RADIATION EFFECTS IN SOLIDS*)

(mainly in metals)

J. W. Glen

CONTENTS

General Principles

§ 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
§ 2. The nature of radiation damage . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
§ 3. Theory of radiation damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
§ 4. Annealing of radiation damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

Experimental Studies of Radiation Effects

§ 5. Effect of radiation on the electrical resistance of pure metals . . . . . 455
§ 6. Effect of radiation on the electrical resistance of alloys . . . . . . . . . 460
§ 7. Annealing of the additional resistance caused by irradiation . . . . . . 472
§ 8. Effect of radiation on the mechanical properties of metals . . . . . . . 486
    8.1. Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
    8.2. Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
    8.3. The “stress—strain” curve for single crystals . . . . . . . . . . . . . . . 491
    8.4. The “stress—strain” curve for polycrystals . . . . . . . . . . . . . . . . 494
    8.5. Internal friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
    8.6. Elastic constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
§ 9. Phase transitions arising as a result of irradiation . . . . . . . . . . . . 498
§ 10. Effect of radiation on the diffraction of X-rays and on density . . . 500
§ 11. Other effects in metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
    11.1. Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
    11.2. Thermoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
§ 12. Effect of radiation on the properties of semiconductors . . . . . . . . 503
    12.1. Electrical effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
    12.2. Other effects in semiconductors . . . . . . . . . . . . . . . . . . . . . . 518

*) Advances in Physics 4, No. 16, 381—478 (1955). Translated from the English by A. Kh. Breger, edited by Prof. G. S. Zhdanov.

§ 13. Analogous radiation effects in nonmetals . . . . . . . . . . . . . . . . . . . . . . . . . . 520
    13. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
    13. 2. Mechanical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
    13. 3. Diffraction of X-rays, electrons, and neutrons;
        density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
    13. 4. Diffusion and electrical conductivity . . . . . . . . . . . . . . . . . . . . . . . 526
    13. 5. Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
    13. 6. Magnetic susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
    13. 7. Optical effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

§ 14. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
    14. 1. Nature of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
    14. 2. Energy required to create a defect . . . . . . . . . . . . . . . . . . . . . . . 528
    14. 3. Degree of disorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
    14. 4. Annealing of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

Cited literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

GENERAL CONSIDERATIONS

§ 1. Introduction

The theory of scattering of particles emitted in radioactive decay was created at the initial stage in the development of nuclear physics. Indeed, the success of Rutherford’s scattering formula led to the recognition of the nuclear hypothesis: the only way to explain the observed number of particles scattered through angles greater than a right angle was to assume that these particles are deflected by a positive charge located at the center of the atom, with a radius considerably smaller than the radius of the atom but carrying a large part of the atom’s mass. This center of the atom was called the nucleus, and the success of the ideas on the structure of matter that arose on the basis of this assumption is demonstrated by the profound understanding of physical and chemical processes achieved since this discovery.

In most cases the experiments by means of which information about the nucleus is obtained consist in studying the radiation emitted when a substance (whose nuclei are being investigated) is bombarded by a beam of known particles, i.e., by measuring the scattering, absorption, and emission of particles. In the early experimental works attention was concentrated on the information that the study of scattering gave concerning the particles or nuclei under consideration, while the disturbances caused by this scattering in the structure of the substance as a whole were rarely studied. Exceptions were works on the theory of the sputtering of atoms from surfaces, on the study of the metamict state of minerals, and on the coloration of alkali halides. Later, the creation of various accelerators and atomic reactors made powerful radiation sources available. With the aid of these sources it became possible to produce substantial changes in the macroscopic properties of substances as a result of bombarding their

over an appreciable interval of time. In addition, the need arose to study these effects in order to judge the behavior of various components and parts of reactors.

The purpose of the present article is to review the development of ideas concerning the influence of irradiation on the physical properties of solids and, in particular, on the properties of metals.

In order to limit the scope of the review, we shall not consider chemical changes caused by radiation, for example the formation of hydrogen peroxide from ice or the cross-linking of polymers; only changes that cause destruction of the lattice of a solid without altering the nature of the molecules of which it consists will be considered.

Since the development of this field is not complete, it is at present impossible to give a satisfactory theoretical interpretation of radiation damage. However, at the beginning of the review some general considerations will nevertheless be given concerning the type and character of the expected effects; then the observed effects will be considered.

Detailed review articles on radiation effects in solids were previously published by Slater^200 in 1951, by Dienes^56b in 1953, and by Kinchin and Pease^117b in 1955; one should also mention the shorter reviews by Lisen^130a,b, Seitz^196, Koehler and Seitz^122a,b, Calkins^35a,b, and Mott^157.** The influence of radiation on the mechanical properties of solids was considered in Dienes’s review^56c. It is also necessary to mention several reviews on related questions: Oatley^164 on the action of radiation on glass, Brumm^29 on the influence of defects in crystal lattices (including defects caused by irradiation) on the electrical resistance of metals, and Przibram’s book^180 on the coloration and luminescence of minerals.

§ 2. Nature of Radiation Damage

The detailed picture of the damage arising under the action of radiation depends both on the nature of the irradiated substance (metal, semiconductor, solid with ionic or atomic bonds) and on the nature and energy of the bombarding particle (heavy ion, alpha particle, proton, electron, neutron, X-rays, etc.). Nevertheless, one can set forth certain general considerations that help in understanding the processes occurring in this case

* For the Russian translation see UFN 47, No. 1, 51 (1952).

* A translation of the theoretical part of review (117b) will be published in the next issue of UFN. (Translator’s note.*)

* In the domestic literature a review by A. I. Zakharov has been published (UFN 57, No. 4, 525, 1955), as well as an article by S. T. Konobeevskii (Atomic Energy 1, No. 3, 1956), etc. See also the collection of translations The Effect of Radiation on Semiconductors and Insulators, Moscow, 1954. (Translator’s note.)

and to explain the differences between individual cases. A particle penetrating into a solid body, colliding with atoms, may produce one of three effects:

a) the particle may collide with one or several orbital electrons,

b) the particle may collide with the nucleus itself, and

c) the particle may cause certain changes in the nucleus, either exciting it or causing a transformation in it.

In the present review only elastic collisions will be considered. Inelastic collisions, generally speaking, lead to the formation of other chemical substances, and although these effects may be of great importance and must always be taken into account in interpreting results, in this article we shall not touch upon them.

In an elastic collision with a bombarding electron, an electron in the lattice usually receives enough energy to leave the atom to which this electron belongs. However, such displacements in a metal do not lead to noticeable changes, since the electron can return to its low-energy state, transferring its excess energy to other electrons and to the lattice in the form of thermal motion. In insulators, displaced electrons may find themselves in the conduction band (analogously to the phenomenon of photoconductivity), or they may be trapped and cause separation of ions in an ionic substance (analogously to the photographic process). These effects can readily be produced by light; the action of other types of radiation is, generally speaking, analogous to the action of light. This phenomenon is well known and will not be considered here. In an elastic collision with a nucleus, part of the energy of the incident particle will be transferred to the nucleus, and if this amount of energy is sufficient, such an impact will displace the nucleus from its position in the lattice. If the bombarding particle retains enough energy also to leave the lattice site, that site remains vacant. However, if the nucleus that originally occupied this site has been displaced only a small distance, it may (spontaneously or as a result of thermal fluctuations) return to its place. If both the nucleus and the bombarding particle have moved away sufficiently rapidly, the final result of the collision will be the formation of a vacant site in the lattice (hereafter called a “vacancy”) and of an atom introduced into an interstitial position (hereafter an “interstitial atom”). At a sufficiently high temperature, interstitial atoms or vacancies, or both, may diffuse in the lattice, and if they come sufficiently close to one another, they may recombine. It is also possible that vacancies or interstitial atoms may assemble in rows (clusters), and if the latter are sufficiently large, they may unite to form li-

linear dislocation rings (screw dislocations cannot be formed in this case). Consequently, from this point of view the effect of irradiation consists in the formation of vacancies and interstitial atoms in excess quantities compared with their number at thermal equilibrium.

If the bombarding particle has a very large energy, then either the recoil atom or the incident particle itself may participate in further collisions—with energy sufficient to knock atoms out of their equilibrium positions. If the cross section for such collisions is large, then a very large number of atoms may be displaced in a small volume. In this case it may prove inappropriate to consider the disturbance from the standpoint of individual vacancies or interstitial atoms, and it may be more expedient to regard such a disturbance as an effect equivalent to the release of a large amount of energy in a small volume, with an instantaneous rise of temperature in this volume to very high values. Such a local introduction of considerable amounts of energy is often called a “thermal spike.” If we now turn to those macroscopic changes that should be expected under the influence of nuclear displacement, we see that two principal effects may occur.

1. If the solid was in an equilibrium state before irradiation, then this equilibrium may be disturbed. Thus a nonequilibrium number of vacancies and interstitial atoms appears, ordered alloys become disordered, etc. If the temperature is sufficiently low, annealing of these effects may not occur and a permanent disturbance is formed, whereas at a sufficiently high temperature rapid annealing of the disturbances will take place.

2. If the substance was initially not in equilibrium, but was in a nonequilibrium state as a result of cooling to a low temperature (as, for example, in the case of a quenched disordered alloy which would become ordered upon slow cooling), then irradiation may bring such a system closer to equilibrium. Consequently, as a result of the formation and annihilation of a “vacancy—interstitial atom” pair, a structure may arise that is closer to equilibrium than the one that existed before this process, since if such an approach to equilibrium is possible at all, then the changes leading to equilibrium will be energetically more favorable than any other mode of transformation.

§ 3. Theory of Radiation Damage

The theory of radiation damage in solids is not yet complete. Calculations of the character and dimensions of the damage are divided into two parts: a) calculation of the degree of the initial damage and b) estim-

J. W. Glen

as well as the degree of instability of this defect and, consequently, the rate of annealing (self-annealing).

In calculating the first stage of this process it is usually assumed that the collision of the bombarding particle and an atom situated at a lattice site may be regarded as a collision of two free particles, and that the principal role of the crystal lattice is to prevent the displacement of atoms until they possess an energy less than some critical energy \(E_d\). The various attempts that have been made to create a theory of atomic displacements have recently been set out in detail in a review by Kinchin and Pease \(^{116}\). Here we shall note only the nature of the results obtained, without going into the details of the calculations. The first estimates of the nature and magnitude of radiation damage were made by Wigner, and for this reason radiation damage is sometimes called the Wigner effect. However, during the war work on this question was classified, and there are no accessible declassified references. The first openly published fundamental theoretical works on radiation damage were those of Seitz \(^{196a}\) and Ozerov \(^{166}\). Seitz’s calculation was criticized, since he used the Born approximation for calculating collisions, for which this approximation is unsuitable; nevertheless the results of this calculation are often used to calculate the order of magnitude of the primary damage. Ozerov’s calculation (damage caused by neutrons and fission products), as well as the later calculations of Brinkman \(^{27a,b}\) and of Snyder and Neufeld \(^{206a,b}\), are free from this shortcoming.

In the case of charged particles, theory shows that if the velocity of these particles exceeds some definite value (depending on the type of substance bombarded), then they give up the greater part of their energy by exciting electrons, and only approximately \(\dfrac{1}{1000}\) of the energy is transferred to nuclei. However, below this critical velocity the greater part of the energy loss occurs in elastic collisions with nuclei. If, further, it is assumed that a nucleus which has received an energy greater than \(E_d\) is always displaced from its position, then it is possible to calculate the actual number of pairs of the type “vacancy—interstitial atom” that are formed. Roughly speaking, one such pair is formed for every \(50\text{–}100\ \mathrm{eV}\) of energy expended in elastic collisions with nuclei. The critical velocity for electronic excitation in the case of insulators is approximately equal to the velocity of an electron having the ionization energy, whereas for metals it is, in order of magnitude, equal to the velocity of electrons at the Fermi surface. Thus, for any individual case one can calculate the energy expended on displacements and obtain an estimate of the number of “vacancy—interstitial atom” pairs formed. In this calculation one may take into account the possibility of colli-

interactions of displaced atoms with other atoms, as well as displacements of the latter from the positions they occupy in the lattice.

In the case of bombardment by neutrons, practically all the energy of these particles is expended on displacing atoms, which may also move sufficiently rapidly to cause excitation of electrons. Calculations show that neutrons produce 10–100 times more displacements in the higher-energy region, since electronic excitation plays a considerably smaller role in this case. Thus, according to Seitz’s theory, a neutron with an energy of 2 MeV produces 6000 displacements in aluminum, whereas an alpha particle with an energy of 5 MeV produces only 60 displacements, and a proton with an energy of 20 MeV produces 80. Snyder and Neufeld \(^{2066}\) examined in detail the theory of neutron irradiation and gave an approximate rule according to which recoil atoms arising in collisions with neutrons lose, in the formation of “vacancy—interstitial atom” pairs, about half of their recoil energy if their energy is less than \(e^2/h\). Conversely, if the energy of the recoil atoms is greater than this quantity, then an approximately constant amount of energy is expended in forming a pair.

The results of this calculation reduce to two formulas determining the number of vacancies or interstitial atoms produced by a neutron of energy \(E\) in a monatomic solid consisting of heavy or medium atoms of mass \(M\):

\[ G(E) \simeq \frac{(nE-\alpha)^2}{4\alpha nE} \qquad \text{for } E \leq \frac{\gamma}{n}, \]

\[ G(E) = \frac{(nE-\alpha)^2 - (1-\overline{R})(nE-\alpha-\gamma)^2}{4\alpha nE} \qquad \text{for } E \geq \frac{\gamma}{n}, \]

where

\[ \gamma = \frac{Me^4}{2\hbar^2}; \qquad n = \frac{4M}{(M+1)^2}; \]

\(\alpha\) is the binding energy of an atom in the lattice; \(\overline{R}\) is a slowly varying function of the atomic number. The extension of this theory to polyatomic solids was briefly set forth by Harrison \(^{91}\). In these calculations the authors neglected the possibility that the moving particle (which itself is usually a displaced atom) remains in a vacant site. This possibility was taken into account by Kinchin and Pease \(^{1176}\), who, however, neglected losses of kinetic energy in collisions. They also found that half of the kinetic energy of a moving atom (if its energy is insufficient to cause ionization) will be expended in forming “vacancy—interstitial atom” pairs. However, if the loss of kinetic energy is taken into account, this fraction will probably lie between \(1/2\) and \(1/4\).

In all the above-mentioned theories it was assumed that atoms possessing energy sufficient for displacement from their positions

in the lattice, do in fact shift. If this assumption is incorrect, then a smaller number of “vacancy—interstitial atom” pairs will be produced. Simpson, Harwitt, and Klensi\(^ {191}\) drew attention to this circumstance in order to explain discrepancies between the theoretical and experimental data, which will be considered below.

The energy of the fragments is sufficient for these particles to lose approximately equal amounts of energy both in that part of their path in which, during the slowing down of the fragments, the process of electronic excitation predominates, and in the remaining part of the path. In this case the atoms displaced by the fragments from their positions in the lattice possess a sufficient reserve of energy to produce about three additional displacements. Thus it may be shown that a pair of uranium fission fragments produces about 25,000 displaced atoms.

The next important feature of radiation damage is that the distribution of this damage is usually far from uniform both macroscopically—because of the insufficient penetrating power of the particles—and microscopically—because a single particle (neutral or charged) produces a large number of vacancies and interstitial atoms. These effects can be avoided in bombardment by high-energy electrons, which can produce one “vacancy—interstitial atom” pair per electron and also have a large penetrating power. However, the number of defects produced by electrons is considerably smaller than the number of defects produced in bombardment with available sources of other particles. Electrons also lose a large part of their energy in other ways, so that in this case the ratio of heat released to the number of displacements is considerably larger than for other particles. For these reasons electron bombardment is used mainly in special cases; examples of the use of electron bombardment will be given below.

Gamma rays undergo very little direct interaction with nuclei and, consequently, the principal displacements under gamma irradiation are produced by recoil electrons in Compton collisions. According to Dagdale\(^ {616}\), measurements have shown that this effect is not as small as might have been expected. In this case the damage should be distributed fairly uniformly and may therefore lead to changes in the properties of a solid over a greater thickness than in bombardment by electrons used as primary particles. For heavy charged particles one can overcome some of the disadvantages associated with the short range of these particles by using very thin specimens; although even in this case most of the damage will occur near the end of the particle’s range, while if the specimen thickness is less than the range length, most of the damage that the particle could produce if its entire range were used will not be realized, and the ratio of electronic

of excitation (and, consequently, the amount of heat) to the number of defects formed increases by several hundred times. Shved and Grötzinger^194 proposed a device that makes it possible to introduce an absorber into the beam in such a way that the thickness of the absorbing material through which the particles pass before they reach the specimen varies linearly and periodically from zero to the value of the particle range.

Another solution to the problem of radiation damage was given by Brinkman^27a,b. He believes that, whereas a rapidly moving atom creates vacancies and interstitial atoms as the primary form of defects, in the case when the atom has slowed down sufficiently, the amount of energy expended in collisions not leading to displacements will be so great that an entire region will melt and then recrystallize again. The author asserts that this differs from the earlier concept of “thermal spikes” in that the high initial density of vacancies and interstitial atoms undergoes more or less complete annealing, and that the defects remain in the form of dislocation loops and small regions with a new orientation. Brinkman calls this region a “displacement spike”; he calculated that for heavy atoms these defects will be the only substantial form of damage, whereas in the case of light elements pairs of the “vacancy—interstitial atom” type will predominate, since the formation of such pairs requires a considerably smaller amount of energy than the melting of an entire region. Brinkman’s conclusion regarding the almost complete recombination of vacancies and interstitial atoms is based on the fact that the cooling of a metal heated to a high temperature proceeds slowly enough for these defects not to have time to stabilize. Apparently, this is not a general case. If it did occur, then a light annealing of some part of the defects would take place as a result of the destruction of dislocation rings of various diameters. If, however, this is not so, then a “displacement spike” is a small region of the crystal that was effectively melted and then quenched.

Another special case was considered by Smoluchowski^203a,b, who pointed out that at very high energies (~400 MeV) the number of nuclear “star” collisions may be sufficient to lead to an increase in the number of displacements with increasing energy of the bombarding particles.

§ 4. Annealing of radiation damage

If, after irradiation at a low temperature, a specimen is heated, there will be a tendency for any radiation defects existing in the form of unstable configurations—for example, in the form of a large number of vacancies or interstitial atoms—to anneal. Therefore, the study of the kinetics of recovery of damage represents

method of investigating the nature of defects, and also gives information on the behavior of various types of lattice defects. The greater part of theoretical work on the annealing of radiation damage has been carried out with the aim of explaining individual experimental results, and examples of such theories may be found in the following sections, where the corresponding experiments are described. Here it is sufficient to point to one or two of the most recent attempts, in order to show what processes are being considered in this connection. Fletcher and Brown^74 indicated that if the defect undergoing annealing consists of vacancies and interstitial atoms, then three types of recovery processes are possible.

1. The interstitial atom and the vacancy are at a short distance from one another and recombine when the temperature is raised sufficiently; this gives a process of the unimolecular-reaction type, or a superposition of several such processes.

2. The interstitial atoms and vacancies are sufficiently far apart from one another that there is a finite probability of these defects escaping from the region of mutual influence; in this case the corresponding capture function is more complex.

3. Vacancies that move away from their corresponding interstitial atoms (Fletcher and Brown consider only this case) diffuse and recombine with other interstitial atoms (this leads to the equation of a bimolecular reaction) or drift to surfaces or to dislocations. Consequently, the annealing of individual “vacancy—interstitial atom” pairs represents the sum of at least three terms. For a comparison of the conclusions of this theory with experimental results, see § 12.

Another theory of the annealing of lattice defects was given by Dienes^56a to explain observations on the recovery of the resistance of copper. He assumes that the activation energy of recovery changes with the number of lattice defects present. Such a dependence of the activation energy should not lead to a change in the character of the graph of $\lg t$ as a function of $\frac{1}{T}$ (where $t$ is the time required for annealing of the given state, $T$ the temperature); but the slopes of such graphs should systematically change for different degrees of annealing. This is analogous to the effect observed in the case when the process is described by an equation for a reaction of higher order with a constant activation energy. Marx^150 pointed out that such an apparent increase in the order of the process occurs when the defects are initially distributed nonuniformly. An explanation of annealing by considering dislocation voids was mentioned in § 3. Of course, the presence of noticeable effects caused by the formation of defects in considerable excess over the equilibrium number should be expected, as Rothstein^190a; 6 emphasized, only at temperatures at which the rate of annealing is very small. He calculated

degree of disorder that will exist in the stationary state reached during irradiation. With a low annealing rate at low temperatures, many physical properties may acquire “anomalous” values. Thus, materials that reach a stationary state in a reactor, when the ambient temperature is lowered, will possess a number of properties usually associated with high temperature.

Another type of annealing that must also be considered in the study of radiation effects is annealing caused by the irradiation itself. In addition to local increases in temperature, the bombarding particles and displaced atoms may in some way eliminate existing defects and also form new ones. Various mechanisms of this phenomenon have been considered by Barnes and Mazey^10.

EXPERIMENTAL STUDIES OF RADIATION EFFECTS

We shall not consider in this article the experimental techniques used for irradiating solids; these techniques are very diverse. However, mention should be made of several works devoted to experimental technique. The Atomic Energy Research Division of North American Aviation has prepared a number of papers on the use of the cyclotron for studying radiation effects, especially at low temperatures (Yockey, Fillmore, Hunt, Andrio, Glasgou, Weber, Jempson, Pepper, and Carter^228; in a more concise form—Yockey, Fillmore, Glasgou, Hunt, and Pepper^227). Descriptions of reactors specially constructed for testing materials are contained in the papers by Huffman^98 and O’Connor and Foster^162. Special X-ray cameras for studying irradiated substances possessing considerable radioactivity have been described by Cummings, Kaulitz, and Sanderson^50, and also by Bredig, Klein, and Borie^26. The experimental conditions of various experiments are given in Table V.

§ 5. Effect of radiation on the electrical resistance of pure metals

One of the best indicators of the degree of perfection of a crystal lattice is its electrical resistance. Results obtained from experiments on measuring the resistance of metals subjected to cold working have shown that this property is restored at lower temperatures than certain mechanical properties, for example hardness. This led to the suggestion that hardness is associated chiefly with the number and configuration of dislocations in a substance, whereas resistance is to a greater extent a measure of the number of vacancies and interstitial ato-

If this point of view is correct, then the resistance should change substantially under the action of irradiation, and the temperature and character of this annealing should in turn confirm or refute the correctness of the assumption according to which the change in the resistance of a metal subjected to cold working is mainly connected with the presence of vacancies and interstitial atoms.

The first systematic study of this question was carried out by Martin, Ostermann, Eggleston, Mackie, and Tarpley^149, who irradiated aluminum and copper (as well as copper–gold alloys, which will be discussed below) with alpha particles in the Berkeley cyclotron. As a result of irradiating specimens at \(-150^\circ\text{C}\), large changes in the electrical resistance of both metals were detected, and annealing of these changes began already at \(-80^\circ\text{C}\). When the specimen was heated to room temperature, no changes in resistance or in the temperature coefficient of resistance were observed in comparison with the corresponding values before irradiation, although, as we shall see below, the hardness of copper under these conditions still differs noticeably from its hardness before irradiation. Cold working usually leads to changes in the resistance of copper at room temperature. To explain this result it is necessary to assume either that the increase in resistance is associated with the presence of dislocations, or that the vacancies and interstitial atoms formed in radiation damage are closer to one another than the vacancies and interstitial atoms formed during cold working, or, finally, that during cold working a larger number of vacancies than interstitial atoms is formed (or vice versa), and, consequently, complete annealing by recombination of these defects is impossible. This last explanation is quite probable, since the formation of an interstitial atom requires the expenditure of a larger amount of energy than the formation of a vacancy, whereas the interstitial atom that is formed is significantly more mobile. Thus, in radiation damage it is most probable that it is precisely the mobility of interstitial atoms that chiefly determines the annealing of the electrical resistance. According to Huntington’s calculation^996, the magnitude of the activation energy is \(1/4\ \text{eV}\).

If the increase in resistance is in fact due to scattering by interstitial atoms and vacancies, then it should not depend on temperature provided that no annealing occurs, and, consequently, at low temperatures after irradiation one should expect a considerably larger relative change in residual resistance. This was observed by Randolph^181a,b, who found that, whereas at room temperature the change in the resistance of molybdenum was only \(4\%\), at \(1.2^\circ\text{K}\) this change reached \(200\%\). In both cases the changes were measured after irradiation at \(-100^\circ\text{C}\), so that at room temperature some annealing probably occurred in the specimens. In more careful

In the experiments performed, Overhauser^165b found that, apart from annealing effects, the additional resistance caused by deuteron bombardment does not depend on temperature in the interval from \(-125^\circ\mathrm{C}\) to room temperature.

Bowen and Rodeback^24a,b reported results contradicting those set forth above. In their experiments the change in electrical resistance was measured as a function of temperature after bombardment, and also after cold working. Using Grüneisen’s formula, they calculated the change in the characteristic temperature. For irradiated copper it was found that, along with a large change in the residual resistance, there was also a change in the temperature-dependent part, leading to a change in the characteristic temperature by \(45^\circ\). After annealing, both the temperature-dependent and temperature-independent parts were restored, and when a graph was constructed on which the two components were plotted against one another, a smooth curve was obtained. For copper subjected to cold working, the curve of the dependence of the residual resistance on the change in the characteristic temperature was very close to the curve corresponding to the irradiated specimen.

In this analysis it is assumed that, owing to internal stresses caused by radiation damage, the vibration spectrum of the lattice is shifted toward low frequencies and, consequently, a larger amount of energy will accumulate in the thermal vibrations of the lattice. This energy may constitute a large part of the energy accumulated in irradiated substances or in substances subjected to cold working. An interpretation of the temperature-independent part by considering point and boundary scattering centers was proposed by Rodeback^187.

The change in resistance under the action of radiation for various metals has still not been systematically studied. In order to clarify the influence of crystal structure on radiation effects, Rock and Wirt^225,226a,b,c carried out experiments with iron, nickel, and cobalt, since these metals have similar properties from almost all other points of view. After bombardment at \(-150^\circ\mathrm{C}\) by a flux of \(10^{17}\) deuterons (with an energy of \(10\ \mathrm{MeV}\)) per \(1\ \mathrm{cm}^2\), the increase in resistance amounted to \(50\%\) in the case of iron, and \(10\%\) in the case of cobalt and nickel. Similar results were also obtained as a result of neutron bombardment at room temperature. These experiments show that in a metal with a body-centered cubic lattice, irradiation leads to more substantial effects than in metals possessing a close-packed lattice.

Kinchin (according to Dargeil’s report^616) studied changes in the resistance of tungsten, molybdenum, and platinum irradiated in a hollow uranium block (in order to increase the number of fast neutrons) up to doses of about \(10^{19}\) fission neutrons per \(1\ \mathrm{cm}^2\). The change in resistance

for tungsten was about 10%, for molybdenum about 7%, whereas the resistance of platinum changed to a considerably smaller extent (about 1% at \(5\cdot 10^{18}\) neutrons/cm\(^2\) and about 2% at \(1.5\cdot 10^{19}\) neutrons/cm\(^2\)). Rack and Wert \(^{226a}\) also studied changes in the resistance of titanium (hexagonal lattice) and vanadium (body-centered cubic lattice). In these metals a very large change in resistance was found in comparison with the changes in the resistance of iron, nickel, and cobalt. However, since the initial resistance of titanium and vanadium is considerably higher than the resistance of the latter three metals, the effect expressed in percent proves to be smaller for titanium than for cobalt, and for vanadium the smallest of all the metals. Since the percentage change in the resistance of iron (the largest of the five metals studied) anneals out considerably faster than the analogous changes in the other metals, the overall result of this work is rather unconvincing.

The magnitude of the effect after prolonged bombardment at low temperature was studied by MacReynolds, Ogburn, McKeown, and Rosenblum \(^{142a,b}\). After bombardment with a dose of \(1.1\times 10^{19}\) neutrons/cm\(^2\) at \(-195^\circ\)C, the change in the resistance of copper was 20%, and of aluminum 33%.

The lowest temperature at which radiation studies have so far been carried out was 10°K. Cooper, Koehler, and Marx \(^{46a,b}\) bombarded copper, silver, and gold at this temperature. They found that the resistance increased, with the rate of this increase decreasing during the course of bombardment, as shown in Fig. 1. In addition, it was found that the “resistance—neutron flux” curves were different at 12°K and 16°K. The first effect may be due to annealing under the action of bombardment and was considered from this point of view by Barnes and Mazeikin \(^{10}\); the second effect, if it actually exists, apparently indicates thermal annealing at these temperatures. However, Cooper, Koehler, and Marx found no changes in resistance in specimens that were held for some time at the bombardment temperature.

Pirshtein, Ingham, and Smoluchowski \(^{170}\) used protons of very high energy (from 100 to 400 MeV) as bombarding particles. They bombarded a thin tungsten wire in a proton synchrotron to doses up to \(10^{16}\) protons/cm\(^2\). In this case the resistance of the wire changed by 0.3% (at 260 MeV) to 0.71% (at 410 MeV). Smoluchowski, Pirshtein, and Ingham \(^{204}\) proposed that at these high energies the particles emitted from the “stars” during nuclear disintegration constitute an important source of defects. A calculation based on this assumption led to reasonably good agreement with the experimental results, whereas according to Seitz’s theory the magnitude of the defects in such

thin specimens must be inversely proportional to the particle energy.

Other determinations of the magnitude of changes in the resistance of metals under the action of radiation were carried out in experiments designed to study the annealing of these changes. These works will be considered below (see § 7).

Here we shall consider one more experiment. This is one of five experiments that were performed in order to determine the energy necessary for the formation of radiation damage in a metal, and it is the third in chronological order. In all these experiments, as the

Fig. 1. Increase in the resistance of copper, silver, and gold during bombardment by deuterons with an energy of 12 MeV at 12° K (Cooper, Koehler, and Marx\(^{466}\)).

bombarding particles, electrons were used, since in this case the amount of energy transferred to the atoms is comparatively small. If the electron energy varies from 0.1 to 1.0 MeV (for example, when electrons are accelerated by means of a Van de Graaff generator), then the maximum energy transferred to an atom (in any collision) is from 5 to 50 eV. This energy is, in order of magnitude, equal to the energy required to displace an atom from its position in the lattice. Thus, the experimental method consists in bombarding with particles of different energies and in determining the threshold value below which no effects are observed. Eggen and Laubenstein\(^{64}\) carried out such experiments, in which the resistance of copper was measured during bombardment by electrons. The specimens were thin copper plates; irradiation was carried out at the temperature of liquid

air. The curve characterizing the dependence of the rate of change of resistance on the electron energy crossed the abscissa axis (which corresponds to the absence of disturbance) at \(0.49 \pm 0.02\) MeV, which corresponds to a displacement energy in copper of \(25 \pm 1\) eV. It is impossible to establish the accuracy with which this quantity was determined, since the details of the experiments are unknown.

§ 6. The Effect of Irradiation on the Electrical Resistance of Alloys

One may expect that in alloys effects similar to those observed in pure metals will occur; however, in this case other phenomena may also take place. One may expect that unstable phases, for example those formed during the crystallization of quenched alloys, will decompose under the action of irradiation. In lattices possessing a superstructure, special phenomena may occur.

Billington and Siegel \(^{17}\) and Merei and Taylor \(^{158a,b,c}\) studied the action of neutron bombardment on a supersaturated solid solution of beryllium in copper, and also on other crystallizing under quenching and unsaturated solid solutions. The results of the study of the solution of beryllium in copper showed that in this alloy there is a greater increase in resistance caused by neutron bombardment than in pure copper or in any other alloy (including some quenched alloys). Merei and Taylor believe that this phenomenon is connected with the formation of nuclei of the stable phase; this explanation is also in agreement with most changes in other properties. Thus, the effect of irradiation at room temperature is similar to the effect occurring during low-temperature annealing (for example, at \(75^\circ\)C), in which an increase in resistance also occurs as a result of the formation of small nuclei of the crystallizing phase; however, these two effects are not entirely identical to one another. Low-temperature annealing increases the resistance considerably more rapidly in polycrystals, which is usually associated with the preferential formation of nuclei at grain boundaries. However, the experiments of Merei and Taylor show that the change in resistance under irradiation is the same both in polycrystalline specimens and in single crystals. They attribute this phenomenon to the random formation of nuclei (in this case not at grain boundaries), probably caused by the greater ease of microdiffusion associated with the presence of an excess number of vacancies and interstitial atoms formed during irradiation. Richards \(^{185}\) pointed out that the radiation effects are perhaps closer to the effects of cold working than to low-temperature annealing. Merei and Taylor explain the fact that they did not find similar effects in other alloys, crystall-

...observed during quenching, by one or several of the following causes:

1) The atoms of the base metal may be insufficiently heavy for each incident neutron to produce the formation of a large number of displacements.

