THE EFFECT OF RADIATION ON THE PHYSICAL PROPERTIES AND STRUCTURE OF A SOLID BODY

A. I. Zakharov

INTRODUCTION

Under the action of various kinds of radiation, most solid bodies change many of their physical properties. In recent years researchers’ attention has been directed to the action of radiation on crystalline structure, electrical resistance, hardness, heat capacity, thermal conductivity, and other properties of a solid body. Changes in physical properties under the action of radiation have been studied in metals, alloys, and nonmetallic solid bodies: ionic, valence, and molecular compounds. Nuclear reactors, elementary-particle accelerators, and radioactive isotopes have been used as radiation sources.

Research in the field of the action of radiation on the physical properties of materials is of great interest both for understanding the structure of a solid body and for the practical use of substances with new properties obtained as a result of irradiation.

Although investigations in the field of the action of radiation on a solid body have been carried out for a number of years, the experimental data obtained are nevertheless insufficient for presenting a complete picture of the processes that occur in a solid body when radiation acts upon it. Theoretical studies in this field are also far behind. Up to the present time there have been few theoretical works on the study of the interaction of particles of intermediate energies with the atoms of a substance. These investigations are of special interest, since the passage of particles of intermediate energies through matter causes the greatest structural changes.

Previously published review articles1,2 summarize the experimental and theoretical material in the field of research on the action of radiation on solids up to 1952.

The present review sets forth the principal works published in foreign journals in recent years. Along with them, works by Soviet investigators are briefly described; these works were reported at the July session of the Academy of Sciences of the USSR on the peaceful use of atomic energy.

At the beginning of the review, the existing theoretical concepts are briefly presented, with the aid of which the behavior of solids under the action of radiation is currently explained. After the theoretical considerations have been examined, the experimental material is set forth.

I. THEORY OF THE ACTION OF RADIATION ON SUBSTANCES

1. Irradiation by Charged Particles

When passing through a solid, a charged particle loses kinetic energy in two ways: as a result of elastic collisions with the nuclei of stationary atoms and as a consequence of excitation or ionization of the atoms of the substance.

Elastic scattering3,4. In elastic collisions with stationary atoms of a substance, a charged particle transfers to them part of its energy. The energy transferred in the primary elastic collision may be sufficient to cause the displacement of neighboring atoms in the crystal lattice by several interatomic distances.

In general, elastic collisions lead to two kinds of results. First, they cause oscillations of atoms in the crystal lattice, i.e. they lead to heating of the material. Second, as a result of elastic collisions, some atoms are torn out of their normal positions in the crystal lattice, as a result of which interstitial atoms and vacancies are formed. The second of these two processes can take place if the stationary atom receives a certain minimum energy \(E_d\), exceeding the energy necessary for the adiabatic displacement of the atom from its normal position in the lattice into an interstice. The assumption that \(E_d\) is of the order of 25 eV for the atoms of most metals, ionic and valence crystals has been confirmed experimentally5.

The fraction of the energy expended in elastic collisions that is used for the formation of displaced atoms is, in the examples considered here, approximately one half.

Excitation of electrons and ionization of atoms. The magnitude of the energy expended per unit path of the moving particle

on ionization of atoms, is expressed by the relation

\[ -\left(\frac{dE}{dx}\right)_e= \frac{4\pi z^2 e^4}{mv^2}\,N_0 Z_2 \lg\frac{\varepsilon}{B}, \tag{1} \]

where

\[ \varepsilon=\frac{m}{M}E, \]

\(E\) is the kinetic energy of the incident particle, \(M\) is its mass, \(m\) is the electron mass, \(ze\) is the charge of the moving particle, \(v\) is its velocity, \(Z_2\) is the number of electrons in a stationary atom, \(N_0\) is the density of stationary atoms, and \(B\) is an energy parameter, equal in order of magnitude to the mean geometric value of the ionization potentials of the various electrons of the atoms of the substance.

In the region of energies where \(\varepsilon \gg B\), the fraction of energy expended on ionization of atoms, relative to the energy lost in elastic collisions, is of the order of \(10^3\). But as the energy of the moving particle decreases, this fraction rapidly decreases owing to the reduction of energy losses to ionization of atoms.

Ionization of the atoms of a substance by a heavy moving particle occurs under the condition that the parameter \(\varepsilon\) is greater than some quantity proportional to the ionization energy of the atoms. It is assumed that the moving particle ceases to excite a given group of bound electrons when its parameter \(\varepsilon\) falls to a value equal to \(\frac{1}{8}E_e\). Usually the excitation energy of the valence electrons is taken as the value of \(E_e\). As energy is lost to ionization, the parameter \(\varepsilon\) decreases to a value below \(\frac{1}{8}E_e\), after which the moving particle loses energy only as a result of elastic collisions.

The above conclusions on the energy loss of a moving particle to ionization of atoms are valid only for insulators. In a metal, part of the energy of the moving particle is lost in excitation of the electron gas.

If the “zero energy” of the Fermi gas is denoted by \(\varepsilon_0\), the result of the calculation is as follows:

1) For a parameter \(\varepsilon\) of the moving particle much greater than \(\varepsilon_0\), the energy lost in excitation of the electron gas is expressed by the relation

\[ -\frac{dE}{dx} = \frac{\pi Z_1^2 e^4}{\varepsilon}\,N_0 n \left(\lg\frac{\varepsilon}{\varepsilon_0}+1.08\right), \tag{2} \]

where \(Z_1\) is the atomic number of the moving particle, and \(n\) is the number of free electrons per atom.

2) For a parameter \(\varepsilon\) of the moving particle much smaller than \(\varepsilon_0\), the expression for the energy lost in excitation of a free

of the electron gas, will take the form

\[ -\frac{dE}{dx}=12\pi N_0 n e A_0 Z_1^{1/3}, \]

where \(A_0=76.8a_0^2\) (\(a_0\) is the Bohr radius). According to the last equation, the energy loss for electron excitation decreases linearly with decreasing \(\varepsilon\). This occurs because free electrons can absorb field energy of arbitrarily low frequency.

3) For a value of the parameter \(\varepsilon\) close to \(\varepsilon_0\), the loss of energy through electron excitation reaches its greatest value. The calculation gives the relative value of the energy loss scattered in elastic collisions to the energy loss for electron excitation, and also an estimate of the value of \(\varepsilon\) at which elastic collisions begin to predominate. It is assumed that excitation of the electrons of the substance ceases as soon as \(\varepsilon\) decreases to the threshold value \(\varepsilon_t\). The value of \(\varepsilon_t\) for metals is a function of \(Z\) and \(n\) and lies in the range from \(0.1\) to \(10\) eV.

Formation of recoil atoms. In its motion a charged particle loses part of its energy in elastic scattering. Approximately half of the energy lost in elastic scattering is expended on knocking atoms out of sites in the crystal lattice. In the collision of a moving particle with an immobile atom, kinetic energy is transferred to the latter, the mean value of which (when the particle energy exceeds \(E_d\)) is given by the expression

\[ \bar{E}=E_d \lg\left(\frac{E}{E_d}\frac{4\mu^2}{M_1M_2}\right), \tag{3} \]

where \(M_1\) and \(M_2\) are the masses of the moving particle and the immobile atom, and \(\mu\) is the reduced mass.

The logarithm has a mean value from 3 to 15. Consequently, the mean kinetic energy of the recoil atom is 3–15 times greater than the energy \(E_d\). Thus, in an elastic collision the recoil atom is capable of knocking atoms out of sites in the crystal lattice. The recoil atom expends all its energy only on elastic collisions. This follows from the smallness of the parameter \(\varepsilon\).

When the energy of secondary recoil atoms is greater than \(E_d\), tertiary atoms, etc., may be knocked out.

2. Irradiation with Fast Neutrons

In an elastic collision with the nucleus of an atom of the substance, a fast neutron transfers to the latter a considerable kinetic energy. The mean value of the kinetic energy transferred in an elastic collision of a neutron with the nucleus of an immobile atom of mass \(M\)

is given by the expression

\[ \bar{E}=\frac{2M}{(M+1)^2}E_0, \tag{4} \]

where \(E_0\) is the initial kinetic energy of the neutron, whence it follows that the recoil atom even of heavy elements has a comparatively large kinetic energy. For example, a copper nucleus (\(M=64\)) receives on the average a kinetic energy of \(67\,000\) ev in an elastic collision with a neutron of energy \(2\) Mev. Thus, recoil atoms have kinetic energy sufficient to knock atoms of the substance out of the sites of the crystal lattice. Of course, the primary recoil atom may also lose energy in exciting electrons and ionizing atoms, but this energy is very small in view of the fact that the recoil atom has a large mass and, consequently, a small parameter \(\varepsilon\). The loss of energy by a recoil atom in elastic scattering is predominant. The comparatively low energy of recoil atoms makes it possible in calculations to use the Bohr model \(^{6}\). In this case the number of interstitial atom–vacancy pairs formed is determined approximately by the formula

\[ B(E)\approx \frac{M}{(M+1)^2}\frac{E_0}{E_d}. \tag{5} \]

Most often, irradiation of materials with fast neutrons is carried out in nuclear reactors near uranium rods. The neutron energy distribution under these conditions is close to the distribution of fission neutrons of \(U^{235}\). The energy of fission neutrons lies in a wide range from \(0\) to \(15\) Mev. The neutron energy distribution is given by the empirical formula

\[ N(E)=\operatorname{sh}(2E)^{1/2}e^{-E}, \tag{6} \]

where \(E\) is the energy in Mev. The number of displacements formed in \(1\ \mathrm{cm}^3\) per second upon irradiation by a flux of \(N(E)\,dE\) neutrons having energies from \(E\) to \(E+dE\) and velocity \(v\) will be:

\[ J=\int vN(E)\sigma(E)B(E)\,dE, \tag{7} \]

where \(\sigma(E)\) is the cross section for collision of a neutron with an atom of the substance. When irradiated with fast neutrons, the material ultimately undergoes changes of the kind that also occur under irradiation with fast charged particles. The change in the properties of a solid body results from the displacement of atoms from their normal positions in the crystal lattice into interstices. Such displacements are formed under irradiation both by charged particles and by neutrons. However, there are substantial differences between irradiation of a substance by neutrons and by charged particles:

1. Under irradiation by fast neutrons, a smaller fraction of the energy is spent on excitation of electrons than under irradiation by charged particles.

1. Fast neutrons have a greater mean free path than charged particles. In view of this, when irradiating with neutrons one can create defects having a uniform concentration in large volumes of material. Charged particles produce defects in a thin layer (less than 1 mm) of the material on the side of irradiation, and the concentration of defects is nonuniform over the thickness of the layer.

3. Fission fragments

The nuclei of many isotopes (thorium-232, uranium-235, plutonium-239, lithium-6, boron-10, etc.) are capable of fission after capturing neutrons. Atoms of any fissionable material, for example uranium-235, can be distributed uniformly in the volume of another nonfissionable substance. Upon capture of a neutron, the uranium-235 nucleus fissions into two fragments possessing a very large kinetic energy, of the order of 150 MeV. The fission process is usually asymmetric; the most probable mass values of the fission fragments are located near 95 and 139. The fission fragments are in an ionized state over the greater part of their path; the degree of ionization decreases as the fragments slow down. The value of the parameter \(\varepsilon\) for this pair of fragments is approximately 500 eV and 260 eV. Consequently, as the fission fragments slow down, most of the energy is spent on electron excitation and ionization of atoms. The magnitude of the energy loss for excitation of electrons by fission fragments is given by the relation

\[ -\left(\frac{dE}{dx}\right)_e=\frac{4\pi e^4}{mv^2}Z_1^2N_0G(\varepsilon), \tag{8} \]

where \(Z_1\) is the atomic number of the fission fragment, and \(G(\varepsilon)\) is a linear function depending on \(\varepsilon\), which has the value 16 at \(\varepsilon=500\) eV and zero at \(\varepsilon=0\).

It has been found theoretically that fission fragments lose about 2.7% of their energy to elastic scattering during the period in which electron excitation predominates. An additional 0.3% of the energy is lost to elastic scattering after electron excitation has ceased. About half of this energy is spent on displacing primary atoms in the crystal lattice. The primary recoil atoms in the case of uranium have a kinetic energy of about 375 eV and additionally displace three atoms. From the combination of these quantities it is determined that a pair of fission fragments produces about 25,000 atomic displacements in metallic uranium.

When the atomic weight of the substance into which the fissionable material is introduced is decreased, the number of atomic displacements produced by one pair of fission fragments decreases. Thus, for example, a pair of uranium-235 fission fragments in graphite produces only 8300 atomic displacements. The decrease in the number of displaced atoms in this case is due to the relative increase in the energy loss by fission fragments to electron excitation.

4. General picture of possible primary and secondary processes under irradiation

The general picture of the processes occurring under the action of radiation on a solid is complex and still little studied. The considered processes of ionization and formation of recoil atoms when a fast particle passes through matter occur both in simple substances and in chemical compounds.