2) The activation energy of diffusion may be too small.

3) The size of the nuclei required for fulfillment of the stability condition may be too large.

4) The nuclei may be too small to exert an influence on the resistance.

This interpretation of the large change in resistance in a solid solution of beryllium in copper was confirmed in experiments by Cleland, Billington, and Crawford^39. They irradiated quenched copper–beryllium alloys in a graphite reactor at \(\sim 120^\circ\mathrm{K}\) and at \(\sim 300^\circ\mathrm{K}\). The authors found that the increase in resistance at \(\sim 120^\circ\mathrm{K}\) amounted to only \(\frac{1}{4}\) of the change in resistance produced as a result of analogous irradiation at \(300^\circ\mathrm{K}\). However, brief subsequent irradiation at \(300^\circ\mathrm{K}\) leads to an increase in the resistance to the value that could have been expected if all the irradiation had been carried out at \(300^\circ\mathrm{K}\). Such behavior is regarded as proof that a large part of the increase in resistance is due to a process based on thermal activation, for example microdiffusion.

Alloys in which superstructures can form behave similarly to alloys that crystallize during quenching. At low temperatures two conditions may be realized: first, in which the metal is slowly cooled and is in an ordered state, and second, in which the metal, quenched from a temperature above the transition temperature, is disordered. Thus, radiation damage can produce two effects: displaced atoms and vacancies, on returning, may fall into other lattice sites (i.e., not into the sites in which they were located before irradiation), which will lead to disordering of a completely ordered alloy; but, on the other hand, they may fall into lattice sites with near order, which may lead to ordering of a disordered specimen. The first experiments of this kind were published by Siegel^199. He found that at a dose of \(3.3\cdot 10^{19}\) neutrons/\(\mathrm{cm}^2\) the resistance of an ordered alloy increased from \(4.6\) to \(10.1\cdot 10^{-6}\ \Omega\cdot\mathrm{cm}\), whereas the resistance of the disordered alloy increased from \(11.2\cdot 10^{-6}\ \Omega\cdot\mathrm{cm}\) only to \(11.3\cdot 10^{-6}\ \Omega\cdot\mathrm{cm}\). Siegel attributes this difference to disordering during bombardment. At the same time, the small change in the resistance of the disordered specimen is completely explained by nuclear transformations occurring in the course of irradiation. A similar result was obtained by Martin et al.^149, who bombarded

by alpha particles, Cu₃Au and CuAu at \(-150^\circ\) C. As in the preceding case, in the ordered specimens there was a large increase in resistance, whereas in the disordered specimens almost no changes were observed. Measurements of the lattice parameters confirmed this explanation; this proved especially convincing in the case of CuAu, where after irradiation with a dose of \(33\) μca-h the tetragonal ordered lattice was completely transformed into a cubic one. On the other hand, Adam and Dalgdeil \(^{2}\) found that irradiation of an ordered copper–gold alloy with slow neutrons at first leads to an increase in order, as is demonstrated by measurements of the unit-cell dimensions, the appearance of additional superstructure lines, and a decrease in electrical resistance. Upon further irradiation the resistance again increased, but disappearance of the superstructure lines was not observed.

Fig. 2. Change in the resistance of disordered and ordered Cu₃Au specimens during neutron bombardment at \(80^\circ\) C (Glick, Brooks, Wittig, and Johnson \(^{84}\)).

The change in resistance during bombardment was studied in greater detail by Glick, Brooks, Wittig, and Johnson \(^{84}\). Bombarding Cu₃Au with neutrons at \(80^\circ\) C, they found (Fig. 2) that in the initially ordered specimen, with a resistivity of \(5.2\ \mu\Omega\cdot\text{cm}\), there was at first a rapid decrease in resistance. The resistance reached a minimum lying 3% below the initial value at an integral dose of \(0.4\cdot 10^{19}\), and then increased approximately linearly, reaching (at an integral dose of \(20\cdot 10^{19}\ \text{neutr}/\text{cm}^{2}\)) a value 60% greater than the initial resistance. The resistance of the initially disordered specimen gradually decreased and, at a dose of \(5\cdot 10^{19}\ \text{neutr}/\text{cm}^{2}\), was 92.5% of the initial value; then the resistance slowly increased to a value 4.2% below the initial value (at a dose of \(20\cdot 10^{19}\ \text{neutr}/\text{cm}^{2}\)). To explain these results it is necessary to assume that irradiation can lead both to ordering and to disordering, the former leading to an increase in the resistance of the initially disordered specimen, which is attributed to contamination of the alloy by mercury formed from gold in the course of bombardment.

(to the end of the experiment more than 1% of the gold is transformed into mercury). The initial decrease in the resistance of the ordered specimen is more surprising; apparently, it is connected with an increase in the degree of order, caused by more intense diffusion, which takes place at the beginning of irradiation but ceases at the moment when the number of mixed atoms becomes sufficient for substantial disruption of the superstructure. These considerations are also confirmed by the results of another experiment, carried out by Glick and Wittig ^85. These authors irradiated specimens at 140° C, i.e., in the temperature region in which the diffusion rate should be considerably greater than in the experiments described above. In specimens which, before irradiation, were in the ordered state, a 6% decrease in resistance was observed at a dose of \(0.4 \cdot 10^{19}\) neutrons/cm\(^2\), followed by a slow increase in resistance to 4% greater than the initial value at a dose of \(14 \cdot 10^{19}\) neutrons/cm\(^2\). On the other hand, in a specimen which before irradiation had been in the disordered state, a decrease in resistance was found which, at a dose of \(2.5 \cdot 10^{19}\) neutrons/cm\(^2\), saturated and reached a value 17% less than the initial one. A control experiment, carried out at the same temperature, showed that the resistance of a disordered specimen not subjected to irradiation decreased by only 4%.

Fillnow, Haltman, and Mechlin ^71 simultaneously carried out hardness measurements and X-ray studies. It turned out that the hardness increased both in ordered and in disordered specimens. On the X-ray photographs of disordered specimens no changes were found, while the ordered specimens gave X-ray photographs on which the lines became sharper after irradiation; these X-ray photographs also showed that the long-range order parameter decreased somewhat. In the disordered substance no changes in the lattice parameter were found; the lattice parameter of the ordered substance decreased substantially.

Bombardment of \(\mathrm{Cu}_3\mathrm{Au}\) was also studied by Blewitt and Coltman ^226. They found that bombardment by a flux of \(10^{12}\) neutrons/cm\(^2\)·sec at 200° C leads to a gradual decrease in resistance. After shutdown of the reactor the fall in resistance ceased after 12 hours, which should be compared with the relaxation time of the unirradiated substance at this temperature—\(10^5\) hours. This effect shows almost definitely that defects in the irradiated substance are mobile, and makes it possible to estimate the mean path of an introduced atom and vacancy up to the moment of their recombination. Experiments on disordering ordered \(\mathrm{Cu}_3\mathrm{Au}\) show that each collision affects \(10^4\) atoms. From the tendency toward saturation of the ordering process during one month at an integral dose of \(10^{18}\) neutrons/cm\(^2\) it follows that if one adopts for the fast-neutron cross section some value, for example 3 barns,

then one can calculate the total number of atoms displaced as a result of collisions with the bombarding neutrons. This number turns out to be equal to \(10^{17}\). Since the total number of atoms in a \(\mathrm{cm}^3\) is approximately \(10^{23}\), it follows that each collision with a neutron affects a volume containing \(10^6\) atoms, and in this volume a state of saturation is produced. Since this number exceeds the number of atoms actually displaced—\(10^4\)—Blewitt and Koehler conclude that vacancies and interstitial atoms migrate for some time before recombination, and that this process is accompanied by a certain ordering. The discrepancy between the value of the integral dose leading to saturation found by these authors and the value found by Glick and co-workers at a lower temperature is apparently explained by the lower mobility of the “vacancy—interstitial atom” pairs at the lower temperature. On the other hand, the overall ordering and, consequently, the change in resistance attributed to one “vacancy—interstitial atom” pair should not be a function of temperature, provided that all pairs annihilate in the same way. Another prediction that can be made on the basis of the hypothesis of ordering due to migration of “vacancy—interstitial atom” pairs is that the ordered regions should, in order of magnitude, correspond to the region ordered by one initial particle, i.e. about 100 Å. If one assumes that at saturation the substance consists entirely of ordered regions (domains), then, from the value of the resistance, it can be estimated that the average size of these regions is about 60–65 Å. On the other hand, in a second article Koehler and Blewitt\({}^{44a}\) report that measurement of the width of the superstructure line on the x-ray pattern leads to an average size of 125 Å. Finally, Koehler and Blewitt\({}^{44b}\) report that when the flux is increased by a factor of 4, the rate of approach to order likewise increases by a factor of 4, whereas in another specimen bombarded at \(-150^\circ\mathrm{C}\), which initially corresponded to the degree of order in equilibrium at \(376^\circ\mathrm{C}\), no decrease in resistance was observed (as occurred under bombardment carried out at \(150^\circ\mathrm{C}\)); only a very slight decrease in resistance was observed. Subsequent annealing of this specimen led to the expected decrease in resistance.

Similar experiments were carried out by Dickson and Bouman\({}^{58}\), who irradiated \(\mathrm{Cu}_3\mathrm{Au}\) with \(\alpha\)-particles of energy 36 MeV. If the ordered alloy was irradiated at \(-180^\circ\mathrm{C}\), the initial rate of disordering was \(3.3\cdot 10^{-17}\ \mu\Omega\cdot\mathrm{cm}\) per \(\alpha\)-particle/\(\mathrm{cm}^2\), whereas bombardment at \(220^\circ\mathrm{C}\) led to a decrease in the rate of disordering by a factor of 6. This shows that vacancies and interstitial atoms at high temperatures are mobile and order a large part of the disordered material. Starting from

of the ordering rate at \(220^\circ\mathrm{C}\) can account for only \(5\%\) of this difference.

All these experiments agree with the assumption that ordering of disordered alloys occurs only as a result of the diffusion of vacancies or interstitial atoms, and that at sufficiently low temperature this diffusion is impeded. This means that the ordering of disordered alloys is a process closer to the annealing of radiation damage in pure metals than to the formation of such damage.

Thus, we have given a qualitative explanation of ordering under the action of radiation; however, so far we have not touched on the process of disordering. The magnitude of this effect is too great for it to be fully explained by the “quenching” of thermal spikes. Two possible theories have been proposed. According to the first theory, put forward by Kinchin and Pease \(^{117a}\), disordering is explained by a large number of collisions in which moving atoms exchange places with stationary atoms. Thus, in each collision one atom of the ordered lattice is replaced by an atom from the random distribution. According to the other theory, proposed by Seitz \(^{196b}\), disordering is explained by elastic deformations arising as a result of thermal stresses around displacement spikes.

In neutron irradiations in a reactor, exact control of the energy spectrum is impossible. A more rigorous way of investigating these effects is the production of defects in the lattice by irradiation with high-energy electrons. In this case not only are effects associated with nuclear transformations eliminated, but there also is no accumulation of a large number of defects in small volumes, since the number of secondary collisions in this case will be significantly smaller than under neutron irradiation. Experiments of this kind were carried out in two laboratories. At Harwell, Adam, Green, and Dugdale \(^{3}\) found that irradiation with electrons of energy \(1\ \mathrm{MeV}\) does not lead to a change in the resistance of an ordered specimen, but upon subsequent annealing at \(100^\circ\mathrm{C}\) or \(130^\circ\mathrm{C}\) there is a decrease in resistance of approximately \(2\%\). The authors explain this phenomenon as follows. A completely annealed ordered specimen corresponds to the degree of order in equilibrium at approximately \(250^\circ\mathrm{C}\). An increase in the number of vacancies and interstitial atoms leads to the fact that at low temperature some atomic displacements occur and, consequently, a higher degree of order can be obtained. Similar experiments using gamma rays were described by Dugdale \(^{616}\). In this case, atomic displacements probably occurred as a result of collisions with electrons interacting with the gamma rays. The advantage of this method of producing displacements is that the distribution of defects is ob—

is more uniform than under direct bombardment by electrons. The annealing of these specimens is being studied.

Similar experiments were carried out in the USA by Dixon, Meechan, and Brinkman[^60]. They repeated the observations of Adam, Green, and Dagdale and, in addition, carried out irradiation at \(-195^\circ\text{C}\) with an integral dose of \(3.4 \cdot 10^{19}\) electrons in order to determine whether any disordering would occur. However, in these experiments no changes in resistance were detected, and annealing at room temperature for 50 hours led to a decrease in the resistance (measured at \(-195^\circ\text{C}\)) by \(2.7\%\), with subsequent fluctuations exceeding the experimental errors (about \(1\%\)). The absence of an increase in resistance not only shows that no disordering occurred in this case, but also that some of the vacancies and interstitial atoms that had formed recombined even at this low temperature. Thus, the principal difference between the defects arising under bombardment by electrons, neutrons, or alpha particles is that electrons cannot produce disorder in an ordered alloy. This assertion seems very well founded, since none of the above-mentioned mechanisms leading to disordering can occur under electron bombardment, with the possible exception of a small number of collisions as a result of which atomic replacements take place. Indeed, under electron bombardment each vacancy and each interstitial atom is in fact isolated, and therefore the tendency toward disordering will in this case be less than during annealing and slow cooling of the metal.

A nonequilibrium number of defects can also be produced by other methods. Quenching from a high temperature will lead to the formation of a number of vacancies corresponding to the high temperature, but in this case, of course, the alloy will remain in the disordered state. Nevertheless, there remains the possibility of comparing the values of the activation energy of the ordering processes. Quenching from a temperature somewhat below the transition temperature should lead to an ordered alloy with a state rather far from complete order and with a nonequilibrium number of vacancies. Finally, cold working also leads to the formation of vacancies and interstitial atoms, chiefly as a result of the motion of dislocations relative to one another. Thus, it is possible to create various states which in one respect or another are similar to radiation damage. Therefore Dagdale and Green[^62] investigated the effect of quenching from \(380^\circ\text{C}\), i.e. from a temperature somewhat below the critical one, and the influence of deformation at room temperature on the character of annealing at \(100^\circ\text{C}\). In both cases an increase in order was observed, and, as in the case of irradiation, it

could be explained by the motion of vacancies with an activation energy equal to 0.9 eV.

Stello\(^{208}\) also investigated the relative rates of ordering in CuAu after various types of treatment. It could not be assumed that samples subjected to cold working order with the same activation energy as was the case in a sample disordered as a result of heat treatment. After bombardment with \(\alpha\)-particles with an energy of 40 MeV, the ordering (if it can be regarded in this case as a single process) had an activation energy 20% greater than in samples disordered as a result of heat treatment.

The most complete study of various ordering processes was carried out by Brinkman, Dixon, and Meechan\(^{28a,b}\). They indicate that a gold atom introduced into an interstitial site has an energy approximately 5 eV greater than an introduced copper atom, and thus the probability of transition of an introduced copper atom into a lattice site occupied by a gold atom, and of displacement of this gold atom into an interstitial site, is extremely small. This means that migration of interstitial atoms cannot lead to ordering and, consequently, the ordering observed in \(\mathrm{Cu}_3\mathrm{Au}\) is almost entirely due to vacancy migration. This conclusion is confirmed by observations of the ordering rate of \(\mathrm{Cu}_3\mathrm{Au}\) samples quenched from various temperatures; in these samples the ordering process takes place in the same temperature interval and at a rate that increases with the temperature from which the sample quench was begun, i.e., with an increase in the number of vacancies present. On the basis of this hypothesis, Brinkman, Dixon, and Meechan interpret the results obtained in experiments on bombardment of \(\mathrm{Cu}_3\mathrm{Au}\) as follows.

Electron bombardment at low temperatures apparently leads to the formation of equal numbers of vacancies and interstitial atoms. At low temperature, the interstitial atoms become mobile and occupy some vacancies; some of the interstitial atoms will then emerge at the surface, while the corresponding number of vacancies will remain in the lattice. Thus, ordering becomes possible upon raising the temperature. If the sample was initially in an ordered state, then these vacancies will lead to the formation of additional order in the already existing large regions. Electron bombardment at higher temperatures leads to greater mobility of both vacancies and interstitial atoms, and the vacancies can again lead to ordering, particularly in those cases where there is already a considerable degree of order. This situation differs from that arising during quenching in that here there are no multiple vacancies and there are interstitial atoms.

Irradiation in a reactor and in a cyclotron at low temperatures leads to the formation of a considerably larger number of vacancies and interstitial atoms than does electron bombardment. In addition, under bombardment with heavy particles the number of lattice disturbances, in particular the degree of disordering, is also greater than under electron bombardment. The interstitial atoms, as in other cases, become mobile at a temperature somewhat below room temperature and will recombine with vacancies, except for a small number of atoms that reach the surface of the crystal, dislocations, or other boundaries. Thus, the number of vacancies remaining in the lattice will be approximately the same as under electron bombardment, and these vacancies will undergo ordering when the temperature is raised to about \(150^\circ\mathrm{C}\). This effect will be substantially more significant if the specimen was initially ordered, since it is much easier to order vacancies if partially ordered regions already exist. In order to order a disordered specimen, irradiation must in fact be carried out at a temperature at which both vacancies and interstitial atoms are mobile, and when a considerably larger number of vacancies can take part in the ordering process.

This conclusion is in complete agreement with the experimental facts. Brinkman, Dixon, and Meechan bombarded \(\mathrm{Cu}_3\mathrm{Au}\) foil at \(-100^\circ\mathrm{C}\) with protons of energy \(9\ \mathrm{MeV}\). At a dose of \(5\cdot10^{17}\ \text{protons}/\mathrm{cm}^2\), the resistance increased by \(4.25\ \mu\Omega\cdot\mathrm{cm}\). The resistance of the disordered specimen is \(0.65\ \mu\Omega\cdot\mathrm{cm}\); consequently, disordering leads to an increase in resistance of \(3.60\ \mu\Omega\cdot\mathrm{cm}\). Both the ordered and the disordered specimens lost \(60\%\) of the additional resistance in the temperature range up to \(0^\circ\). In this same range, as we shall see below, a large part of the additional resistance of pure copper is lost. At these temperatures no ordering occurs in the disordered specimen, either in this case or in the experiments with electron bombardment, since the resistance of the disordered specimen after bombardment followed by “pulsed” annealing up to \(130^\circ\mathrm{C}\) was still higher than its initial value. The change in resistance of the ordered specimen was approximately the same upon heating to \(0^\circ\mathrm{C}\), which apparently is convincing evidence in favor of the assumption of migration of interstitial atoms at this temperature. This evidence will be used in the next section to interpret annealing effects in pure metals. Brinkman, Dixon, and Meechan, in experiments with proton bombardment, confirmed that in the course of annealing of disordered specimens up to \(200^\circ\mathrm{C}\) no ordering occurs; however, bombardment at \(200^\circ\mathrm{C}\) leads to a decrease in the rate of ordering.

The same was found by other authors as well (Adam and Dattadeyl$^{2}$, Glick et al.$^{24}$, Blewitt and Coltman$^{226}$).

Further experiments on the alloys Cu$_3$Au and CuAu were carried out by Cook and Cushing$^{45a,b}$, who gave a somewhat different interpretation of their results. They irradiated three series of specimens in the Canadian NRX reactor under different conditions. The first series of specimens was irradiated in uranium with a cadmium filter, in order to obtain a powerful flux of fast neutrons without thermal neutrons. The second series of specimens was irradiated with the usual neutron spectrum of the reactor, and the third series was irradiated with the usual neutron spectrum of the reactor with a cadmium filter to filter out thermal neutrons. The authors found that the flux of fast neutrons led to disordering of ordered specimens, but gave no appreciable effect upon irradiation of disordered specimens. At the same time, irradiation with thermal neutrons led to a decrease in resistance and, consequently, to ordering of both ordered and disordered specimens. This conclusion was made on the basis of differences in the effects in the second and third series of experiments.

The results obtained under bombardment with fast neutrons in these works are explained by the authors by considering thermal wedges, which lead to disordering; in this way excellent agreement is obtained between the theoretical and experimental curves. Taking a reasonable value (5 barns) for the average total scattering cross section of fast neutrons, they found that one thermal wedge leads to the disordering of $10^4$ atoms. The ordering effects are fully explained by the authors by the presence of mercury atoms arising as a result of nuclear transformations caused by thermal neutrons. In the case considered by them, such an explanation is reasonable if the experiments show that only thermal neutrons lead to ordering, since capture is the principal process in which thermal neutrons participate. On the contrary, proceeding from these considerations, it is completely impossible to explain the experiments described above, in which electron and proton bombardment likewise led to an increase in the degree of order. In addition, as Cook and Cushing suppose, a priori one may expect that the presence of impurity atoms will lead to an increase in resistance. It is possible that these authors did not observe ordering of disordered alloys because in their experiments the bombardment was carried out at too low a temperature. Apparently, in the present case, as in other experiments, the initial decrease in resistance of the ordered alloy in the flux of thermal neutrons is due to ordering as a result of vacancy migration. It is somewhat strange that Cook and Cushing did not observe a similar change in resistance in the experiments with a cadmium filter. Dattadeyl found a decrease in resistance

in an ordered specimen of Cu$_3$Au irradiated in the BEPO reactor vessel at 50° C with a cadmium filter. Blewitt and Coltman$^{226}$ subjected to detailed criticism the interpretation given by Cook and Kashing. They pointed out that the effects can be observed only at a concentration of mercury atoms of about $1 : 10^8$. Blewitt and Coltman explain the discrepancy found by Cook and Kashing in experiments carried out with and without a converter by introducing the assumption that the increased flux of fast neutrons (in the presence of the converter), owing to the possible formation of clusters of defects, provides on the whole fewer opportunities for the annihilation of vacancies, despite their large number.

In addition to the investigations set forth above, radiation effects in alloys in which “order—disorder” transitions occur have been studied on specimens of brass and of the nickel—manganese system. Eggleston and Bowmen$^{66}$ irradiated beta brass with alpha particles at $-100^\circ$ C. Beta brass cannot be disordered on quenching from a temperature above the transition temperature, chiefly because of the high rate of relaxation at temperatures lying considerably below the transition temperature. However, the large increase in resistance caused by irradiation (approximately 4 times greater than the relative increase in the resistance of copper under the same conditions) makes it very probable that irradiation leads to some disordering. The fact that this additional resistance is rapidly annealed at $-40^\circ$ C makes this interpretation quite plausible.

The influence of irradiation by fast neutrons in a reactor on the properties of nickel and manganese alloys containing from 16.5 to 31.9 atomic % manganese was studied by Aronin$^{9a,b}$. These alloys in the ordered state, in the form of the Ni$_3$Mn superstructure, are ferromagnetic; therefore Aronin, in addition to measuring resistance, carried out measurements of magnetic induction. He found (as also in the case of Cu$_3$Au) that the resistance of ordered alloys increases as a result of bombardment. The interpretation of this phenomenon in terms of disordering was confirmed by a decrease in the internal magnetic induction. At low manganese contents (from 16 to 22 atomic %) the decrease in inductive resistance and the increase in ohmic resistance do not occur as rapidly as might be expected, and this is attributed to the superposition of a new effect; bombardment of thermally quenched alloys of such composition leads to a considerable increase in magnetic induction and in the temperature coefficient of resistance, and also to a noticeable decrease in resistance. At the same time, in similar experiments carried out with alloys of higher manganese content, small changes in the opposite direction were observed. These changes differ substantially from the effects caused by cold working, which often have the opposite sign.

These results lead to the supposition that large changes in disordered structures are caused by ordering due to the motion of vacancies. It remains unclear, however, why this phenomenon occurs in alloys containing less than 22 atomic % manganese; it is possible that these alloys contain a larger number of natural vacancies than an alloy of stoichiometric composition.

For the stoichiometric alloy (24 atomic % manganese), Aronin studied the effects arising under bombardment of thermally disordered specimens, as well as of specimens disordered as a result of cold working. In both cases a tendency was found toward transition into another state with intermediate properties. The results of bombardment of ordered \( \mathrm{Ni}_3 \mathrm{Mn} \) can be interpreted theoretically as an exponential change of the order parameter with flux, provided that (as follows from theory) the order parameter changes linearly with induction and quadratically with resistance. Aronin analyzed Ziegel’s results on \( \mathrm{Cu}_3 \mathrm{Au} \), assuming that the additional resistance is proportional to the square of the order parameter, and showed that these results also agree with an exponential dependence on the order parameter. Another calculation, which can be made on this basis, shows that one neutron with an energy of \(1\) MeV in the process of disordering leads to the displacement of 5000 atoms, i.e., affects a region with a diameter of approximately \(70\) Å.

Smoluchowski showed that the decrease in resistance occurring under bombardment of alloys is due not only to a change in the degree of order, but may be connected with a change in the characteristic temperature caused by a change in the elastic constants. Such a change should influence the temperature-dependent part of the resistance. To test these considerations, Rosenblatt, Smoluchowski, and Dienes \(^{188}\) irradiated alpha brass of various compositions (10, 20, 30% zinc) in an atomic reactor. Since alpha brass is essentially a disordered alloy, it could be assumed that any decrease in resistance would be due to a change in the elastic constants. However, the decrease is observed not only at room temperature, but also at the temperatures of liquid hydrogen and liquid helium; consequently, an explanation based on a change in the characteristic temperature cannot be adequate. Annealing experiments showed that at \(170^\circ\mathrm{C}\) the resistance assumes its initial value. Kitting \(^{112a,6}\) found no signs of order in X-ray and neutronographic studies of brass crystals (70% copper and 30% zinc) annealed at \(190^\circ\mathrm{C}\). His data show that the critical temperature must in any case be no higher than \(95^\circ\mathrm{C}\). At the same time, the drop in resistance during irradiation at room temperature apparently shows that at this temperature there is some degree of order.

§ 7. Annealing of the Additional Resistance Caused by Irradiation

In considering the action of radiation on alloys we saw that some effects occur only in those cases when the introduced atoms and vacancies are mobile. In the section devoted to the influence of irradiation on the resistance of pure metals, it was shown that these effects are more pronounced in those cases when the irradiation was carried out at a temperature below room temperature. In this it is understood that the disturbance in the lattice arising as a result of bombardment at low temperature is appreciably annealed upon heating to room temperature.

In the present section we shall consider experiments set up to study the kinetics of this process of defect recovery. Before proceeding to the presentation of the results of individual experiments, it is probably useful briefly to consider a model for the kinetics of thermally activated recovery, with the help of which a large part of the data is analyzed. If the resistance is partially due to certain defects which can be annealed, and if the resistance of each defect is always one and the same, then the annealing of the resistance will obey the same equations as the annealing of the number of defects. Further, if the defects are annealed as a result of migration through the lattice to some capture site (i.e., to annihilation of the defect), and if each jump of a defect in the process of migration requires a certain activation energy \(Q\), then the annealing process will be described by the well-known equations for chemical reactions of first or second order in the case where the defects are initially distributed at random, or by certain other simple equations in those cases where the distribution of defects can be described by some mathematical formula. In particular, if this process is described by a first-order equation, then the rate of decrease in the number of defects is equal to

\[ \dot n = -\frac{n\nu}{x} e^{-\frac{Q}{RT}}, \tag{1} \]

where \(n\) is the number of defects, \(x\) is the number of displacements of a defect before its annihilation, \(\nu\) is the atomic frequency, \(Q\) is the activation energy, and \(T\) is the absolute temperature. If the process obeys a second-order equation, then an analogous expression is obtained, in which \(n^2\) will enter instead of \(n\). In each of these cases the activation energy can be found by changing the temperature and subsequently solving the equations for the rate of the process immediately before the change and after the change. Thus, if \(r\) is the ratio of the rates after and before the change from temperature \(T\)

up to temperature \(T'\), then

\[ Q=\frac{T\cdot T'}{T'-T}\,R\ln r . \tag{2} \]

Such a calculation is entirely correct if the activation energy is not a function of temperature, even in the case when it depends on \(n\). In practice, however, we are not dealing (except in special cases) with simple processes. Therefore, if an analysis such as the one we have just considered shows that the activation energy is a function of temperature, this may mean that either there is a single process whose activation energy actually depends on temperature, or that several different processes are taking place simultaneously. In the first case one has to solve the differential equation

\[ RT^2\frac{d}{dT}(\lg n)=Q-T\frac{dQ}{dT}. \tag{3} \]

In the second (and, apparently, more probable) case the treatment proves to be more complicated, since the annealed state of all the various processes will be a function of the temperature history of the specimen; consequently the total annealing process cannot be described by simple kinetic equations. In this case it is usually assumed that all processes with activation energies below a certain value will be annealed out very rapidly during isothermal annealing, whereas processes whose activation energies are above this value will not be annealed at all. Moreover, it may be considered that the annealing observed at a given temperature is due to processes with activation energies lying in a very narrow interval, the midpoint of which is determined by equation (2). However, too much hope should not be placed in these results until the assumptions on which they are based have been confirmed and an appropriate theory has been created.

After these remarks we shall turn to a presentation of the experimental results. Dugdale \(^{61a,b}\) studied the annealing of the additional resistance arising in platinum both under the action of irradiation in a reactor and as a result of cold working. Specimens were placed in the BEPO reactor (Harwell) and irradiated with a flux of thermal neutrons of about \(4\cdot 10^{18}\ \text{neutrons}/\text{cm}^2\) at approximately \(50^\circ\text{C}\). After such irradiation the resistance of the specimens, measured at the triple point of water, increased by \(0.3\%\). Approximately \(15\%\) of this increase in resistance was annealed in two stages: at \(70^\circ\text{C}\) for 646 hours and at \(90^\circ\text{C}\) for 336 hours. The annealing curves made it possible to calculate the activation energy, yielding the value

1.19 eV, in excellent agreement with the value 1.20 eV found in exactly the same investigation of a specimen whose resistance, as a result of cold working, had increased by 1.5%. This is a serious indication that in both cases one and the same mechanism of the phenomenon was involved. In a later work by Kinchin (reported in the article by Daggdale \(^{616}\)) this investigation was extended to tungsten and molybdenum. In tungsten, 20% of the additional resistance is annealed out at temperatures between 70 and 270°C with an activation energy from 1.2 to 1.6 eV; in molybdenum, 60% of the additional resistance is annealed out between 100 and 160°C with an activation energy from 1.25 to 1.35 eV, and 30% is annealed out between 190 and 270°C with an activation energy of 1.46 eV. In the study of molybdenum specimens, measurements of the stored energy were also made simultaneously.

In most work on the annealing of the resistance due to irradiation, the objects of study have been noble metals and especially copper. Marx, Cooper, and Henderson \(^{151}\), Henderson, Cooper, and Marx \(^{94}\), and Marx, Köhler, and Wert \(^{152}\) reported the first investigations of low-temperature bombardment of copper, silver, and gold, as well as nickel and tantalum. They measured the change in the resistance of these metals arising as a result of deuteron bombardment at \(-140\) and \(-150^\circ\)C and found an increase in resistance, which confirmed the theoretically expected dependence on atomic number and bond strength. In addition, the authors found that these effects at the two indicated temperatures are different. Recovery of defects at these temperatures evidently occurred with an activation energy of about 0.2 eV. Other observations by these authors have now been considerably surpassed by later works of Cooper, Köhler, and Marx \(^{466}\), and therefore we shall not consider them further.

The annealing of radiation-induced disturbances in copper was systematically studied by Eggleston \(^{656,\text{в}}\) and by Overhauser \(^{165\text{a},\,\text{б},\,\text{в}}\). To study the recovery of the residual resistance of copper after bombardment with alpha particles at \(-150^\circ\)C, Eggleston used the method of “pulsed” annealing. He found that, for annealing between \(-65\) and \(-20^\circ\)C, the activation energy is 0.717 eV. The experimental data in this temperature range are described by a third-order reaction equation. He also found that, for annealing at temperatures between 250 and 325°C, the activation energy is 2.12 eV, and the experimental data are described by a fourth-order reaction equation. In addition, Eggleston compared the annealing of the resistance of irradiated copper with that of copper wires subjected to cold working in liquid helium. Approximately up to \(-80^\circ\)C the annealing rates in these two cases were the same, but above this temperature the annealing of the radiation-induced disturbance proceeded faster than the annealing of the disturbance due to cold working. To explain this

phenomena assume that in the case of cold working the resistance is due to dislocations, or that in the case of radiation damage vacancies and interstitial atoms accumulate, and therefore annealing in this case proceeds more readily than in the case of cold working, when the defects are distributed more uniformly in the lattice.

Here it should be noted that MacReynolds et al. \(^{142a,b}\) studied the annealing of the additional resistance and of the critical shearing stress of copper and aluminum after low-temperature neutron bombardment. The additional resistance was partly annealed between \(-80\) and \(+20^\circ\) C with an activation energy of \(0.6\) eV, while the critical shearing stress did not change. The remaining part of the change in resistance and the critical shearing stress were annealed between 300 and \(400^\circ\) C with an activation energy of 2 eV. In aluminum both these properties were annealed simultaneously between \(-80\) and \(-20^\circ\) C with an activation energy of \(0.55\) eV, the annealing process being described by a second-order reaction equation.

Overhauser \(^{165a,b}\) bombarded a copper wire with deuterons of energy 12 MeV at \(-180^\circ\) C and studied the recovery of defects during isothermal anneals at temperatures from \(-185\) to \(+167^\circ\) C. He measured the resistance very accurately and found that the additional resistance \(r\), due to irradiation, does not depend on temperature, or at least is expressed by the equation \(r = r_0(1 + aT)\), where \(a < 0.0002\). Apparently these results are in contradiction with the data of Bowden and Rodeback \(^{24a,b}\), set forth in § 5. A direct comparison of the results of these two experiments is difficult, first because the measurements were made at different temperatures, and second because the experimental details are not described in the paper by Bowden and Rodeback. However, it seems unlikely that the temperature-dependent part of the resistance was changed by the irradiation only at low temperatures.

Overhauser’s main experimental results concern the kinetics of annealing. He found that even at \(-185^\circ\) C annealing proceeds to a sufficient extent to explain a large part (if not all) of the drop in the “resistance—flux” curve, and that the recovery of resistance at these low temperatures and in the interval up to \(-60^\circ\) C cannot be explained by any process with a single activation energy. On the contrary, the apparent activation energy is approximately proportional to the absolute temperature and is \(0.44\) eV at \(-100^\circ\) C. This result requires further consideration, since Overhauser, in calculating the activation energy, used equation (2), and, as stated above, such a calculation is valid only if the activation energy is independent of temperature. Indeed, if the activation energy is proportional to temperature, then substitution into equation (1) shows that the rate of the process should not depend on temperature, which by

in fact does not take place. If it is assumed that this process is some single process with a variable activation energy, then Overhauser’s results can be explained by assuming that the left-hand side of equation (3) is proportional to the temperature and that the solution of the resulting differential equation has the form

\[ Q = BT \lg T + CT , \]

where \(B\) and \(C\) are constants. It is then assumed that

\[ \frac{dp}{dt} = AT^{30}, \]

if one uses the slope of the straight line obtained in Overhauser’s experiments. Thus it becomes clear that the whole concept based on the use of an activation energy is of little value. In fact it seems more probable that it is not the activation energy of a single process that changes, but that we are dealing with a large number of superposed processes. In this case, if the processes occurring at the two temperatures used to determine the activation energy are different, then what determines the annealing rate may turn out to be not the activation energy, but the number of defects taking part in these two processes. It may be stated with confidence that below \(-100^\circ\)C the annealing of radiation damage does not obey a simple activation equation or any small number of such equations. Approximately half of the additional resistance is annealed in this temperature region.

In the interval from \(-60^\circ\)C to room temperature the recovery (in good agreement with Eggleston’s observations) can be described as a single process with an activation energy of \(0.68 \pm 0.02\) eV, and this process accounts for approximately one quarter of the additional resistance. Another quarter of the additional resistance is not annealed in the temperature interval studied. This process was described by a reaction equation of order 2.5, whereas one can hardly expect it to obey an equation of order higher than the second. However, this is in agreement with Eggleston’s observations, and Overhauser explains it by the influence of stresses arising in the lattice. Marx\(^{150}\), as well as Koehler\(^{122a}\), pointed out that this phenomenon may be connected with the accumulation of defects, which should lead to a reaction with a higher apparent order than for the same process in the case of uniformly distributed defects. Dienes\(^{56a}\) proposed another possible explanation. If the activation energy is a linearly decreasing function of the number of existing defects, then the annealing curves should be

similar to analogous curves for the process with constant activation energy, but of higher order. Unfortunately, the stage up to which annealing proceeds at a given temperature is, in these experiments with pulsed annealing, always approximately the same, and therefore it is unclear whether the activation energy is constant during annealing at a given temperature; it seems more probable that this is not the case.

Oberhauser interprets these results in the following way. Low-temperature annealing is due to the recombination of introduced atoms and vacancies, and the change in activation energy is due to the different initial distances between the recombining introduced atoms and vacancies. The recovery process at temperatures above \(-40^\circ\)C at small concentrations is due to the volume diffusion of vacancies and their annihilation with introduced atoms by a process described by a second-order equation. At higher concentrations the recovery process deviates from this usual equation because of the presence of lattice stresses arising around interstitial atoms. If this interpretation is correct (and this, apparently, is so, since in quenched metal and in metal subjected to cold working the same activation energy was found, as will be indicated below), then measurements of self-diffusion, which give the sum of the activation energies for formation and migration, make it possible to isolate the activation energy of the vacancy-formation process, equal to \(1.39\) eV, which may be compared with the calculated value of about \(1.5\) eV. However, further work, which will be described below, casts doubt on the correctness of such an assumption.

In a later paper Oberhauser\(^{165в}\) measured the energy released upon heating irradiated copper from \(-150^\circ\)C to room temperature after bombardment with a flux of \(0.9 \cdot 10\) deuterons/\(\text{cm}^2\) with an energy of \(12\) MeV. He obtained these data with a very accurate measurement of the temperature of the irradiated and unirradiated specimens and of the vessel in which both specimens were heated simultaneously (the specimens being placed at symmetrical points in the vessel). In this way he was able to find the dependence of the rate of energy release on temperature, shown as curves in Fig. 3. The total amount of heat released on heating to room temperature was about \(0.05\) cal/g. Since, according to Huntington’s calculation\(^{99б}\), the energy of a “vacancy—interstitial atom” pair is \(5\) eV (this figure can hardly be in error by more than a factor of two), this experiment makes it possible to estimate the number of pairs present in the substance after bombardment. It turned out that the number of pairs is \(5 \cdot 10^{-5}\), which should be compared with the value \(2.5 \cdot 10^{-3}\) calculated by Seitz’s theory using the value of the displacement energy found by Etten and Laubenstein. Since, simultaneously with the measurements of the released energy, Oberhauser also measured changes

of resistance, he was able to relate the amount of energy released to the decrease in resistance, and in this way a value of \(1.7 \pm 0.2\) cal/2/µohm·cm was obtained. This value may be used in calculating the experimental value of the resistance of one pair of defects, if the formation energy found by Huntington is adopted. Such a calculation gives \(11\ \mu\Omega\cdot\text{cm}\) per one atomic percent of defect pairs. This figure should be compared with the value 2.7 calculated by Dienesberger[^110], Abel[^1], and Blatt[^20]. The discrepancy of about a factor of 4 is more likely to be explained by the inaccuracy of the resistance calculation than by the calculation of the defect-formation energy. However, Blatt, Hughes, and Rubenstein1 point out that calculations of the resistance due to the presence of small concentrations of gallium, germanium, and arsenic in copper lead to values twice as large as the observed quantities, and that in this case the theory leads to discrepancies of opposite sign compared with those mentioned above. Overhauser (see Koehler[^122a]) also calculated the energy required for the annealing of “vacancy—interstitial atom” pairs situated close to one another; in doing so he changed the parameters in his equations to take into account the activation energy of vacancy diffusion, equal to \(0.68\ \text{eV}\). Various geometrical configurations give energy values of 0.20; 0.32; 0.42; 0.46; 0.50 and other higher values, expressed in electron-volts. It is assumed that in very low-temperature annealing of radiation damage the lowest of the above energy values may be used.

Fig. 3. Release of latent energy during annealing of two samples of irradiated copper. Weight of each sample 0.219 g (Overhauser[^165]).

Apparently, the works of Hoffmann and Reiser[^95] and of Geisler[^183] are of interest; they found analogous annealing effects in copper films deposited in vacuum on glass at temperatures from \(-150\) to \(-100^\circ\text{C}\). In this case the difference in resistances

was considerably greater (about 700% of the annealed resistance), but the phenomenologically calculated activation energy had the same value.

As was already indicated in § 5, Cooper, Koehler, and Marx46a,b bombarded copper, silver, and gold at a temperature of about 10° K. They found no annealing in those cases where the specimens were held for some time at the bombardment temperature, while after annealing the resistance of copper and silver (but not gold) decreased sharply at 40 and 30° K, respectively, as shown in Fig. 4. They believe that this phenomenon may be associated with recombination—

Fig. 4. Temperature annealing of the resistance of specimens of copper, silver, and gold irradiated at a temperature of about 10° K (Cooper, Koehler, and Marx46b).

—of closely spaced pairs “vacancy—interstitial atom”; at the same time these authors point out that migration of interstitial atoms requires only 0.07 eV, and therefore migration can also occur at these temperatures. The integral deuteron dose in the experiments of Cooper, Koehler, and Marx was practically the same as in the experiments of Overhauser165a,b,c, and it should be noted that the additional resistance retained in the specimens of Cooper, Koehler, and Marx upon heating to 90° K was about \(1 \cdot 10^{-7}\ \text{ohm}\cdot\text{cm}\), whereas the change in resistance according to Overhauser’s data was \(0.7 \cdot 10^{-7}\ \text{ohm}\cdot\text{cm}\). Thus it is evident that the results of these two experiments are very close and can be compared with one another. Moreover, the data presented show that at these temperatures the effect of low-temperature bombardment with subsequent annealing is essentially the same as the effect of “high-temperature” bombardment—

rolling. Overhauser found that, in the two annealing stages which he observed, the ratio of the amount of released stored energy to the magnitude of the annealed-out resistance is the same. If it is assumed that the same ratio exists also in low-temperature annealing, then Overhauser’s results can be extrapolated to this temperature region and one can find, for example, the number of defects formed at \(10^\circ \mathrm{K}\). Since about 55% of the increase in resistance is annealed out between 10 and \(90^\circ \mathrm{K}\), the degree of disorder in these specimens is approximately 2.6 times greater than the degree of disorder that was annealed out in Overhauser’s experiments, i.e. a displacement of about \(1.3\cdot 10^{-4}\) of the total number of atoms occurred. This value should be compared with the figure \(2.5\cdot 10^{-3}\), calculated from Seitz’s theory using the displacement energy found by Ergin and Laubenstein. In doing so it should be borne in mind that, since the latter value was determined at the temperature of liquid air, it may be somewhat overestimated. Taking this circumstance into account may further worsen the agreement between the two above-mentioned quantities. This discrepancy will also be considered in § 14.3.

The interpretation of these experiments was subsequently considered by Brinkman, Dixon, and Meechan \(^{28a,\,6}\). Apparently, the annealing observed at \(-30^\circ \mathrm{C}\) is a firmly established phenomenon associated with the motion of certain types of defects—either vacancies or interstitial atoms. In order to decide precisely which type of defect takes part in this process, Brinkman, Dixon, and Meechan consider the annealing of the additional resistance caused by cold working of copper. If it is assumed that cold working also leads to the formation of both interstitial atoms and vacancies, but that, unlike irradiation, the process of cold working produces a considerably larger number of vacancies than interstitial atoms, then it is possible that the annealing in copper subjected to cold working at \(-30^\circ \mathrm{C}\), observed by Eggleston \(^{65a}\), is due to the same defect that causes annealing in irradiated copper. It is also possible that the annealing observed between 100 and \(200^\circ \mathrm{C}\) (Bowen, Eggleston, and Crouchot \(^{23}\)) is due to the annealing of some defect that is completely absent in irradiated copper when it reaches these temperatures, since in that case no annealing is observed. Brinkman, Dixon, and Meechan further point out that the annealing kinetics of this process, at least in its early stages, is much closer to the kinetics of migration of point defects to some “trap” at the surface than to the kinetics described by the equation of a chemical reaction. For example, the infinite initial slope of the curve describing this process is regarded by the authors as strong evidence that it is due to the migration of point defects to grain boundaries or to edge dislocations. If both pro-

If the annealing processes (at \(-30^\circ\) and about \(150^\circ\) C) are due to point defects, then the low-temperature annealing must be due to interstitial atoms, since only under this condition can one explain why annealing at the higher temperature occurs in cold-worked specimens and does not occur in irradiated specimens. Interstitial atoms compensate almost all the vacancies in an irradiated specimen, but their number is insufficient to produce the same effect in a material that has undergone cold working.

In arriving at this conclusion, Brinkman, Dixon, and Meechan pointed out that the activation-energy values for these two processes in pure copper (\(0.7\) and \(1.2\) ev) are practically the same as those found in the case of \(\mathrm{Cu}_3\mathrm{Au}\), and that the interpretation of these phenomena can in fact be made on the basis of the analogy in the properties of these two substances.

However, this scheme predicts that in quenched copper the low-temperature stage of annealing should not occur at all, since in this case there should be no interstitial atoms at low temperature. Further, since experiments by Menintveld\({}^{146}\) showed that the annealing stages of copper and gold subjected to cold working are to a considerable degree the same, the experiments of Kauffman and Koehler\({}^{116}\) on the annealing of quenched gold confirm this conclusion. Kauffman and Koehler found annealing below room temperature and calculated from their experiments that the activation energy is \(0.68\) ev. They attribute this annealing to vacancy migration, and since their experiments on quenching from different temperatures led to an activation energy of vacancy formation equal to \(1.28\) ev, this assumption seems very reasonable, since the sum of the two activation energies given must be equal to the observed activation energy for self-diffusion—\(1.965\) ev. Thus, these two quantities are in good agreement with each other.

To explain these results according to the scheme of Dixon, Brinkman, and Meechan, it would be necessary to assert that copper and gold are not similar to each other (which seems unlikely), or that the annealing process is due to some other defects (interstitial atoms or divacancies) present in the quenched material. However, in the presence of divacancies ordering in \(\mathrm{Cu}_3\mathrm{Au}\) should occur, which, in the opinion of Brinkman, Dixon, and Meechan, is a process analogous to that considered above.

Thus, if the experiments of Kauffman and Koehler are regarded as reliable, then in the scheme described there is a serious discrepancy, and it appears most desirable to repeat these experiments with copper in order to eliminate the difficulty connected with comparing two different metals. Meechan and Eggleston\({}^{155}\) performed an experiment that led to a result somewhat different from the results of Kauffman and Koehler\({}^{116}\). They measured the resistance of copper and gold

at various temperatures and suggested that the deviations from the parabolic dependence are due to the presence of vacancies. They calculated the values of the vacancy-formation energies in copper and gold (respectively \(0.90 \pm 0.05\) and \(0.67 \pm 0.07\) eV) and then, using the values of the activation energies for self-diffusion, found that the activation energy for vacancy migration is \(1.17\) eV in copper and \(1.54\) eV in gold. The results presented were in good agreement with the scheme of Dienes, Brinkman, and Meechan, but this experimental method is less direct than the method of Kauffman and Koehler, and it is far from obvious that the “resistance—temperature” curve for a metal in the absence of vacancies has no terms of order higher than the second, as was assumed by Meechan and Eggleston.

A further difficulty in the scheme of Dienes, Brinkman, and Meechan arises from the fact that, according to this scheme, the behavior of copper and \(\mathrm{Cu}_3\mathrm{Au}\) is assumed to be the same. Recent experiments on the determination of threshold energies for the electron-bombardment effect have shown that in copper the displacement energy is \(25\) eV (Eggleston and Laubenstein\({}^{64}\)), whereas in \(\mathrm{Cu}_3\mathrm{Au}\) this energy is less than \(13.5\) eV (Dugdale\({}^{616}\)). It is obvious that, with such large discrepancies in the displacement-energy values, it seems unlikely that the values of the other energies would be practically identical in these two substances. However, until further studies of the annealing kinetics have been carried out (in particular, for quenched copper and \(\mathrm{Cu}_3\mathrm{Au}\)), all these questions cannot be resolved. If these two substances are different, then the activation energy, equal in the case of copper to \(0.7\) eV, may represent vacancy migration, while the process proceeding with an activation energy of \(1.2\) eV must still be explained additionally. Something similar was found in copper (Bowen, Eggleston, and Crowthor\({}^{23}\); Smart, Smith, and Phillips\({}^{201}\)) and in gold subjected to cold working (Meechan and Dienes\({}^{154}\)), but not in the case of quenched materials. Thus there remains the possibility that this phenomenon is to some extent associated with dislocations, although it is difficult to understand fully what occurs in this case, especially if one assumes (as was done by Brinkman, Dienes, and Meechan) that the kinetics in this case are the same as in three-dimensional migration of defects to boundaries. If it were found that the process with an activation energy of \(1.2\) eV represents vacancy migration, then the process with an activation energy of \(0.7\) eV in the quenched substance could be ascribed to the existence of divacancies, which, according to the calculation of Bartlett and Dienes\({}^{11}\), should be significantly more mobile than single vacancies. It is possible, however, that their detailed calculation contains errors; Lomer (private communication) pointed out that an essential assumption in this calculation is a hexagonal close-packed lattice. It is assumed thereby that atoms cannot leave the plane

lattice. Moreover, in Lomer’s opinion, the calculation of the forces between neighboring atoms following the nearest neighbors, carried out by Bartlett and Dienes, is open to doubt.

In the preceding exposition we concentrated attention on the values of the activation energy obtained from various annealing experiments. However, these experiments can also yield other information, and the most interesting among these concerns the time required for annealing to take place (the approximation proposed by Koehler\({}^{122б}\)). Lomer and Cottrell\({}^{138}\) pointed out that, if the activation energy is known and if some assumptions are introduced about the frequency of vibrations, then from the annealing data one can derive the average number of jumps made by a defect before its annihilation occurs. If such a calculation is carried out, a rather strange result is obtained. At temperatures below \(-100^\circ\)C the number of jumps found in this way is about \(10^8\), whereas at temperatures above \(-60^\circ\) it is about 10. For a normal number of vacancies and interstitial atoms in the lattice, one should expect the number of jumps to be about \(10^4\), and this number may increase somewhat with temperature, since the number of sites at which the defect can be captured decreases. Thus, we have an anomalously large number of jumps at low temperatures and an anomalously small number at high temperatures.

Lomer and Cottrell considered various possible explanations of these anomalies. At high temperatures the observed effect could occur if the defects important in this temperature region could not move freely through the lattice, but were captured near impurity atoms. In this case the activation energy of annealing would not coincide with the activation energy for defect diffusion, but would be equal to the sum of this energy and the activation energy of the process of removing the defect from the region close to the impurity atom. Therefore, if the defect began to move, it could rapidly diffuse to a boundary, since the thermal activation would be significantly greater than the energy required only for diffusion; thus a simple calculation leads to an anomalously small number of jumps.

It seems that this explanation agrees well with the experimental facts, but it should be noted that the activation energy found in this way (if the defects are vacancies) would not be the activation energy for diffusion of a free vacancy and, consequently, would not be equal to the difference between the values of the activation energy of self-diffusion and vacancy formation. Since Kaufmann and Koehler\({}^{116}\), in their quenching experiments, measured both this energy and the energy of formation, and since the sum of these energies gave the activation energy of self-diffusion, such an explanation in this case cannot be applied if the value of the vacancy-formation energy found in that work is considered correct, rather than ...

in the experiments of Meechan and Eggleston^155. A further conclusion from this theory, subject to experimental verification, is that the activation energy of annealing may depend substantially on the character of the impurities present in concentrations of about \(1:10^4\), which may explain the discrepancy between the results obtained in different laboratories.

To explain a very large number of jumps at low temperatures, Lomer and Cottrell suppose that interstitial atoms cannot move through the lattice in three directions, but that their motion is restricted only to lines. Then the value \(10^8\) would have the correct order of magnitude and would be in agreement with a concentration of \(10^{-4}\) vacancies per lattice site. The supposition of such linear motion of interstitial atoms would be necessary if these atoms were located not at the center of the lattice cube, but in a close-packed row, the stress being compensated by compression of the atoms along one close-packed direction, thereby producing a defect called by Frenkel and Kontorova^81 a “crowdion,” and by Paneth^168—crowdion*). Defects of this form could move only along the close-packed directions in which the stresses relax, and in this way it would be possible to explain all the results. However, the question of the stability of defects of this type has not yet been studied. In the work of Seitz and Stumpf^82 only the length of such a defect was calculated.

At this stage in the development of the theory, other possible forms of annealing of radiation defects in solids evidently arise. Thus, for example, a “crowdion” may be trapped near a vacancy located at a short distance from its axis, and while this defect cannot annihilate with the vacancy at this temperature as a result of the motion of the “crowdion,” with a sufficiently high rise in temperature the vacancy may diffuse, enter this defect, and annihilate with the “crowdion.” For this process it is also required that the vacancy make a very small number of jumps, and thus one may give another explanation of the small number of jumps at high temperature for the case of radiation damage (this explanation, of course, is unsuitable for the case of quenching).

Vacancies located very close to a “crowdion” may move with an activation energy lower than the activation energy for ordinary vacancy diffusion, and this may be an alternative explanation for the existence of regions with different activation energies, where an activation energy of \(0.2\) ev is associated with the motion of the “crowdion,” and an energy of \(0.7\) ev with vacancy migration. It may be supposed that determining the order of the reaction could give

) In what follows, to denote dislocations of this type the term “crowdion” is used. (Translator’s note.)*

Table I

Activation-energy and annealing-temperature values found for copper, silver, and gold and their alloys

Substance	Treatment method	Activation energy (eV)	Annealing temperature (°C)	Reference
Cu	Deuteron bombardment	0.1–0.2	−233	46a
Ag	Deuteron bombardment	0.1–0.2	−243	46a
Cu	Deuteron bombardment	Varies with temperature	From −165 to −60	165a,b
Cu	Cold working	Scatter	< −140	65a
Cu	» »	0.44	From −140 to −70	65a
Cu	» »	0.20	From −150 to −50	146
Ag	» »	0.18	From −150 to −80	146
Au	» »	0.29	From −150 to −50	146
Cu	Deuteron bombardment	0.68	From −60 to 170	165a,b
Cu	α-particle bombardment	0.72	From −65 to −20	65v
Cu	Neutron bombardment	0.6	From −80 to 20	142b
Cu	Cold working	0.67	From −70 to 20	65a
Cu	» »	0.88	From −50 to 50	146
Ag	» »	0.65	From −80 to 0	146
Au	» »	0.69	From −50 to 50	146
Au	Quenching	0.68	From −30 to 15	111b
Cu₃Au	Proton bombardment	—	From −60 to 0	286
Ag—Zn	Quenching	0.8	From 40 to 80	189
Cu	Cold working	1	From 80 to 200	201
Cu	» »	1.23	From 100 to 250	23
Cu	High temperature (resistivity measurement)	1.17	—	155
Au	Cold working	1.29	From 150 to 200	154
Au	High temperature (resistivity measurement)	1.54	—	155
Cu₃Au	Electron bombardment, cold working, or quenching	0.9	From 100 to 130	3; 286; 62
Ag—Zn	Quenching	1.1	From 40 to 80	189
Cu	α-particle bombardment	2.12	From 250 to 325	65v
Cu	Neutron bombardment	2	~ 320	142b
Cu	Self-diffusion	2.05	—	144

basis for choosing one of these two possibilities, since the annihilation processes of pairs and “vacancy—caterpillar” systems located close to one another are monomolecular processes, whereas the migration and annihilation of interstitial “caterpillar” atoms and vacancies are bimolecular processes. However, the ability of radiation-induced defects to accumulate at particular sites in the lattice usually hinders the realization of this possibility, leading to an anomalously high apparent reaction order (Eggleston \(^{65б,в}\)). Apparently, in considering the results of experiments with specimens in which the defects were produced by electron bombardment, the difficulties indicated do not arise.

In addition, to explain a small number of transitions at high temperatures one may assume that vacancies combine in pairs, and these double vacancies move with a considerably lower activation energy.

Thus, at present it is impossible to say which of the processes is decisive for annealing at any stage, even in the most thoroughly studied metal—copper. Therefore the known data are presented by us in the form of two tables: Table I, in which the activation energies found and the annealing temperatures are given, and Table II, containing schemes proposed to explain the annealing of copper. The reader may find a further discussion of this problem in the work of Van Bueren \(^{34}\).

§ 8. Influence of radiation on the mechanical properties of metals

8.1. Creep

The first report on the influence of radiation on mechanical properties was a paper in which the increase in the creep rate of cadmium single crystals under bombardment by alpha particles from polonium was studied. Andrade \(^{4а,б}\) found that bringing the source into contact with the crystal caused an immediate increase in the rate of flow (up to fivefold). The effect was more noticeable if the source was brought up to the crystal shortly after the start of the experiment, i.e., when the crystal was in the transitional region of creep retardation. At a later stage on the creep curve no noticeable effects were obtained. Andrade suggested that this effect may be due to the formation of slip planes under the influence of alpha particles, while the later stages of creep are associated with further slip along existing planes and therefore alpha radiation at this stage no longer has an effect. Unfortunately, in none of his experiments did Andrade check whether the creep would take on a lower value if the radiation source were removed; Andrade’s experiments were interrupted because of the war. Recently Meakin \(^{145а,б}\) attempted to repeat these experiments; however, although he had a more powerful polonium source

Table II

Schemes proposed for explaining the annealing of copper*)

Energy, ev	Temperature, °C	Brum29	Brinkman et al.286	Ziger195	Lomer and Cottrell138 scheme I	Lomer and Cottrell138 scheme II
0.1—0.2	−233	Migration of interstitial atoms	Annihilation of pairs located far from one another	Annealing of molten regions	Migration of interstitial atoms	Migration of “caterpillars”
From 0.2 to 0.5	From −160 to −60	Migration of vacancy clusters	The same	Migration of vacancy clusters	Liberation of trapped interstitial atoms	Liberation of trapped “caterpillars”
0.7	From −60 to 50	Migration of vacancies	Migration of interstitial atoms	Migration of interstitial atoms	The same	Diffusion of vacancies toward “caterpillars”
1.2	100	—	Migration of vacancies	Migration of vacancies	Migration of vacancies	—
2.1	320	Self-diffusion	Self-diffusion	Self-diffusion	Self-diffusion	Self-diffusion

*) In this table, the authors’ names in the first row indicate in which works the principal features of the schemes presented in the table should be sought. At the same time, only Ziger’s scheme195 is given in the table in full. In other cases, the details of the schemes presented in the table may differ from the views set forth at the time by the indicated authors.

\((5 \cdot 10^8\ \alpha\text{-particles}/\text{cm}^2 \cdot \text{sec})\), than Andrade \((1.5 \cdot 10^8\ \alpha\text{-particles}/\text{cm}^2 \cdot \text{sec})\), no effect was detected. At the same time it was observed that bombardment for 1–2 hours before the start of the experiment led to a certain decrease in the creep rate. A similar experiment, carried out by Schmid and Lintner \(^{192a,6}\) on zinc single crystals, showed that in this case bombardment with polonium \(\alpha\)-particles led to an increase in the strength of the crystal during creep. Their method of testing consisted in allowing the crystal to creep for one minute, removing the stress for 3 minutes, then again

Fig. 5. Creep curves of zinc crystals under irradiation by alpha particles (●——●) and without irradiation (○— —○). Specimens tested without irradiation for 1 minute, then a 3-minute pause, tested under irradiation, a 3-minute pause, etc. (Schmid and Lintner \(^{192б}\)).

for one minute the crystal was subjected to creep, and so on. Such creep curves were recorded in the presence of a radiation source. The authors found that the creep rate under irradiation was only half that without irradiation (this fact would not have been so striking if creep curves had been recorded for some time after irradiation), as is shown in Fig. 5. This effect is very difficult to explain, since the irradiation was very weak (sources with activity less than 20 mCu were used), and if these effects were due to the formation of a surface film, then before the next measurement without irradiation annealing should not have occurred. However, as can be seen from Fig. 5, some annealing nevertheless apparently takes place. One experiment, carried out with a neutron source (radon—beryllium), showed the opposite effect, namely a small (20%) increase in the creep rate (Fig. 6). It is to be hoped that such tests will be continued, with the radiation source

will be brought up to the crystal and removed from it during the measurement of creep (the test method used by Machlin). At such low irradiation doses, it is hardly possible to expect measurable effects throughout the entire thickness of the material. Nabarro\(^{159}\) estimated the creep that may be expected in a solid in the presence of an additional number of vacancies and interstitial atoms produced as a result of neutron bombardment, and found that this effect is, generally speaking, very small. Some experiments carried out with polycrystalline specimens were published.

Fig. 6. Creep curves of zinc crystals under irradiation with neutrons from a radon–beryllium source (●——●) and without irradiation (○— — —○). The test method is the same as in the experiments presented in Fig. 5 (Schmid and Lintner\(^{1926}\)).

Jones, Munro, and Hancock\(^{109a,b}\) studied the creep of polycrystalline aluminum during bombardment in the Canadian NRX reactor by a fast-neutron flux of \(1.3\cdot 10^{12}\) neutrons/\(\text{cm}^2\cdot\text{s}\). This experiment was carried out by measuring the rate of radial expansion of a tube subjected to internal pressure; the radial increase was measured from the change in the pressure of air flowing through a circular opening around the tube. The results showed that irradiation does not lead to large changes in the creep rate.

Jepson, Mather, and Yockey\(^{104}\), and Andro, Jepson, Mather, and Yockey\(^{b}\), Jepson, Mather, Andrew, and Yockey\(^{103}\) published the results of tests of aluminum under bombardment in a cyclotron. Under bombardment by a flux of \(1.2\cdot 10^{13}\) \(\alpha\)-particles/\(\text{cm}^2\cdot\text{s}\) they found no noticeable changes. In fact, both Jones et al. and Jepson—

Johnson et al. found a decrease in the wing speed during bombardment that did not exceed the experimental errors. Wittig \(^{222a,b}\) bombarded copper wire \(0.5\ \mathrm{mm}\) in diameter with deuterons in a cyclotron. The author believes that his experiments were carried out in the second stage of the creep curve, but from the curves presented in his works it follows that a slowing of creep occurred in this case. No effects were observed (measurement accuracy \(\pm 20\%\)); since the vacancy concentration, estimated from the deuteron flux \(10^{12}\ \mathrm{cm}^{-2}\cdot\mathrm{sec}^{-1}\), is \(1:10^7\) atoms, this is not very surprising. One might have expected the appearance of some effect due to the presence of thermal wedges, but even in this case, because a noticeable increase in temperature occurs only in a small volume, and also because of the short duration of this temperature rise, it is hardly possible to obtain measurable effects caused by the direct action of radiation or by the influence of radiation damage, as occurs in surface catalysis in the form proposed by Andrade.

There is also a report on experiments carried out at Purdue University. A preliminary description of the apparatus was given by Gossick \(^{87a,b}\) and Pizarro \(^{174}\), who intended to measure the yield point and Young’s modulus of molybdenum, as well as the flow of polycrystalline copper specimens \(0.3\ \mathrm{mm}\) in diameter, before and after deuteron bombardment. Preliminary results of the creep measurements showed that, at small fluxes, no appreciable changes in the creep rate are observed (Lark—Horowitz \(^{126b}\)).