In addition, in solid chemical compounds, under the action of radiation, excitation of molecules may occur, followed by their decomposition. Upon dissociation of molecules of a chemical compound, ions and radicals are formed, which may either be neutralized or, by combining with one another, create chemical compounds of the original or of a different composition.

A scheme of the general picture of possible primary and secondary processes under the action of radiation on matter\(^8\) is given in Fig. 1.

II. ACTION OF RADIATION ON METALS AND ALLOYS

1. Nature of radiation-induced disturbances

When metals are irradiated with high-energy particles, recoil atoms are formed which cause disturbances of the crystal lattice. These disturbances in the substance can be represented by a certain visual model. At the first moment after receiving an impulse from the particle, the recoil atom has a high velocity and loses kinetic energy partly to the excitation of electrons. As the kinetic energy of the recoil atom decreases, the fraction of energy lost to elastic scattering increases.

In a short time of the order of \(10^{-11}\) sec, in the vicinity of the motion of the recoil atom the temperature rises to \(10^4{}^\circ\mathrm{K}\). In regions where the temperature reaches a value above the melting temperature at the given pressure, the concentration of atoms in interstices and vacancies amounts to several percent. Consequently, in these regions an interstitial atom is separated by two or three interatomic distances from a vacancy. Such a spatial distribution of atoms causes local stresses. With a very high quenching rate of the molten regions, density relaxation does not have time to occur. Relaxation can occur only when the relaxation time is much less than the lifetime of the given volume in the melt.

In work\(^9\) the existence is assumed of two regions of defects of the crystal lattice which arise during the interaction of a fast particle with the atoms of the substance. The first region

Fig. 1. Possible primary and secondary processes during irradiation.^8

Text appearing in the figure:

• Fast particle
  (primary, secondary)
• Fast ion, recoil atom
• Neutron

• $\gamma$- or X-rays

• Continuous X-ray radiation

• Excitation of inner electrons
• Excitation of valence electrons
• Interstitial atom—vacancy
• Excitation of molecules
• Cherenkov radiation

• Nuclear reaction

• X-ray radiation

• Recombination radiation
• Radiation losses
• Luminescence
• Dissociation
• Ionization
• Secondary ions
• Chain reaction
• Chemical reaction
• Primary-ion reaction
• Recombination
• Radicals
• Heat

“thermal wedging” was considered by Seitz\(^{3}\) and represents a region of interstitial atoms and vacancies. The second region of “displacement wedging,” proposed by Brinkman, is a direct continuation of the first region.

In Fig. 2 a schematic section is given of the disturbance caused by a recoil atom in the crystal lattice of a metal. The narrow channel below point \(A\) represents a region of interstitial atoms and vacancies. Above point \(A\) lies the region of “displacement wedging.” It is assumed that in this region melting of the metal and its solidification take place. During the existence of the molten state, an exchange of atoms by random displacements has time to occur. Therefore the atoms in the molten cavity have time to occupy new positions. Consequently, upon solidification a multitude of small crystallites of entirely new orientation is formed.

Heating of the region of “displacement wedging” occurs under the action of three factors: 1) due to the elastic collision of the recoil atom with the atoms of the substance without displacing the latter by more than a lattice parameter; 2) due to the energy transferred to the atoms of the substance through electrons that were excited by the recoil atom; 3) due to the release of energy as a result of the restoration of disturbances in the preceding region of defects.

The energy communicated by the recoil atom to the electrons is distributed among a large number of electrons. Thus, the action of the second factor is insignificant. Heating of the region of “displacement wedging”—

Fig. 2. Schematic representation of a model of radiation damage in a metal\(^{9}\).

“wedging” occurs chiefly due to the action of the first and third factors. However, at first the action of the first factor predominates, and only later does the third factor begin to act. As a result of these successive processes the crystal lattice is heated above the melting temperature. Melting evidently occurs in a cylindrical region along the path of the recoil atom.

In the calculations the parameter \(E_t\) is introduced. The parameter \(E_t\) may be characterized as the energy of the primary recoil atom for which the mean free path between significant collisions becomes of the order of the interatomic distance. Table I gives the values of the energy \(E_t\) for various elements. The table was calculated on the basis of theoretical deductions made by Brinkman. From an analysis of the values in the table one may conclude that in light elements the regions of “thermal wedging” predominate, whereas in heavy elements the regions of “displacement wedging” predominate. Thus, the proposed model shows that radiation damage is different in the case of light and heavy elements.

Table I

\(Z\)	Element	\(r_0\), Å	\(E_t\), eV	\(Z\)	Element	\(r_0\), Å	\(E_t\), eV
11	Na	3,708	180	56	Ba	4,34	860
12	Mg	3,190	550	57	La	3,73	4 200
13	Al	2,856	1 200	58	Ce	3,64	5 900
19	K	4,618	140	59	Pr	3,633	6 000
20	Ca	3,93	420	60	Nd	3,62	6 500
21	Sc	3,205	2 500	63	Eu	3,960	1 500
22	Ti	2,91	5 000	64	Gd	3,554	8 300
23	V	2,627	9 600	65	Tb	3,508	10 000
24	Cr	2,493	15 000	66	Dy	3,499	10 000
26	Fe	2,476	20 000	67	Ho	3,480	11 000
27	Co	2,501	20 000	68	Er	3,459	12 000
28	Ni	2,486	23 000	69	Tm	3,446	13 000
29	Cu	2,551	23 000	70	Yb	3,866	3 700
30	Zn	2,659	19 000	71	Lu	3,439	13 000
37	Rb	4,87	150	72	Hf	3,14	33 000
38	Sr	4,30	610	73	Ta	2,854	73 000
39	Y	3,59	3 000	74	W	2,734	110 000
40	Zr	3,16	9 000	75	Re	2,734	105 000
41	Nb	2,853	25 000	76	Os	2,670	150 000
42	Mo	2,720	36 000	77	Ir	2,709	120 000
44	Ru	2,644	51 000	78	Pt	2,769	110 000
45	Rh	2,685	47 000	79	Au	2,878	80 000
46	Pd	2,745	43 000	81	Tl	3,401	16 000
47	Ag	2,882	31 000	82	Pb	3,493	14 000
48	Pb	2,972	21 000	90	Th	3,59	9 000

\(r_0\) — distance between atoms.

Usually the energy of melting required at atmospheric pressure per atom is of the order of 0.1–0.2 eV. When a region of “displaced wedging-in” is formed, the metal located inside it is subjected to high pressure from the surrounding atoms. Therefore the energy expended on melting increases, but its value remains below 0.5 eV. Since part of the energy is lost in heating atoms along the boundary of the molten region and in exciting electrons, the melting energy per atom of a region of “displaced wedging-in” is taken to be of the order of 1 eV.

Using these considerations, one can, for copper irradiated with neutrons of energy 2 MeV, find the average number of atoms that have formed a region of “displaced wedging-in,” which turns out to be of the order of \(2 \cdot 10^4\) atoms. If one assumes that the region of “displaced wedging-in” has a spherical shape, then the diameter of the sphere will be of the order of 75 Å.

To prove the existence in a metal of molten so-called regions of “displaced wedging-in,” a metastable alloy of iron in copper was used \(^{10}\). The alloy contained 2.4 weight percent iron. Specimens of this chemical composition, quenched from a temperature above 700° C, were paramagnetic. Annealing or plastic deformation transforms the specimens into the ferromagnetic state. The ferromagnetic precipitate is relatively stable under subsequent thermal and mechanical action. Specimens containing a ferromagnetic phase were irradiated with protons of energy 9 MeV. It was found that the ferromagnetic phase decreases at a rate of 0.5% for each \(\mu\text{A-hour}/\text{cm}^2\) of proton flux. The decrease of the ferromagnetic phase under irradiation is associated with the formation, at the sites of collisions of protons with atoms of the substance, of molten regions, within whose volume quenching of the single paramagnetic phase from the melt occurs.

The existence of regions including interstitial atoms and vacancies is confirmed by experiments \(^{11}\) carried out on metals having similar physical properties but different crystal structures. If two metals are taken, one of which has a body-centered cubic lattice, packing coefficient 0.69, and the other a close-packed hexagonal or face-centered cubic lattice with packing coefficient 0.74, then one may assume that, in the less dense packing, under radiation damage, the formation of interstitial atoms and vacancies is more probable than in the denser packing, all other conditions being equal.

Three metals were taken for treatment: iron, nickel, and cobalt. These metals have similar physical and chemical properties, with the exception of crystal structure. Iron has a cubic body-centered lattice, nickel a face-centered cubic lattice, and cobalt a close-packed hexagonal...

hexagonal lattice. Samples of the metals listed were irradiated with deuterons of energy 12 MeV. The temperature of the samples during irradiation was \(-150^\circ\)C. The change in properties was observed from the change in electrical resistance, the measurement of which was carried out at a temperature of \(-180^\circ\)C. The measurements showed that, at a total flux of

\[ 10^{17}\ \frac{\text{deuterons}}{\text{cm}^2}, \]

iron increases its resistance by 50%, while nickel and cobalt increase it by 10%.

Irradiation by fast neutrons of iron and nickel samples in a nuclear reactor was also carried out. As a result of irradiation, the resistance of the iron sample increased by 10%, and that of the nickel sample by 1%.

These experiments show that, for the same irradiation dose, the change in properties is more considerable in the metal that has the less dense crystal structure. Consequently, the nature of the crystal structure is a factor determining the degree of disturbance of the crystal lattice of a substance under irradiation by fast particles. In addition, this confirms the proposition that the disturbances of the crystal lattice causing changes in many physical properties of a substance are interstitial atoms and vacancies.

2. Change in the Properties of Ordering Alloys

Recently, the effect of neutron irradiation on alloys of the Ni—Mn type with a content from 16.5 to 31.9 at.% Mn\(^{12}\) has been studied in detail. It was found that the action of radiation on the physical properties of alloys differs both from the action of plastic deformation and from the action of heat treatment by quenching.

Irradiation of the samples was carried out with fast neutrons, the mean value of whose energy spectrum was 0.5 MeV. The total flux of fast neutrons had values

\[ 0.55 \cdot 10^{20}\ \frac{n}{\text{cm}^2} \quad \text{and} \quad 0.92 \cdot 10^{20}\ \frac{n}{\text{cm}^2}. \]

Irradiation of ordered alloys causes disordering. In Figs. 3 and 4 it is seen that the curves of electrical resistance and magnetic saturation for irradiated samples lie between the curves of ordered and disordered alloys. With more considerable irradiation, the curves of electrical resistance and magnetic saturation are situated closer to the curves for the alloy disordered by quenching. The change in properties has a nonlinear dependence on the chemical composition of the alloys. The greatest effect is observed in alloys containing from 16.5 to 22 at.% Mn.

It is often erroneously assumed that the effect of radiation on the properties of a solid is similar to the effect of cold working by pressure,

and they also ascribe to them one and the same mechanism of the processes taking place. However, investigations of changes in the electrical and magnetic properties under irradiation of previously disordered alloys do not confirm a complete similarity between radiation disturbances and disturbances produced by cold working. In Figs. 5–7 are shown curves of electrical resistivity, the temperature coefficient

Fig. 3. Effect of irradiation on the electrical resistivity of previously ordered alloys \(^ {12}\).

Fig. 4. Effect of irradiation on the magnetic saturation of previously ordered alloys \(^ {12}\).

Fig. 5. Effect of irradiation on the electrical resistivity of thermally disordered alloys \(^ {12}\).

Fig. 6. Effect of irradiation on the temperature coefficient of electrical resistivity of thermally disordered alloys \(^ {12}\).

of electrical resistivity and magnetic saturation as functions of chemical composition for irradiated and deformed specimens previously disordered by quenching. These curves are plotted relative to the alloys disordered by quenching, whose properties were taken as the initial ones. For alloys irradiated with neutrons, the curves of electrical resistivity, the temperature coefficient of electrical resistivity, and magnetic saturation as functions of manganese content have a completely different form in comparison with the curves for alloys subjected to deformation. The curves for alloys subjected to deformation are located for the most part below the zero line. The greatest effect of both treatments is observed for alloys containing from 16.5 to 22 at. % Mn, and the effect of irradiation on the physical properties of alloys of this composition is opposite to the effect of plastic deformation.

Fig. 7. Effect of irradiation on the magnetic saturation of thermally disordered alloys \(^{12}\).

Fig. 8. Effect of irradiation on the electrical resistivity, the temperature coefficient of electrical resistivity, and the magnetic saturation of a \(\mathrm{Ni}_3\mathrm{Mn}\) alloy previously disordered by quenching and by cold working \(^{12}\).