8.2. Hardness. Apparently, among mechanical measurements the simplest is the measurement of indentation hardness, and a number of investigators have used this property to obtain some idea of the behavior of metals after irradiation. Billington and Siegel \(^{17}\) studied the influence of irradiation in an atomic reactor on the hardness (Rockwell—\(R_F\)) of annealed copper and copper subjected to cold working. For annealed copper the hardness (Rockwell) changed from \(R_F 43\) to \(R_F 90\), and for a copper specimen subjected to cold working—from \(R_F 93\) to \(R_F 97\). In “copper—beryllium” alloys the hardness changed with the change in electrical resistance. An increase in hardness was also observed in stainless steel, Monel metal, 65/35 brass, and silicon bronze.

Geib and Grace \(^{83a,b}\), Harmon, Eidam, and Geib \(^{89}\), Harmon, Horvath, and Geib \(^{90}\) studied the influence of deuteron bombardment on the hardness of molybdenum, using a Knoop indenter with various loads. Despite the large scatter of the experimental results, which can partly be explained by different grain orientation and other removable causes, an increase in the hardness of the annealed specimen can be observed. Later experiments, carried out—

considerably smaller degrees of irradiation, led to significantly smaller changes. Thus, these results should not be accorded great importance until further investigations have been carried out. It should be noted that the appearance of the specimen changed after irradiation: a surface film of unknown composition appeared on it, which could be removed with trichloroethylene; however, this film could nevertheless influence the hardness.

To avoid the influence of thermal spikes, Dixon and Meechan ^59 used electrons with an energy of 1 MeV to bombard copper at \(-20^\circ\mathrm{C}\). Hardness measurements showed an increase from 44.3 to 47.7 \(VPN\)*); approximately half of this increase was annealed out at \(170^\circ\mathrm{C}\) over 8 hours, which can be attributed chiefly to quenching caused exclusively by the presence of vacancies and interstitial atoms.

Merrey and Taylor ^158a, b, c, whose results on measuring the electrical resistance of the “copper—beryllium” system were described above, also found that the hardness of a large number of solid solutions of these alloys increased as a result of irradiation by 10–20 \(VPN\), and in the Cu—Be alloy by approximately 40 \(VPN\). This increase was in no way connected with an increase in resistance. The indicated difference between alloys that crystallize upon solidification is attributed to the fact that particles of different sizes are needed for these two effects. Fillnow, Haltman, and Mehl ^71 measured the hardness of their \( \mathrm{Cu}_3\mathrm{Al} \) specimens by Vickers; in disordered specimens the hardness increased from 100 to 121 \(VPN\), and in ordered ones from 110 to 158 \(VPN\), with the larger change being mainly associated with a further increase in the degree of order. This was confirmed by an increase in the sharpness of the lines on the X-ray diffraction patterns of these specimens.

8.3. Stress–strain curve for single crystals. Blewitt and Coltman ^22a investigated the influence of irradiation in an atomic reactor on the stress–strain curves of copper single crystals at room temperature and at the temperature of liquid nitrogen. The first experiments showed that a specimen irradiated with a dose of \(1.8 \cdot 10^{18}\) fast neutrons/\(\mathrm{cm}^2\) and tested at room temperature had a critical shear stress of \(1.94\ \mathrm{kg}\cdot\mathrm{mm}^{-2}\), instead of \(0.24\ \mathrm{kg}\cdot\mathrm{mm}^{-2}\) for an unirradiated specimen. Further experiments by Jameson and Blewitt ^102a, b showed that in irradiated single crystals the slip lines were grouped more closely together and more cross-slip was observed than in unirradiated crystals. When a new slip system arose, a decrease in stress occurred. All these effects are similar to phenomena observed in unirradiated

*) Measurements by the Vickers normal-pyramid method.

alpha brass. When the measurement temperature was lowered (but not the temperature at which the irradiation was carried out) to 78°K, the critical shear stress increased still further (for unirradiated crystals it did not depend on temperature). However, the initial rate of hardening was so greatly reduced as a result of the treatment that this curve could not be distinguished from the curve for an unirradiated crystal after approximately 20% elongation. Cross slip was not so evident, and the slip lines were situated closer to one another and were grouped in smaller numbers than at room temperature. Some irradiated crystals fractured brittly at 78°K after several strong jolts.

Redman, Coltman, and Blewitt \(^{184}\) studied the recovery of the critical shear stress of copper crystals. They annealed the specimens at temperatures between 300 and 400°C. No recrystallization was observed, although the critical shear stress had been exceeded by an amount from 0.2 to 3.5 \(kg \cdot mm^{-2}\). The relaxation time for recovery of the critical shear stress varied from 400 hours at 305°C to 11 minutes at 385°C, and the activation energy proved to be 2.2 eV. This value of the activation energy is greater than the activation energy found for the recovery of the electrical resistance; it is of the same order of magnitude as the activation energy for self-diffusion, i.e., the process of formation and motion of vacancies.

MacReynolds, Austine, Mackeown, and Rosenblatt \(^{142a,b}\) studied the change in the critical shear stress of copper and aluminum after intensive neutron bombardment at a temperature below \(-150^\circ\)C and found a change of several hundred percent. For copper they found that this change was annealed out approximately at 320°C, simultaneously with the annealing of that part of the increase in resistance which remained after the low-temperature anneal. In the case of aluminum, both these properties were annealed out in the range from \(-80\) to \(-20^\circ\)C. The activation energies were found to be, respectively, 2 and 0.55 eV.

Kunz and Holden \(^{125a,b}\) studied the influence of neutron bombardment on the “stress—strain” curves of single crystals. They worked at a total flux approximately equal to 0.1 of the flux used in the work of MacReynolds et al., and irradiated the specimens at room temperature. It is therefore not surprising that for lead crystals they found no changes; other specimens—iron and zinc—showed appreciable changes. Annealing of iron crystals at temperatures between 200 and 500°C led to the determination of the activation energy for recovery of the yield point, equal to 3.1 eV, i.e., to the same value as the activation energy of self-diffusion. Holden and Kunz \(^{96}\), Kunz and Holden \(^{125b}\) proposed that, since the change in the yield point is annealed out

only with the activation energy of self-diffusion, then the principal mechanism may be the formation of agglomerates of interstitial atoms. However, the x-ray data are difficult to interpret in this way. Therefore the agglomerates of interstitial atoms must be similar to Preston–Guinier zones. The authors proposed carrying out the following experiments in order to resolve this problem: 1) irradiation at 78° K, which according to their theory should produce a smaller effect on the shear stress if the interstitial atoms do not form agglomerates (although, as we have already seen, MacReynolds et al.^{142б} found that the critical shear stress in any case increases more appreciably at this temperature); 2) measurement of the electrical resistance parallel and perpendicular to the basal plane in metals with a hexagonal structure. In such cases the agglomerates should form parallel to the basal plane and, consequently, should exert different effects on the resistance in these two directions. Holden and Kunz also showed that, if the environment of dislocations by point defects is important, specimens in which there are imperfections should be subjected to mechanical aging.

Kelly ^{114a, б} studied the effect of bombardment by alpha particles at \(-100^\circ\) C on the structure of slip bands in aluminum with the aid of an electron microscope. He found that in specimens tested at \(-196^\circ\) C there was an increase in slip along the given plane, in comparison with unirradiated specimens tested (in bending) at the same stresses. In specimens tested at room temperature this effect was not found, which is not unexpected if one takes into account the annealing results obtained by MacReynolds et al. Testing of specimens at \(-78^\circ\) gave less definite results. One should mention an analogous result obtained by Maddin and Cottrell ^{143}, who found that quenched aluminum crystals show a considerable increase in the yield point, a decreased rate of mechanical quench aging, and coarser slip bands than crystals subjected to slow cooling. This effect can be explained by impulses caused by vacancies on dislocations, and occurs at room temperature, since in this case there are no interstitial atoms that could recombine with vacancies. In the case of irradiation the influence on the critical shear stress may likewise be due to vacancies and interstitial atoms migrating to dislocations, although it seems that annealing should proceed by a different route, and the arguments advanced by Kunz and Holden still require verification. If the interstitial atoms are mobile at temperatures below that of liquid nitrogen, then they may cause the increase in the yield point observed at this temperature, or, on the other hand, the density of defects may be sufficient

in order for the dislocations to capture a sufficient number of these defects to raise the yield point even in the absence of migration. At present, however, the hardening mechanism is still unknown, and further experiments must be carried out to test the various theories.

8.4. Stress–strain curve for polycrystals. One of the most noticeable effects of irradiation on mechanical properties is its influence on the “ductile–brittle” transition. This phenomenon was observed in molybdenum by Brèch, Makhu, and Hokenbery \(^{33a,b}\). Neutron irradiation at a dose of \(1.9\) to \(5.9 \cdot 10^{20}\) neutrons/cm\(^2\) led to an increase in the transition temperature

Fig. 7. Load–elongation curves for irradiated and unirradiated molybdenum at room temperature (Brèch, Makhu, and Hokenbery \(^{33b}\)).

from the “ductile–brittle” transition from \(-30\) to \(+70^\circ\)C, and thus the effect on the stress–strain curve at room temperature was most striking (Fig. 7). Brèch et al. carried out tensile tests at temperatures from \(21.8\) to \(100^\circ\)C and plotted the relative stress as a function of temperature. It was shown that the brittle-strength curves and the plastic-flow curves increased, the latter increasing considerably more, which leads to a rise in the transition temperature (Fig. 8). Since the microstructure of the specimen did not change during irradiation, Brèch et al. attributed this effect to the influence of point defects.

Makin (private communication) tested various metals after irradiation in an atomic reactor with a dose of \(5 \cdot 10^{19}\) neutrons/cm\(^2\). He found that the yield point of molybdenum increased at room temperature and at \(150^\circ\)C by 4%; for titanium the increase at

temperature of liquid air was 15%, and at 200° about 7%. In nickel this effect was still greater: the yield point at 78° doubled, and at 300° increased by 35%. The ductility, measured by the reduction in elongation, decreased in the same way as the rate of hardening, so that the area of the “stress—strain” curve for nickel changed only insignificantly.

Fig. 8. Yield point and tensile strength for molybdenum as a function of grain size, neutron irradiation, and temperature. The tensile-strength curves are shown to the left of the vertical lines, and the yield curves to the right (Brosch, Makylio, and Hokenberry \(^{336}\)).

slightly. An analogous result was obtained in the study of copper. Copper and nickel specimens were annealed, with the change in the yield point of copper annealed between 300 and 360° C, with an activation energy of 2.05 eV, while in nickel annealing occurred between 340 and 400° with an activation energy of 2.63 eV. However, in this case some annealing apparently also occurred between 100 and 300°. Evidently, annealing of nickel proceeded considerably faster (about 100 times) than annealing of copper. Experiments to verify this phenomenon, and also to study the influence of neutron dose and preliminary cold working, are continuing. These experiments should be extended to other metals.

Meyer \(^{156}\) studied the effect of deuteron bombardment on the notch sensitivity of mild steel and found that the “ductility—brittleness” transition temperature increased from \(-1\) to \(18^\circ\)C and was not a linear function of dose. The Knoop hardness also increased from 180 to 380. The annealing behavior in this case differed from the annealing of specimens hardened as a result of treatment, and occurred between 260 and \(480^\circ\)C with a variable activation energy; the \(-5\%\) effect caused by cold working was annealed out between 315 and \(371^\circ\).

Steele and Wallace \(^{207}\) studied the effect of neutron bombardment on the “stress—strain” curves of a number of aluminum alloys in the annealed state, as well as in the states of strain hardening and aging. Generally speaking, they found that both the yield strength and the ultimate tensile stress increase, this increase being greatest for annealed specimens. On the other hand, in strain-hardened alloys this increase was sufficient to raise the tensile strength to values exceeding those obtained with optimum strain hardening. Ductility in most cases (but not always) decreased. The strain-hardening exponent (i.e., the best power law satisfied by the actual “stress—strain” curve) was greater for irradiated specimens, which agrees with earlier observations on the increase in the yield strength, but leads to a decrease in the rate of hardening. A positive aspect of these experiments is the testing, under irradiation conditions, of 20–25 specimens of each alloy, which makes it possible to check the reproducibility of the results.

The influence of irradiation on various structural materials was studied by Sutton and Lizer \(^{212a, b}\). They present tables showing the effect of doses up to approximately \(3 \cdot 10^{20}\) thermal neutrons/cm\(^2\) (about \(1 \cdot 10^{20}\) fast neutrons/cm\(^2\)) at temperatures from 20 to \(250^\circ\)C on the hardness of various steels and alloys based on nickel, cobalt, and zirconium, on the tensile strength and ductility of the same substances, and also of tungsten, tantalum, and certain alloys of these metals. In addition, other properties were studied: the behavior of certain grades of boiler steel under impact, the density of steels and alloys of nickel and cobalt, and the magnetic susceptibility and electrical resistance of steels. The results obtained by these authors show that, as a result of irradiation, greater hardening occurs in softer materials than in harder materials, and that the effect of irradiation on steels is not a simple function of carbon content. These effects tend toward saturation before complete embrittlement of the materials. As in other experiments described above, the “ductility—brittleness” transition temperature in-

failed. Setton and Liser do not consider these effects to be worthy of much attention from designers, although they should nevertheless be taken into account. Measurements of magnetic susceptibility showed that there is a certain tendency toward a phase transition from austenitic to ferritic iron (this leads to an increase in susceptibility by 600% after irradiation with a dose of \(10^{19}\) neutrons/cm\(^2\)), but Setton and Liser do not consider the degree of transformation sufficient for a noticeable increase in the corrosion susceptibility of ordinary stainless steels.

Typical figures for the effects observed by Setton and Liser (percentage increases) are as follows: for hardness—in carbon steels 40%, in stainless steels 100%, in nickel 140%, in zirconium 100%; for the tensile strength—in carbon steels 10%, in stainless steels 20%, in nickel 40%, in zirconium 5%; for the yield strength—a twofold increase compared with the increase in the tensile strength.

8.5. Internal friction. Li and Nowick \(^{133}\) carried out a study in order to clarify the question of the effect of irradiation in a reactor on the internal friction of a copper–aluminum alloy (17 at.%). They found no effect and, since quenching this alloy from a high temperature had a noticeable effect on the relaxation time at temperatures from 114 to 162°C, the authors believe that this negative result shows that the vacancies formed as a result of irradiation are largely eliminated by other defects that are mobile at temperatures below room temperature. There are no other data on measurements of internal friction in irradiated metals.

8.6. Elastic constants. The effect of irradiation on elastic constants was the subject of theoretical calculations by Dienes \(^{56a}\), who found that interstitial atoms should produce a significantly greater effect than vacancies. Although this calculation was subsequently called into question (Nabarro \(^{159б}\), Dienes \(^{56б}\)), it still seems probable that the increase in the bulk modulus of elasticity in the presence of interstitial atoms should be greater than the decrease of this modulus in the presence of the same number of vacancies. To confirm these considerations, Dienes \(^{56б}\) reported that (according to preliminary data of Bowman and Tarpinian) the Young’s modulus of copper increases by 10% upon irradiation in a cyclotron. The final results of this work have not yet been published. In contrast to these results, Charlesby, Hancock, and Sansom \(^{37a, б}\) found no significant effect of irradiation in a reactor on the elastic modulus of austenitic steel. For this purpose they carried out a very ingenious experiment in which watch springs were subjected to irradiation in a reactor. In addition, Kunz and Holden \(^{125a, б}\) reported that, when copper was irradiated in a reactor with a dose of \(2.4 \cdot 10^{18}\) neutrons/cm\(^2\), there was no

no changes in the elastic constants exceeding the accuracy of the measurements (about 1%) were found. Both of these investigations were carried out at the ordinary temperature existing in the reactor, and it is possible that the effect reported by Dienes occurred at a lower temperature.

Dicamp and Crittenden \(^{55}\) reported that, as a result of irradiating copper with a dose of \(9 \cdot 10^{16}\) deuterons of energy \(20\) MeV at \(-175^\circ\)C, the shear modulus decreased by approximately 1.5%. About \(1/3\) of this change in the modulus was annealed out at \(-125^\circ\); at \(-75^\circ\) a further, very slight annealing took place. The annealing of the decrease in the modulus was completed between \(-50^\circ\) and \(+100^\circ\). In the opinion of Dicamp and Crittenden, the form of the curve describing the course of annealing of the shear modulus with temperature shows that the low-temperature recovery corresponds to a redistribution of dislocations until the latter are captured by vacancies or interstitial atoms, and that the subsequent annealing is based on the motion of interstitial atoms and the annihilation of vacancies. This explanation assumes that the recovery of the shear modulus is due to the formation or release of dislocations. On the other hand, it may be expected that point defects also reduce the shear modulus, and in that case the whole effect may be due to the disappearance of these defects. Apparently, the results of the recent work of Dicamp \(^{54}\), in which the bombarding particles were electrons of energy \(1\) MeV, speak in favor of this latter explanation. Unfortunately, in that work the value of the shear modulus of the irradiated specimen is not given, but annealing led to the following changes: from \(-196\) to \(-50^\circ\)C—an increase of 4%; from 25 to \(+50^\circ\)—no changes; at \(75^\circ\)—a decrease of 0.5%; from 100 to \(200^\circ\)—no changes; from \(250\) to \(350^\circ\)—a decrease of 2%. An explanation of these effects is difficult, but a study of their connection with the annealing of other properties of irradiated copper might shed light on the processes of clustering and annihilation of vacancies and interstitial atoms, which are the only primary disturbances produced by 1 MeV electrons.

§ 9. Phase transitions arising as a result of irradiation

In § 6 we already considered examples of systems in which the presence of an increased number of vacancies and interstitial atoms formed during irradiation can facilitate the approach of the system to phase equilibrium, as well as other cases in which irradiation led to departure from the equilibrium position. Examples of this phenomenon were observed not only in measurements of electrical resistance, but also in the study of other properties.

It is known that gray tin at low temperatures is in a stable phase state; white tin at these temperatures is metastable. Flimen[^72a-b] and Flimen and Dienes[^73] observed that the rate of transformation of white tin (irradiated at the temperature of liquid nitrogen in the Brookhaven reactor) into gray tin, measured at \(-50.3^\circ\mathrm{C}\), was considerably higher than in an unirradiated specimen. To measure the rate of transformation of unirradiated and irradiated specimens, as well as of a specimen seeded with gray tin, a dilatometer was used. The irradiated specimen had a somewhat longer induction period than specimens seeded with gray tin and, apparently, a lower transformation rate; but both of these quantities in the irradiated specimens were reproduced much better than in the seeded specimens. X-ray investigation showed that, in the course of irradiation, no appreciable amounts (0.05%) of gray tin were formed and that, consequently, the action of the radiation is due mainly to defects formed during irradiation which, upon heating, either themselves play the role of nuclei of the new phase or (as a result of diffusion) promote the formation of such nuclei.

The return of an alloy to its stable state was used by Dienes[^53a-b] to determine the threshold energy for the formation of defects. From an alloy of copper with iron (2.4% by weight) there crystallizes a phase containing iron and having a lattice close to the face-centered cubic lattice of copper; aging at elevated temperature leads to the growth of this crystallizing phase. After transformation of this phase into the stable body-centered cubic form, the iron becomes ferromagnetic and, thus, magnetic saturation provides a direct method for measuring the amount of transformed substance. This transformation can be initiated by point defects formed as a result of bombardment. Therefore, carrying out experiments with electron bombardment of various energies, Dienes was able to find the threshold energy for vacancy formation, equal to \(0.45\) MeV, which corresponds to a displacement energy of \(23\) eV, if one assumes (as Dienes[^53a] initially did) that only copper atoms are displaced.

If one assumes that iron atoms are displaced, then a value of the displacement energy of \(27\) eV is obtained; and if one assumes that either of these displacements can lead to the transformation, then the latter figure is the correct one. In a recent paper Dienes[^53b] developed arguments in favor of the assumption of displacement of iron atoms and showed that the curve of the dependence of the intensity of magnetization on the energy of the bombarding particles has the same form as the theoretically expected curve in the case in which each displacement causes the transition of 200 atoms into the body-centered cubic lattice.

The same alloy was used by Denny \(^{58в}\) to verify another basic postulate of the theory of radiation-induced disturbances. If the crystallizing phase passes completely into the ferromagnetic form, then no thermal or mechanical treatment can return it to the paramagnetic form, except heating this phase to a temperature above the temperatures of existence of both phases. An alloy with the phase crystallized in it, in this ferromagnetic state, was irradiated with protons of energy \(9\) MeV, and it was found that the amount of ferromagnetic phase decreases. Denny attributes this phenomenon to local heating in the thermal wedge or, more probably, in the displacement wedge, since it must encompass the volume of a particle of the crystallized phase. Thus, these changes are evidence for the existence of such wedges, since at present there are no other explanations of these facts. However, this phenomenon may be explained by invoking the mechanism of collisions occurring during atomic displacements (Kinchin and Pease \(^{117а, б}\)), if a sufficient number of displaced iron atoms replace copper atoms in the body-centered lattice. Another example of a metal returning to its stable form under the action of radiation is provided by the austenitic steels studied by Sutton and Lizer \(^{212а, б}\) in the experiments described in § 4. In these steels the magnetic susceptibility increased by \(600\%\), which indicates some transition to the ferritic form.

§ 10. Effect of radiation on X-ray diffraction and on density

Any noticeable changes in the lattice caused by radiation should lead to some changes in X-ray diffraction patterns. In addition to the effect on superstructure alloys and phase changes, which were discussed above, investigators looked for effects in stable, pure substances. Thus, Sidhu and Henry \(^{198}\) studied powder photographs of beryllium, graphite, diamond, and aluminum after bombardment by neutrons produced in a cyclotron by the reaction \(\mathrm{Be}(\alpha,n)\). Noticeable changes were found on the X-ray patterns of some of the substances listed*). Warren \(^{219а, б, в, г}\) found no line broadening when copper and zirconium were bombarded in a cyclotron, nor under electron bombardment of germanium. On the X-ray pattern of an aluminum single crystal after six months’ irradiation in the Hanford reactor, no measurable line broadening was detected either. Irradiation in the reactor of \(\mathrm{Cu} + 2\%\mathrm{Si}\) had no effect on the integral intensities, on the positions, or on the widths of the maxima; however, subsequent etching—

*) The authors did not indicate on the X-ray patterns of precisely which substances the changes were observed.

...by any of the three reagents used for this purpose gave very broad maxima, while etching the irradiated material with the same reagents produced no changes.

Adam (reported by Dugdale \(^{616}\)) at a measurement accuracy of \(1:20\,000\) found no changes in the dimensions of the unit cell and no broadening of the lines on the radiograph of platinum, whose resistivity changed by \(2\%\), but did find a measurable increase in the interplanar spacing \((1:10\,000)\) in molybdenum powder, whose resistivity as a result of irradiation changed by \(12\%\). Kunz and Holden \(^{125a,b}\) found line broadening on radiographs of copper and magnesium, and also broadening and displacement of the maxima on the radiograph of brass (without specifying the composition). Adam (private communication) found a rather surprising effect in the hexagonal alloy \(\mathrm{WAl}_5\). Upon irradiation of this alloy there occurred an expansion of the lattice by approximately \(0.1\%\) in the direction of the \(c\)-axis and some contraction in the direction of the \(a\)-axis. These changes are considerably larger than the changes in lattice parameter usually observed in metals; it may therefore be supposed that this alloy possesses certain nonmetallic properties. Tucker and Sampson \(^{215a,b}\) indicated that X-ray measurements of lattice parameters should be much more sensitive to the presence of interstitial atoms than to vacancies, and calculated that in this way \(0.01\%\) of interstitial atoms could be detected. The circumstance that, as indicated above, such changes have not been found in some metals is probably very good evidence that, in these metals, by the time the experiment temperature is reached, interstitial atoms are already absent. Thus this method is a valuable means of clarifying the question of the participation of interstitial atoms in the annealing process. Therefore the statement by Tucker and Sampson that the appreciable effect expected by them is observed experimentally in substances irradiated with neutrons is of interest. MacDonald and Kiritida \(^{141}\) studied the change in the volume of copper under deuteron irradiation. Their latest results, reported by Kiritida \(^{115}\), are that a dose of \(1.15\cdot 10^{17}\) deuterons \(/\mathrm{cm}^2\) at the temperature of liquid nitrogen leads to an increase in volume by \(0.034\%\) (if averaged over the deuteron range). Annealing of this damage proceeds as follows: \(10.8\%\) at temperatures below \(-105^\circ\mathrm{C}\), no annealing between \(-105\) and \(-25^\circ\); \(2.9\%\) between \(-25^\circ\) and \(0^\circ\); no annealing between \(0^\circ\) and \(+190^\circ\); \(3.6\%\) from \(190\) to \(260^\circ\), and \(2.9\%\) from \(260\) to \(400^\circ\). Even at \(400^\circ\) about \(80\%\) of the effect remained. However, bombardment at room temperature gave only approximately \(1/10\) of the effect obtained as a result of the same bombardment at the temperature of liquid nitrogen and subsequent annealing at room temperature. The magnitude of the effect at the lower temperature is equivalent to approximately \(1/10\) of the expansion of atomic volume attributed to one displaced atom (if one calculates the number of displaced...

atoms according to Seitz’s theory). The author reports that no changes in the lattice parameters were found in this case (the measurements were made with an accuracy of up to 0.02%; the paper does not indicate at what temperature this observation was made).

§ 11. Other Effects in Metals

11.1 Diffusion. One may expect that additional vacancies and interstitial atoms present in an irradiated substance increase the diffusion coefficient. However, direct measurements of diffusion are possible only at temperatures at which the diffusion coefficient is sufficiently large; at such temperatures the number of equilibrium natural vacancies is considerably greater than the number of vacancies formed as a result of irradiation. Lomer\({}^{137}\) calculated for the case of copper that there is only a rather narrow temperature region around \(450^\circ\) K in which this effect can be observed. Above \(550^\circ\) K the number of vacancies formed as a result of irradiation will already be negligible, while below \(350^\circ\) K the diffusion coefficient will be too small for it to be measurable by ordinary methods even in the presence of irradiation-induced vacancies. The situation in other substances is apparently analogous, and it is therefore not surprising that so far there have been no papers reporting the observation of a significant influence of irradiation on diffusion.

Johnson and Martin\({}^{106}\) applied the tracer-atom method to measure the self-diffusion of silver during irradiation with protons of energy 110 MeV, and also without irradiation. In this case no changes were found either in single crystals or in polycrystalline specimens. Experiments in the temperature range from 600 to \(900^\circ\) C led to the determination of the activation energy, \(1.82 \pm 0.03\) eV, and of the value of the diffusion coefficient \(D_0 = 0.11 \pm 0.05\ \text{cm}^2/\text{sec}\).

Callendin, Ridolfo, and Poole\({}^{36}\) observed an effect that may be described as a diffusion process. They found that cobalt, covered with a layer of gold and then placed between graphite disks 4.5 mm thick and irradiated in a reactor, diffuses into the graphite (in the latter, activity with the half-life of \(\mathrm{Co}^{60}\) was detected). They suggested that this “diffusion” is a direct result of the passage of cobalt atoms through the gold layer under the influence of bombardment.

The results for “copper—gold” alloys, presented in § 6, can also be interpreted as a consequence of an increase in the diffusion rate. Apparently, in these experiments the diffusion rate, in accordance with Lomer’s theory, increases many times over, since at the temperatures at which these experiments were carried out the diffusion rate is ordinarily too small for measurement by ordinary methods.

11.2. Thermoelectric effect.

Andrews, Jeppson, and Yockey\(^{7}\) studied the effect of bombardment by alpha particles in a cyclotron on the thermopower of iron, constantan, chromel, alumel, platinum, and an alloy of platinum with 10% rhodium. With a measurement accuracy of \(3 \cdot 10^{-7}\) volt/°C, no changes in thermopower were found. The experiments were carried out at temperatures up to 500° C. Another negative result was reported in the work of Jamison and Bloit\(^{102}\), who studied copper—constantan and iron—constantan pairs at the temperature of liquid nitrogen in the Oak Ridge reactor. In these experiments no changes were detected either, with a measurement accuracy of \(0.01\) mv, the hot junction being immersed in ice. Palladino\(^{167}\) also reported a negative result; in that work the practical difficulty was emphasized that most materials for lead-in wires likewise undergo damage.

A positive result was established by Andrews and Davidson\(^{5}\) in experiments on the bombardment of iron and constantan wires with protons of energy 10 Mev, the specimens under study being cooled during irradiation to a temperature below 0° C. After irradiation these wires were annealed at various temperatures, and then the difference in thermopower between the irradiated and unirradiated sections was measured;

§ 12. Effect of radiation on the properties of semiconductors

12.1. Electrical effects.

The study of radiation effects in semiconductors has been the subject of numerous investigations. The results obtained are also important for understanding data on radiation effects in ordinary metals; therefore we consider it necessary to review these works.

According to the electron theory of metals, electrons in a solid are found in various bands of energy values, arising as a result of the broadening of atomic energy levels. If between two neighboring energy bands there is a definite gap, which is a forbidden band, and if there is a sufficient number of electrons to fill all the energy bands up to the lowest band, then at sufficiently low temperatures, at which this gap is large in comparison with \(kT\), the given substance is an insulator.

Semiconductors are those substances to which, in pure form, the above-described picture of insulators is applicable, but in which impurities or defects introduce other levels that give rise to some conductivity. Thus, for example, if an impurity atom is introduced with a number of electrons greater by one than the number of electrons of the semiconductor atom, then the semiconductor will possess one electron in excess of the number necessary to fill the band (known as the “filled band”), and this electron

will lie in the orbit of the impurity atom (a “localized level”). Often such a localized level lies very close to the upper band, called the conduction band. In this case only a very small activation is needed for this electron to pass into the conduction band and somewhat increase the conductivity. Such a substance is called an \(n\)-type semiconductor (since, in this case, the electricity is carried by negative carriers). Impurities of this kind are sometimes called donors.

Similarly, if an impurity atom has one electron fewer than the semiconductor atom, it may be considered to form a localized vacant energy level for an electron of the filled band; this level may be occupied by some electron from the filled band with an energy considerably smaller than the energy required for the electron to pass directly into the conduction band. If this level is thus occupied, then a hole will remain in the filled band, and this hole will behave in exactly the same way as a positively charged carrier of electricity. Semiconductors of this type are therefore called \(p\)-type semiconductors, and such impurity atoms are called acceptors. The sign of these carriers of electricity can be determined from the sign of the Hall coefficient—the transverse potential produced by a unit current flowing perpendicular to a magnetic field.

Impurities that introduce empty levels above the forbidden band can remove electrons from the conduction band; such levels are called electron traps. On the other hand, impurities that create filled levels below the forbidden band can give electrons to holes located in the filled band; these levels are called hole traps.

The usual method of preparing semiconductors consists in introducing a small number of impurity atoms that act as donors or acceptors for electrons. However, vacancies in the lattice or interstitial atoms can produce an analogous effect, and thus one may expect bombardment by nuclear particles to influence the semiconductor properties. Two further effects are also known that can be caused by bombardment; however, from the standpoint of comparison with the phenomena occurring in metals and considered in the present review, these effects are not of direct interest to us. First, nuclear transmutations may also lead to the formation of new impurity atoms; however, consideration of these effects, although they do exert a substantial influence on semiconductor properties, lies outside the scope of our review. Second, transient effects may occur, based on the excitation of electrons during bombardment, but these effects have no analogues in metals. Nevertheless, the phenomena indicated must always be taken into account in the interpre—

tation of experimental data. An essential difference is that effects due to vacancies or introduced atoms (if they are not transient in the sense in which electronic excited states are transient) can be removed by heat treatment, whereas effects associated with nuclear transformations, obviously, cannot be removed by such treatment. A complete review of all effects connected with the irradiation of semiconductors, covering work up to 1950, was given by Lark-Horovitz \(^{126a}\) *).

[In the figure: vertical axis \(\sigma\) \((\Omega^{-1}\,\mathrm{cm}^{-1})\); horizontal axis \(d = 10^{15}\,(\mathrm{cm}^{-2})\). Curve labels: “\(p\)-type germanium”; “\(n\)-type germanium”.]

Fig. 9. Change in the conductivity of germanium irradiated with neutrons as a function of dose (Fan and Lark-Horovitz \(^{70}\)).