Irradiation of alloys previously disordered by quenching and disordered by cold deformation causes different changes in the physical properties. In Fig. 8 are shown curves of the change in electrical resistivity, the temperature coefficient of electrical resistivity, and magnetic saturation as functions of the total irradiation of specimens disordered both by quenching and by deformation. The chemical composition of these alloys was close to \(\mathrm{Ni}_3\mathrm{Mn}\). The change in electrical resistivity is opposite in sign for quenched-

ordered and deformed specimens. If in specimens disordered by quenching irradiation slightly lowers the electrical resistance, then in deformed specimens the electrical resistance increases by 5%. The temperature coefficient of electrical resistance and the magnetic saturation change under irradiation in approximately the same way as the electrical resistance. The values of the electrical resistance, the temperature coefficient of electrical resistance, and the magnetic saturation for both kinds of specimens, upon irradiation with a total flux of fast neutrons of the order of \(9\cdot 10^{19}\ \dfrac{n}{\mathrm{cm}^2}\), become the same, i.e., saturation sets in.

Important results were obtained in irradiating the alloy \(\mathrm{Cu}_3\mathrm{Au}\) with fast neutrons \(^{13,14}\) in a nuclear reactor at a temperature of \(80^\circ\mathrm{C}\). Figure 9 gives the results on the effect of irradiation on the electrical resistance of preliminarily ordered and disordered alloys.

Fig. 9. Effect of fast neutrons on the electrical resistance of ordered (2) and disordered (1) \(\mathrm{Cu}_3\mathrm{Au}\) alloys.

The electrical resistance of the disordered specimens decreases until the total flux reaches \(4\cdot 10^{19}\ \dfrac{n}{\mathrm{cm}^2}\) and thereafter remains constant, having a value 7% less than the initial one (curve 1). The electrical resistance of the ordered specimens (curve 2) at first falls rapidly. After irradiation with a total flux of \(0.4\cdot 10^{19}\ \dfrac{n}{\mathrm{cm}^2}\), its value becomes 3% less than the initial one. It is supposed \(^{15}\) that the decrease in electrical resistance for the ordered \(\mathrm{Cu}_3\mathrm{Au}\) alloy is connected not only with additional ordering, but also with a change in the characteristic Debye temperature as a result of a change in the modulus of elasticity under irradiation. After this the electrical resistance increases linearly. Upon irradiation with a total flux of \(2\cdot 10^{20}\ \dfrac{n}{\mathrm{cm}^2}\), the resistance increases by 60% in comparison with the initial value \(^{16}\).

From the results set forth it is concluded that irradiation in a reactor has a dual tendency: both disordering of ordered—

daughter alloys and ordering of disordered alloys, if the electrical resistivity is taken as the measure of the degree of order.

X-ray investigations of irradiated alloys show that superstructure lines disappear as a result of the action of radiation \(^{2,17,18,19}\). When ordered alloys \(\mathrm{Cu_3Au}\), \(\mathrm{CuAu}\) are irradiated with alpha particles of energy \(33\ \mathrm{MeV}\), they pass into the disordered state, and in this transition the lattice constants change. The ordered structure of the \(\mathrm{CuAu}\) alloy has a tetragonal lattice, while the disordered one has a face-centered cubic lattice. Figure 10 shows the transition of the tetragonal structure into the cubic one under irradiation with alpha particles. Figure 11 gives the change in the lattice constant of the ordered \(\mathrm{Cu_3Au}\) alloy as a function of the irradiation dose.

Fig. 10. Change in the crystal-lattice constants of the ordered \(\mathrm{CuAu}\) alloy under irradiation with \(\alpha\)-particles of energy \(33\ \mathrm{MeV}\) \(^{2}\).

In work \(^{12}\), on the basis of experimental data, the number of displaced atoms in an alloy of composition \(\mathrm{Ni_3Mn}\) is calculated for each primary collision of a fast neutron of energy \(0.5\ \mathrm{MeV}\) with the nucleus of a stationary atom.

The average number of displaced atoms \(dQ\) in the crystal lattice is proportional to the neutron flux \(dn\), i.e. \(dQ = k\,dn\). The number of primary elastic collisions per atom for a neutron flux \(dn\) is determined from the expression \(dC = \sigma\,dn\), where \(\sigma\) is the cross section for elastic scattering of fast neutrons by atoms of the alloy. Consequently, the number of displaced atoms in each primary collision with a fast neutron is determined by the ratio

\[ \frac{dQ}{dC} = \frac{k}{\sigma}. \tag{9} \]

Fig. 11. Change in the crystal-lattice constant of the ordered \(\mathrm{Cu_3Au}\) alloy under irradiation with \(\alpha\)-particles of energy \(33\ \mathrm{MeV}\) \(^{2}\).

The value of \(\sigma\) for Ni and Mn is equal to \(3 \cdot 10^{-24}\ \mathrm{cm^2}\). The value of the coefficien-

ta \(k\) is determined from irradiation experiments. For this purpose, curves of the dependence of electrical resistivity and magnetic

Fig. 12. (1) Dependence between the degree of long-range order and electrical resistivity. (2) Dependence between the degree of long-range order and magnetic saturation in the alloy \(\mathrm{Ni_3Mn}^{12}\): \(\bigcirc\) — ordered alloy, \(\oplus\) — irradiated with a fluence \(0.55\cdot 10^{20}\ \dfrac{n}{\mathrm{cm}^2}\), \(\bullet\) — irradiated with a fluence \(0.92\cdot 10^{20}\ \dfrac{n}{\mathrm{cm}^2}\).

saturation on the degree of long-range order are constructed in advance (Fig. 12). From the known values of electrical resistivity for two irradiation levels, from the curves of Fig. 12 the corresponding degrees of long-range order are determined to be 0.45 and 0.22.

The degree of long-range order \(S\) has an exponential dependence on the total neutron fluence \(n\):

\[ S = S_0 e^{-kn}, \tag{10} \]

where \(S_0\) is the degree of long-range order before irradiation, and \(k\) is a constant coefficient characterizing the material.

The values found for the degree of long-range order for two irradiation doses make it possible to construct the dependence of \(\ln \dfrac{S}{S_0}\) on the total fluence of fast neutrons. The curve of this dependence is shown in Fig. 13, from the slope of which the value

\[ k = 1.5\cdot 10^{-20}\ \frac{\mathrm{cm}^2}{n} \]

is determined.

Fig. 13. Dependence of \(\ln S/S_0\) on the total fluence of fast neutrons for the alloy \(\mathrm{Ni_3Mn}^{12}\).

It is possible to determine the number of displaced atoms in the \(\mathrm{Ni_3Mn}\) alloy for each primary collision of a fast neutron. It turns out to be equal to 5000.

3. The effect of radiation on phase transformations

The study of the action of radiation on the process of phase transformation in a solid is of considerable interest. At present several works are known ^20, ^21, ^22 in which data are presented on the influence of radiation on phase transformations in a solid.

Irradiation with fast neutrons affects the process of the polymorphic transformation of white tin into gray tin ^20. Thin tin plates were irradiated in a nuclear reactor at the temperature of liquid nitrogen. At this temperature the rate of transformation of one tin phase into another is very small. After irradiation the specimens were kept for a long time at a temperature of \(-196^\circ\text{C}\).

The irradiated specimens were compared with unirradiated ones. The surface of the irradiated specimens was covered with tubercles of gray tin, whereas the unirradiated specimens had a clean surface. Consequently, irradiation promotes the transformation of white tin into gray tin. The increase in the rate of the phase transformation is probably associated with an increase in the thermodynamic potential of the atoms due to the appearance of internal stresses. It is possible that regions of crystal-lattice disturbances formed under irradiation are sites of nucleation of the new phase.

The action of neutron irradiation on phase transformation was observed in stainless steels from the anomalous increase in magnetic susceptibility ^21. The action of neutron irradiation on the decomposition of austenite in chromium–nickel alloys containing \(20.5\%\) Cr, \(10.9\%\) Ni, and \(1.49\%\) Mn was studied by a magnetic method ^22. Alloys of similar composition under ordinary conditions are in the austenitic state; however, the \(\gamma\)-phase is thermodynamically unstable at room temperature. In the austenitic state these alloys have the face-centered cubic lattice of \(\gamma\)-iron, but the stable state at room temperature is a mixture of austenite and ferrite.

It was found that neutron irradiation causes a small increase in the ferrite phase, the amount of this phase increasing both with increasing irradiation time and with increasing amount of the initial ferrite component. This makes it possible to suppose that irradiation causes rather an increase in the rate of growth of existing nuclei than the appearance of new ferrite growth centers. This assumption is also confirmed by the fact that a 17-fold increase in dose causes only a 2–3-fold increase in magnetic saturation at a considerable content of the \(\gamma\)-phase.

4. The effect of radiation on diffusion in alloys

When irradiated with heavy particles of high energy, regions are formed in the material that contain disturbances of the crystal lattice in the form of interstitial atoms and vacancies (holes). It is known that defects of this kind play the predominant role in dif-

diffusion of metal atoms; therefore irradiation should greatly increase the rate of diffusion.

The effect of irradiation on diffusion was studied in a disordered alloy, Cu\(_3\)Au. In this alloy each atom has a tendency toward ordering, which takes place by diffusion. For an unirradiated disordered specimen at a temperature of \(+200^\circ\)C, the time required for ordering is of the order of \(10^5\) hours, whereas for specimens irradiated with fast neutrons with a total flux of \(10^{18}\ \dfrac{n}{\text{cm}^2}\), the ordering time under the same conditions becomes only 10–12 hours \(^{23}\).

An X-ray study of irradiated specimens \(^{24}\) of Cu\(_3\)Au made it possible, from the half-width of the superstructure lines, to determine the size of the ordered regions; their diameter proved to be of the order of 125 Å. From the size of the ordering regions one may conclude that defects of the interstitial atom–vacancy type travel a considerable distance before they disappear.

An experiment involving irradiation, at a temperature of \(150^\circ\)C, of previously disordered Cu\(_3\)Au specimens with various fluxes of fast neutrons shows the degree of the effect of irradiation on diffusion in alloys \(^{25}\). Some specimens were kept in a flux of \(1 \cdot 10^{12}\ \dfrac{n}{\text{cm}^2\,\text{sec}}\), and others in a flux of \(2.5 \cdot 10^{11}\ \dfrac{n}{\text{cm}^2\,\text{sec}}\). In specimens irradiated with the weaker flux, the electrical resistance decreased by one half in 24 hours. Specimens in the more intense flux reached the same resistance four times faster than the specimens in the weak flux.

When lithium was irradiated with slow neutrons it was found that the rate of diffusion of silver in it increases by more than a factor of 10 \(^{26}\). A silver foil 12 \(\mu\) thick, clamped between two lithium plates, when irradiated with a flux of \(10^{12}\ \dfrac{n}{\text{cm}^2\,\text{sec}}\) for 34 hours at a temperature of \(16^\circ\)C, dissolved completely in the lithium, whereas without irradiation this was not observed. The diffusion coefficient of silver in lithium at \(16^\circ\)C under irradiation was found to be \(2.4 \cdot 10^{-10}\ \text{cm}^2\,\text{sec}^{-1}\), while at the same temperature without irradiation it was \(0.1 \cdot 10^{-10}\ \text{cm}^2\,\text{sec}^{-1}\). The effect of irradiation is equivalent to raising the temperature from \(16^\circ\)C to approximately \(140^\circ\)C.

The increase in the diffusion rate in lithium is due to the formation of defects in the crystal lattice when it is bombarded by fragments of lithium nuclei. Such fragments are helium and tritium nuclei formed in the nuclear reaction.

In addition to activation of diffusion under irradiation with fast neutrons, the phenomenon of direct transfer of atoms of a substance over considerable distances has been observed \(^{27}\).

The experiments were carried out on flat cobalt specimens coated with a thin layer of gold. During irradiation with fast neutrons, cobalt disks were placed between two graphite plates. After irradiation, radioactive cobalt-60 was found in the graphite plates. It is believed that the cobalt atoms were transferred as a result of an elastic collision between cobalt nuclei and high-energy neutrons. This experiment makes it possible to suppose that a similar type of atomic transfer takes place in other materials irradiated with high-energy heavy particles. Consequently, irradiation with fast particles causes a “mixing” of the atoms of a substance.

5. Change in the Elastic Properties of Metals and Alloys

The influence of irradiation on the elastic properties of materials is considered as the result of the presence of interstitial atoms and vacancies (holes) formed upon irradiation by high-energy particles $^{28}$.

The elastic modulus is very sensitive to disturbances of the crystal lattice with the formation of interstitial atoms. With the formation of each interstitial atom–vacancy pair, the potential elastic energy of the system of ions of the crystal lattice increases.

Fig. 14. Shear stress–relative shear curve for a copper single crystal $^{31}$.

Calculations that have been made show that 1% of interstitial atoms increases the Young’s modulus of copper by 9.2% and that of sodium by 3%. More refined calculations $^{29,30}$ established that 1% of interstitial atoms in copper increases the elastic modulus by 6.3%, while 1% of vacancies decreases the elastic modulus by 1.5%.

Experimental data confirm the theoretical conclusions1. A copper single crystal irradiated with fast neutrons changes its elastic properties.

Fig. 14 gives the curve of the dependence of shear stress on the magnitude of the relative shear for irradiated and unirradiated copper specimens. The shear strength limit was determined for an unirradiated copper crystal to be equal to \(0.241\ \mathrm{kg/mm^2}\), and for an irradiated one, \(1.938\ \mathrm{kg/mm^2}\). The curve of the dependence of the shear strength limit on the total flux of fast neutrons is given in Fig. 15. During

Fig. 15. Effect of irradiation with fast neutrons on the shear strength limit of a copper single crystal1.

irradiation with fast neutrons, copper is strengthened. A strong similarity is noted between radiation hardening and the hardening influence of impurities. It is assumed that interstitial atoms and vacancies manifest themselves similarly to impurity atoms.

Mechanical tests of copper single-crystal specimens irradiated with fast neutrons at a temperature of \(-78^\circ\mathrm{C}\) showed a significant increase in the strength limit2. Often in tests the irradiated specimens failed by brittle fracture. Brittle fracture was usually preceded by several clicks, as the result of the formation of cracks on the surface of the specimen.

Irradiation with a total flux of fast neutrons of \(1.3 \cdot 10^{19}\) of aluminum, beryllium, and silicon bronze at a temperature of \(-150^\circ\mathrm{C}\) causes an increase in the strength limit by several hundred percent in the low-temperature region3.

Single crystals of iron and zinc, as a result of irradiation with fast neutrons, increase their yield point4. This change in mechanical properties is completely restored at a temperature of \(200\text{—}500^\circ\mathrm{C}\) over the course of \(10^4\) minutes.

When irradiated with fast neutrons, tungsten lowers its strength limit, whereas tantalum, on the contrary, raises it5.

The mechanical properties of metals change not only under the action of irradiation with heavy particles, but also under irradiation with light—

… particles^35. Irradiation of copper with electrons of energy 1.25 MeV increases the hardness from 44.3 to 47.7 kg/mm². Annealing at a temperature of 170°C for 8 hours partially restores the hardness.

It should be noted that the effect of irradiation is sharply manifested in metals that have been preliminarily annealed. Annealing of metals removes all internal stresses. The atoms occupy more stable positions. The entire system lowers its free energy. During annealing, order increases in alloys. If, in pure metals, interstitial atoms and vacancies are taken as the second component, then it may be considered that during annealing the degree of order increases owing to the disappearance of interstitial-atom—vacancy pairs. During irradiation of metals, interstitial-atom—vacancy pairs are formed, which cause changes in the mechanical properties. If, however, the metal has previously been subjected to deformation, then the order in the arrangement of atoms in the crystal lattice will be disturbed; therefore, in such a metal one cannot expect a significant change in the mechanical properties upon irradiation. Experiments^36 have shown that irradiation of annealed molybdenum specimens with deuterons of energy 10 MeV and a total flux of 5.1 μA·h/cm² increases the hardness by 12%. Irradiation without annealing of cold-rolled specimens, however, does not cause a change in hardness. In a similar way, depending on the initial state, the hardness of nickel and zirconium changes upon irradiation with neutrons^21.

Fig. 16. Increase in the hardness of low-carbon steel upon irradiation with deuterons of energy 18.6 MeV^37.

Upon irradiation of alloys, changes in mechanical properties occur just as in most pure metals: the strength limit, modulus of elasticity, hardness, etc., increase^21.

In one of the works^37, studies were carried out on the effect of irradiation with deuterons on the hardness and impact toughness of low-carbon steel. The deuterons had an energy of 18.6 MeV. The hardness of low-carbon steel increases as the irradiation dose increases. From the curve in Fig. 16 it is seen that the hardness increased from 180 units for the unirradiated material to 400 units for the material irradiated with a total flux of 60 μA·h/cm².

The action of irradiation with deuterons on the impact toughness of low-carbon steel is similar to cold working. As in irradiation

...and cold working increases the brittle-fracture temperature. A feature of the change in impact toughness under irradiation is that, up to a certain threshold of the total deuteron flux, the brittle-fracture temperature does not change. Thus, for example, a deuteron flux of \(16.2\) \(\mu\text{kA}\cdot\text{h}/\text{cm}^2\) does not change the brittle-fracture temperature, whereas a flux of \(29.6\) \(\mu\text{kA}\cdot\text{h}/\text{cm}^2\) raises the temperature by \(18^\circ\text{C}\) (Fig. 17). It is known that plastic deformation gradually raises the brittle-fracture temperature. For this steel, at deformations of 1, 5, and 10%, the brittle-fracture temperature rises, respectively, by 8.5, 9.5, and \(14.5^\circ\text{C}\).

Fig. 17. Curves of impact toughness for specimens irradiated with a total deuteron flux of 29.5 \(\mu\text{kA}\cdot\text{h}/\text{cm}^2\) (solid curve) and unirradiated specimens (dashed curve) \(^{37}\).

Annealing of deformed specimens takes place in the interval \(55^\circ\text{C}\) and is completely finished at \(370^\circ\text{C}\), with a constant activation energy. The recovery of defects in irradiated specimens, however, extends over the temperature interval from 260 to \(480^\circ\text{C}\). The activation energy of recovery in the case of irradiation increases as the annealing temperature rises. The different character of the recovery of disturbances caused by deformation and by irradiation indicates the different nature of the defects. It may be supposed that, as a result of irradiation, interstitial atoms and vacancies are produced in the material in equal amounts, whereas in cold working this equality is absent.

The mechanical properties change especially strongly upon irradiation of ordering alloys. Upon irradiation with a total flux of fast neutrons \(3\cdot10^{20}\ \dfrac{n}{\text{cm}^2}\), specimens of the alloy \(\mathrm{Cu}_3\mathrm{Au}\) show a considerable increase in hardness both for the ordered and the disordered alloy \(^{38}\). The Vickers hardness of disordered specimens under irradiation increases by 21 units (initial hardness 100). The hardness of the ordered material under irradiation increases by 48 units (initial hardness 110).

The mechanical properties of quenched solid solutions of sparingly soluble components at room temperature, as a result of irradiation, change not through the formation of defects in the crystal lattice, but through aging, i.e., the precipitation of a second phase from the solution. Experiments[^39] on irradiation of a quenched solid solution of a Cu—Be alloy containing 2% Be were carried out in such a way as to determine whether strengthening occurs because of disturbances of the crystal lattice or because of precipitation of a second phase. Specimens of Cu—Be were irradiated at two different temperatures, 120° K and 300° K. It turned out that the electrical resistance for the specimen irradiated at 300° K increased four times more strongly than for the specimen at 120° K. If the specimen is irradiated for some time at a temperature of 120° K and then for a short time at 300° K, the effect obtained is the same as if it had been irradiated at 300° K. Upon irradiation with fast neutrons of a quenched solid solution of Cu—Be, a considerable increase in hardness occurs.

Additional proof that the hardness and other mechanical properties of the copper–beryllium alloy are due to precipitation of a second phase as a result of increased diffusion is provided by data obtained under irradiation by fast neutrons of saturated and unsaturated solid solutions[^40]. After irradiation with an integrated flux of \(2.3 \cdot 10^{18}\ \dfrac{n}{\mathrm{cm}^{2}}\), the hardness of the saturated solid solution of beryllium in copper increased by 40 Rockwell units, and the electrical resistance by 10%. At the same time, for the unsaturated solid solution of beryllium in copper, under the same irradiation the hardness increases by 20 Rockwell units, and the electrical resistance by 0.5%.

6. Annealing of radiation damage

For understanding the nature of radiation damage, the study of the restoration of physical properties during annealing is essential. A number of works have been devoted to this question. In work[^41], processes occurring during annealing in copper wire previously irradiated with deuterons of energy 12 MeV were investigated. The increase in the electrical resistance of copper at a temperature of \(-180^\circ\)C as a function of the integrated deuteron flux is shown in Fig. 18. The initial slope of the curve is approximately 4 times greater than the slope of the remaining part. When the flux reaches \(1 \cdot 10^{17}\ \dfrac{\text{deuterons}}{\mathrm{cm}^{2}}\), the bombardment was stopped, and the temperature of the specimen decreased to \(-185^\circ\)C. At this temperature a noticeable annealing is observed: over 22 hours the electrical resistance decreased by 6%. Short bombard—

restored the electrical resistance. The shape of the curve after partial annealing is the same as under the initial irradiation. The behavior of the curve during partial annealing in the low-temperature region indicates that irradiation produces defects which can be restored at the temperature of liquid nitrogen. The activation energy at a temperature of \(-180^\circ\)C has a value of the order of \(0.2\) eV. Figure 19 gives the temperature dependence of the activation energy. Above \(-30^\circ\)C the activation energy is constant and is \(0.68\) eV. Annealing in this region is due to a single process. It is assumed that at this temperature recombination of interstitial atoms with migrating vacancies occurs.

Fig. 18. Increase in the electrical resistance of copper as a function of the total deuteron flux at a temperature of \(-180^\circ\)C. The decrease in resistance at a flux of \(10^{17}\ \dfrac{\text{deuterons}}{\text{cm}^2}\) is due to thermal recovery \(^{41}\).

Interstitial atoms and vacancies are produced by irradiation in equal amounts. If the atomic component of each kind of defect is denoted by \(f\), then it may be assumed that recombination during vacancy migration obeys the law

\[ \frac{df}{dt}=-cf^2, \tag{11} \]

where \(c\) depends only on temperature. The electrical resistance during irradiation increases proportionally to \(f^2\). If expression (11) is chosen correctly, then its values must coincide with the experimental curve of the change in electrical resistance during isothermal annealing (Fig. 20). The experimental curve of the change in electrical resistance during annealing satisfies the equation

Fig. 19. Dependence of the activation energy on temperature \(^{41}\).

\[ \frac{d(r-r_0)}{dt}=-A(r-r_0)^n, \tag{12} \]

where \(r_0\) is the resistance of the irradiated copper after annealing. However

the value of $n$ is not 2 but 2.5. This increase in the number $n$ is connected with the influence of elastic stresses caused by interstitial atoms.

Figure 21 shows a graph of the overall recovery of the electrical resistance of copper for various temperatures during the first 100 minutes. The peak in the region of $-30^\circ$ C characterizes a single process. The disappearance of interstitial atom—vacancy pairs in this temperature region proceeds by a diffusion path. This process takes place through migration of vacant sites. Interstitial atoms do not move at this temperature. However, stresses in the lattice, created by interstitial atoms or by impurity atoms, promote the displacement of empty sites. Thus, for example, an admixture of lead in an amount of 1% accelerates the self-diffusion of silver by a factor of 2[^42].

Fig. 20. Change in the electrical resistance of copper during isothermal annealing at a temperature of $-18.3^\circ$ C[^41].

For copper, annealing at a low temperature restores 50% of all defects produced by irradiation at a temperature of $-180^\circ$ C. This recovery is due to recombination of neighboring interstitial atom—vacancy pairs.

Fig. 21. Decrease in the electrical resistance of irradiated copper during the first 100 min. for each annealing temperature. The solid line connects the points calculated for the case of a single process with an activation energy of 0.68 eV[^41].

From a temperature of $-30^\circ$ C to room temperature, annealing of 25% of the total number of defects occurs. The remaining 25% of radiation defects are recovered in the temperature range from 20 to 170° C.

Defects recovered at high temperature still have no explanation. One supposition is that these defects are caused by local heating, which arises

at the expense of the energy of the bombarding particles. During the slowing down of the particles, small regions of the substance along their path may melt and rapidly cool, so that disordered regions will arise. To anneal them, the recrystallization temperature is required. Some part of the defects may consist of interstitial atoms, which cannot recombine because of the absence of vacancies, owing to the capture of the latter by other defects and by the surface.

A comparison was made between the annealing of defects obtained under irradiation and the annealing of defects caused by cold working. Isothermal annealing of deformed copper43 showed that recovery of the defects occurs in the region of two temperatures.

Fig. 22. Comparison of the annealing of defects caused by cold working with the annealing of defects caused by radiation irradiation3.

In the vicinity of \(-110^\circ\mathrm{C}\) the activation energy of recovery is \(0.44\) eV, and near \(-30^\circ\mathrm{C}\) the value of the activation energy is \(0.67\) eV. Consequently, the activation energies of recovery are close to one another for both types of defects, which indicates the existing similarity of the defects produced. However, a comparison of the influence of annealing on the dependence of the temperature coefficient of electrical resistance for copper that had been irradiated and treated by deformation showed a characteristic difference in the processes occurring in the two cases2. In Fig. 22 the course of the change in the temperature coefficient of electrical resistance during annealing is compared for deformed copper and copper irradiated with deuterons.

Recovery of the electrical resistance of Cu, Ag, Au, Ni, Ta irradiated with deuterons of energy \(12\) MeV was carried out over a wide temperature range from \(10\) to \(300^\circ\mathrm{K}\)44.