Early investigations (Lark-Horovitz, Blair, Davis, and Tendam \(^{128}\)) showed that, when various types of germanium are bombarded with neutrons, the resistance of pure germanium and of \(p\)-type germanium decreases, while \(n\)-type germanium is converted into \(p\)-germanium, i.e., it appears that the primary effect is the introduction of acceptor defects. Figure 9 presents curves describing an experiment of this kind, taken from a later work. Neutron irradiation leads to the same result (Davis, Johnson, Lark-Horovitz, and Siegel \(^{52}\); Johnson and Lark-Horovitz \(^{107}\)). However, only part of the neutron defects was annealed at \(400^\circ\mathrm{C}\), whereas

) See the translation in UFN 50, 51, 1953, and also the collection of translations The Action of Radiation on Semiconductors and Insulators, Moscow, 1954. (Translator’s note.*)

defects caused by deuteron bombardment were completely annealed at this temperature. The conductivity of \(n\)-germanium rapidly decreased to a certain minimum, followed by a slower increase. Upon irradiation with cadmium screens, this minimum was reached at a later stage than in graphite, and heat treatment restored the initial state. In contrast to these results obtained in experiments with germanium, silicon, \(\mathrm{Cu}_2\mathrm{O}\), and selenium (also semiconductors), independently of the type of conductivity, showed an increase in resistance as a result of bombardment both by deuterons and by neutrons, with heat treatment leading to restoration of the initial properties (Johnson and Lark-Horovitz \(^{107}\), Lark-Horovitz, Becker, Davis, and Fan \(^{127}\)). Thus, there is a substantial difference between germanium and other semiconductors. In addition, new absorption bands were found in silicon, which facilitated the interpretation of the phenomena occurring in this case. These bands were studied by Becker, Fan, and Lark-Horovitz \(^{12}\), Fan \(^{68}\), and Fan and Becker \(^{69}\). A considerable decrease in absorption in the long-wavelength region and the appearance of a new band are consistent with the idea of the introduction of electron and hole traps.

The number of holes formed on average per incident neutron was studied by Crawford and Lark-Horovitz \(^{49a,b}\). They found that \(n\)-germanium loses electrons at an initial rate of 3 electrons per incident fast neutron, while \(p\)-germanium acquires holes at a considerably lower rate—approximately 0.6–0.8 hole per incident neutron. It should be noted that these quantities are affected by the prior history of the specimen and by temperature (see Cleland, Crawford, Lark-Horovitz, and Pigg \(^{41}\); Cleland, Crawford, Lark-Horovitz, Pigg, and Young \(^{42}\)).

Similar experiments with polonium alpha particles (Bretten and Pearson \(^{25}\)) showed that with such bombardment the conversion of \(n\)-germanium into \(p\)-germanium also occurs. At first there is a loss of 78 electrons per alpha particle, and after conversion the rate of introduction of holes is 8.6 holes per alpha particle. Some of these holes disappear with time at room temperature after the cessation of bombardment, leaving two holes per alpha particle. The initial high rate of electron loss agrees with the number of displaced atoms \(^{59}\) per alpha particle with an energy of 5 MeV, calculated from Seitz’s theory.

However, if the initial concentration of holes is sufficiently large, then bombardment of \(p\)-germanium leads to a decrease in conductivity (Crawford, Cleland, Lark-Horovitz, Pigg, and Young \(^{48}\); Cleland, Crawford, Lark-Horovitz, Pigg, and Young \(^{42}\)). The concentration of holes to which all specimens tend after prolonged bombardment and which, consequently, determines the increase or decrease

conductivity, itself is a function of temperature. For example, this concentration at \(55^\circ\mathrm{C}\) is \(5\cdot 10^{17}\) holes per \(\mathrm{cm}^3\), and at \(-78^\circ\mathrm{C}\) it is \(4\cdot 10^{16}\) holes per \(\mathrm{cm}^3\). Successive bombardments of a specimen with a hole concentration between these two values at the two indicated temperatures lead to successive increases and decreases of the conductivity. Similar effects were obtained upon irradiation with deuterons (Forster, Fan, and Lark-Horovitz\(^{78}\)). It was also found that the number of carriers lost per incident deuteron, for \(n\)- and \(p\)-germanium and low-resistivity \(p\)-silicon, is respectively 11, 4, and 31.

The theory of this effect was developed by James and Lark-Horovitz\(^{101}\). If the interstitial atoms produced as a result of bombardment acted as donors, and the vacancies as acceptors, then bombardment would not lead to conversion of \(n\)-type germanium into \(p\)-type, since equal numbers of donors and acceptors would be formed and they would essentially cancel one another. The real process must be more complicated than the simple formation of electron acceptors.

James and Lark-Horovitz believe that the best explanation is to consider doubly ionized states of interstitial atoms and vacancies. Let us consider an interstitial germanium atom with one electron removed from it; this electron will be attracted to the \(\mathrm{Ge}^{+}\) ion and will move around this ion in an orbit whose diameter exceeds the interplanar distance because of the dielectric constant of germanium. Its binding energy is about \(0.05\,\mathrm{eV}\). If we now consider separately the \(\mathrm{Ge}^{+}\) ion, then the next removed electron will move in an orbit around the \(\mathrm{Ge}^{++}\) ion with an energy 4 times greater than the energy of the first electronic orbit, and probably still considerably higher, because its orbit is too small for a simple calculation based on the use of the dielectric constant measured for a large mass of material. Indeed, on the basis of the experimental results requiring explanation, one may say that this ionization energy is, in order of magnitude, comparable to the width of the forbidden energy band. Thus the energy levels may be represented as shown in Fig. 10.

Similar arguments may be used in considering the levels formed by vacancies. If the \(\mathrm{Ge}^{++++}\) ion is removed from the lattice, the band structure will be shifted upward at the vacant site and localized states will be formed above the filled band. Suppose that four states are split off and, consequently, in order to preserve neutrality it is necessary to remove four electrons; the holes thereby created will move toward the excess charge and will release four states above the band. In order to remove one of these holes, i.e., in order to fill the hole with an electron, it is necessary to expend

some amount of energy; for the second hole a larger amount of energy will be required. The third and fourth holes need not be considered. If only three states are split off, then upon the removal of four electrons only three holes can pass into these states, while the fourth hole will revolve around the negative charge in an orbit similar to the orbit of the hydrogen atom, and a state will be formed with an energy \(0.05\ \text{eV}\) greater than the energy of the filled band. If only two levels are split off, then two hydrogen-like orbits will arise, and so on.

Fig. 10. Level diagram for vacancies and incorporated atoms in germanium: (a) if the level is occupied, the incorporated atom is neutral; (b) if the level is free, the incorporated atom is doubly charged; (c) if the level is occupied, near the vacancy there is a charge equal to the charge of two electrons; (d) if the level is free, near the vacancy the charge is zero.

The difference between these schemes consists in the fact that the energy levels for holes are different. Let us suppose that the levels are to some extent similar to the levels shown in Fig. 10, i.e., that the ionization levels of the first two holes and the excitation level of the second electron are located near the lower edge of the forbidden band.

Each “vacancy—incorporated atom” pair represents two vacant levels which can capture two electrons from the conduction band, if (as occurs in an \(n\)-type semiconductor) there are any conduction electrons that can be captured. Thus, for germanium samples with high conductivity, two electrons can be captured by each displaced atom; and in those cases where the initial number of electrons is smaller, the number of captured electrons will likewise be somewhat smaller. The maximum resistance will be reached in those cases where the bombardment continued until all conduction electrons were captured on low-lying levels and the upper level created by the incorporated atom also became free. At this stage only one of the vacant levels will be used for capturing the initial elec-

trons to the conduction band, and the other will be needed in order to carry out the transition of electrons from the upper implantation level. Thus a bombardment twice as long as could be estimated from the initial slope of the curve is necessary. This prediction is in good agreement with experiment. Further bombardment leads to the formation of one unoccupied vacancy level near the filled band, and this may lead to a gradual increase in the \(p\)-type conductivity.

To explain other results obtained on silicon, it is only necessary to assume a different arrangement of levels, due to the fact that the value of the dielectric constant of silicon differs from that for germanium. Apparently, in the final state of heavily irradiated silicon there remain only levels which are difficult to fill from the filled band or to excite to the conduction band. This may be directly connected with the considerably greater energy of secondary ionization for holes formed from vacancies arising after removal of silicon atoms. In this state the upper two levels always prove to be unoccupied, and the lower two always filled.

Fig. 11. Conductivity of two samples of germanium after bombardment by electrons as a function of electron energy (after Klontz \(^{119a}\)).

One of the most interesting experiments with semiconductors consists in measuring the energy required for the formation of a stable “implanted atom—vacancy” pair. This experiment was carried out by Klontz (\(^{119a,b,c}\); see also Klontz and Lark-Horovitz \(^{120a,b,c}\)). A sample of germanium, cooled to the temperature of liquid nitrogen, was bombarded on a Van de Graaff generator at various precisely determined energies. It was found that the threshold for the change in conductivity lies near \(0.6\) MeV. If the conductivity is plotted on a graph as a function of the energy of the bombarding particle, one obtains a curve increasing with increasing energy, the initial curvature up to the linear region being due to the impossibility for electrons in this region to penetrate through the entire sample (Fig. 11). The actual value of the threshold, \(0.65\) MeV, would correspond to an electron which, in a head-on collision with a stationary germanium atom, could transfer to this atom \(30\) eV.

Thus, 30 eV is the energy required to displace one atom into an interstitial position, known as the Wigner-effect energy. Varley (private communication) pointed out that if the thermal vibrations of a germanium atom are taken into account, then the energy transferred to this atom may be larger. Allowance for this effect leads to an increase in the energy required for the formation of a stable “vacancy–interstitial atom” pair by approximately 2%. Other possible errors are introduced by the method of determining the threshold, particularly because the displacement cross section, as well as the volume of the correspondingly irradiated material, decrease rapidly with energy. Nevertheless, these experiments provide a good means of quantitatively determining the Wigner-effect energy. Kohn^124 indicated that some of the nearest interstitial positions may be reached at considerably lower energies than those calculated theoretically; and if this is so, it is assumed either that such interstitial positions are unstable at the temperature of Klontz’s experiment, or that, if they are stable, they do not give the necessary acceptor levels. This, as Kohn suggests, is consistent with the lower values of the Wigner-effect energy found in other substances.

The lifetime of carriers present in smaller numbers is a more sensitive measure of defects in semiconductors than is resistance; the use of this property for determining the threshold was first proposed by Rappaport^{182a,6}. This method was applied in the work of Loferski and Rappaport^136. They irradiated germanium and silicon electron-voltaic cells with electrons of energies from 0.5 to 1.3 MeV on a Van de Graaff generator and measured the short-circuit current. It was found that the short-circuit current decreases with time only in the case when the electron energy is above a certain critical voltage. According to the theory of this effect, the quantity \((J_s)^{-2}\) should be proportional to the number of defects formed. Therefore, if one plots \((J_s)^{-2}\) versus time, a straight line should result, whose slope \(\nu\) is proportional to the rate of defect formation.

Thus, if one then plots “\(\nu\)—electron energy,” the resulting curve intercepts on the energy axis the value of the electron energy capable of displacing atoms from their lattice sites. The results obtained are shown in Fig. 12, from which it can be seen that the effect was observed in germanium (an \(n\)-type specimen with an initial resistivity of \(0.2–0.4\ \Omega\cdot\mathrm{cm}\)) at energies above \(0.510\ \mathrm{MeV}\), while in silicon (a \(p\)-type specimen with an initial resistivity of \(35\ \Omega\cdot\mathrm{cm}\)) the effect was observed even at \(0.3\ \mathrm{MeV}\), and the abscissa of the point of intersection of the extrapolated portion of the curve was \(0.28\ \mathrm{MeV}\). These values of the energies of the bombarding particles lead to values of the displacement energy

23 eV for germanium and 27.6 eV for silicon*). The quoted value of the displacement energy for germanium is considerably lower than the value obtained by Klontz (30 eV), and the discrepancy exceeds the experimental errors. Since the experiments of Loferski and Rappaport were carried out at room temperature, thermal vibrations of the atoms in this case are of great importance, and the effect discussed in connection with Klontz’s experiment may explain the discrepancy of 2.5 eV. However, this is, of course, not sufficient to raise the value found by Loferski and Rappaport to that obtained by Klontz.

Unfortunately, Loferski and Rappaport used the same electrons both for exciting the element and for producing defects. Electrons with energies below the value at which a permanent defect is produced could affect the lifetime of carriers represented in smaller numbers. However, if such a defect is permanent, it should not grow without limit, and Loferski and Rappaport found that at 0.51 MeV the short-circuit current gradually decreased over the course of 20 minutes. In addition to studying the threshold, Klontz showed that electrons have the same effect on n- and p-type germanium as other particles. He found the number of electron traps per incident electron at various energies (at 0.7 MeV—\(10^{-3}\) traps/\(\mathrm{cm}^{3}\) for each incident electron per \(\mathrm{cm}^{2}\); at 1.5 MeV—1.1; at 1.8 MeV—2.5). In addition, he studied annealing effects.

Fig. 12. Slope in the plot “\((J_s)^{-2}\)—time,” which should have been proportional to the number of defects present, as a function of the energy of the bombarding electrons (Loferski and Rappaport \(^{136}\)).

* Addition made in proof. Rappaport and Loferski (private communication) later found measurable effects at lower energies, and the value of \(E_d\) according to their data is 12.9 eV both for germanium and for silicon.

Klontz[^1196] also studied the effect of electron bombardment on a \(p\)-type germanium specimen with extremely high resistance. Just as in the case of neutrons, in this case bombardment at the temperature of liquid nitrogen leads to a decrease in resistance. Here the resistance tends toward the same limiting value that is reached when the conductivity of the \(p\)-type is increased in specimens with low conductivity, or in specimens belonging to the \(n\)-type. Annealing at room temperature proved sufficient to produce almost complete recovery, and even at the temperature of liquid nitrogen some changes were observed.

Cassins[^51] bombarded germanium with ions from \(H^1\) to \(Sb^{51}\) with energies of about 5 \(Kev\). The effects that he observed in the change of diode characteristics are consistent with the formation of a \(p\)-type layer on the surface. Cassins believes, however, that his results do not agree with the simple Lark-Horovitz theory, since they require the presence of two types of acceptor defects and since saturation occurs at a concentration of only \(1 : 10^6\). Furthermore, the depth of penetration apparently does not depend on the nature of the ion. Cassins explains his results by using the concept of a thermal wedge. The results of analogous experiments are presented in the work of Lourens, Gibson, and Grenville[^129].

The comparatively simple explanation of all the effects by considering energy levels associated with vacancies and interstitial atoms is complicated by the phenomena observed when germanium is bombarded at the temperature of liquid nitrogen with subsequent heating. Under these conditions Forster, Fan, and Lark-Horovitz[^786], and Fan and Lark-Horovitz[^70], found that, as a result of bombardment with deuterons of energy 9.3 \(Mev\), conversion of \(n\)-type into \(p\)-type occurs, and there is the same decrease in conductivity of a high-conductivity \(p\)-type specimen as at room temperature. They also found an unusual effect when the temperature was raised. For temperatures below \(141^\circ K\), both the resistance and the Hall coefficient increased, while above this temperature they again decreased until, at room temperature, their magnitude was six orders of magnitude lower than the value at the end of irradiation (the measurements were made at one and the same temperature, \(90^\circ K\)). Thus, as a result of annealing, in a specimen that originally belonged to the \(n\)-type, a significantly greater conversion into \(p\)-type occurred than as a result of irradiation; moreover, this conversion was so substantial that a \(p\)-type specimen with the same resistance as the resistance of the irradiated specimen at the end of the bombardment process increased its resistance as a result of bombardment at \(90^\circ K\). It is assumed here that a large number of donor impurities are annealed below room temperature. This result is confirmed by mobility measurements. Analogous experiments with electron bombardment led to entirely different

results. Annealing at 90 or 130° K after irradiation led to a decrease in the Hall coefficient and the resistance, and as a result of further annealing at 170° K both of these quantities were restored to values very close to those which they had at the end of the bombardment. Subsequent annealing at still higher temperatures led to restoration of the properties that had existed before irradiation. Other experiments of the same type, in which the resistance and Hall coefficient were measured during low-temperature bombardment and annealing, were described in the papers of Klontz¹¹⁹⁶,ᵇ, Pepper, Klontz, Lark-Horovitz, and McKay¹⁷², Klontz, Pepper, and Lark-Horovitz¹²¹, Stockmann, Klontz, Fen, and Lark-Horovitz²¹¹, as well as Brown, Fletcher, and Wright³²⁶ and Shulman, Brown, and Fletcher¹⁹⁷. The results of experiments in which irradiation with neutrons was carried out at 110° K are presented in the papers of Crawford, Cleland, Holmes, and Jigg⁴⁷ and Cleland, Crawford, and Jigg⁴³. The fact that different annealing processes occur below room temperature, and also that bombardment by electrons and by heavy particles leads to different results, shows that a simple representation of defects as isolated vacancies and interstitial atoms must be complicated. The general idea underlying this model may be retained, but the number of types of defects considered must be increased by including various clusters of defects.

With the research techniques presently available, one can determine the positions of various levels that arise owing to the presence of defects, and further work should be devoted to a careful study of these positions and of their relation to the behavior of the defects. Fen and Lark-Horovitz⁷⁰ outlined paths for investigations of this kind and reported some preliminary results.

The various effects found in silicon and germanium were compared with similar effects that arise upon quenching (which may lead to the formation of vacancies, and perhaps also interstitial atoms), since these structures are very open. Taylor²¹³ found that in quenched germanium only hole traps are observed, whereas in silicon there are both electron and hole traps. The dependence of the number of these traps on the quenching temperature made it possible to calculate the formation energy, which for germanium was found to be \(1.8—5 \cdot 10^{-4}\,T\) eV per atom. Mayburg obtained similar results for germanium and studied the annealing process; to explain these processes he used the concept of vacancies and interstitial atoms essentially in the same way as was done in considering experiments on radiation damage. He found that below 516° C the best model for annealing is one in which interstitial atoms are captured by dislocations. He therefore believes that in germanium interstitial atoms are more mobile than vacancies.

Ellis and Greiner^67 studied the properties of plastically deformed germanium, and in this case, as under irradiation, it was found that specimens of the \(n\)-type, in which considerable disturbances had occurred, were converted into \(p\)-type specimens. These results, however, differ somewhat from those obtained under irradiation, since Lipson, Burstein, and Smith^135 found that in germanium subjected to cold working the internal absorption edge is shifted, whereas in irradiated germanium no such shift occurs; furthermore, the diffuse part (“tail”) of the absorption edge has a different character in these two cases.

Here one should also mention the work of Taylor, Odell, and Fan^214, who found that the high non-ohmic resistance of grain boundaries in \(n\)-type germanium is eliminated if the germanium, as a result of irradiation or hot working, is converted into \(p\)-type, and also the work of Florida, Holt, and Stephen^77, who showed that in point-contact transistors the effects of hole accumulation resulting from neutron bombardment are reduced (mainly owing to a decrease in the lifetime of the holes).

Brown and Fletcher^30, Fletcher, Brown, and MacLeod^75, Brown, Fletcher, and MacLeod^31, Brown, Fletcher, and Wright^32a, and Fletcher and Brown^74 studied the annealing of radiation damage in germanium at temperatures above room temperature. Germanium specimens, initially belonging to the \(n\)-type with a conductivity of about \(1\ \mathrm{siemens/cm}\), were bombarded at room temperature with electrons of energy \(3\ \mathrm{MeV}\), and were then annealed at various temperatures from 140 to \(360^\circ\mathrm{C}\). The annealing curves at different temperatures could be superposed on one another by a suitable choice of time scales; however, the shape of these curves does not correspond to a simple kinetic process. From the values of the factors required to bring together the curves corresponding to different temperatures, an activation energy of \(1.7\ \mathrm{eV}\) was found, although the experimental points fitted somewhat better on a curve corresponding to the assumption that the initial stages of the recovery process occurred with a somewhat lower activation energy, amounting to about \(1.6\ \mathrm{eV}\). The theory of this recovery process was considered by Fletcher and Brown^74. They believe that annealing is the sum of three terms.

1) A monomolecular term due to the recombination of “vacancy—interstitial atom” pairs located close to one another; this process has an activation energy that depends on the initial distance between the vacancies and interstitial atoms and therefore can be represented as the sum of a series of terms for all possible positions. This sum, as has already been mentioned, can be calculated for the case of face-centered cubic metals. Fletcher and Brown carried out such a calculation for the germanium lattice. Thus, the number of “vacancy—interstitial atom” pairs disappearing”】【final -offsetof
this way can be calculated.

during the annealing process is equal to

\[ N_M=\Sigma_1 N_i e^{-t/\tau_1}, \]

where \(N_i\) is the number of introduced atoms located at a distance of \(i\) lattice sites from their vacancies; \(\tau_1\) is the transition time required for the first displacement (which will be the longest in the entire recombination process), and \(\Sigma_1\) is the sum over all lattice sites within a certain radius.

2) The second process will occur when the vacancy and the introduced atom formed simultaneously are so far apart from one another that they lie outside the sphere of their interaction. In the process of diffusion, the mobile defect (according to the assumption of Fletcher and Brown—the vacancy) may approach its partner sufficiently closely and annihilate. The number of defects annihilating by this mechanism on the basis of continuum theory may be determined by the equation

\[ N_L=\Sigma_2 N_i\frac{r_c}{r_i}\frac{1}{\sqrt{\pi}}\Phi\left[\frac{r_i-r_c}{(2<b^2>)^{1/2}}\left\{\frac{\tau}{t}\right\}^{1/2}\right], \]

where \(r_i\) is the distance of the \(i\)-th site from its vacancy, \(b\) is the magnitude of the change in \(r_i\) for each transition, \(<>\) denotes averaging over all possible transitions, and \(\Sigma_2\) is the sum over all lattice sites lying outside the radius \(r_c\).

3) Finally, we must take into account the number of lattice sites that disappear as a result of bimolecular recombination of introduced atoms with vacancies that were initially at a large distance from these atoms. This leads to one more term for the decrease in the number of pairs (it is possible that there may be still other terms caused by capture at surfaces or dislocations)

\[ N_B=\frac{\Sigma_2 N_i\left(1-\frac{r_c}{r_i}\right)} {1+4\pi r_c^2<b>\left\{\frac{t}{\tau}\right\}\Sigma_2 N_i\left(1-\frac{r_c}{r_i}\right)}. \]

The total number of disappearing pairs of vacancies and introduced atoms is therefore determined by the equation

\[ N=N_M+N_L+N_B. \]

After some time, \(N_M\) will become a very small quantity, since \(\tau_1<\tau\), and the second mechanism requires many displacements with time \(\tau\), whereas the monomolecular mechanism requires, in essence, only one displacement with time \(\tau_1\).

In comparing such a complex theory with experiment, a number of possibilities arises. A successful theory must not only reproduce

annealing curve (with such a large number of parameters this can be done with the aid of any theory), but it must also lead to plausible values of the constant quantities used in this connection, for example, the transition time \(\tau\) and the radius of the elastic region around the interstitial atom \(r_c\).

Brown, Fletcher, and Wright \(^{32a}\) consider various possibilities and come to the conclusion that, in their experiments, only the first two terms play an essential role and that the first monomolecular term has two components. Since the radius \(r_c\) has such a value that the interstitial atom is surrounded by approximately three shells of neighboring atoms, they assume that the nearest possible positions for vacancies—at least at room temperature—are unstable.

They do not consider it possible to reconcile the experimental data with the calculation by using only the second and third terms and assuming that the first process occurs entirely at a temperature below room temperature, since the activation energy varies with temperature (the second and third terms require a constant energy), and also because the transition time calculated for this case is \(10^{17}\) sec (which should be compared with the expected value \(\sim 10^{13}\), which agrees with another method of treating the experimental results). Another difficulty in such a consideration is that, after both processes are completed, \(10\%\) of the existing change remains, which must now be associated with diffusion to surfaces or dislocations. Even under this condition, this phenomenon can be explained only if the interstitial atom moves or, conversely, if it is an acceptor rather than a donor. The authors do not consider any of these possibilities acceptable.

Taking into account the results obtained in experiments with the “copper—gold” system, which definitely indicate that in this case interstitial atoms are more mobile, the supposition that in germanium the mobile defects are vacancies may seem strange. It should be borne in mind, however, that germanium, which has the diamond structure, is very far from close packing and that, therefore, the properties of interstitial atoms in the germanium lattice must differ substantially from the properties of interstitial atoms in a close-packed lattice. There are a number of natural sites in the lattice which can be occupied by interstitial atoms and with respect to which one may assume that, when such a site is occupied by an interstitial atom, only a small elastic distortion arises in the lattice. In a close-packed lattice there are no such places. Of course, these considerations are not proof that the activation energy for diffusion of interstitial atoms has the same magnitude or is even higher than the activation energy for diffusion of vacancies; however, they at least show that this is not excluded on the basis

RADIATION EFFECTS IN SOLIDS

all analogy with metals, which have close packing. However, Mayburg’s results \(^{153}\) show that the most mobile defects in germanium may be interstitial atoms.

Another result, reported by Fletcher, Brown, and Reit \(^{78}\), is that the rate of change of electrical conductivity varies in the course of electron bombardment. This cannot be due to approach to the Fermi level, and therefore the authors carried out additional experiments to determine whether this phenomenon could be connected with annealing occurring under the influence of the bombardment. If this actually proved to be the cause of the indicated changes, one might expect that bombardment at 1.5 MeV would lead to annealing of the defects caused by the preceding bombardment at 3 MeV, and also that, under prolonged bombardment by monoenergetic electrons, a saturation state should be reached. Neither of these effects was in fact observed, and therefore Fletcher, Brown, and Reit came to the conclusion that the indicated phenomenon must be due to a microscopically inhomogeneous distribution of impurities.

In other semiconductors, bombardment led to a decrease in electrical conductivity. Pitt, Cleland, Crawford, and Lark-Horovitz \(^{173}\) found that, under irradiation in a reactor, the electrical conductivity of cuprous oxide plates decreases at first very rapidly (as does the forward conductivity of rectifiers made of \(\mathrm{Cu_2O}\)). The reverse conductivity decreases only slightly. The effects in silicon have already been considered above: in \(n\)-type and \(p\)-type specimens the electrical conductivity decreases. Odenkrahtz \(^{163}\) studied the effect of bombarding lead sulfide semiconductors with polonium \(\alpha\)-particles. He found that at first the conductivity increased by several percent, and then decreased to \(1/3\) of its initial value, several days being required for recovery.

Cleland and Crawford \(^{40a,b,c}\) reported that another semiconductor which changes its type of conductivity as a result of neutron bombardment is indium antimonide. In this case holes disappear from \(p\)-type material four times faster than electrons from \(n\)-type specimens of low conductivity, with both types tending to change into \(n\)-type with a carrier concentration of about \(10^5\) electrons/\(\mathrm{cm}^3\) at liquid-nitrogen temperature. Pepper, Klontz, Lark-Horovitz, and Mackay \(^{172}\) studied the change in the Hall coefficient and resistance in the course of electron bombardment; these two quantities change in the same way in \(p\)-type specimens, whereas for \(n\)-type the Hall coefficient passes through a maximum negative value and then becomes positive. It should be expected that in this case these phenomena must be more complex than the corresponding effects in germanium, since in the present case there are two possible types of interstitial atoms and two types of vacancies. Until it is...

an explanation has been given for the data obtained in experiments with germanium; apparently, it is impossible to create a theory for more complex semiconductors. In addition to the semiconductors mentioned, gallium antimonide has also been investigated. In this case Kleland and Crawford^40r found that neutron irradiation leads to a decrease in the carrier concentration in samples with high electrical conductivity of both the \(p\)- and \(n\)-types. At the same time, the rate of recovery of the changes was approximately the same for both cases, and no changes in the type of conductivity were observed. Some annealing of the disturbances was observed at \(120^\circ\text{C}\), and at \(500^\circ\) the number of acceptor centers in \(p\)-type samples increases appreciably, whereas in \(n\)-type samples the number of donors decreases appreciably. Irradiation of the resulting \(n\)-type samples with low conductivity (such low conductivity is not achieved by other methods of treatment) showed that, in these samples, the rate of removal of carriers does not depend very strongly on the initial carrier concentration, while in \(p\)-type samples it falls rapidly with decreasing initial concentration. This apparently indicates that, if this effect had not reached saturation earlier, gallium antimonide would have changed from \(n\)-type to \(p\)-type.

A special case, intermediate between a metal and a semiconductor, is graphite, in which the conduction bands and valence bands touch or even partially overlap. Kinchin^116 summarized data on the effects observed upon irradiation of graphite. The resistance of graphite increases as a result of irradiation, and this increase is the greater the higher the temperature at which the measurements are made; the Hall coefficient, initially negative, increases during bombardment and becomes positive. If the Hall coefficient is measured at low temperature, then, for a given irradiation, the value of this coefficient passes through a maximum, after which further irradiation again leads to a decrease in the coefficient. These data were used by Johnston^108 to calculate the density of defects. After irradiation with a dose of \(5\cdot 10^{19}\) thermal neutrons per \(1\ \text{cm}^2\), the density of defects capturing electrons was \(10^{20}\) per \(1\ \text{cm}^3\).

12.2. Other effects in semiconductors. It might have been expected that a change in the number of carriers in germanium would affect diamagnetism. Stevens, Kleland, and Crawford^210, as well as Stevens^209a, reported measurements they had performed on \(n\)- and \(p\)-type samples. In \(p\)-type samples, irradiation leads to a decrease in diamagnetic susceptibility at low temperatures (in agreement with what was predicted on the basis of electrical effects). In \(n\)-type samples no changes were observed; Stevens attributes this fact to an insufficient initial carrier concentration, as well as to the possible presence of inhomogeneities.

Shulz-Dubois, Nisenoff, Feh, and Lark-Horovitz ^193, after neutron bombardment of silicon-coated boron, found electron-spin resonance in \(p\)-type samples; before irradiation such effects had not been observed. Consequently, these measurements constitute a research method that can yield useful additional data for the interpretation of various effects.

Binny and Liebshutz ^19a,b,c,d studied X-ray diffraction patterns and electron-diffraction patterns of irradiated germanium and silicon. They drew attention to diffuse scattering of X-rays, since this scattering should be sensitive to local disturbances in the lattice and, consequently, should make it possible to calculate elastic constants by the Wuster method. They also studied Kikuchi lines in electron-diffraction patterns, since these lines are extremely sensitive to the presence of lattice distortions. The X-ray studies were carried out on samples irradiated in a cyclotron at \(-5^\circ\) C, and the electron-diffraction studies on samples irradiated at the temperature of liquid nitrogen in an atomic reactor. No changes were observed on any of the X-ray diffraction patterns or electron-diffraction patterns, and no changes were found in the dimensions of the unit cell of germanium irradiated with neutrons. By contrast, for silicon Binny and Liebshutz ^19c found definite changes in the diffuse scattering of X-rays, corresponding to large changes in the elastic constants \(c_{11}\) and \(c_{12}\). The change in the characteristic temperature, calculated on the basis of these quantities, is in agreement with the observed change. According to Weissman and Chang ^220, as a result of irradiation in a reactor the lattice period of a germanium single crystal along the \(a\) axis changed by 0.02%; at the same time, the width of the \((111)\) reflection increased by more than a factor of three.

Keesom, Lark-Horovitz, and Pearlman ^113a,b,c found that, as a result of deuteron or neutron bombardment, in the equation for the specific heat of silicon at low temperatures the linear term, which takes into account the role of electrons, decreases significantly. Thus, a decrease in the number of carriers as a result of bombardment is confirmed. They also found a decrease in the characteristic temperature (from electrical measurements). To explain the magnitude of the observed change in the characteristic temperature, Dienes and Kleynman ^57 proposed that some additional lattice disorder, different from vacancies and interstitial atoms, must be taken into account. They suggested that in the structures of silicon and diamond some covalent single bonds are broken and transformed into double bonds. Calculations showed that each fast neutron leads to the formation of a region 45 Å in diameter in which the rupture of many bonds occurs, leading to a weakening of the lattice and to a considerable decrease in the elastic constants. This process has no analogue in metals. Other effects

bombardment in covalent and ionic compounds will be considered in § 13.

The graphite lattice also changes as a result of bombardment. The interplanar spacing \(c\) as a result of bombardment (at a dose of \(10^{20}\) neutrons/cm\(^2\)) increases at room temperature by \(1.3\%\) (private communication from Simmonds) and by \(4.75\%\) at \(-196^\circ\) C (Kitting\({}^{112г}\)). At a lower temperature the expansion of the lattice is not proportional to the dose. At the same time the reflections on the X-ray photographs broaden considerably and give long “tails.”