Bombardment of these metals with deuterons at a temperature of \(10^\circ\mathrm{K}\) causes a greater increase in electrical resistance than at the temperature of liquid nitrogen. This is associated with partial recovery

of disturbances of the crystal lattice occurring at the temperature of liquid nitrogen, whereas at a temperature of \(10^\circ\) K no recovery takes place.

Upon irradiation of Au, Ag, and Cu, a dependence of the increase in electrical resistivity on \(Z\) is observed, which agrees with Seitz’s calculations.

During annealing of irradiated specimens, an increase is observed in the rate of decrease of electrical resistivity in two temperature regions, \(30\)—\(40^\circ\) K and \(220\)—\(250^\circ\) K. In copper, near a temperature of \(40^\circ\) K, about \(50\%\) of the electrical resistivity acquired upon irradiation is recovered. In silver, near a temperature of \(30^\circ\) K, about \(20\%\) of the acquired electrical resistivity is recovered. The activation energy at this temperature for Cu and Ag is \(0.1\) eV. Recovery of the electrical resistivity during annealing in the region \(220\)—\(280^\circ\) K for Cu, Ag, and Au amounts, respectively, to 18, 19, and \(44\%\) of the total increase in electrical resistivity upon deuteron irradiation.

The recovery of disturbances in metals was investigated not only from the change in electrical properties during annealing, but also by the behavior of other physical properties. In work \(^{45}\), the recovery of stored energy during annealing of copper specimens irradiated with deuterons was studied. A system with a distorted crystal lattice has a greater free energy than one with a regular lattice. Upon irradiation, disturbances of the crystal lattice are formed and the free energy increases. The recovery of disturbances proceeds at different rates during annealing in different temperature regions. When defects of the crystal lattice disappear, the excess energy is released in the form of heat.

Fig. 23. Annealing of stored energy for two specimens irradiated with deuterons \(^{45}\):

\(1\)—fluence \(0.9 \cdot 10^{17}\ \dfrac{\text{deuterons}}{\text{cm}^{2}}\),

\(2\)—fluence \(1.5 \cdot 10^{17}\ \dfrac{\text{deuterons}}{\text{cm}^{2}}\).

As a result of a calorimetric measurement of the heat released during annealing of irradiated copper specimens, the dependence of the rate of release of stored energy on the annealing temperature was obtained. Figure 23 shows the recovery of stored energy during annealing for two copper specimens irradiated with a total fluence of \(0.9 \cdot 10^{17}\ \dfrac{\text{deuterons}}{\text{cm}^{2}}\) and \(1.5 \cdot 10^{17}\ \dfrac{\text{deuterons}}{\text{cm}^{2}}\). The different shape of the curves for the two specimens below \(-80^\circ\) C is due to the different temperature of the specimens during irradiation. The annealing process at

at low temperature occurs by recombination of very close interstitial-atom—vacancy pairs. The peak of the curve at \(-15^\circ\text{C}\) is due to the disappearance of interstitial-atom—vacancy pairs as a result of internal diffusion. The total stored energy between \(-80^\circ\text{C}\) and \(+20^\circ\text{C}\) was found by integrating the curves in Fig. 23; it is equal to \(0.052\ \dfrac{\text{cal}}{\text{g}}\). If it is assumed that an energy of \(5\ \text{eV}\) is required to form an interstitial-atom—vacancy pair, then from the obtained value of the stored energy one determines a defect concentration of the order of \(5\cdot 10^{-5}\).

During annealing, complex processes of restoration of disturbances of the crystal lattice take place.

It is assumed that at very low temperature migration of double vacancies occurs. In the temperature region in which interstitial-atom—vacancy pairs disappear, neighboring vacancies combine, forming large vacancy clusters. When the vacancy density is greater than the equilibrium one, the vacancies will combine into groups in the form of planes and dislocation rings. This assumption is confirmed by the fact that, under neutron irradiation of a copper single crystal, there is an insignificant change in electrical resistivity, whereas the yield stress increases by 1000%, and this is not completely removed even at a temperature of \(400^\circ\text{C}\), although the electrical resistivity is fully restored at a lower temperature.

The existence of vacancy clusters is proved experimentally\(^{46}\). Nickel was deposited on a mica substrate at a temperature of \(75^\circ\text{C}\), at a constant rate of \(60\ \text{\AA}/\text{s}\), to a thickness of \(2000\ \text{\AA}\). The deposition was carried out at a pressure of \(4\cdot 10^{-5}\) mm Hg. During annealing, a rapid drop in electrical resistivity occurs near \(+150^\circ\text{C}\), whereas the microstresses of the film increase after a minimum at a temperature of \(+225^\circ\text{C}\). The hardness behaves in the same way during annealing of the film. The increase in microstresses after the minimum at \(+225^\circ\text{C}\) is explained by the formation of group vacancies in the form of shields and rings.

III. EFFECT OF NEUTRON IRRADIATION ON THE PHYSICAL PROPERTIES AND STRUCTURE OF GRAPHITE

Graphite is used in nuclear reactors as a neutron moderator; therefore the study of changes in its physical properties is of special practical interest.

Irradiation of graphite was carried out in a nuclear reactor both near the uranium rod and at some distance from it\(^{47}\). The greatest total neutron flux was \(10^{21}\ \dfrac{n}{\text{cm}^2}\).

As a result of irradiation, the electrical resistance of graphite may increase up to threefold. In the initial moment, the increase in electrical resistance depends on the irradiation intensity. At irradiation intensities equal to \(2\cdot 10^{12}\dfrac{n}{\text{cm}^2\,\text{sec}}\), \(10^{13}\dfrac{n}{\text{cm}^2\,\text{sec}}\), and \(2\cdot 10^{13}\dfrac{n}{\text{cm}^2\,\text{sec}}\), the rates of increase of electrical resistance were, respectively, in the ratio \(1:4.7:10\).

Upon annealing irradiated graphite, the electrical resistance is intensively restored in the region of two temperatures, \(400\)—\(500^\circ\text{C}\) and above \(1000^\circ\text{C}\). It has been observed that slightly irradiated graphite recovers the greater part of the acquired electrical resistance in the first temperature region. In strongly irradiated graphite, the main decrease in electrical resistance is shifted beyond \(1000^\circ\text{C}\). Graphite irradiated with slow and resonance neutrons, i.e., far from uranium rods, restores its electrical resistance only in the first temperature region. Consequently, the stable defects whose annealing at temperatures above \(1000^\circ\text{C}\) is associated with the restoration of electrical resistance are produced by fast neutrons.

The specific volume of graphite increases noticeably only when irradiated by neutrons near uranium. The increase in specific volume proceeds slowly with increasing irradiation dose. The process of increase in specific volume belongs to the secondary processes with which the stable increase in electrical resistance is associated.

The thermal conductivity of graphite under irradiation decreases by as much as 20 times. With a considerable increase in the irradiation dose, the temperature dependence of the thermal conductivity of graphite becomes similar to the temperature dependence of the thermal conductivity of graphite having fine crystallites. This shows that, in graphite, irradiation causes fragmentation of the crystals.

The release of stored energy in graphite during annealing was studied. Calorimetric determinations showed that up to \(600^\circ\text{C}\) about \(80\ \text{cal}/\text{g}\) is released. As the irradiation dose increases, the release of energy shifts into the region of high annealing temperatures. The maximum on the curve of the rate of heat release as a function of the annealing temperature lies in the region of \(250^\circ\text{C}\), and with increasing irradiation dose the maximum shifts toward higher temperatures. The position of the high-temperature branches of these curves rises progressively with increasing irradiation dose, which indicates the presence of stored energy still preserved up to an annealing temperature of \(600^\circ\text{C}\).

It was also established that the change in Young’s modulus and in hardness coincides with the dependence of electrical resistance on irradiation dose. The change in Young’s modulus and in the hardness of graphite under irradiation is connected with primary defects that accumulate rapidly.

X-ray studies carried out by S. T. Konobeevskii and co-workers showed that, as a result of irradiation, the structure of graphite changes greatly. Under the action of irradiation, the distance \(c\) between basal planes increases, whereas

the mean distance \(a\) between atoms within the nets decreases. In the overall complexity, however, an increase in volume occurs, since the increase in \(c\) outweighs the decrease in \(a\). If it is assumed that the decrease in the mean distance between atoms in the net is due to the formation of vacancies, while the increase in the mean distance between basal planes is caused by interstitial atoms, then this agrees with the supposition that vacancies reduce the interatomic distance five times less than interstitial atoms increase it \(^{48}\).

When X-ray patterns taken from irradiated and unirradiated graphite specimens are compared, large changes are visible, consisting in a displacement of the interference lines, their broadening, a decrease in intensity, and even complete disappearance at large angles of reflection.

From analysis of the broadening of the lines it was possible to obtain the dependence of the reduction in crystallite sizes on the irradiation dose. It turns out that the fragmentation of crystallites occurs mainly along the \(a\)-axis. Annealing at \(1050^\circ\mathrm{C}\) causes an insignificant restoration of crystallite sizes.

As a result of neutron irradiation, structural defects of two types are formed in graphite.

The first type of defects rapidly accumulates with increasing irradiation dose up to an equilibrium concentration. These defects, in all probability, are isolated, closely spaced interstitial-atom—vacancy pairs. The stability of this sort of defect is not high; they are completely annealed at a temperature of \(500\)—\(600^\circ\mathrm{C}\). The first type of defect in graphite is associated with changes in electrical resistivity, Young’s modulus and hardness, as well as some part of the thermal conductivity and stored energy released during low-temperature annealing.

The second type of defect is manifested in changes of such properties as volume change, further change in thermal conductivity, the appearance of a stable excess electrical resistivity, and high-temperature stored energy. These defects are formed more slowly with increasing irradiation dose, and their creation requires a harder neutron spectrum. It is supposed that defects of the second type are substantial regions of a disturbed crystal lattice, including a large number of atoms. These regions lead to fragmentation of the crystallites. Annealing of this sort of defect occurs only at the recrystallization temperature, i.e., about \(2000^\circ\mathrm{C}\).

IV. CHANGE IN THE PROPERTIES OF SEMICONDUCTORS UNDER IRRADIATION

The effect of irradiation on the physical properties of semiconductors Ge, Si, Se, InSb, Cu\(_2\)O, and others has been studied by many investigators \(^{49-67}\). Irradiation was carried out with various kinds of radiation: fast neutrons, alpha particles, deuterons, and electrons.

The behavior of semiconductors under irradiation is varied. Thus, for example, when “hole”-type germanium is irradiated by any high-energy particles, the electrical conductivity increases. The electrical conductivity of “electron”-type germanium, on the contrary, at the beginning of irradiation decreases, and after reaching a minimum increases. The sign of the Hall-effect coefficient shows that, upon irradiation of “electron”-type germanium, a transition to the “hole” type takes place. Upon irradiation of silicon, selenium, and Cu₂O, a decrease in electrical conductivity always occurs, which is explained by the formation under irradiation of traps both for electrons and for holes.

Fig. 24. Threshold for displacement of atoms of “electron”-type germanium under irradiation with electrons².

High-energy particles, in elastic collisions with the atoms of a solid, produce disturbances in the crystal lattice in the form of pairs consisting of an interstitial atom and a vacancy. To move a germanium atom from a lattice site into an interstice, it is necessary to impart to it an energy of a definite magnitude⁵⁰. Figure 24 shows the curve of the change in electrical conductivity of “electron”-type germanium as a function of the energy of the electrons with which it was irradiated. From the curve it is evident that the electrical conductivity of germanium begins to decrease when it is irradiated with electrons of energy higher than 0.63 MeV. The decrease in electrical conductivity is associated with the formation of disturbances of the crystal lattice. The energy 0.63 MeV is taken as the threshold for formation of interstitial-atom–vacancy pairs. The threshold value of the electron energy makes it possible to determine the energy expended in moving a germanium atom, which proves to be equal to 30.5 eV.

1. Change in the electrical properties of “electron”-type germanium

“Electron”-type germanium has electronic conductivity, which is due to the transition of electrons from an impurity level into the upper unfilled conduction band.

When Ge is irradiated with neutrons⁵¹,⁵², two kinds of impurities are formed. As a result of elastic collisions of a Ge atom with fast neutrons, interstitial atoms and vacancies (holes) are formed, which manifest themselves as carriers of positive electricity. As a result of the capture of slow neutrons by the nuclei of germanium isotopes, there are formed—

... nuclei of new elements are formed. One part of the atoms of the new elements formed in the nuclear reaction become impurities that provide donor-type conductivity (electronic), while another part provide acceptor-type conductivity (hole). In neutron nuclear reactions two predominant isotopes are formed: in the form of a “hole” impurity—gallium, and an impurity of the “electronic” type—arsenic. The amount of impurities formed upon the capture of neutrons by the nuclei of germanium isotopes depends on the magnitude of the activation cross section. The activation cross section for the formation of an isotope that is an impurity of the acceptor type is greater than for the formation of an impurity of the donor type; therefore, as a result of nuclear reactions, carriers of positive electricity are produced.

The influence of impurities formed in nuclear reactions is small in comparison with the effect of disturbances caused by fast neutrons. The effect of irradiation by fast neutrons on the conductivity of germanium of the “electronic” type is especially noticeable.^54 Figure 25 shows the dependence of conductivity on the total neutron flux. The initial slope of the curve is proportional to the magnitude of the irradiation. From the slope of the straight-line part of the curve one can determine the mean number of electron traps \(k\) per neutron of the given energy spectrum of neutrons.

Fig. 25. Electrical conductivity of germanium of the “electronic” type as a function of the total neutron flux at room temperature.

From the initial slope of the curve of the dependence of electrical conductivity on the total neutron flux, the mean value \(k\) is found, which in this case is equal to 3.2 acceptors for each incident neutron.

The minimum of conductivity on the curve corresponds to the moment of transition of germanium of the “electronic” type into the “hole” type.

The less steep slope of the curve after the transition of germanium of the “electronic” type into the “hole” type is due to several factors: first, to the rate of recombination of lattice defects, which depends on the density of defects; second, to the number of centers capable of being ionized thermodynamically and thereby influencing the increase in the concentration of holes.

Two factors affect the increase in “hole” conductivity: 1) annealing of lattice defects, 2) increase in the concentration of posi-

charge carriers. In order to shorten the annealing process, irradiation of germanium was carried out at the temperature of dry ice. The conductivity curve for low temperature has a form similar to the curve obtained at room temperature. However, the minimum of the conductivity as a result of irradiation at the temperature of dry ice is found at lower values of the total neutron flux than at room temperature. The existence of the transition of germanium of the “electronic” type to the “hole” type under irradiation with fast neutrons is also confirmed by the fact that the magnetic susceptibility decreases in this transition. In work 55 the magnetic susceptibility was measured. In view of the small effective mass of the electrons, the diamagnetic susceptibility of germanium of the “electronic” type is greater than that of the “hole” type. Upon irradiation of germanium of the “electronic” type, the diamagnetism decreases. This agrees with the change in the values of the Hall-effect coefficient.

Irradiation with alpha particles of energy 5.3 MeV causes a change in the electrical conductivity of germanium of the “electronic” type. The character of the change in properties under this irradiation coincides with the behavior of the properties under irradiation with fast neutrons 56. It was found that one alpha particle in germanium of the “electronic” type transfers 78 electrons from the conduction region. After a certain dose of irradiation of a single crystal of germanium of the “electronic” type, the electrical conductivity reaches a minimum, which indicates the complete absence of electrons in the conduction band. Further irradiation with alpha particles increases the electrical conductivity, which is a sign of the transition of germanium to the “hole” type. From the rate of increase of the conductivity it was found that 8.6 holes are formed per incident alpha particle. It was noted that, of every 8.6 holes formed, after holding at room temperature only two remain.

Fig. 26. Electrical conductivity of “hole”-type germanium as a function of the time of irradiation with fast neutrons at room temperature 54.

2. Change in the electrical properties of “hole”-type germanium

The typical dependence of the electrical conductivity of “hole”-type germanium on the total neutron flux at room temperature is shown in Fig. 26. Calculations made from the slope of the electrical-conductivity curve showed that for each incident neutron there is formed

0.8 holes. The slope of the curve decreases as the total flux is increased, which indicates saturation. The saturation effect under irradiation is connected chiefly with annealing of the defects formed.

Experiments57 carried out on neutron irradiation of germanium samples of the “hole” type showed a decrease in electrical conductivity at low temperature and an increase at high temperature. The curve of electrical conductivity as a function of the total flux and the temperature of irradiation is given in Fig. 27. The decrease in electrical conductivity under neutron irradiation in the low-temperature region is explained by the raising of the acceptor impurity levels, for which traps are created as a result of irradiation; the number of current carriers decreases. Consequently, the electrical conductivity of germanium falls with increasing total flux of fast neutrons through the sample.

Fig. 27. Change in the electrical conductivity (solid line) of “hole”-type germanium under neutron irradiation in various temperature regions; the dashed line shows the course of the temperature57.

3. Change in the physical properties of silicon, indium antimonide, and other semiconductors

Neutron irradiation of silicon of both types (“electron” and “hole”) causes a decrease in electrical conductivity. This is due to the fact that the impurity levels in “electron”-type silicon are lowered, and in “hole”-type silicon they are raised. Owing to this, irradiation creates not current carriers, but traps for them. A similar phenomenon also occurs in “hole”-type germanium when irradiated in the low-temperature region57, 58.

Bombardment with 10 MeV deuterons of “hole”-type silicon lowers the electrical conductivity59. At the first moment of irradiation each deuteron creates a trap, on the average, for 31 holes.

The effects produced in germanium and silicon by nuclear irradiations have some similarity to the effects arising under high-temperature heating followed by quenching60. During quenching in silicon, disturbances of the crystal lattice in the form of interstitial atoms and vacancies produced on heating are fixed; these manifest themselves as traps for both current carriers.

When cuprous indium is irradiated with fast neutrons, traps are created for both types of charge carriers—both electrons and holes[^61]. However, “hole” traps are four times more effective than electron traps. Therefore cuprous indium of any type, as a result of irradiation, acquires a very low electronic conductivity. A similar effect is obtained when “hole-type” cuprous indium is irradiated with electrons of energy 4.5 MeV[^62]. Under this irradiation the Hall-effect coefficient and the electrical resistivity increase monotonically, but their ratio decreases with increasing radiation dose.

Irradiation of semiconductors causes changes in them not only in electrical, but also in mechanical and thermal properties. From the change in the diffuse scattering of X-rays from a silicon single crystal, the elastic constants were determined[^63]. A change in the values of the elastic constants of silicon as a result of neutron irradiation was observed.

After irradiation in a nuclear reactor, the heat capacity and the characteristic Debye temperature of silicon decrease noticeably[^64], and the heat capacity stably retains its new value upon heating to 780° K.

The high electrical resistance of the “hole-electron” barrier in germanium makes it possible to use it as a counter of particles with high ionizing power[^65]. It was noted that a point contact of a conductor with a “hole-type” germanium crystal can be used to count alpha particles of polonium and beta particles of RaE. When individual ionizing particles pass through a germanium crystal, they produce pulses. The magnitude and time constant of the pulse depend on the resistance of the barrier and on its power. The resistance of the barrier can be varied by changing the temperature; the power of the barrier depends on the size of the crystal. The magnitude and duration of the pulse when a particle passes through the crystal may be judged from the following[^2]: an electron with energy 0.7 MeV increases the electrical conductivity of the barrier by a pulse by approximately a factor of 10, with a pulse duration of 10 μsec.

The optical properties of semiconductors undergo significant changes as a result of irradiation[^2]. When silicon of both types is acted upon by neutrons and deuterons, a new narrow absorption level appears for light with \(\lambda = 1.75\,\mu\). The appearance of the new absorption level is due either to excitation of hole traps with high discrete energy levels, or to excitation of discrete low levels of electron traps.

4. Annealing of Defects in Semiconductors

Disturbances of the crystal lattice formed during irradiation are partially restored even after holding at room temperature. Thus, for example, in germanium at room temperature annealing occurs of 75% of the defects caused by neutron-

irradiation. The restoration of the properties of irradiated germanium has a complex dependence on time. The annealing process in time breaks down into several stages.

In work \(^{66}\) the mechanism of annealing is considered for the simplest type of defects, when only one interstitial atom is associated with each vacancy. Under irradiation by heavy particles, entire clusters of interstitial atom–vacancy pairs are undoubtedly formed.

During annealing in an irradiated material, recombination occurs between interstitial atoms and vacancies located both inside the deformed region of the crystal lattice and outside it. The presence of two processes of recombination of interstitial atom–vacancy pairs is confirmed experimentally \(^{67}\). For “electronic”-type germanium irradiated with electrons of energy \(3\) MeV, different activation energies are obtained at different annealing temperatures. It increases from \(1.6\) eV at \(140^\circ\)C to \(1.8\) eV at \(300^\circ\)C. This is in agreement with the assumption that at low temperature recombination occurs for the nearest interstitial atom–vacancy pairs, separated from one another by a potential barrier which, because of the presence of a stress field, has a height lower than that of the barrier between any atom and a vacancy in the undeformed space of the crystal.

V. RADIATION DEFECTS IN INSULATORS

Most insulators are complex chemical compounds. They are nonplastic, and have very low electrical and thermal conductivity. Possessing characteristic physical properties, insulators are more sensitive to the action of radiation in comparison with metals. If metals, when irradiated with gamma rays and electrons, almost do not change their properties, then many insulators, even under the action of small radiation doses, noticeably change many physical properties.

When chemical compounds are irradiated, in addition to the phenomena that occur in metals and simple substances (crystal-lattice defects of the interstitial atom–vacancy type), dissociation of molecules and the formation of new chemical substances as a result of reactions between ions and radicals are possible.

1. Glass and ionic compounds

The optical properties of insulators are very sensitive to the action of radiation. The change in optical properties in insulators is associated with the formation, upon irradiation, of electron traps which, upon capturing free electrons, form color centers. Some chemical substances, such as, for example, silver chloride, form color centers even when illuminated with ordinary light.

When irradiated with gamma rays, lead glasses, which are usually used as shielding against radiation when working with radioactive substances, change color[^68]. The transmission coefficient for light rays after irradiation of the glass with gamma rays decreases noticeably. Significant irradiation doses, of the order of \(10^{10}\) roentgens, can cause destruction of the glass.

The coloring of glass cannot be attributed to defects of the crystal lattice, since glass is an amorphous substance. The change in optical properties is caused by other phenomena. Two mechanisms are assumed: first, electron traps bind ions into neutral atoms and, consequently, colloidal coloring occurs; second, oxidation–reduction processes occur in the exchange of electrons between ions of various kinds.

Quartz glass[^69], when irradiated with a neutron flux of the order of \(2 \cdot 10^{20}\ n/\text{cm}^2\), increases its density from 2.21 to 2.25 g/cm\(^3\). In addition, an increase in the refractive index is observed from 1.45706 to 1.46687 (the sodium \(D\) line).

An X-ray study of irradiated quartz glass reveals broadening of the main diffraction peak, and it shifts toward larger values of \(\sin \theta/\lambda\). The total area occupied by the diffraction curve for irradiated specimens increases slightly in comparison with the initial pattern.

It is assumed that all changes in the properties of quartz glass are due to rupture of chemical bonds of the silicon–oxygen framework under neutron irradiation.

Of particular interest is the irradiation of crown and flint glasses with krypton ions[^70] having an energy of 60 keV and a total flux of 20 \(\mu\)A-hours/cm\(^2\). As a result of irradiation, the properties of the surface layer of the glass change: reflection from the surface decreases, and transmittance increases. The acquired properties are not changed by the action of strong acids or by heating to \(400^\circ\)C. Usually the phenomenon associated with a decrease in the reflection of light rays from the surface in the antireflection treatment of optics is explained by the existence of a surface layer one quarter of a wavelength thick. However, it is known that inert ions under irradiation penetrate to a depth on the order of ten wavelengths; therefore the surface layer, it would seem, should be considerably thicker than a quarter of a wavelength. Irradiation of glass with other heavy particles of high energy does not cause similar changes in properties. Therefore additional investigations are required to clarify the mechanism causing these changes in the properties of glass.

Irradiation of sodium chloride crystals with alpha particles leads to the formation of color centers[^71]. Irradiation of the crystals that is considerable in magnitude leads to a purplish coloration, which appears as a result of the precipitation of colloidal sodium. Upon annealing...

the coloration disappears. The annealing process is accompanied by blue luminescence.

X-rays and gamma rays, when passing through an aluminum oxide crystal, color it violet[^72]. When an aluminum oxide crystal is irradiated in a nuclear reactor, additional absorption bands appear for light waves of length 2040 Å and 2600 Å. The absorption band at 2040 Å is ten times more intense than the absorption band with wavelength 2600 Å.

When lithium fluoride is irradiated with neutrons, defects are formed that are connected not only with the elastic scattering of fast neutrons, but are also caused by the products of the nuclear reaction after the capture of slow neutrons by the nuclei of the lithium-6 isotope. The reaction proceeds:
\[ \mathrm{Li}^{6}+n^{1}\to \mathrm{H}^{3}+\mathrm{He}^{4}+4.8\ \text{MeV}. \]
The tritium nucleus receives an energy of 2.74 MeV, and the α-particle 2.06 MeV; both of these particles have energy sufficient to create defects in the crystal lattice independently.

An X-ray study of LiF irradiated by a total flux of slow neutrons of the order of \(7.5\cdot 10^{17}\ n/\text{cm}^{2}\) showed that in this material internal stresses arise between individual significant regions of the substance, and not within the volume of an elementary cell[^73]. It is assumed that the stresses arise as a result of the displacement of a large number of atoms in the (001) plane. This displacement extends over hundreds of angstroms; it may be separated from a similar displacement by a distance of the order of 500 Å. The regions located between shear defects are in a stressed state, and it is they that chiefly account for the broadening of the diffraction lines.