§ 13. Analogous radiation effects in nonmetals

13.1. Introduction. A review of radiation damage, even if concerned chiefly with effects in metals, would be incomplete if it did not contain descriptions of analogous effects in nonmetals. The basic mechanism which we have considered as determining the phenomena observed in metals may equally well occur in any solid. At the same time, in substances in which displaced electrons can also lead to effects stable in time, other phenomena must also be taken into account. It might have been supposed that effects due to displaced atoms could be distinguished from purely electronic effects both theoretically and experimentally, since it seemed that only heavy particles could displace atoms from their positions in the lattice. Unfortunately, it turned out that this assumption is not entirely justified. The effects arising on irradiation with X-rays and with heavy particles proved to be similar to one another. Moreover, it was shown that some phenomena arising under the action of X-rays in ionic solids can be explained only if it is assumed that such irradiation leads to the displacement of atoms. The process underlying these displacements is, in essence, probably electronic and, apparently, does not occur in metals. However, in studying substances with intermediate properties one must always reckon with this possibility. Up to now two mechanisms have been proposed for the displacement of atoms in ionic solids under the action of X-rays: according to the first mechanism (Maxham\({}^{148}\), Pratt\({}^{175}\)) it is assumed that vacancies are removed from dislocations, possibly under the action of excitons; according to the second mechanism (Varley\({}^{217а,б}\)), multiple ionization by radiation can force an initially negative ion to leave its position under the action of electrostatic forces repelling this ion from its positively charged neighbors, thereby creating a “vacancy—interstitial atom” pair. Owing to the existence of these effects, great caution must be exercised in comparing the results

tates obtained for nonmetals and for metals. In this section we shall only mention some of those effects which at present seem closest to the corresponding phenomena in metals, or which most clearly illustrate the processes underlying these effects, without attempting an exhaustive survey of this large and complex question.

13.2. Mechanical properties. A number of papers report significant changes in the plastic properties of ionic crystals. Wogan, Leivo, and Smoluchowski \(^{218}\), and Smoluchowski, Leivo, Pirlshtein, Smith, and Wogan \(^{205}\) found that irradiation of sodium chloride by protons leads to an increase in its hardness (measured with a Tukon instrument) from 16.3 to 36. Uestrehl \(^{221a,b}\) confirmed this result and also reported a similar increase in hardness under electron bombardment and under irradiation by x-rays. In fact, under all the indicated methods of bombardment there was an increase in hardness by more than 100%, with annealing of these effects occurring between 150 and 300° C.

An even greater increase in the hardness of sodium chloride (up to 46 \(VPN\)) was obtained upon irradiation with alpha particles (under electron irradiation the hardness increased to 36 \(VPN\), under x-ray irradiation—to 33.4 \(VPN\)). The fact that these effects can be caused by radiation that is incapable of displacing an atom by direct collision shows that some one of the mechanisms considered in the preceding paragraph (or an analogous one) must be involved.

It was further found that irradiation lowers the internal friction in ionic crystals (Frankl and Read \(^{80}\), Frankl \(^{79}\)) and increases the yield point (after a certain decrease at small doses, Pratt \(^{175}\)). Pratt attributes this initial decrease to the release of individual irregularities from dislocations, and the subsequent increase to the formation of new irregularities.

The Young’s modulus of ionic crystals, according to the data of Wogan, Leivo, and Smoluchowski \(^{218}\), also increases under proton irradiation; on the other hand, Gordon and Nowick \(^{86}\) reported that x-ray irradiation increases the modulus \(c_{11}\) only in rock salt subjected to cold working. In their experiments irradiation effectively increased the modulus by the amount of the decrease that had occurred during the preliminary cold working. In this case there may be a substantial difference between the effects arising under the influence of different kinds of radiation.

13.3. Diffraction of x-rays, electrons, and neutrons; density. A number of experiments were carried out to study the influence of irradiation on lattice parameters, determined by x-ray methods, and on density. If the results of such experiments are compared, then it would probably be possible

distinguish lattice disturbances in which vacancies predominate and states in which vacancies and interstitial atoms are present in approximately equal numbers. Unfortunately, the published measurements do not agree with one another. Binder and Sturm \(^{18\,a,b}\) and Keating \(^{112}\) studied the action of atomic-reactor radiation on lithium fluoride. Since lithium, when bombarded with neutrons, gives a triton and an alpha particle with an energy of \(4.8\) MeV, a considerable disturbance of the lattice may occur in this case. Binder and Sturm found that the discrepancy between the changes in the x-ray and macroscopic density amounts to \(6\%\), so that, apparently, the disturbance is not limited merely to the formation of vacancies. However, Keating found no changes in the lattice parameters upon irradiation with a flux of \(7.5\cdot 10^{17}\) neutrons/\(\text{cm}^2\), although in his experiments there was a broadening of the lines and a decrease in extinction, which makes these results doubtful. Warren \(^{219\,a,b,c,d}\) also found that the principal effect in the irradiation of LiF is the broadening of the maxima; he attributed this to the great variety of interplanar spacings occurring in the crystal. The integrated intensity of the (002) maximum also increased, whereas the intensity of the (004) and higher-order maxima did not increase. On the other hand, Berry \(^{16}\) found that irradiation of potassium chloride by Roentgen rays leads to an increase in the lattice dimensions, which becomes saturated when a relative increase of \(1\cdot 10^{-5}\) is reached. According to other investigators, saturation of the change in length occurs at a relative elongation of \(20\cdot 10^{-5}\). Berry believes that his results confirm the presence of vacancies, although calculations ought to be made in order to decide whether the observed expansion of the lattice can be caused by the presence of vacancies or whether this expansion is evidence for the formation of a small number of interstitial atoms under the action of Roentgen rays.

Further proof of changes in the volume of lithium fluoride was obtained by Primak, Delbecq, and Yuster \(^{177,179}\). They found that nonuniformly irradiated crystals possess double refraction, and interpreted this double refraction as a photoelastic effect caused by a change in the volume of the irradiated regions of the crystal. After irradiation with a flux of \(10^{13}\) deuterons per \(1\ \text{cm}^2\), the change in volume, calculated on the basis of the data on double refraction, was from \(2\) to \(9\cdot 10^{-5}\), depending on the depth. Since the number of vacancies could also be determined from the density of coloration, it proved possible to compare the expansion of the crystal with the density of vacancies. It was found that the discrepancy between these two quantities does not exceed the experimental errors.

Leivo \(^{131}\) found that the density of potassium chloride (determined by measuring the temperature of suspension in 1–3 dibromopropane) as a result of irradiation with protons of energy \(360\) MeV for one

hour, decreases by \(5\cdot 10^{-5}\ \text{g}/\text{cm}^3\). A similar effect was also found by this author under irradiation with X-rays. Leibow and Smoluchowski \(^{132}\), with more prolonged irradiation, obtained an effect four times as large. A study of the surface of these crystals by Smith, Leibow, and Smoluchowski \(^{202}\), using interferometric methods, gave no evidence that these density changes are caused by diffusion, but the authors report that slip lines were often visible in the irradiated regions.

Lin and Russell \(^{134}\) measured the change in the length of KCl and NaCl crystals under X-ray irradiation and compared the results with data on the density of \(F\)-centers found by an optical method. The results differed by no more than 5%; for example, in KCl the change in length per unit length was \(1.36\cdot 10^{-6}\), and the number of vacancies, calculated on the basis of this value, was \(6.6\cdot 10^{16}\ \text{cm}^{-3}\); on the other hand, the number of vacancies found from optical data was \(6.7\cdot 10^{16}\ \text{cm}^{-3}\). This fact again shows that X-rays in ionic crystals form vacancies and, perhaps, interstitial atoms.

In covalent compounds these phenomena may lead to even more substantial changes, and in some cases the crystal lattice is destroyed under bombardment and passes into a glassy state. This effect has long been known to mineralogists, since in some minerals containing atoms of radioactive isotopes as principal constituents or as impurities, processes occur as a result of which the mineral, while remaining crystalline in external appearance, shows no anisotropy, cleavage, or X-ray patterns, unlike other crystalline substances. This state is called metamict. The most remarkable fact is that some substances become metamict, while others do not. This problem was considered by Primak \(^{176}\) on the basis of data obtained during neutron bombardment of a number of substances in a reactor (see also Primak, Fuchs, and Day \(^{178}\)). He found that irradiation in a reactor: (a) has no effect on the Debyegrams of beryllia, \(\mathrm{GeO_2}\), germanium, silicon, corundum, or rutile; (b) causes small increases in the lattice constants of MgO (0.1%), spinel (0.12%), and \(\mathrm{CaF_2}\) (0.08%); (c) causes large changes (without an increase in the diffuseness of the lines) in diamond (0.9%), silicon carbide (0.68% along the \(a\) axis and 0.68% along the \(c_0\) axis), chrysoberyl, and phenacite; and (d) leads to an increase in the diffuseness of the lines in the X-ray patterns of quartz, tridymite, and cristobalite. Primak concluded that the large effects were determined not by the crystalline structure or by the type of bond, but only by the existence of a metastable glassy state.

The limiting state to which this process can proceed is well illustrated by the behavior of the mineral zircon [Harley and Fairbairn \(^{100a,b}\), Holland and Gottfried \(^{91}\)]; this mineral may contain

various amounts of uranium and thorium as impurities, and thus there are specimens of this mineral that have received different irradiation doses—up to \(10^{16}\) alpha particles per \(1\ \mathrm{mg}\).

The intensity of the lines on zircon X-ray diffraction patterns decreases with dose and becomes comparable with the background at a dose of \(6\cdot 10^{15}\) alpha particles per \(1\ \mathrm{mg}\). At the same time a shift of the diffraction maxima occurs, and at a certain intermediate stage a second maximum appears, which Holland and Gottfried attribute to the existence of a second phase. With a further increase in dose this maximum also disappears and becomes indistinguishable from the background. All these data (especially if one takes into account that the irradiation of the minerals occurred over more than a thousand million years) show that the annealing rate at ordinary temperatures is quite negligible; on the other hand, metamict minerals almost always recrystallize upon heating, but the original lattice is not necessarily formed.

An interesting case of metamictization caused by irradiation in a reactor is the metamictization of quartz, which never occurs in nature. Since quartz is sometimes found near radioactive deposits, this apparently indicates that gradual annealing can take place at ordinary temperatures. However, the rate of this process is such that it is of no significance in laboratory studies. Wittels\(^{225}\) found that after irradiation quartz at first becomes more anisotropic, the lines on Debyegrams broaden considerably and become diffuse, and the symmetry of Lauegrams also disappears. At this stage the change in density, according to X-ray data, is \(4.8\%\), and according to mechanical measurements \(3.5\%\). Further irradiation [Wittels and Sherrill\(^{224}\)] leads to an even greater decrease in density, down to \(14.7\%\), and to the disappearance of the lines on X-ray diffraction patterns; the crystals no longer have latent heat in the \(\alpha \rightleftarrows \beta\) transformation, and piezoelectric crystals no longer resonate. Thereafter specimens that before irradiation had been quartz, cristobalite, tridymite, and quartz glass transformed into a single phase—an optically isotropic glass with specific gravity 2.26. In all cases, as a result of annealing at \(930^\circ\mathrm{C}\), this glass recrystallized into quartz. The early stages of this disorder were also studied by Johnson and Pizzo\(^{105}\), who found that at first there is a rather rapid decrease in the frequency of a quartz crystal vibrator, caused by ionization, and also a slow linear contraction, attributed to the formation of defects by neutrons. After neutron irradiation the quartz became transparent, and subsequent irradiation with X-rays no longer led to its coloration or to a change in frequency. One of the features of radiation damage in quartz, noted by Wittels and Sherrill\(^{224}\), is that the change in density accelerated during irradiation up to a dose of \(10^{20}\) neutrons/\(\mathrm{cm}^2\). Primak\(^{1766}\) suggested that this is caused by thermal spikes, which give a large

effect, when the thermal conductivity of quartz decreases as a result of the presence of disturbances that arose at the initial stage of irradiation.

Boron compounds have also been studied in considerable detail, since under irradiation in a reactor the reaction \(B^{10}(n,\alpha)\) gives large effects. Pils[^131] studied a number of boron compounds and found changes in the lattice parameters of the order of 1% at doses of \(10^{18}\) thermal neutrons per \(1\ \text{cm}^2\). It was found that an increase in the dimensions of the unit cell along the \(c\) axis and a decrease along the \(a\) axis occur with noticeable saturation at fairly early stages of irradiation. However, other effects—for example, broadening of some lines in the X-ray patterns—do not exhibit saturation. Apparently this is due to the limitation of the number of possible interstitial atoms, whereas other defects, for example such as orientational disturbances, may continue to form. Tucker and Senio[^216a,^b,^g] studied in detail the action of heavy particles on boron carbide and obtained very noticeable effects. They found contraction in the direction of the \(c\) axis and expansion in the direction of the \(a\) axis, as well as changes in the mean positions of some atoms and very strong diffuse scattering. Likewise, under proton irradiation of diamond, the scattering angle of X-rays increases by \(10'—30'\) (Hayes and Smoluchowski[^93]) and a new maximum appears in the X-ray pattern (Robinson, Lee, and Smoluchowski[^186]).

Antal, Weiss, and Dienes[^8] proposed using the passage of long-wavelength neutrons through a substance to determine the number of defects in irradiated solids and reported that preliminary results of experiments with \(Al_2O_3\) gave encouraging results. If the neutron wavelength is large compared with any Bragg-scattered wave, then only defects can cause scattering of neutrons from the beam, and this will be the sole cause of attenuation of the neutron flux, provided, of course, that the nuclei under consideration do not capture neutrons. Further, the scattering of neutrons by a defect will be the same as by the nucleus under consideration and can be precisely determined from nuclear experiments. Consequently, this method in principle permits a direct determination of the number of defects. The practical application of such a method may be somewhat limited. The restriction to substances with low capture cross sections does not permit the study of very many materials, and in order to be able to measure the attenuation accurately the specimen must probably be very large (of the order of a meter in length). Further, it is unclear how the formation of “clusters” of defects will affect the attenuation of the neutron flux.

Another substance in which, apparently, a phase transition occurs (besides those mentioned in § 9) is phosphorus. Chipman, Warren, and Dienes[^38] found that irradiation increases the lattice dimension of black phosphorus along the \(c\) axis by \(0.03 \pm 0.02\%\), and also that new lines appear in the X-ray pattern. Some of these lines were identified as lines of red phosphorus. In addition to these X-ray...

graphic changes, the specimen became stronger and harder and showed a tendency toward reduced water absorption.

13.4. Diffusion and electrical conductivity. It is believed that in ionic substances electrical conductivity is due to the diffusion of vacancies of positive ions. Consequently, irradiation should have approximately the same effect on electrical conductivity as on diffusion. X-ray irradiation leads to a decrease in the diffusion coefficient of sodium ions in sodium chloride (Mapother^147), and also reduces the electrical conductivity of potassium chloride (Nelson, Sproull, and Caswell^160). These effects are consistent with the observations cited above, which showed that X-ray irradiation lowers internal friction. However, Nelson et al. found that further irradiation again leads to an increase in electrical conductivity; they obtained this result also under neutron irradiation.

Pirlshtein^169a,b,c (see also Smoluchowski^203b) studied in detail the effect of bombardment of sodium and potassium chlorides with protons of energy 400 MeV and with gamma rays. He confirmed that at small doses the electrical conductivity decreases, while at large doses the electrical conductivity increases again. In addition, the author found that the annealing characteristics of these defects were very complex. At first, during annealing, the electrical conductivity rapidly falls to \(1/100\) of the conductivity of the unirradiated control specimen, and then, with further heating, the electrical conductivity increases (with the presence of some oscillations) to the value corresponding to the unirradiated substance. Smoluchowski^203a,b considered these results taking into account the formation, aggregation, and disappearance of vacancies and interstitial atoms, but the question of the role of the separate processes at the various stages is still far from being resolved.

13.5. Thermal conductivity. Berman, Klemens, Ziman, and Fry^15, Berman^13, and Klemens^118 investigated the influence of neutron irradiation on the thermal conductivity of quartz at low temperatures. As a result of irradiation the thermal conductivity of quartz decreased, especially in the region of the conductivity maximum, near 12° K; at sufficiently large doses this maximum was suppressed. At this stage the curve in “conductivity—temperature” coordinates was similar to the analogous curve for quartz glass (in accordance with the observations of Uittels and Sherrill^224). On annealing, a gradual restoration of the initial properties occurred. These results were analyzed by Klemens^118, taking into account scattering caused by defect clusters, which affect low-frequency phonons at low temperatures. Assuming reasonable sizes for the defect clusters, Klemens found that the cluster density is \(10^{-7}\) per atom. Apparently, the concept of defect clusters can adequately explain the available data.

Berman, Foster, and Rosenberg^14 obtained similar results in an analogous study of synthetic sapphire crystals.

In this case the result can be interpreted if it is assumed that one neutron affects a region containing 4000 atoms in a long narrow volume. A rather similar effect was obtained upon irradiation with gamma radiation, but apparently saturation of the disorder occurred earlier than the complete decrease in thermal conductivity obtained upon neutron irradiation was reached. In contrast to neutron irradiation, irradiation of diamond with gamma rays produced no effect.

13.6. Magnetic susceptibility. If vacancies or interstitial atoms possess their own magnetic moment, then irradiation should lead to an increase in the degree of paramagnetism of the substance, and in accordance with this McClelland^139 and McClelland and Donio^140 observed a decrease in diamagnetic susceptibility as a result of irradiation in quartz, fused quartz, recrystallized aluminum oxide, and magnesium oxide; on the contrary, no changes were observed in spinel, sapphire, and BeO. If the paramagnetism is due to the formation of defects with spin equal to \(1/2\), then the number of such defects can be estimated. At a dose of \(3.76 \cdot 10^{19}\) neutrons/\(\mathrm{cm}^2\), the following data were obtained (number of defects per molecule):

\[ \begin{aligned} \text{in quartz glass} &\quad —\ 2.1 \cdot 10^{-3};\\ \text{in crystalline quartz} &\quad —\ 3.2 \cdot 10^{-3};\\ \text{in recrystallized aluminum oxide} &\quad —\ 2.4 \cdot 10^{-3};\\ \text{in magnesium oxide} &\quad —\ 0.65 \cdot 10^{-3}. \end{aligned} \]

In the first three substances a certain saturation of the effect was observed. In magnesium oxide (in two separate experiments), at a dose of \(0.52 \cdot 10^{19}\) neutrons/\(\mathrm{cm}^2\), the effect was very small, whereas at a dose of \(3.76 \cdot 10^{19}\) neutrons/\(\mathrm{cm}^2\) the effect was 8 times greater. Consequently, at least in this case, the phenomenon proves to be more complex than the simple formation of paramagnetic defects. Stevens^2096 measured the temperature dependence of the susceptibility of quartz crystals. Before irradiation, the diamagnetic susceptibility over a considerable interval does not depend on temperature, whereas after irradiation it decreases noticeably with increasing temperature. This confirms the assumption that paramagnetic centers arise. After some irradiation the number of apparent centers decreases with further irradiation, although the density still continues to decrease. Apparently this phenomenon may be explained by the fact that at first the disorder has the form of paramagnetic defects, for example interstitial atoms, while with further irradiation quartz approaches a glassy state and, after some time, the number of interstitial atoms actually decreases.

Döamel, Freymann, and Freymann^63 proposed using the effect of irradiation on the absorption of electromagnetic radiation as a useful method for studying radiation disorder. They measured the effect of neutron irradiation of zinc oxide on absorption in the region

0.2–1000 kilocycles per second, and found a noticeable effect; from the relation between the frequency of maximum absorption and the temperature it is possible to calculate the activation energy. Paramagnetic-resonance methods can also be used to study the nature of defects. Griffiths, Owen, and Ward \(^{88a,b}\) studied this effect in quartz and diamond; the theory of the method was considered by Obrien and Pryce \(^{161}\). It has been possible to show that the defects producing the “smoky” coloration of quartz are in fact aluminum impurities.

13.7. Optical effects. Generally speaking, optical effects in nonmetals caused by irradiation are similar to the effects that arise with other methods of coloration, but absorption bands sometimes appear which do not arise with the other methods. However, the interpretation of these phenomena is still at an initial stage; moreover, the general effects are apparently not analogous to optical effects in metals and therefore will not be considered in greater detail.

§ 14. Conclusion

In this section an attempt is made to bring together the various data presented above in order to give a general picture of the processes that occur in radiation damage.

14.1. Nature of the damage. Damage caused by irradiation of solids—apart from chemical, electronic effects and nuclear transformations—can best be described in terms of the formation of vacancies and interstitial atoms. With the exception of the case of electron bombardment, this damage is distributed nonuniformly and is concentrated in small volumes of the substance. If the temperature is sufficiently low and the initial substance is in a stable state, then no other effects are observed. If the substance is not in a stable state, then the brief existence of “vacancy–interstitial atom” pairs, which, generally speaking, are unstable, may lead to the formation of nuclei of a more stable phase.

If heavy bombarding particles are used, local effects may arise which are best described in terms of the heating of a small volume of the substance to a high temperature, with subsequent quenching of this volume. This was shown for the disordering of ordered alloys and, more convincingly, in the case of the formation of regions of an unstable phase in an alloy of 2.4% Fe in Cu (Denny \(^{53b}\)). However, this result may also be interpreted by considering collisions that lead to atomic replacements (Kinchin and Pease \(^{117a,b}\)).

14.2. Energy required to produce damage. In order to find the energy required to produce…

disturbances, it is necessary to use for bombarding solids particles whose energy can conveniently be varied near this threshold value. For this purpose the most convenient bombarding particles are electrons, and a number of experiments were carried out in which electrons of various energies were used to produce radiation damage. The greatest energy at which no effect occurs is taken as the energy at which the electron (in a head-on collision with a nucleus) cannot transfer to the lattice an amount of energy sufficient to displace this atom to the distance at which it would be in a stable state in an interstice. The distance between the vacancy and the interstitial atom located in the nearest stable lattice site is unknown and may be a function of temperature. Nevertheless, these experiments do give a measure of the energy required to form “vacancy—interstitial atom” pairs. A summary of the experimental data on this question, which are of fundamental interest in the study of radiation damage, is given in Table III.

The last column of this table gives the values of the energy that an electron (with the energy given in the preceding column) transfers to the atom in a head-on collision. The accuracy of determination of these quantities is of the order of several percent. So far there are no exact theoretical values with which these results could be compared. Huntington \(^{99a}\) has reported that he is attempting such a calculation, but at present the best theory gives, for the minimum energy required to create a “vacancy—interstitial atom” pair in copper, \(34\) eV. The assumptions made in this calculation are such that the value of \(25\) eV found by Eggan and Laubenstein is in satisfactory agreement with this figure.

14.3. Degree of damage. The theory of effects caused by isolated vacancies and isolated interstitial atoms has not been developed sufficiently for it to be used with confidence and, moreover, it is very difficult to take into account effects associated with accumulations of defects. In this connection, very few experimental studies contain reliable estimates of the actual number of displaced atoms. If the theoretical calculations of Dienes and Blat \(^{20}\) are accepted, then measurements of electrical resistance can be used for this purpose. This was done by Harrison and Seitz \(^{92}\), who used experimental data obtained by Cooper, Koehler, and Marx \(^{466}\) on the influence of neutron bombardment at \(10^\circ\) K. The number of displacements determined in this way is \(1/5\) of the number of displacements calculated according to the theory of Snyder and Neufeld \(^{206}\). If, however, resistance measurements at liquid-nitrogen temperature are used for this purpose, the analogous data differ by a factor of \(7.3\). A similar calculation, applied to the change in resistance caused in copper by electron bombardment at a temperature

Table III

Experiments carried out to determine the formation energy of a “vacancy—implanted atom” pair

Author	Bombarded substance	Measured property	Threshold energy (MeV)	Energy transferred to the atom (eV)
Clontz \(^{119a}\) . . . . . . . . .	\(n\)-germanium at \(-196^\circ\)C	Resistance	0.63	30
Loferski and Rappaport \(^{136}\) . .	\(n\)-germanium and \(p\)-silicon at room temperature	Lifetime of carriers whose concentration is minimal	0.51 (Ge) 0.28 (Si)	23 (Ge) 27.6 (Si)
Denny \(^{536}\) . . . . . . . . .	Iron–copper alloy	Saturation magnetization	0.45	27 (if an iron atom is displaced) 23 (if a copper atom is displaced)
Etgen and Laubenstein \(^{64}\) . . .	Copper	Resistance	0.49	25
Dageid \(^{616}\) . . . . . . . .	\(\mathrm{Cu}_3\mathrm{Au}\)	Ordering	0.3	10

RADIATION EFFECTS IN SOLIDS

liquid nitrogen, gives a number of defects 5.7 times smaller than according to the theory. Harrison and Seitz suggested that the constancy of this discrepancy shows that either the resistance calculations carried out by Dienes and Blatt give values that are too high by a factor of 5, or else the theory of Snyder and Neufeld is incorrect (in particular, the assumption that all atoms receiving an amount of energy greater than the threshold value are actually displaced from their positions in the lattice). Blatt, Hughes, and Rubenstein1 indicated that a similar calculation of the resistance due to small concentrations of gallium, germanium, and arsenic in copper gives a value twice as large as the experimental value. Thus, the resistance calculation may lead to a number of displaced atoms that is overestimated by approximately a factor of 2. On the other hand, if in the theory of Snyder and Neufeld one takes into account the possibility of collisions leading to replacement of atoms (according to Kinchin and Pease2), then the number of displaced atoms is reduced by a factor of 2. Thus, these two estimates can be satisfactorily reconciled without the need to change the adopted assumption about the displacement of atoms receiving the threshold energy.

However, this question is more complicated than could be supposed only on the basis of resistance data. Measurements of stored energy, performed by Overhauser3, represent another method for estimating the degree of disorder arising in copper under deuteron bombardment, if one adopts some value for the energy stored by one “vacancy—interstitial atom” pair. The calculation of this energy is apparently more reliable than calculation based on the change in resistance and, taking the value 5 eV, Overhauser found that the concentration of pairs in his specimen after bombardment with a dose of \(10^{17}\) deuterons/\(\text{cm}^2\) is \(5 \cdot 10^{-5}\). Since the resistance of these specimens is also known, this gives an independent estimate of the resistance of a “vacancy—interstitial atom” pair, yielding a value of \(11\ \mu\Omega\cdot\text{cm}\) per 1% displacements. This figure should be compared with the value \(2.7\ \mu\Omega\cdot\text{cm}\) per 1% displacements calculated by Dienes and Blatt. Thus, this estimate shows that the resistance calculations give a value underestimated by a factor of 4, and, if this interpretation is accepted, then the number of defects found in the low-temperature irradiation experiments (Cooper, Koehler, and Marx) would differ from the number calculated according to the theory of Snyder and Neufeld by a factor of 20. On the other hand, if it is assumed that the resistance calculations carried out by Dienes and Blatt are correct, then the energy stored by a “vacancy—interstitial atom” pair must be of the order of 1.2 eV. All the data set forth above are summarized in Table IV, which gives mutually consistent values for interpreting the results obtained by Cooper, Koehler, and Marx. In compiling this table it was assumed that all the additional resistance is due to

by the presence of vacancies and interstitial atoms. If the circumstance that \(1/4\) of the additional resistance (according to Overhauser) is not annealed at room temperature means that this resistance is due to some other cause, then the concentration of interstitial atoms in the last column of this table should be reduced by 10%. However, since the interpretation of the annealing process is still somewhat doubtful (for example, migration of vacancies at room temperature may not take place), it was decided not to introduce this correction into the table. In any case, the table shows the limits within which the number of interstitial atoms should lie.

Table IV

Possible interpretations of the additional resistance \(-2.1 \cdot 10^{-7}\ \Omega\cdot\text{cm}\), found by Cooper, Koehler, and Marx \(^{466}\) after bombardment with a dose of \(1.1\cdot 10^7\) deuterons with energy \(12\ \text{MeV}\cdot\text{cm}^{-2}\) at \(10^\circ\) K

(The figures in bold were obtained as a result of theoretical calculations)

Author	Resistance of 1% interstitial atoms \((\mu\Omega\cdot\text{cm})\)	Stored energy per one interstitial atom **) \((\text{eV})\)	Concentration of interstitial atoms
Huntington \(^{996}\) . . . . . . .	11	5	\(1.9\cdot 10^{-4}\)
Dienesberger \(^{110}\) and Blatt \(^{20}\)	2.7	1.2	\(7.8\cdot 10^{-4}\)
Blatt, Hughes, and Rubenstein \(^{21}\)	1.3	0.6	\(15.6\cdot 10^{-4}\)
Snyder and Neufeld \(^{2066}\) (doubled values) *)	1.0	0.44	\(21.5\cdot 10^{-4}\)
Snyder and Neufeld \(^{2066}\)	0.49	0.22	\(43.0\cdot 10^{-4}\)

*) A factor of 2 was adopted to take into account collisions leading to atomic displacements (Kinchin and Pease \(^{117a,b}\)); in this case the calculation of Snyder and Neufeld almost coincides with the original calculation of Seitz \(^{196a}\).

**) Taking Overhauser’s value for the ratio of stored energy to resistance.

For estimating the degree of disorder, the following additional methods were proposed. Measurement of the lattice parameters (Tucker and Simpson \(^{2156}\)); this method also has a somewhat uncertain theory. Diffraction of neutrons of large wavelength (Antal, Weiss, and

Dienes\(^{8}\); in this case the theory is rigorous if the damage consists of simple vacancies and interstitial atoms, but the experimental difficulties may prove considerable, since large specimens are necessary for the investigation and, moreover, a uniform distribution of non-accumulating defects will apparently occur only when gamma radiation is used, and in this case very large doses are required. However, even under conditions where the accumulation of defects is of no serious importance, the number of substances with a sufficiently small neutron-capture cross section is small.

If the theory of James and Lark-Horovitz\(^{101}\) has any meaning, then the initial rate of disappearance of carriers from semiconductors with high conductivity probably provides a good estimate of the number of defects formed. The first results, obtained by Crawford and Lark-Horovitz\(^{49a,b}\), and also by Bretton and Pearson\(^{25}\), show that, under these assumptions, 1.5 vacancies are formed per incident neutron, and 39 vacancies per alpha particle; the latter figure (Cleland, Crawford, and Pigg\(^{43}\)) means that 2.5 vacancies are formed per fast neutron. The degree of radiation damage after prolonged irradiation will be determined by the balance between newly created defects and annealing effects—thermal or induced by irradiation.

The question of the distribution of damage should be considered. Generally speaking, this distribution will be extremely nonuniform, because the damage is grouped around those positions where collisions of incident particles with lattice atoms occur. The volume of a thermal spike can be estimated on the basis of disordering effects, and the volume disordered by one neutron contains about \(10^{4}\) atoms (Cook and Kashin\(^{45a,b}\); Aponin\(^{96}\)).

14.4. Annealing of damage. Since this question was considered in sufficient detail in § 7, here we shall only summarize the principal results. Various combinations of vacancies and interstitial atoms can recombine if they possess different activation energies. Pairs of vacancies and interstitial atoms located close to one another (or, possibly, local molten regions, if one uses the concept of thermal spikes) are almost certainly the most readily disappearing form of damage in metals and can be annealed at the temperature of liquid air. The activation energy will depend on the distance between the interstitial atom and the vacancy, so that the annealing curve will correspond to the sum of several monomolecular reactions.

The next simple process is the migration of interstitial atoms. Although “crowdions” may exist, these defects (interstitial atoms) may be captured by vacancies on other lines of close packing instead of annihilating. Reliable calculations for this process are not yet available. In specimens in which damage is produced by electrons, accumulation can hardly be expected...

vacancies, but they can be detected in specimens with more substantial disordering or in specimens in which thermal wedges have formed.

Vacancy migration can occur at an activation energy of 0.7 eV or 1.2 eV; it can be slowed as a result of the capture of vacancies by impurity atoms, and after this migration recovery can be accelerated through the formation of vacancy pairs. Finally, in those cases where self-diffusion proves possible, any dislocations caused by thermal stresses can move and either disappear or, at the very least, polygonize. In copper this process occurs with an activation energy of about 2.1 eV.