Neutron irradiation of lithium fluoride crystals, as well as potassium chloride crystals, causes a change in coloration[^74]. In lithium fluoride a resonance absorption appears for a wavelength of 3400 Å, disappearing only upon heating to 500° C.

X-ray studies of neutron-irradiated single crystals of boron carbide showed significant structural changes[^75].

Upon irradiation by a total flux of thermal neutrons \(3\cdot 10^{20}\ n/\text{cm}^{2}\), the lattice contracts in the direction of the \(c_{0}\) axis by 1.38% and expands in the direction of \(a_{0}\) by 0.89%. The relative positions of the atoms in the lattice change. On the Laue photograph the interference spots are surrounded by a strong diffuse background. The thermal factor assumes values in the \(c_{0}\) direction 6 times greater than in the \(a_{0}\) direction.

The change in the diffraction pattern on the Laue photograph is due to the anisotropy of the lattice defect, which forms in a chain of three carbon atoms arranged along the \(c_{0}\) axis. Upon irradiation the middle carbon atom of this chain is knocked out into the interatomic space. The remaining two carbon atoms strive to compensate for the removal of the third by drawing closer together, carrying the boron atoms along with them. This

causes compression of the lattice in the direction \(c_0\) and expansion in the direction \(a_0\).

Upon heating to a temperature of \(900^\circ\text{C}\), the displaced carbon atoms return to their normal positions. However, after annealing, part of the diffuse background remains on the Laue diagram; this is due to the products of the decay of boron nuclei—lithium and helium atoms.

In one of the works\({}^{76}\), the effect was studied of \(\alpha\)-particles formed in the decay of uranium, thorium, and their daughter isotopes on the density, lattice constants, and optical properties of Ceylon zircon. The radioactive elements uranium and thorium are present in small quantities in zircon, and their concentration is easily determined from the \(\alpha\)-activity. The total number of decays per unit quantity of substance is determined by calculation (the age of the zircon is taken to be \(570 \cdot 10^6\) years). The density of zircon, with increasing irradiation dose, at first decreases slowly, then more rapidly, and finally, asymptotically approaching the value \(3.96\ \text{g}/\text{cm}^3\) at an irradiation dose of \(1.2 \cdot 10^{16}\) \(\alpha\)-decays per \(1\ \text{cm}^2\). Zircon containing no uranium and thorium has a density of \(4.700\ \text{g}/\text{cm}^3\). The lattice parameters increase with increasing irradiation dose by \(1.5\)—\(2\%\). At a dose of \(0.449 \times 10^{16}\ \alpha/\text{cm}^2\), the increase of the lattice parameters ceases, i.e., saturation sets in. The refractive power of zircon decreases with increasing irradiation dose. The mean and anomalous refractive index at a dose of \(0.15 \cdot 10^{16}\ n/\text{cm}^2\) asymptotically approaches the value 1.810.

Fig. 28. Thermal conductivity of crystalline quartz and quartz glass\({}^{78}\): 1 — crystalline unirradiated quartz; 2 — after the first irradiation—1.0 conventional units; 3 — after the second irradiation—1.4 conventional units; 4 — after the third irradiation—16.5 conventional units; 5 — unirradiated quartz glass.

The change in many physical properties of crystalline substances is usually explained on the basis of the formation of defects of the interstitial atom—vacancy type. With the aid of this model, the distortion of the lattice of alpha-quartz under irradiation with fast neutrons is explained\({}^{77}\). The density of quartz, measured by two methods—by weighing and by X-ray analysis—decreased by approximately \(4\%\). The lattice constants for unirradiated quartz had the dimensions: \(a = 4.903\ \text{Å}\) and \(c = 5.393\ \text{Å}\). After irradiation the constants changed in the following way: \(a = 5.01 \pm 0.01\ \text{Å}\) and \(c = 5.41 \pm 0.02\ \text{Å}\). The anisotropy of expansion

in the direction of the \(a\) axis is caused by the placement of displaced atoms in the interstices in this direction. For irradiated quartz, on X-ray diffraction patterns the diffraction lines at \(2\theta > 90^\circ\) are strongly broadened. From this one may suppose that irradiation produces internal stresses. Annealing at a temperature of \(485^\circ\)C does not change the stresses and distortions in alpha-quartz.

Under the action of neutrons quartz noticeably decreases its thermal conductivity in the low-temperature region \(^{78,79}\). Fig. 28 shows the change in the thermal conductivity of quartz. The change in thermal conductivity is not proportional to the irradiation dose. For relative irradiation doses of \(1:2.4:18.9\), the change in thermal conductivity is \(1:1.7:18\). The nonproportionality of the decrease in thermal conductivity to the irradiation dose is evidently connected with the redistribution of defects during the irradiation process. Annealing of irradiated quartz causes an increase in thermal conductivity. The results of experiments on the restoration of the thermal conductivity of quartz upon annealing are given in Fig. 29. The maximum thermal conductivity occurs at \(15^\circ\)K and decreases linearly with increasing temperature. After prolonged annealing at a temperature of \(700^\circ\)C, the thermal conductivity below \(25^\circ\)K becomes less than that of irradiated quartz (intersection of the curves \(I_1\) and \(H_8\)). The decrease below \(25^\circ\)K in the thermal conductivity for annealed specimens leads to the supposition that the number of group defects decreases during heat treatment. Heat treatment of unirradiated crystals does not cause a change in thermal conductivity in the low-temperature region.

Fig. 29. Thermal conductivity of crystalline quartz after considerable annealing for three irradiations \(I_1, I_2, I_3\) \(^{78}\):

Curve	Annealing temperature, °C	Annealing time, hours
\(H_1\)	300	8
\(H_2\)	400	6
\(H_3\)	510	6
\(H_4\)	565	6
\(H_5\)	540	60
\(H_6\)	540	677
\(H_7\)	600	1
\(H_8\)	700	6

Quartz, upon irradiation with fast neutrons, decreases its refractive index and also noticeably changes its heat capacity.

The changes in properties described above for quartz occur upon irradiation of magnesium oxide, spinel, and sapphire \(^{80}\).

Recently a number of studies have been carried out on the influence of radiation on the electrical conductivity of alkali-halide compounds.

Alkali-halide crystals have ionic conductivity of electricity. Usually the mechanism of ion displacement is associated with the presence of defects in the crystal lattice^79,81^. As is known, irradiation of a substance by some kind of nuclear radiation causes the formation of defects in the crystal lattice. At first glance it would seem that irradiation with any dose, with the formation of defects in the crystal lattice of the substance, should lead to an increase in electrical conductivity. However, experiments have shown that small doses of irradiation by high-energy protons cause a decrease in the electrical conductivity of sodium chloride, whereas under irradiation with a considerable total flux of protons \(\left(10^{15}\ \dfrac{\text{protons}}{\text{cm}^2}\right)\) with an energy of \(350\ \text{MeV}\), sodium chloride crystals increase their electrical conductivity by more than a factor of ten^82^.

Fig. 30. Dependence of the radioactive intensity on the square of the distance from the surface of the crystal^84^. Holding temperature \(427^\circ\text{C}\). Diffusion time 3.75 days. Diffusion coefficient for the unirradiated crystal \(1\cdot 10^{-11}\ \text{cm}^2/\text{sec}\). Unit of length \(4.884\cdot 10^{-4}\ \text{cm}\): ○ — unirradiated; ● — irradiated.

A decrease in electrical conductivity was also found in potassium chloride under the action of small doses of gamma rays^83^. Prolonged irradiation by gamma rays and neutrons, on the contrary, increases the electrical conductivity.

The study of sodium diffusion in a sodium chloride crystal in the temperature region below \(550^\circ\text{C}\) showed that under the action of X-rays the diffusion coefficient decreases; this is in agreement with the decrease in ionic conductivity under the action of small radiation doses^84^. Figure 30 gives the dependence of the radioactive intensity of sodium on the square of the distance from the surface for irradiated and unirradiated crystals. The decrease both in the ionic conduction of the current and in atomic diffusion at small irradiation doses has not yet found a satisfactory explanation.

2. Nature of Radiation Damage in Homeopolar Crystals

Diamond, silicon, and a number of other substances have a homeopolar crystal structure.

The change in physical properties under radiation damage to the crystal lattice is explained on the basis of the nature of the chemic-

…of chemical bonds in compounds of the homeopolar type. Instead of a model of disturbances of the interstitial-and-vacancy type, another model is proposed, which is based on the well-known tendency of carbon or silicon to replace single bonds by double ones. Thus, the recoil atom formed as a result of an elastic collision with a fast particle breaks single bonds, which are transformed into a system of double and single bonds. The change of bonds leads to a change in the physical properties of the substance. Upon irradiation with fast neutrons, in the places where recoil atoms are formed, separate disordered regions of diameter of the order of 45 Å are produced, containing approximately \(10^4\) carbon atoms \(^{85}\). These regions are mechanically weak and are regarded as holes in diamond. Such a model of radiation damage makes it possible to explain satisfactorily the decrease in the characteristic Debye temperature, and the change in the heat capacity and elastic modulus of diamond and silicon under irradiation with fast neutrons.

3. The Action of Radiation on Zinc Sulfide Phosphor

It was found \(^{86}\) that, upon irradiation with \(\alpha\)-particles, the luminescence of zinc sulfide weakens. The photoconductivity and dielectric constant of zinc sulfide decrease after irradiation. Irradiation causes a shift of the luminescence spectrum toward long wavelengths.

Fig. 31. Effect of neutron-irradiation exposure on the luminescence coefficient of zinc sulfide \(^{87}\):
1 — ultraviolet excitation (high intensity); 2 — ultraviolet excitation (low intensity); 3 — X-ray excitation; 4 — ultraviolet excitation with quenching infrared illumination.

Interesting results were obtained in studying the action of fast neutrons on the physical properties of copper-activated zinc sulfide \(^{87}\). Irradiation was carried out with a total flux of fast neutrons from \(1.2 \cdot 10^{15}\) to \(2 \cdot 10^{17}\ \text{n}/\text{cm}^2\).

Studies showed that neutron irradiation weakens luminescence. In Fig. 31 the weakening of the total luminescence is shown as a function of the irradiation dose. The weakening of luminescence is caused by the transfer of a portion of the electrons into traps with low energy levels. Upon irradiation, a limited number of deep electron traps is created in the material and, consequently, the less—

the greater their depth. Therefore, for x-ray excitation, as is seen in Fig. 31 (curve 3), saturation is reached earlier than for softer exciters.

Fig. 32. Growth of luminescence^87: 1 — unirradiated specimen, ultraviolet excitation; 2 — 16-hour irradiation in a nuclear reactor, excitation by x-rays; 3 — 16-hour irradiation, ultraviolet excitation.

The intensity of luminescence increases upon excitation over a certain time. The increase of luminescence is characterized by the resolving time, i.e., the period during which the luminescence reaches the greatest intensity for the given state of the substance and the given exciter. Upon irradiation, the resolving time of luminescence is greatly extended (Fig. 32).

Neutron irradiation increases the rate of phosphorescence decay (Fig. 33). The decay of phosphorescence is a complex phenomenon. To explain most cases of phosphorescence decay, two simple mechanisms are cited. First-order decay is considered, in the case of light emission, to be due to the slow release of electrons from traps into the conduction band. Second-order decay is considered to be a process caused by recombination in the conduction band and holes in the filled band. However, the phenomena that occur are considerably more complex.

Neutron irradiation shifts the luminescence spectrum toward shorter waves. In previous work, under irradiation with alpha particles, a shift of the luminescence spectrum toward longer waves was observed.

Fig. 33. Decay of phosphorescence for an unirradiated specimen and specimens irradiated in a nuclear reactor for 1, 2, 4, and 8 hours^87.

A nonidentical behavior of the dielectric constant has been noted at different excitation intensities of irradiated and unirradiated phosphor. If for an unirradiated phosphor the dielectric

constant depends linearly on the logarithm of the excitation intensity, then for an irradiated phosphor at low excitation intensity the dielectric constant is greater than for a nonirradiated one; as the excitation intensity increases, the dielectric constant becomes smaller than for the nonirradiated material.

Changes in the dielectric properties of phosphors under irradiation can be used as an indicator of significant doses of radioactive irradiation. Thus, for example, a capacitor with an admixture of zinc sulfide in polystyrene before irradiation had a capacitance of 2000 µµf; after irradiation by X-rays for 1 minute with a dose of 48 roentgens, its capacitance doubled \(^{88}\).

At a high temperature, of the order of \(700^\circ\)C, annealing of phosphors occurs. All properties of the phosphors assume their original values.

VI. IRRADIATION OF SOLID MOLECULAR COMPOUNDS

Irradiation in molecular compounds causes fundamental changes in physical and chemical properties. Under the action of nuclear radiations, processes of three main types occur: destruction (splitting of molecules into parts), cross-linking of molecular chains, and decomposition of molecules with the formation of gaseous products \(^{87}\). All three processes take place in the substance during irradiation simultaneously, but the relation between them depends primarily on the chemical nature of the polymer and its molecular structure. Therefore, as a result of irradiation, different molecular compounds may change their properties in a very diverse manner.