Unfortunately, many of the assertions made above are conjectural, and we are still far from a complete understanding of the process of annealing of point defects in metals. Experiments carried out on quenched specimens (which should contain only vacancies) using precision methods for determining lattice periods (which should be more sensitive to the presence of interstitial atoms than to the presence of vacancies, especially if the interstitial atoms are not gathered into “caterpillars”) may help to clarify the various possibilities given in Table II. Until such experiments have been performed, it is impossible to say what the state of radiation damage is at any temperatures above 50° K, even in the most thoroughly studied metal—copper.

In other metals, for example in aluminum, where the repulsion of closed shells is of considerably less importance, and in iron with its body-centered cubic lattice, the relative values of the activation energies for defect motion, the geometry of the defect clusters that form, and even the nature of the individual interstitial regions may be completely different; and in order to create a more or less complete theory of the annealing of radiation damage, many more investigations involving comparative study of different metals must be carried out.

ADDENDUM IN PROOF

Prof. Schmid has drawn my attention to two further papers in which the influence of irradiation on the properties of metals was studied. In the first paper (Schmid and Lindner4) the influence of electron bombardment on the creep of zinc crystals is reported; hardening was usually found in these experiments. In the second paper (Neumann and Schmid5) changes in resistance observed in Cu—Be alloys after slight bombardment by alpha and beta particles are reported. No changes in microhardness were found in this case. A review article on radiation damage was published by Schmid and Lindner6 in 1955.

TABLE V

SUMMARY OF THE CONDITIONS UNDER WHICH THE EXPERIMENTS WERE CONDUCTED AND OF THE RESULTS OF MOST OF THE WORKS MENTIONED IN THIS REVIEW

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Al and Cu	$\alpha$	33 MeV	—	$-150^\circ$C; room temperature	Resistance	Large change if irradiated at $-150^\circ$C. No changes if irradiated at room temperature	149
Mo	$d$	10 MeV	—	$-100^\circ$C	Same	Increase by a factor of 3 if measured at $1.2^\circ$K. Increase by 4% if measured at room temperature	181a, b
Cu	$\alpha$	33.6 MeV	$1.7 \cdot 10^{17}$	—	Resistance and characteristic temperature	The characteristic temperature increases by 45° (when calculated from the resistance)	24a, b
Cu	$d$	12 MeV	$1.1 \cdot 10^{17}$	$-180^\circ$C	Resistance	Change independent of temperature (therefore the characteristic temperature does not change)	1656
Fe, Ni, Co	$d$	10 MeV	$10^{17}$	$-150^\circ$C	Same	In iron, larger changes occur than in metals with close packing	226в
W, Mo, Pt	$n$	Reactor	$\sim 10^{19}$	$30^\circ$C	Same	Changes: in W $\sim 10\%$; in Mo—7% and in Pt—1%	616

Substance	Type	Irradiation source / energy	Fluence	Temperature	Measured quantity	Effect	Ref.
Cu, Al	$n$	Reactor	$1.1 \cdot 10^{19}$	From $-150$ to $-195^\circ\mathrm{C}$	Resistance	If measurements are made at $-195^\circ\mathrm{C}$, the resistance increases by 20% (Cu), 33% (Al)	142б
Cu, Ag, Au	$d$	12 MeV	$1.1 \cdot 10^{17}$	$-261^\circ\mathrm{C}$	Same	Increase by 13% (Cu), 15% (Ag, Au); not annealed at $-261^\circ\mathrm{C}$	466
W	$p$	From 100 to 400 MeV	$10^{16}$	Room temperature	Same	Change by 0.49% at 130 MeV, by 0.33% at 260 MeV, and by 0.71% at 410 MeV	170
Cu	$e$	From 0.45 to 1 MeV	—	Liquid air	Same	Threshold energy of electrons at which the effect arises is $0.49 \pm 0.02$ MeV; this corresponds to a displacement energy of $25 \pm 1$ eV	64
Cu + 2 wt.% Be	$n$	Reactor	$4 \cdot 10^{19}$ (integr.)	$40^\circ\mathrm{C}$	Resistance of a quenched specimen	Increase by 18%	17
Cu + 13.5 at.% Be	$n$	Reactor	$2.3 \cdot 10^{18}$ (integr.)	—	Same	Increase by 11%	158в
Cu + 2 wt.% Be	$n$	Reactor	—	$-150^\circ\mathrm{C}$	Same	Increase by $\dfrac{1}{4}$ of the magnitude of the increase found at $40^\circ\mathrm{C}$; upon heating it reaches the same magnitude	39
Cu$_3$Au	$n$	Reactor	$3.3 \cdot 10^{10}$ above 50 keV	$40^\circ\mathrm{C}$	Resistance	In the ordered specimen, an increase from $4.6$ to $10.1 \cdot 10^{-6}$ ohm·cm; in the disordered specimen, no changes	199
CuAu and Cu$_3$Au	$\alpha$	33 MeV	$3.7 \cdot 10^{17}$	$-150^\circ\mathrm{C}$	Same	In ordered specimens, an increase; in disordered specimens, no changes	149
Cu$_3$Au	$n$	Reactor	—	—	Same	In ordered specimens, first a decrease in resistance, then an increase	2

Continuation of Table V

Irradiated substance	particle	energy	integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Cu₃Au	n	Reactor	2·10²⁰ thermal	80° C	Resistance	In the ordered specimen, a rapid decrease followed by a gradual increase to a resistance 60% above the initial value. In the disordered specimen, a decrease, saturating at a resistance 7% below the initial value, and then a slow increase in resistance	84
Cu₃Au	n	Reactor	1.4·10²⁰ thermal	140° C	Same	In the ordered specimen, a decrease by 6% followed by an increase to a resistance 4% greater than the initial value. In the disordered specimen—a decrease, saturating at a resistance 17% below the initial value	85
Cu₃Au	n	Reactor	3·10²⁰ thermal	80° C	Hardness and lines on radiographs	In the disordered specimen, an increase from 100 to 121 VPN; no changes in the radiographs. In the ordered specimen, an increase from 110 to 158 VPN and an increase in the sharpness of the lines on the radiographs	71

Alloy	Radiation	Source / energy	Dose	Temperature	Method / measured quantity	Result / remarks	Ref.
Cu₃Au	$n$	Reactor	$\sim 2.1 \cdot 10^{18}$	$200^\circ\mathrm{C}$	Resistance	A delay of 12 hours after shutdown of the reactor. It is assumed that this is a relaxation time	226
Cu₃Au	$n$	Reactor	—	—	Lines on X-ray diffraction patterns. Resistance	It is assumed that after irradiation of the ordered alloy the crystallite size is 125 Å	44a
Cu₃Au	$n$	Reactor	$1.2 \cdot 10^{16}$ fast	$-160^\circ\mathrm{C}$	Lines on X-ray diffraction patterns. Resistance	In an ordered specimen there is a small increase, which decreases only upon annealing	44б
Cu₃Au	$\alpha$	36 MeV	—	$-180^\circ\mathrm{C}$	Same	The initial rate of disordering is 6 times greater than at $220^\circ\mathrm{C}$	58
Cu₃Au	$\dot e$	1 MeV	$3 \cdot 10^{17}$	From 40 to $45^\circ\mathrm{C}$	Same	No changes. Annealing at $100^\circ\mathrm{C}$ leads to a decrease in the resistance of the ordered specimen	3
Cu₃Au (ordered)	$\gamma$	Co⁶⁰	$6 \cdot 10^{16}$	—	Same	Annealing at $128^\circ\mathrm{C}$ for 500 min leads to a decrease in resistance by $3 \cdot 10^{-8}\ \Omega\cdot\mathrm{cm}$; it is assumed that vacancies are formed	61б
Cu₃Au	$\dot e$	0.3 MeV	—	—	Same	An ordering effect is observed; it is assumed that vacancies are formed and that the threshold for their formation is below 13.5 eV	61б
Cu₃Au	$e$	1 MeV	$3 \cdot 10^{19}$	$-195^\circ\mathrm{C}$	Same	No changes. Annealing at room temperature leads to a decrease with subsequent fluctuations of resistance	60

Continuation of Table V

Irradiated substance	particle	energy	integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Cu—Au	$\alpha$	39.6 MeV	$4.1 \cdot 10^{17}$	$< -150^\circ$C	Resistance	The rate of ordering, both for ordered and for disordered samples, was measured at different temperatures.	208
Cu$_3$Au	$p$	9 MeV	$5 \cdot 10^{17}$	$-100^\circ$C	Same	In ordered samples, an increase by 4.25 $\mu\Omega\cdot$cm; in disordered samples, by 0.65 $\mu\Omega\cdot$cm; 0.6 of this value anneals at $0^\circ$C.	286
Cu$_3$Au and Cu—Au	$n$	Reactor	$\sim 10^{20}$	$\sim 30^\circ$C	Resistance and lines on X-ray diffraction patterns	Thermal neutrons lead to ordering of both ordered and disordered samples. Fast neutrons disorder ordered samples.	45a, b
$\beta$-brass	$\alpha$	33 MeV	$2.6 \cdot 10^{17}$	$< -100^\circ$C	Resistance	Increase by 100%; disordering is assumed.	66
Ni$_3$Mn	$n$	Fast	$0.9 \cdot 10^{20}$; $> \dfrac{1}{2}$ MeV	$\sim 50^\circ$C	Resistance and magnetic induction	In ordered samples, an increase in resistance and a decrease in induction. In disordered samples, a decrease in resistance and a large	9a, b

Material	Type	Source	Dose	Temperature	Measured quantity	Results	Ref.
α-brass	$n$	Reactor	One week in the Brookhaven reactor	$50^\circ\mathrm{C}$	Resistance	Increase in induction only at contents from 16 to 22% Mn. Decrease even if measurements are carried out at the temperature of liquid helium. Anneals at $170^\circ\mathrm{C}$	188
Pt	$n$	Reactor	$4\cdot 10^{18}$	$\sim 50^\circ\mathrm{C}$	Resistance and annealing	Increase by 0.3%; approximately 15% of this amount anneals with $Q = 1.2\,\text{eV}$	61a, б
W, Mo	$n$	Reactor	$\sim 10^{19}$	$30^\circ\mathrm{C}$	Annealing of resistance	Mo: $Q$ Cu changes from 1.25 to $1.35\,\text{eV}$ upon annealing of 60% of the resistance change between 100° and $160^\circ\mathrm{C}$; upon annealing of 30% of the change between 190° and 270°—$Q = 1.46\,\text{eV}$. W: upon annealing of 20% of the resistance change between 70° and $270^\circ\mathrm{C}$, $Q$ changes from 1.2 to $1.6\,\text{eV}$	61б
Cu, Ag, Au, Ni, Ta	$d$	12 MeV	$2.7\cdot 10^{17}$	$-140$ and $-150^\circ\mathrm{C}$	Resistance and annealing	The change is greatest in Ni and Ta. Recovery is observed at $-165^\circ\mathrm{C}$ with $Q = 0.15\,\text{eV}$ (Cu, Ag, Au) and $0.20\,\text{eV}$ (Ni, Ta)	151
Cu	$a$	35 MeV	$1.5\cdot 10^{17}$	$-150^\circ\mathrm{C}$	Resistance	Annealing: between $-20^\circ$ and $-65^\circ\mathrm{C}$, $Q = 0.717\,\text{eV}$; between 250° and $350^\circ\mathrm{C}$, $Q = 2.12\,\text{eV}$	65б, в
Cu	$d$	12 MeV	$1.1\cdot 10^{17}$	$-180^\circ\mathrm{C}$	Same	Annealing: below $-60^\circ\mathrm{C}$, $Q \sim T$; from $-60^\circ\mathrm{C}$ to room temperature, $Q = 0.68\,\text{eV}$. At $167^\circ\mathrm{C}$, 25% of the total resistance change is retained	165a, б

Continuation of Table V

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Cu, Al	$n$	Reactor	$1.1\cdot 10^{19}$	From $-150$ to $-195^\circ$C	Resistance	Cu: annealing in two stages—from $-80^\circ$ to $20^\circ$C and with critical shear stress from $300^\circ$ to $400^\circ$C. Al: annealing with critical shear stress from $-80^\circ$ to $-20^\circ$C	142b
Cu	$d$	12 MeV	$10^{17}$	$-150^\circ$C	Released energy	In the course of annealing at room temperature, $1.2$ cal/g is released	165b
Cu, Ag, Au	$d$	12 MeV	$10^{17}$	$-261^\circ$C	Resistance	In copper, about 40% of the additional resistance is annealed at $-233^\circ$C. In silver—20% at $243^\circ$C. In gold there is no sharp change in resistance	46a
Cd single crystals	$\alpha$	5.3 MeV	$1.5\cdot 10^8$ per sec.	—	Creep rate	Increase by up to 5 times only under longitudinal flow.	4a, 6
Cd single crystals	$\alpha$	5.3 MeV	$5\cdot 10^9$ per sec.	Room temperature	Creep	No effect. If the bombardment is followed for 1–2 hours by a creep test, the creep rate as a result of irradiation decreases by approximately 30%	145a, 6

Material	Radiation	Energy	Dose	Temperature	Property	Effect	Reference
Zn single crystals	$\alpha,\ n$	$5.3$ MeV	—	—	Creep	Hardening, i.e., slowing of creep. Apparently, neutrons produce the opposite effect	192a, b
Al polycrystals	$n$	Reactor	$1.3\cdot 10^{12}$ (with energy above $1$ eV) per sec.	$50^\circ$ C	Creep rate	No changes	109
Al polycrystals	$\alpha$	$38$ MeV	$1.2\cdot 10^{12}$ per sec.	From 150 to $320^\circ$ C	Creep rate	No significant changes	103
Cu polycrystals	$d$	$16$ MeV	$10^{12}$ per sec.	$250^\circ$ C	Same	At a pressure of $700\ \mathrm{kg/cm^2}$ no effect (measurement error $\pm 20\%$)	222a, c
Cu	$n$	Reactor	$5\cdot 10^{19}$	$40^\circ$ C	Hardness	In the annealed specimen the hardness changed from $R_F\ 43$ to $R_F\ 90$	17
Cu	$n$	Reactor	$5\cdot 10^{19}$	$40^\circ$ C	Hardness	In the cold-worked specimen: from $R_F\ 93$ to $R_F\ 97$	17
Mo	$d$	From $8.4$ to $10$ MeV	$1.5\cdot 10^{17}$	—	»	Increase from 201 to 253 $VPN$	83a, b; 89, 90
Cu	$e$	$1$ MeV	$5\cdot 10^{18}$	$-20^\circ$ C	»	Increase from 44.7 to 47.7 $VPN$	59
Cu alloys	$n$	Reactor	$2.3\cdot 10^{18}$	—	»	Increase by $\sim 20\ VPN$ for solid solutions and by $\sim 40\ VPN$ for Cu—Be	158b, c
Cu$_3$Au	$n$	Reactor	$3\cdot 10^{20}$	$80^\circ$ C	»	In the disordered specimen from 100 to 121 $VPN$, in the ordered one—from 110 to 158 $VPN$	71
Cu single crystal	$n$	Reactor fast	$1.8\cdot 10^{18}$	—	Critical shear stress	Increase from 0.24 to $1.94\ \mathrm{kg/mm^2}$	22a
Cu single crystal	$n$	Reactor fast	$8\cdot 10^{18}$	—	Slip lines	Accumulation of a larger number of lines	102a

Continuation of Table V

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Cu single crystals	$n$	Reactor	—	—	“Stress—deformation” curve	Changes at 78°K; the critical shear stress increased	102b
Cu single crystals	$n$	Reactor	—	—	Critical shear stress	After an increase (up to 3.5 kg·mm$^{-2}$), annealing in the range 300—400°C. Activation energy 2.2 eV	184
Cu, Al	$n$	Reactor	$1.1 \cdot 10^{19}$	$-195^\circ$C	Same	Increase by a factor of 5. Annealing in Cu at 320°C; in Al from $-80^\circ$ to 20°C. Activation energy 2 eV (Cu) and 0.55 eV (Al)	142b
Fe, Zn, Pb	$n$	Reactor	$10^{18}$	Room	Yield point	Increase by $\sim$2 times in Fe and Zn crystals. In Pb there is no effect. Annealing in Fe with activation energy 3.1 eV	125b
Al	$\alpha$	39.6 MeV	$9 \cdot 10^{16}$	$-100^\circ$C	Slip planes	Stronger slip along the given plane	114a, b
Mo	$n$	Reactor	From 1.9 to $5.9 \cdot 10^{20}$	—	“Stress—deformation” curve	The transition temperature “plasticity—brittleness” rose from 30° to $+170^\circ$C	33a, b
Ni, Cu, Mo, Ti, etc.	$n$	Reactor	$5 \cdot 10^{19}$	100°C	Same	Increase in the yield point from 7 to 100%. Elongation and initial rate of hardening	Makin; private communication

SAE 1019 steel	\(d\)	18.6 MeV	\(3.7 \cdot 10^{17}\)	—	Hardness, etc.	decrease. Annealing of the yield point at 300—360° for Cu \((Q = 2.05\ \text{eV})\) and 340—400° C for Ni \((Q = 2.63\ \text{eV})\). The “ductility—brittleness” transition temperature rose from \(-1^\circ\) to \(+18^\circ\) C. The hardness increased from 180 to 380 (Knoop). The annealing effect lies between 260 and 480° C, with variable activation energy	156
Al alloys	\(n\)	Reactor	\(1.3 \cdot 10^{21}\) total dose; \(10^{20}\) fast	65° C	“Stress—strain” curve	The yield point and tensile strength increase approximately twofold in annealed specimens. Elongation decreases by approximately 20%	207
Steels, Ni- and Co-alloys, Zr	\(n\)	Reactor	\(10^{20}\)	From 20 to 25° C	Hardness; “stress—strain” curve	Hardness increases by 20—150%; yield point by 10—60%; tensile strength by 5—40%. The “ductility—brittleness” transition temperature rises	212a
Cu, 17 at.% Al	\(n\)	Reactor	—	\(-195^\circ\) and 50° C	Internal friction	No changes	133
Austenitic steel	\(n\)	Reactor	\(\sim 10^{19}\)	From 60 to 70° C	Modulus of elasticity	No changes	376
Cu	\(n\)	Reactor	\(2.4 \cdot 10^{18}\)	—	Elastic constants	No changes	125a, b
Cu	\(d\)	20 MeV	\(9 \cdot 10^{16}\)	\(-175^\circ\) C	Shear modulus	Decrease by 1.5%. \(\dfrac{1}{3}\) of this amount anneals at \(-125^\circ\) C; the remaining part anneals between \(-50\) and \(+100^\circ\) C	55

Continuation of Table V

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Cu	$e$	1 MeV	$4.5 \cdot 10^{18}$	$-195^\circ$ C	Shear modulus	Annealing at $-50^\circ$ C gives an increase of 4%; at 75°—a decrease of 0.5%, and in the range 250–350° C a decrease of 2%	54
$\beta$—Sn	$n$	Reactor	$10^{18}$	$-195^\circ$ C	Transformation	Growth of $\alpha$—Sn upon heating is considerably faster than in unirradiated $\beta$—Sn, but slower than in $\beta$—Sn “seeded” with gray tin	73
Cu + 2.4 wt.% Fe	$e$	0.5 MeV	—	—	Magnetization with saturation	Threshold energy for the transformation is 0.45 MeV; at the displacement energy for iron, $27 \pm 2$ eV	53a, б
Cu + 2.4 wt.% Fe	$p$	9 MeV	—	—	Same	With complete crystallization before irradiation, the magnetization decreases, which indicates local melting	53в
Cu, Zr, Ge, Al	$n$	Reactor	6 months at Hanford	—	Lines on X-ray diffraction patterns	No effects	219a, б, в
Cu + 2% Si single crystal	$n$	Reactor	550/atom.	—	Same	No changes, but subsequent etching gives very broad maxima	219г

Pt, Mo	$n$	Reactor	$1.5 \cdot 10^{19}$ fast	—	Lines on X-ray patterns	No changes in Pt. Increase of the interplanar spacing in Mo by $1:10\,000$	61b
Cu, Mg, brass	$n$	Reactor	$\sim 10^{18}$	—	Same	Broadening of the lines in all cases; displacement of the lines in brass	125a, b
WAl$_5$	$n$	Reactor	$\sim 10^{19}$	—	Same	Expansion in the direction of the $c$ axis by 0.1%; slight compression in the direction $a$	Adam, private communication
Cu	$d$	19 MeV	$1.15 \cdot 10^{17}$	$-195^\circ$C	Volume	Increase by 0.034%; 14% of this quantity is annealed at room temperature, but irradiation at room temperature gives only a 0.1% change in volume	115
Ag	$p$	10 MeV	$3 \cdot 10^{14}$ per sec.	—	Self-diffusion	No measurable changes	106
Co, coated with Au	$n$	Reactor	—	—	Diffusion	Apparently, some number of Co atoms pass through the gold layer	36
Fe, Pt, etc.	$\alpha$	40 MeV	—	—	Thermoelectromotive force	No changes down to $3 \cdot 10^{-7}$ V/°C	7
Cu and Fe—constantan	$n$	Reactor	$5 \cdot 10^{16}$	—	Same	No changes with an accuracy up to $10^{-5}$ V between the temperature of liquid nitrogen and ice	102c
Fe	$p$	10 MeV	$5 \cdot 10^{17}$	—	Same	$\sim 0.3$ microvolt per degree between irradiated and unirradiated iron samples	5
Constantan	$p$	10 MeV	$3.8 \cdot 10^{17}$	—	Same	0.1 microvolt per degree between irradiated and unirradiated constantan samples	5

Continuation of Table V

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
Ge	d	10 MeV	—	Room	Resistance	In pure germanium and in p-type germanium, decrease; n-type germanium is converted into p-type	128
Ge	n	Fast	1 day at ORNL	—	Same	In p-type germanium, decrease; in n-type germanium, increase to a maximum, with conversion to p-type and subsequent decrease	107
Si	n	Fast	—	—	» »	Increase in all cases to a value exceeding 10,000 ohm·cm	127
Si	n	Fast	—	—	Absorption bands	A new band and a decrease of absorption in the long-wavelength region indicate the formation of traps for electrons and holes	68, 69, 12
Ge	n	Fast	—	—	Number of holes per neutron	In n-germanium: 3 per fast neutron; in p-germanium, 0.7 per fast neutron	49a, b
Ge	α	5.3 MeV	4.5·10¹⁰	Room	Resistance	n-germanium is converted into p-germanium. At first 78 electrons are lost per α-particle; after conversion, gain—	25

Material	Particle	Energy	Dose	Temperature	Quantity measured	Observations	Ref.
Ge	\(n\)	Fast	\(1.2 \cdot 10^{16}\)	—	Same	8.6 holes per \(\alpha\)-particle are created. In a \(p\)-germanium specimen having low resistivity, the resistance increases under bombardment.	48
Ge and Si	\(d\)	10 MeV	—	—	Number of carriers lost per deuteron	In a \(p\)-germanium specimen with low resistivity — 4; in \(p\)-germanium — 11, in \(p\)-silicon — 31.	78a
Ge	\(e\)	From 0.4 to 1.5 MeV	\(\sim 10^{18}\)	\(-196^\circ\)C	Threshold energy	0.65 MeV for a charge of constant resistance. It is assumed that the displacement energy is 30 eV.	119b
Ge and Si electron-voltaic cells	\(e\)	From 0.3 to 1.5 MeV	—	Room	Short-circuit current	The current increases with the time of bombardment by electrons, if their energy exceeds the threshold energy — 0.51 MeV (for Ge) and 0.28 MeV (for Si). The corresponding displacement energies are: 23 eV (Ge) and 27.6 eV (Si).	136
Ge	\(e\)	4.2 MeV	\(\sim 4.5 \cdot 10^{9}\)	\(-196^\circ\)C	Resistance and annealing	In \(p\)-germanium with initial resistivity \(2.18\ \Omega\cdot\text{cm}\), a decrease in conductivity occurs; it anneals at room temperature.	119c
Ge	Ions from H\(^1\) to Sb\(^{{11}}\)	From 5 to 90 keV	—	—	Diode characteristics	The observed effects are consistent with the assumption of the formation of a surface layer of \(p\)-type.	51
Ge	\(d\)	9.3 MeV	—	\(-170^\circ\)	Hall coefficient	At temperatures below 141° annealing occurs, accompanied by an increase in \(R\) and \(\rho\). At temperatures above 141°K, \(R\) and \(\rho\) decrease.	78b

Continuation of Table V

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
1	2	3	4	5	6	7	8
Ge	n	Reactor	—	From −90 to −160° C	Hall coefficient and resistance	Annealing at temperatures below 140° K leads to an increase in resistance. This process is described by the first-order reaction equation	47
Ge	e	4.5 MeV	—	−186° C	Same	In p-germanium (coated with In) \(R\) and \(\rho\) increase, with \(R/\rho\) constant. With Au coating, \(R\) and \(\rho\) decrease, with \(R/\rho\) passing through a minimum equal to \(1/3\) of the initial value. In n-germanium \(R\) and \(\rho\) increase; \(R\) passes through a maximum negative value and then becomes positive	172
Ge	e	4.5 MeV	—	−186° C	» »	\(R\) and \(\rho\) increase in n- and p-germanium. Annealing was studied	121
n—Ge	n	—	—	—	Barrier at the grain boundary	The high resistance disappeared on transition of n-germanium to p-germanium	214
n—Ge	e	3 MeV	\(10^{14}\)	—	Annealing of resistance	Agrees with theory. From the second part of the process an activation energy of 1.8 eV was found	32a

Material	Type	Irradiation	Dose	Temperature	Measured quantity	Effect	References
\(\mathrm{Cu_2O}\)	\(n\)	Reactor	—	—	Resistance	Increases	173
PbS	\(a\)	\(-5.3\) MeV	—	—	Same	Increases to three times the value after an initial decrease by a few percent	163
Si*	\(n\)	Reactor	—	—	Specific heat	Bombardment leads to a considerable decrease in the role of the linear term in the expression for the specific heat; the characteristic temperature also decreases	113a, b, c
InSb	\(n\)	Reactor	—	\(30^\circ\)C	Hall coefficient	\(p\)-type is converted into \(n\)-type. \(n\)-type tends to be converted into \(n\)-type with high resistivity	40a, b, c
GaSb	\(n\)	Reactor	—	—	Resistance and Hall coefficient	In both \(n\)-type and \(p\)-type, the resistance increases. Changes in the Hall coefficient showed that traps for carriers are formed. The rate of disappearance of carriers in \(p\)-type varies with their initial concentration. In \(n\)-type this phenomenon is not observed	40g
Graphite	\(n\)	Reactor	\(5\cdot10^{19}\) thermal		Resistance, Hall coefficient, and galvanomagnetic effect	The resistance and Hall coefficient increase. The galvanomagnetic effect decreases. The effects are consistent with the formation of electron traps	116
\(n\)—Ge	\(n\)	Reactor	—	—	Magnetic susceptibility	Decrease of diamagnetism	210
\(p\)—Si, coated with B	\(n\)	Reactor	—	—	Electron spin resonance	Observed only in irradiated samples	193

Continuation of Table V

Irradiated substance	Irradiation conditions	Irradiation conditions	Irradiation conditions	Temperature	Property studied	Effect	Literature
	particle	energy	integral flux (number of particles per cm²)
1	2	3	4	5	6	7	8
Ge single crystals	$n$	Reactor	$1.4 \cdot 10^{18}$ slow; $1.2 \cdot 10^{13}$ fast	From 160 to 200° C	Lines on X-ray diffraction patterns	The half-width of the lines increased from 36″ to $3 \tfrac{1}{2}$. Diffuse scattering increased; $a_0$ increased from 5.657₇ to 5.659₂ Å	220
Graphite	$n$	Reactor	$2.1 \cdot 10^{19}$	−196° C	Lines on X-ray diffraction patterns	$c_0$ increases by 4.75%. Reflections on X-ray diffraction patterns broaden and have longer “tails”	112г
NaCl	$p$	400 MeV	—	—	Hardness and elasticity	Hardness increases from 16.3 to 36 $V/P_N$. Young’s modulus also increases	218
Alkali-halide compounds	X-rays $e$ $α$	1 MeV; 40 MeV	—	20° C; 20° C; −170° C	Hardness; »; »	Increases from 16.3 to 33.4 $V/P_N$ (NaCl), from 16.3 to 36 $V/P_N$ (NaCl), from 16.3 to 46 $V/P_N$ (NaCl)	221a, б
NaCl	X-rays	—	—	—	Internal friction	Decreases	80
NaCl	Same	—	—	—	Modulus of elasticity	Increases in specimens subjected to cold working. In this case, the decrease caused by cold working is annealed out	86

LiF	” ”	Reactor	\(6\cdot 10^{16}\)	—	Lattice parameter and density	Changes equivalent within an accuracy of 6%
LiF	” ”	Reactor	\(7.5\cdot 10^{17}\)	—	Lattice parameter	No changes detected. Lines on the radiographs broaden
LiF	” ”	Reactor	8 days in the Argonne reactor	—	Reflections on radiographs	They broaden and become more intense
KCl	” ”	—	—	—	Lattice parameter	Increase of \(a\) by 0.001%
LiF	X-rays or \(d\)	21 MeV	\(10^{13}\)	—	Density from measurements of double refraction	Decrease from 2 to \(9\cdot 10^{-5}\)
KCl	\(p\)	400 MeV	\(5\cdot 10^{15}\)	—	Density	Decrease by \(2\cdot 10^{-4}\ \mathrm{g/cm^3}\)
KCl	X-rays or \(p\)	—	—	—	Surface	Slip lines on the irradiated surface. The effects of irradiation by X-rays and protons are similar, with the exception of effects obtained at large proton doses
KCl, NaCl	X-rays	—	—	—	Changes in length	Agree, to an accuracy of up to 5%, with the optical determination of the density of colored centers
Various covalent compounds	\(n\)	Reactor	—	—	Powder radiographs	In some substances effects are not observed; in others significant effects are found
Zircon	\(\alpha\)	—	\(10^{16}\) per mg	—	Radiographs	The intensity of the lines decreases; the lines merge with the background at a dose of \(10^{16}\) \(\alpha\)-particles per mg

Continuation of Table V

Irradiated substance	Irradiation conditions: particle	Irradiation conditions: energy	Irradiation conditions: integral flux (number of particles per cm²)	Temperature	Property studied	Effect	Literature
Quartz	\(n\)	Reactor	\(6.6 \cdot 10^{19}\) fast	—	Lattice	Becomes more anisotropic; density decreases by 3.5%	223
\(\mathrm{SiO_2}\), various structures	\(n\)	Reactor	\(2 \cdot 10^{20}\) fast	—	Structure	All structures transform into a glass-like form, which after heating recrystallizes with the formation of quartz	224
Quartz oscillators	\(n\)	Reactor	\(10^{19}\)	—	Frequency and change in coloration	The frequency decreases linearly with dose. X-rays no longer color the crystals	105
BN and other boron compounds	\(n\)	Reactor	\(10^{18}\) thermal	—	Lattice parameter and lines in X-ray photographs	The lattice parameter changes by 1%. With increasing dose, this change saturates. The lines broaden, with the broadening of some lines becoming saturated	171
\(\mathrm{B_4C}\)	\(n\)	Reactor	\(3 \cdot 10^{20}\) thermal	—	Same	Compression along the \(c\) axis and expansion along the \(a\) axis. Reflections are very diffuse	216a, b, c, d
Diamond	\(p\)	360 MeV	—	—	X-ray diffraction patterns	The scattering angle increases by \(10'—30'\)	93
Diamond	\(p\)	360 MeV	—	—	Same	An unexpected weak maximum at 0.02 radian	186

Substance	Irradiation	Source or energy	Dose	Temperature	Property investigated	Effect	References
NaCl	X-rays	—	—	\< 550° C	Diffusion	Decrease in rate	147
KCl	γ, n	Co⁶⁰; reactor	—	—	Electrical conductivity	Short-term γ-irradiation leads to a decrease. Prolonged γ- or neutron irradiation leads to an increase	160
KCl, NaCl	p, γ	400 MeV	10¹⁴—10¹⁷	—	Same	With short-term bombardment the decrease is sharp; with prolonged bombardment, an increase. Annealing gives a large decrease followed by an increase	169a, б, в; 203б
Quartz	n	Fast reactor	2·10¹⁹ fast	—	Thermal conductivity	The maximum at 12° K disappears, and the thermal conductivity becomes closer to that of glass	13
Artificial sapphire	n, γ	Reactor	5·10¹⁸	—	Same	Considerable decrease at low temperatures	14
Oxides	n	Reactor	3,8·10¹⁹ fast	—	Magnetic susceptibility	Many oxides become less diamagnetic	140
Quartz	n	Reactor	5·10¹⁹ fast	—	Same	Does not depend on the temperature before irradiation. Decreases with increasing temperature after irradiation. Further irradiation diminishes this effect	209б
ZnO	n	Reactor	1,8·10¹⁶	—	Absorption of electromagnetic radiation	Noticeable changes	63
Quartz, diamond	n	Reactor	—	—	Paramagnetic resonance	Lines were found. In quartz the fine structure of these lines shows that the “smoky” coloration is due to the presence of Al	886

CITED LITERATURE

1. F. Abeles, Comptes Rendus Acad. Sci. 237, 796 (1953).
2. J. Adam, R. A. Dugdale, Nature, Lond. 168, 581 (1951).
3. J. Adam, A. Green, R. A. Dugdale, Phil. Mag. (7), 43, 1216 (1953).
4. E. N. da C. Andrade, a) Nature, Lond. 156, 113 (1945); b) Monogr. Ser. Inst. Metals, No. 13, 133 (1953).
5. A. Andrew, C. R. Davidson, Phys. Rev. (2), 89, 876 (1953).
6. A. Andrew, M. P. Jeppson, R. L. Mather, H. P. Yockey, Phys. Rev. (2), 96, 843, (A) (1954).
7. A. Andrew, M. R. Jeppson, H. P. Yockey, Phys. Rev. (2), 86, 643, (A) (1952).
8. J. J. Antal, R. J. Weiss, G. J. Dienes, Phys. Rev. (2), 98, 1541, (A) (1955).
9. L. R. Aronin, a) U. S. Report AECU-2634 (1953); b) J. Appl. Phys. 25, 344 (1954).
10. R. S. Barnes, M. J. Makin, British Report AERE M/R 1626, 9p. (1955).
11. J. H. Bartlett, G. J. Dienes, Phys. Rev. (2), 89, 848 (1953).
12. M. Becker, H. Y. Fan, K. Lark-Horovitz, Phys. Rev. (2), 85, 730, (A) (1952).
13. R. Berman, Proc. Roy. Soc. A, 208, 90 (1951).
14. R. Berman, E. L. Foster, H. M. Rosenberg, Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 321 (1955).
15. R. Berman, F. E. C. Klemens, F. E. Simon, T. M. Fry, Nature, Lond. 166, 864 (1950).
16. C. R. Berry, Phys. Rev. (2), 93, 1540, (A) (1955).
17. D. S. Billington, S. Siegel, Metal Progress 58, 847 (1950); see also U. S. Report AECD-2810.
18. D. Binder, W. J. Sturm, a) Phys. Rev. (2), 94, 760, (A) (1954); b) Ibid. (2), 96, 1519 (1954).
19. W. P. Binnie, A. M. Liebschutz, a) U. S. Report AECU-2225, 4 (1952); b) U. S. Report COO-102, 15 (1953); c) U. S. Report COO-104, 41 (1953); d) Phys. Rev. (2), 94, 1410, (A) (1954).
20. F. J. Blatt, Phys. Rev. (2), 98, 245, (A) (1955).
21. F. J. Blatt, M. C. Huse, R. A. Rubenstein, Phys. Rev. (2), 93, 1553, (A) (1955).
22. T. H. Blewitt, R. R. Coltman, a) Phys. Rev. (2), 82, 769, (A) (1951); b) Ibid. (2), 85, 384 (1952); Acta Metallurgica 2, 549 (1955).
23. D. B. Bowen, R. R. Eggleston, R. H. Kropschot, J. Appl. Phys. 23, 630 (1952).
24. D. B. Bowen, G. W. Rodeback, a) Phys. Rev. (2), 92, 531, (A) (1953); b) Acta Metallurgica, 1, 649 (1953); see also U. S. Report NAA-SR-251, 17 p.
25. W. H. Brattain, G. L. Pearson, Phys. Rev. (2), 80, 846 (1950).
26. M. A. Bredig, G. E. Klein, B. S. Borie, Jr., Rev. Sci. Instrum. 26, 610 (1955).
27. J. A. Brinkman, a) U. S. Report NAA-SR-198 (1952); b) J. Appl. Phys. 25, 961 (1954).
28. J. A. Brinkman, C. E. Dixon, C. J. Meechan, a) U. S. Report NAA-SR-249 (1953); b) Acta Metallurgica 2, 38 (1954).
29. T. Broom, Advances in Physics 3, 26 (1954).
30. W. L. Brown, R. C. Fletcher, Phys. Rev. (2), 91, 237, (A) (1953).

1. W. L. Brown, R. C. Fletcher, S. Machlup, Phys. Rev. (2), 90, 709 (1953).

2. W. L. Brown, R. C. Fletcher, K. A. Wright, a) Phys. Rev. (2), 92, 591 (1953); b) Ibid. (2), 96, 834, (A) (1954).

3. C. A. Bruch, W. E. McHugh, R. W. Hockenburg, a) U. S. Report KAPL-1095, 54 p. (1954); b) J. Metals 7, 281 (1955).

4. H. G. van Bueren, Zeit. Metallk. 46, 272 (1955).

5. V. P. Calkins, a) Nucleonics 12, 9, 9 (1954); b) Nuclear Engineering, Part II, Chem. Eng. Progr. Symposium Ser. 50, 12, 28 (1954).

6. G. W. Callendine, Jr., V. C. Ridolfo, M. L. Pool, Phys. Rev. (2), 86, 642, (A) (1952).

7. A. Charlesby, N. H. Hancock and H. C. Sansom, a) British Report AERE M/R 1434 (1954); b) J. Nuclear Energy 1, 264 (1955).

8. D. L. Chipman, B. E. Warren, G. J. Dienes, J. Appl. Phys. 24, 1251 (1953); see also U. S. Report BNL-1479.

9. J. W. Cleland, D. S. Billington, J. H. Crawford, Jr., Phys. Rev. (2), 91, 238, (A) (1953).

10. J. W. Cleland, J. H. Crawford, Jr., a) Phys. Rev. (2), 93, 894 (1954); b) Ibid. (2), 94, 1410, (A) (1954); c) Ibid. (2), 95, 1177 (1954); d) Ibid. (2), 99, 637, (A) (1955).

11. J. W. Cleland, J. H. Crawford, Jr., K. Lark-Horovitz, J. C. Pigg, Phys. Rev. (2), 82, 763, (A) (1951).

12. J. W. Cleland, J. H. Crawford, Jr., K. Lark-Horovitz, J. C. Pigg, F. W. Young, Jr., a) Phys. Rev. (2), 83, 312 (1951); b) Ibid. (2), 84, 861 (1951).

13. J. W. Cleland, J. H. Crawford, Jr., J. C. Pigg, Phys. Rev. (2), 98, 1742 (1955).

14. R. R. Coltman, T. H. Blewitt, a) Phys. Rev. (2), 86, 641, (A) (1952); b) Ibid. (2), 91, 235, (A) (1953).

15. L. G. Cook, R. L. Cushing, a) Acta Metallurgica 1, 539 (1953); b) Ibid. 1, 549 (1953).

16. H. G. Cooper, J. S. Koehler, J. W. Marx, a) Phys. Rev. (2), 94, 496 (1954); b) Ibid. (2), 97, 599 (1955).

17. J. H. Crawford, Jr., J. W. Cleland, D. K. Holmes, J. C. Pigg, Phys. Rev. (2), 91, 243, (A) (1953).

18. J. H. Crawford, Jr., J. W. Cleland, K. Lark-Horovitz, J. C. Pigg, F. W. Young, Jr., Phys. Rev. (2), 85, 730, (A) (1952).

19. J. H. Crawford, Jr., K. Lark-Horovitz, a) Phys. Rev. (2), 78, 815 (1950); b) Ibid. (2), 79, 889 (1950).

20. W. V. Cummings, Jr., D. C. Kaulitz, M. J. Sanderson, Rev. Sci. Instrum. 26, 5 (1955).

21. W. D. Cussins, Proc. Phys. Soc. B, 68, 213 (1955).

22. R. E. Davis, W. E. Johnson, K. Lark-Horovitz, S. Siegel, Phys. Rev. (2), 74, 1255, (A); see also U. S. Report AECD-2054.

23. J. M. Denney, a) Phys. Rev. (2), 92, 531, (A) (1953); b) U. S. Report NAA-SR-271, 26 p. (1954); c) Phys. Rev. (2), 94, 1417, (A) (1954).

24. H. Dieckamp, Phys. Rev. (2), 98, 1531, (A) (1955).

25. H. Dieckamp, E. C. Crittenden, Jr., Phys. Rev. 94, 1418, (A) (1954).

26. G. J. Dienes, a) Phys. Rev. (2), 86, 228 (1952); b) Ibid. 87, 666, (1952); c) Ann. Rev. Nuclear Science 2, 187 (1953); d) J. Appl. Phys. 24, 666 (1953); see also U. S. Report BNL-1340; e) Phys. Rev. (2), 91, 1283 (1953)

27. G. J. Dienes, D. A. Kleinman, Phys. Rev. (2), 91, 238, (A). (1953).

28. C. E. Dixon, D. B. Bowen, Phys. Rev. (2), 94, 1418, (A) (1953).

1. C. E. Dixon, C. J. Meechan, Phys. Rev. (2), 91, 237, (A) (1953).
2. C. E. Dixon, C. J. Meechan, J. A. Brinkman, Phil. Mag. (7) 44, 449.
3. R. A. Dugdale, a) Phil. Mag. (7), 43, 912 (1952); b) Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 246 (1955).
4. R. A. Dugdale, A. Green, Phil. Mag. (7), 45, 163 (1954).
5. F. Duhamel, M. Freymann, R. Freymann, Comptes Rendus Acad. Sci. 237, 1684 (1953).
6. D. T. Eggen, M. J. Laubenstein, Phys. Rev. (2), 91, 238, (A) (1953).
7. R. R. Eggleston, a) J. Appl. Phys. 23, 1400 (1952); b) Phys. Rev. (2), 92, 531, (A) (1953); c) Acta Metallurgica 1, 679 (1953).
8. R. R. Eggleston, F. E. Bowman, J. Appl. Phys. 24, 229, (1953).
9. W. C. Ellis, E. S. Greiner, Phys. Rev. (2), 92, 1061 (1953).
10. H. Y. Fan, Phys. Rev. (2), 85, 730, (A) (1952).
11. H. Y. Fan, M. Becker, Reading Conference on Semi-conducting Materials (London: Butterworth), p. 132 (1951).
12. H. Y. Fan, K. Lark-Horovitz, Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 232 (1955).
13. Fillnow, E. K. Halteman, G. F. Mechlin, Phys. Rev. (2), 91, 236, (A) (1953).
14. J. Fleeman, a) Phys. Rev. (2), 91, 237, (A) (1953); b) Ibid. (2), 94, 1422, (A) (1954).
15. J. Fleeman, G. J. Dienes, J. Appl. Phys. 26, 652 (1955).
16. R. C. Fletcher, W. L. Brown, Phys. Rev. (2), 92, 585 (1953).
17. R. C. Fletcher. W. L. Brown, S. Machlup, Phys. Rev. (2), 91, 237, (A) (1953).
18. R. C. Fletcher, W. L. Brown, K. A. Wright, Phys. Rev. (2), 96, 833, (A) (1954).
19. C. D. Florida, F. R. Holt, J. H. Stephen, Nature, Lond. 173, 397 (1954).
20. J. H. Forster, H. Y. Fan, K. Lark-Horovitz, a) Phys. Rev. (2), 86, 643, (A) (1952); b) Ibid. (2), 91, 229, (A) (1953).
21. D. R. Frankl, Phys. Rev. (2), 92, 573 (1953).
22. D. R. Frankl, T. A. Read, Phys. Rev. (2), 89, 663 (1953).
23. J. Frenkel, T. Kontorova, J. Phys. USSR 1, 137 (1939).
24. E. Fues, H. Stumpf, Zeit. Naturforsch. 10a, 136 (1955).
25. I. G. Geib, R. E. Grace, a) Phys. Rev. (2), 86, 643, (A) (1952); correction ibid. 638; b) U. S. Report AECU-2225, 14 (1952).
26. H. L. Glick, F. C. Brooks, W. F. Witzig, W. E. Johnson, Phys. Rev. 87, 1074 (1952); see also U. S. Report WAPD-77.
27. H. L. Glick, W. F. Witzig, Phys. Rev. (2), 91, 236, (A) (1953).
28. R. B. Gordon, A. S. Nowick, Phys. Rev. (2), 98, 1540, (A) (1955).
29. B. R. Gossick, a) U. S. Report AECU-2225, 34 (1952); b) U. S. Report COO-103 (1953).
30. J. H. E. Griffiths, J. Owen, L. M. Ward, a) Nature, Lond. 173, 439 (1954); b) Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 81 (1955).
31. T. C. Harmon, R. Eidam, I. G. Geib, U. S. Report COO-102, 1 (1953).
32. T. C. Harmon, L. Horvath, I. G. Geib, U. S. Report COO-104, 17 (1953).

1. E. G. Harris, Phys. Rev. (2), 98, 1151, (A) (1955).
2. W. A. Harrison, F. Seitz, Phys. Rev. (2), 93, 1530, (A) (1955).
3. S. Hayes, R. Smoluchowski, Phys. Rev. (2), 91, 244, (A) (1953).
4. J. W. Henderson, H. G. Cooper, J. W. Marx, Phys. Rev. (2), 86, 642, (A) (1952).
5. R. W. Hoffman, N. S. Rasor, Phys. Rev. (2), 94, 1406, (A) (1954).
6. A. N. Holden, F. W. Kunz, U. S. Report AECD-3616, 24 p. (1954); see also Nuclear Science Abstracts.
7. H. D. Holland, D. Gottfried, Acta Cryst. 8, 291 (1955).
8. J. R. Huffman, Nucleonics 12, 4, 20 (1954).
9. H. B. Huntington, a) Phys. Rev. (2), 61, 325 (1942); b) Ibid. (2), 91, 1092 (1953); c) Ibid. (2), 93, 1414 (1954).
10. P. M. Hurley, H. W. Fairburn, a) J. Appl. Phys. 23, 1408 (1952); b) Bull. Geol. Soc. Amer. 64, 659 (1953).
11. H. M. James, K. Lark-Horovitz, Zeit. phys. Chem., 198, 107 (1951); see also U. S. Report TID-5011.
12. R. E. Jamison, T. H. Blewitt, a) Phys. Rev. (2), 86, 641, (A) (1952); b) Ibid. (2), 91, 237, (A) (1953); c) Rev. Sci. Instrum. 24, 474 (1953).
13. M. R. Jeppson, R. L. Mather, A. Andrew, H. P. Yockey, J. Appl. Phys. 26, 365 (1955).
14. M. R. Jeppson, R. L. Mather, H. P. Yockey, U. S. Report AECD-3631, 30 p. (1954).
15. F. B. Johnson, R. S. Pease, Phil. Mag. (7), 45, 631 (1954).
16. R. D. Johnson, A. B. Martin, J. Appl. Phys. 23, 1245 (1952).
17. W. E. Johnson, K. Lark-Horovitz, Phys. Rev. (2), 76, 442 (1949).
18. D. F. Johnston, J. Nuclear Energy 1, 311 (1955).
19. E. R. W. Jones, W. Munro, N. H. Hancock, a) British Report AERE M/R 795 (1951); b) J. Nuclear Energy 1, 76 (1954).
20. P. Jongenburger, Phys. Rev. (2), 90, 710 (1953).
21. J. W. Kauffman, J. S. Koehler, a) Phys. Rev. (2), 88, 149 (1952); b) Ibid. (2), 97, 555 (1955).
22. D. T. Keating, a) Phys. Rev. (2), 94, 1429 (A) (1954); b) Acta Metallurgica 2, 885 (1954); see also U. S. Report BNL-1848, 9 p.; c) Phys. Rev. (2), 97, 832 (1955); d) Ibid. (2), 98, 1859 (1955).
23. P. H. Keesom, K. Lark-Horovitz, N. Pearlman, a) Phys. Rev. (2), 89, 900, (A) (1952); b) Science 116, 630 (1952); c) U. S. Report COO-102, 8 (1953).
24. E. M. Kelly, a) U. S. Report NAA-SR-261, 15 p. (1954); b) Acta Metallurgica 3, 101 (1955).
25. H. A. Kierstead, Phys. Rev. (2), 98, 245, (A) (1955).
26. G. H. Kinchin, J. Nuclear Energy 1, 124 (1954).
27. G. H. Kinchin, R. S. Pease, a) J. Nuclear Energy 1, 200 (1955); b) Rep. Progress Phys. 18, 1 (1955).
28. P. G. Klemens, Proc. Roy. Soc. A208, 108 (1951).
29. E. E. Klontz, a) U. S. Report AECU-2267 or AECU-2664 (1952; b) U. S. Report COO-102, 28 (1953); c) U. S. Report COO-104, 13) (1953).
30. E. E. Klontz, K. Lark-Horovitz, a) Phys. Rev. 82, 763, (A) (1951); b) U. S. Report AECU-2225, 56 (1952); c) Phys. Rev. (2), 86, 643, (A) (1952).
31. E. E. Klontz, R. R. Pepper, K. Lark-Horovitz. Phys. Rev. (2), 98, 1535, (A) (1955).

1. J. S. Koehler, a) U. S. Report COO-197 (1953); b) U. S. Report COO-199 (1954).

2. J. S. Koehler, F. Seitz, a) Zeit. Physik 138, 238 (1954); b) Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 222 (1955).

3. W. Kohn, Phys. Rev. (2), 94, 1409, (A) (1954).

4. F. W. Kunz, A. N. Holden, a) Phys. Rev. (2), 94, 1417, (A) (1954); b) Acta Metallurgica 2, 816 (1954); see also U. S. Report KAPL-1066, 45 p. (1954).

5. K. Lark-Horovitz, a) Reading Conference on Semi-conducting Materials (London: Butterworth), p. 47 (1951); b) U. S. Report AECU-2225, 1 (1952).

6. K. Lark-Horovitz, M. Becker, R. E. Davis, H. Y. Fan, Phys. Rev. (2), 78, 334, (A) (1950).

7. K. Lark-Horovitz, E. Bleuler, R. E. Davis, D. Tendam, Phys. Rev. (2), 73, 1256, (A) (1948).

8. R. Lawrance, A. F. Gibson, J. W. Granville, Proc. Phys. Soc., B, 67, 625 (1954).

9. D. O. Leeser, a) Materials and Methods 36, 1, 75 (1952); b) Ibid., 40, 2, 110 (1954).

10. W. J. Leivo, Phys. Rev. (2), 91, 245, (A) (1953).

11. W. J. Leivo, R. Smoluchowski, Phys. Rev. (2), 93, 1415 (1954).

12. C. Y. Li and A. S. Nowick, Phys. Rev. (2), 98, 1531, (A) (1955).

13. L.-Y. Lin, B. R. Russell, Phys. Rev. (2), 99, 657, (A) (1955).

14. H. G. Lipson, E. Burstein, P. L. Smith, Phys. Rev. (2), 98, 1535, (A) (1955).

15. J. J. Loferski, P. Rappaport, Phys. Rev. (2), 98, 1861, (1955).

16. W. M. Lomer, British Report AERE T/R 1540, 10 p. (1954).

17. W. M. Lomer, A. H. Cottrell, Phil. Mag. (7), 46, 711 (1955).

18. J. D. McClelland, U. S. Report NAA-SR-263, 14 p. (1953).

19. J. D. McClelland, J. J. Donoghue, J. Appl. Phys. 24, 963 (1953).

20. W. R. McDonnell, H. A. Kierstead, a) Phys. Rev. (2), 93, 247 (1954); for correction see Ibid. 98, 1870 (1955).

21. A. W. McReynolds, W. Augustyniak, M. McKeown, D. B. Rosenblatt, a) Phys. Rev. (2), 94, 1417, (A) (1954); b) Ibid. (2), 98, 418 (1955).

22. R. Maddin, A. H. Cottrell, Phil. Mag. (7), 46, 735 (1955).

23. M. S. Maier, H. R. Nelson, Trans. A. I. M. E. 147, 39 (1942).

24. M. J. Makin, a) Nature, Lond. 174, 752 (1954); b) Nuclear Energy 1, 181 (1955).

25. J. A. Manintveld, Nature, Lond. 169, 623 (1952).

26. D. Mapother, Phys. Rev. (2), 89, 1231 (1953).

27. J. J. Markham, Phys. Rev. (2), 88, 500 (1952).

28. A. B. Martin, S. B. Austerman, R. R. Eggleston, J. F. McGee, M. Tarpinian, Phys. Rev. (2), 81, 664, (A) (1951).

29. J. W. Marx, Phys. Rev. (2), 91, 1564 (1953).

30. J. W. Marx, H. G. Cooper, J. W. Henderson, Phys. Rev. (2), 88, 106 (1952); see also U. S. Report AECU-2118, 19 p.

31. J. W. Marx, J. S. Koehler, C. Wert, Phys. Rev. (2), 86, 643, (A) (1952).

32. S. Mayburg, Phys. Rev. (2), 95, 38 (1954).

33. C. J. Meechan, G. M. Dieckamp, U. S. Report NAA-SR-1159 (1955).

34. C. J. Meechan, R. R. Eggleston, Acta Metallurgica 2, 680 (1954).

RADIATION EFFECTS IN SOLIDS

1. R. A. Meyer, J. Appl. Phys. 25, 1369 (1954); U. S. Report USNRDL-431, 56 p.

2. L. Mongini, Energia Nucleare, No. 8, 209 (1953).

3. G. T. Murray, W. E. Taylor, a) Phys. Rev. (2), 86, 642, (A) (1952); b) U. S. Report ORNL-1323 (1953); c) Acta Metallurgica 2, 52 (1954).

4. F. R. N. Nabarro, a) Report of the Conference on the Strength of Solids, Bristol, 1947 (London: Physical Society), p. 75 (1948); b) Phys. Rev. (2), 87, 665 (1952).

5. C. M. Nelson, R. L. Sproull, R. S. Caswell, Phys. Rev. (2), 90, 364, (A) (1953).

6. M. C. M. O’Brien, M. H. L. Pryce, Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 88 (1955).

7. J. J. O’Connor, L. S. Foster, Nuclear Engineering, Part II, Chem. Eng. Progr. Symposium Ser., 50, 12, 59 (1954).

8. F. K. Odencantz, Phys. Rev. (2), 88, 166, (A) (1952).

9. K. O. Otley, Glass Ind. 33, 24 (1952).

10. A. W. Overhauser, a) Phys. Rev. (2), 92, 533, (A) (1953); b) Ibid. (2), 90, 393 (1953); see also U. S. Report AECU-2358; c) Ibid. (2), 94, 1551 (1954).

11. J. Ozeroff, U. S. Report AECD-2973 (KAPL-205), 42 p. (1949).

12. N. J. Palladino, U. S. Report WARD-ReS-13, 2 p., referred to in Nuclear Science Abstracts (1954).

13. H. R. Paneth, Phys. Rev. (2), 80, 703, (1950).

14. E. A. Pearlstein, a) Phys. Rev. (2), 91, 244, (A) (1953); b) Phys. Rev. (2), 92, 881 (1953); see also U. S. Report NYO-3127; c) Phys. Rev. (2), 94, 1432, (A) (1954).

15. E. A. Pearlstein, H. Ingham, R. Smoluchowski, Phys. Rev. (2), 98, 1530, (A) (1955).

16. R. S. Pease, Acta Cryst. 7, 663, (A) (1954).

17. R. Pepper, E. E. Klontz, K. Lark-Horovitz, J. MacKay, Phys. Rev. (2), 94, 1410, (A) (1954).

18. J. C. Pigg, J. W. Cleland, J. H. Crawford, Jr., K. Lark-Horovitz, Phys. Rev. (2), 82, 763, (A) (1951).

19. R. A. Pizarro, U. S. Report AECU-2225, 37 (1952).

20. P. L. Pratt, Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 402 (1955).

21. W. Primak, a) Phys. Rev. (2), 95, 837 (1954); b) Ibid. (2), 98, 1854 (1955).

22. W. Primak, C. J. Delbecq, P. H. Yuster, Phys. Rev. (2), 98, 1708 (1955).

23. W. Primak, L. H. Fuchs, P. Day, Phys. Rev. (2), 92, 1064 (1953).

24. W. Primak, P. H. Yuster, C. J. Delbecq, Phys. Rev. (2), 98, 237, (A) (1955).

25. K. Przibram, Verfärbung und Lumineszenz (Wien: Springer), 275 p. (1953).

26. B. W. Randolph, a) Phys. Rev. (2), 85, 710, (A) (1952); b) U. S. Report COO-102, 24 (1953).

27. P. Rappaport, a) Phys. Rev. (2), 93, 246 (1954); b) Ibid. (2), 94, 1409, (A) (1954).

28. N. S. Rasor, Phys. Rev. (2), 98, 1555, (A) (1955).

29. J. K. Redman, R. R. Coltman, T. H. Blewitt, Phys. Rev. (2), 91, 448 (A) (1953).

30. J. T. Richards, Acta Metallurgica 3, 211 (1955).

1. W. H. Robinson, Y.-Y. Li, R. Smoluchowski, Phys. Rev. (2), 94, 1435, (A) (1954).
2. G. W. Rodeback, Phys. Rev. (2), 94, 1046, (A) (1954).
3. D. B. Rosenblatt, R. Smoluchowski, G. L. Dienes, Phys. Rev. (2), 94, 1417, (A) (1954).
4. A. E. Roswell, A. S. Nowick, J. Metals 5 (Trans. A. J. M. E., 197), 1259 (1953).
5. J. Rothstein, a) Phys. Rev. (2), 89, 901, (A) (1953); b) U. S. Report SCEL-E-1127, AD-25284, 76 p. (1953).
6. J. B. Sampson, H. Hurwitz, Jr., E. F. Clancy, Phys. Rev. (2), 99, in press, (A) (1955).
7. E. Schmid, K. Lintner, a) Anzeiger Osterr. Akad. Wiss., Math.-Naturwiss. Klasse 91, 25 (1954); b) Sitzber. Österr. Akad. Wiss. (II), 163, 109 (1954).
8. E. Schulz-Dubois, M. Nisenoff, H. Y. Fan, K. Lark-Horovitz, Phys. Rev. (2), 98, 1561, (A) (1955).
9. P. Schwed, G. Groetzinger, J. Appl. Phys. 23, 234 (1952).
10. A. Seeger, Zeit. Naturforsch. 10a, 251 (1955).
11. F. Seitz, a) Disc. Faraday Soc., No. 5, 271 (1949); b) Physics Today 5, 6, 6 (1952); c) Phys. Rev. (2), 98, 1530, (A) (1955).
12. R. G. Shulman, W. L. Brown, R. C. Fletcher, Phys. Rev. (2), 96, 833, (A) (1954).
13. S. S. Sidhu, C. O. Henry, Phys. Rev. (2), 80, 123, (A) (1950).
14. S. Siegel, Phys. Rev. (2), 75, 1823 (1949).
15. J. C. Slater, J. Appl. Phys. 22, 237 (1951).
16. J. S. Smart, Jr., A. A. Smith, Jr., A. J. Phillips, Trans. A.I.M.E. 143, 272 (1941).
17. W. J. Smith, W. J. Leivo, R. Smoluchowski, Phys. Rev. (2), 94, 1435, (A) (1954).
18. R. Smoluchowski, a) Phys. Rev. (2), 94, 1409, (A) (1954); b) Report of the Conference on Defects in Crystalline Solids, Bristol, 1954 (London: Physical Society), p. 252 (1955).
19. R. Smoluchowski, E. Pearlstein, H. Ingham, Phys. Rev. (2), 98, 1530 (A) (1955).
20. R. Smoluchowski, W. J. Leivo, E. A. Pearlstein, W. J. Smith, W. Vaughan, U. S. Report NYO-3126 (1953).
21. W. S. Snyder, J. Neufeld, a) Phys. Rev. (2), 94, 760, (A) (1954); b) Phys. Rev. (2), 97, 1636, (1955).
22. R. V. Steele, W. P. Wallace, U. S. Report LRL-145, 21 p. (1954).
23. P. G. Stello, U. S. Report NAA-SR-171 (1952).
24. D. K. Stevens, a) U. S. Report ORNL-1599, 37 p. (1954); b) Phys. Rev. (2), 98, 1541, (A) (1955).
25. D. K. Stevens, J. W. Cleland, J. H. Crawford, Jr., Phys. Rev. (2), 94, 1409 (1954).
26. F. Stockman, E. E. Klontz, H. Y. Fan, K. Lark-Horovitz, Phys. Rev. (2), 98, 1535, (A) (1955).
27. C. R. Sutton, D. O. Leeser, a) Nuclear Engineering, Part II; Chem. Eng. Progr. Symposium Ser., 50, 12, 208 (1954); b) Nucleonics 12, 9, 8, (1954).
28. W. E. Taylor, Phys. Rev. (2), 86, 642, (A) (1952).
29. W. E. Taylor, N. H. Odell, H. Y. Fan, Phys. Rev. (2), 88, 867 (1952).
30. C. W. Tucker, Jr., J. B. Sampson, a) Phys. Rev. (2), 94, 1418, (A) (1954); b) Acta Metallurgica 2, 433; see also U. S. Report KAPL-1037 (1955).

1. C. W. Tucker, Jr., P. Senio, a) Acta Cryst. 7, 456; see also U. S. Report AECD-3613, 7 p.; b) U. S. Report KAPL-1180, 37 p. (1954); c) Phys. Rev. (2), 98, 1541, (A) (1955); d) Acta Cryst. 8, 371 (1955).

2. J. H. O. Varley, a) Nature, Lond. 174, 886 (1954); b) J. Nuclear Energy 1, 130; see also AERE M/R 1508, 12 p. (1954).

3. W. H. Vaughan, W. J. Leivo, R. Smoluchowsky, Phys. Rev. (2), 91, 245, (A).

4. B. E. Warren, a) U. S. Reports NYO-767, 4 p. (1951); b) U. S. Reports NYO-3731, NYO-3732, (1952); c) U. S. Report NYO-3734 (1953); d) U. S. Reports NYO-6508, 6 p., NYO-6511, 5 p. (1954).

5. S. Weissman and R. Chang, Phys. Rev. (2), 99, 657 (A).

6. D. R. Westervelt, a) Acta Metallurgica 1, 755 (1953); b) U. S. Report NAA-SR-888, 26 p. (1954).

7. W. F. Witzig, a) U. S. Report AECD-3290, WAPD-43 (1951); b) Phys. Rev. (2), 87, 211, (A) (1952); c) J. Appl. Phys. 23, 1263 (1952).

8. M. Wittels, Phys. Rev. (2), 89, 656 (1953).

9. M. Wittels, F. A. Sherrill, Phys. Rev. (2), 93, 1117 (1954).

10. D. A. Wruck, U. S. Report AD-25100; referred to in Nuclear Science Abstracts (1954).

11. D. Wruck, C. Wert, a) Phys. Rev. (2), 94, 1417, (A) (1954); b) U. S. Report AECU-2906, 26 p. (1954); c) Acta Metallurgica 3, 115 (1955).

12. H. P. Yockey, A. Andrew, F. L. Fillmore, L. E. Glasgow, C. d’A. Hunt, J. H. Pepper, Rev. Sci. Instrum. 25, 1011 (1954).

13. H. P. Yockey, F. L. Fillmore, C. d’A. Hunt, A. Andrew, L. Glasgow, F. R. Weber, Jr., M. R. Jeppson, J. H. Pepper, R. E. Garter, U. S. Report NAA-SR-186 (1952).

14. E. Schmid, K. Lintner, Zeit. Metallk. 46, 71 (1955).

15. B. Neumann, E. Schmid, J. Metals 9, 349 (1955).

16. K. Lintner, E. Schmid, Ergebnisse der Exakten Naturwissenschaften 28, 302 (1955).