Irradiation of various high-polymer compounds was carried out with \(\gamma\)-rays of \(Co^{60}\) (with an activity of 100 g-equiv of radium), \(\alpha\)-particles of radon, and fast electrons.

As a result of studying the mechanical properties under irradiation, their dependence on temperature, and the solubility of polymers in solvents, it was found that in a number of substances—polyethylene, polyvinyl chloride, high-molecular-weight polystyrene, natural rubber, and others—the process of molecular cross-linking predominates; on the contrary, in another group of compounds—polyisobutylene, polyvinyl acetate, polyvinyl alcohol, low-molecular-weight polystyrene, Teflon, and others—the process of destruction predominates, as a result of which the molecular weight of the compound decreases.

Owing to the cross-linking of molecules, polyethylene, upon irradiation, ceases to pass into the viscous-flow state under load in the temperature range \(100\text{–}110^\circ\)C. Samples of “cross-linked” polyethylene lose the ability to dissolve in benzene and toluene.

The elongation at break of polyethylene gradually decreases with the irradiation dose, although the tensile strength decreases much more slowly.

The strength characteristics for polyethylene irradiated with γ-rays can be characterized by the data given in Table II.

Table II

Dose, \(10^6\) roentgens	Tensile strength, \(kg/mm^2\)	Elongation, %
0	1.04	415
45	0.99	135
80	1.08	70

After irradiation in a nuclear reactor, the mechanical properties of polyethylene \(^{31}\) change in approximately the same way as under irradiation with Co-60 γ-rays. This is seen from a comparison of the curves for irradiated and unirradiated polyethylene in Fig. 34. The curves show that after irradiation the mechanical properties of polyethylene change considerably. As the total neutron flux increases, the elasticity of polyethylene decreases. At a total flux of \(12.8 \cdot 10^{18}\ n/cm^2\), polyethylene becomes practically brittle.

Fig. 34. Dependence of stress on relative elongation for unirradiated and irradiated polyethylene \(^{31}\): 1 — unirradiated; 2 — irradiated with a total flux of \(0.23 \cdot 10^{18}\ n/cm^2\); 3 — \(4.14 \cdot 10^{18}\ n/cm^2\); 4 — \(12.8 \cdot 10^{18}\ n/cm^2\).

Fig. 35. Dependence of stress on relative elongation for irradiated and unirradiated polystyrene \(^{31}\).

One of the polymers more resistant to irradiation proved to be polystyrene, which even after consid-

... dose of irradiation only slightly changed its mechanical properties. The stress–relative elongation curve for irradiated and unirradiated polystyrene is shown in Fig. 35.

The decrease in elongation at break for polystyrene and polyethylene under irradiation is the result of the formation of a spatial molecular network arising from the cross-linking of molecules during irradiation.

Phenomena of an entirely different type are observed upon irradiation of polyisobutylene. In this case, processes of degradation and a decrease in the degree of polymerization occur. Under substantial irradiation, polyisobutylene changes from a solid into a viscous liquid. The following change in the molecular weight of polyisobutylene is observed as a function of the dose of irradiation by γ-rays (Table III), where \(M_0\) is the initial average molecular weight, and \(M\) is the molecular weight after irradiation.

Table III

Irradiation time, hours	Dose, \(10^6\) roentgens	\(M \cdot 10^3\)	\(M_0/M\)
0	0	480	1
5	1.4	280	1.7
11.25	3.8	190	2.5
19.3	6.5	110	4.3
34.6	11.7	55	8.7
46	15.6	52	9.4
89.5	30.3	22	21.3

The mechanical properties of Teflon also change in a peculiar manner under the action of radiation. When irradiated with a dose of \(5—8 \cdot 10^6\) roentgens, Teflon becomes extremely brittle and crumbles. Viscous flow in thermomechanical testing of irradiated Teflon begins at a lower temperature than for unirradiated Teflon. This also confirms the presence of degradation processes occurring in Teflon during irradiation.

Upon irradiation of polymers, a third type of process takes place—the formation of gaseous products. This phenomenon is associated with the rupture of chemical bonds at the ends of molecules or in side groups as a result of excitation of the molecule during irradiation. Qualitative and quantitative analysis of the gases released during irradiation of a number of polymers provides some information about the mechanism of this type of process. It has been found that in most cases hydrogen is released in considerable quantity, and fragments of chain molecules containing from 1 to 4 carbon atoms are released in small quantity.

When polymers are irradiated in air, oxidative reactions also occur. Thus, for example, upon irradiation of polytetrafluoroethylene, the oxidation products CO and CO₂ are released.

Electron-diffraction and X-ray studies of the structure of certain polymers during irradiation have shown a transition from the crystalline state to the amorphous state. This transition has been observed at various stages in polyethylene, Teflon, and other polymers under...

at different irradiation doses. As the irradiation dose increases, on the X-ray patterns and electron-diffraction patterns the intensity of the diffraction lines from the crystals decreases and several diffuse rings appear, characteristic of amorphous bodies; their intensity increases with increasing irradiation dose. The transition to the amorphous state is observed upon irradiation of all crystalline polymers. However, the complete transition to the amorphous state occurs at different doses for different polymers.

Irradiation causes a change in the electrical properties of high polymers. During irradiation with $\gamma$-rays, the electrical conductivity of a number of polymers—oxosil, saran, polystyrene, polyethylene, etc.—increases tens of times and depends on the irradiation intensity $^{90}$. After irradiation is stopped, the electrical conductivity returns to its initial value. Upon irradiation of polyethylene with Co-60 $\gamma$-rays it was found that the conductivity $\sigma$ increases with increasing irradiation intensity $I$ according to the law $\sigma \sim I^{3/4}$. The photoconductivity as a function of the radiation intensity is expressed by the relation $\sigma \sim I^{1/2}$. This circumstance raises doubt as to whether the “$\gamma$-conductivity” of polyethylene is electronic conductivity, like the conductivity of photoconducting substances. This doubt is further strengthened by the fact that the “$\gamma$-conductivity” of polyethylene depends on temperature. It is therefore assumed that the conductivity of polyethylene is due to ions.

Subsequent investigations made it possible to clarify more fully the dependence of the electrical properties of polymers on irradiation $^{91}$. It turned out that

Fig. 36. Initial decrease in the electrical resistance of polystyrene as a result of irradiation with $\beta$-rays from a radioactive strontium-90 source (flux density of $\beta$-rays 12 $\mu\text{cal}/\text{cm}^2$) $^{91}$.

when polystyrene is irradiated with $\beta$-particles, its electrical resistance has a complex dependence on the duration of irradiation. As is seen in Figs. 36 and 37, in the first minutes of irradiation the electrical resistance decreases to a certain value, which remains constant for approximately one day, and after this

it begins to increase, reaching the initial value after a month of irradiation. A similar effect of change in electrical resistivity was found in many insulators (polyethylene, polymonochlorotrifluoroethylene, polyether, amber, mica).

In all probability, in explaining the complex dependence of the electrical resistivity of high polymers on the irradiation dose, one should

Fig. 37. Increase in the electrical resistivity of polystyrene as a result of prolonged irradiation with β-rays ^91.

proceed from the fact that the determining role in the behavior of the electrical resistivity is played by the change in the molecular structure of the polymer during irradiation.

CITED LITERATURE

Articles marked with an asterisk have a Russian translation in the collection The Effect of Radiations on Semiconductors and Insulators, IL, Moscow, 1954.

1. J. Sletter, UFN 47, 51 (1952).
2. G. J. Dienes, Ann. Rev. Nuclear Sci. 2, 187 (1953).
   3. F. Seitz, Disc. Faraday Soc. 5*, 271 (1949).
3. N. Mott and H. Massey, The Theory of Atomic Collisions, IL, Moscow, 1951.
4. D. T. Eggen, M. J. Laubenstein, Phys. Rev. 91, 238 (1953).
5. W. S. Snyder, J. Newfeld, Phys. Rev. 97, 1636 (1955).
6. D. Hughes, Neutron Research on Nuclear Reactors, IL, Moscow, 1954.
7. Milton Burton, J. Physic. Chem 51, 611 (1947).
8. J. A. Brinkman, J. Appl. Phys. 25, 961 (1954).
9. J. M. Denney, Phys. Rev. 94, 1417 (1954).
10. D. Wruck, C. Wert, Phys. Rev. 94, 1417 (1954); Acta Metallurgica 3, 115 (1955).
11. L. R. Aronin, J. Appl. Phys. 25, 344 (1954).

1. H. L. Glick, F. C. Brooks, W. F. Witzig, W. E. Jonson. Phys. Rev. 87, 1074 (1952).

2. S. Siegel, Phys. Rev. 75, 1823 (1949).

3. D. B. Rosenblatt, R. Smoluchowski, G. J. Dienes, Phys. Rev. 94, 1417 (1954).

4. H. L. Glick, W. F. Witzig, Phys. Rev. 91, 236 (1953).

5. C. E. Dixon, D. B. Bowen, Phys. Rev. 94, 1418 (1954).

6. L. G. Cook, R. L. Cushing, Acta Metallurgica 1, 539 (1953).

7. L. G. Cook, R. L. Cushing, Acta Metallurgica 1, 549 (1953).

8. J. Fleeman, Phys. Rev. 91, 237 (1953).

9. C. R. Sutton, D. O. Leeser, Iron Age 8, 128 (1954); Iron Age 9, 91 (1954).

10. M. B. Reynolds, J. R. Law Jr., L. O. Sullivan, J. of Metals 7, 555 (1955).

11. T. H. Blewitt, R. R. Coltman, Phys. Rev. 85, 384 (1952).

12. R. R. Coltman, T. H. Blewitt, Phys. Rev. 86, 641 (1952).

13. R. R. Coltman, T. H. Blewitt, Phys. Rev. 91, 236 (1953).

14. V. K. Zavoyskii, B. V. Ershler, Session of the Academy of Sciences of the USSR on the Peaceful Use of Atomic Energy, July 1–5, 1955; Meeting of the Division of Physical and Mathematical Sciences, Publishing House of the Academy of Sciences of the USSR, Moscow, 1955.

15. G. W. Callendine, Jr., Virginia C. Ridolfo, M. L. Pool, Phys. Rev. 86, 642 (1952).

16. G. J. Dienes, Phys. Rev. 86, 228 (1952).

17. F. R. N. Nabarro, Phys. Rev. 87, 665 (1952).

18. G. J. Dienes, Phys. Rev. 87, 666 (1952).

19. G. J. Dienes, J. Appl. Phys. 24, 666 (1953).

20. R. E. Jamison, T. H. Blewitt, Phys. Rev. 91, 237 (1953).

21. A. W. McReynolds, W. Augustyniak, M. McKeowd, Phys. Rev. 94, 1417 (1954).

22. F. W. Kunz, A. N. Holden, Phys. Rev. 94, 1417 (1954).

23. C. E. Dixon, C. J. Meechan, Phys. Rev. 91, 237 (1953).

24. J. G. Geib, R. E. Grace, Phys. Rev. 86, 643 (1952).

25. R. A. Meyer, J. Appl. Phys. 25, 1369 (1954).

26. R. H. Fillnow, E. K. Halteman, G. F. Mechlin, Phys. Rev. 91, 236 (1953).

27. J. W. Cleland, D. S. Billington, J. H. Crawford, Phys. Rev. 91, 238 (1953); D. S. Billington, S. Siegel, Metall Progress 58, 847 (1950).

28. G. T. Murray, W. E. Taylor, Phys. Rev. 86, 642 (1952).

41. A. W. Overhauser, Phys. Rev. 90*, 393 (1953).

1. R. E. Hoffman, D. Turnbull, J. Appl. Phys. 23, 1409 (1952).

2. R. R. Eggleston, J. Appl. Phys. 23, 1400 (1952).

3. J. W. Marx, H. G. Cooper, J. W. Henderson, Phys. Rev. 88, 106 (1952); H. G. Cooper, J. S. Koehler, J. W. Marx, Phys. Rev. 97*, 599 (1955).

4. A. W. Overhauser, Phys. Rev. 94, 1551 (1954).

1. R. W. Hoffman, F. J. Anders, E. C. Crittenden Jr., J. Appl. Phys. 24, 231 (1953).

2. V. I. Klimenkov, Yu. N. Alekseenko, Session of the USSR Academy of Sciences on the peaceful uses of atomic energy, July 1–5, 1955, Meeting of the Division of Physical and Mathematical Sciences, Publishing House of the USSR Academy of Sciences, Moscow, 1955.

3. J. D. Eshelby, J. Appl. Phys. 24, 1249 (1953); C. W. Turcker, Jr., J. B. Sampson, Acta Metallurgica 2, 433 (1954).

4. W. E. Johnson, K. Lark-Horovitz, Phys. Rev. 76, 442 (1949).

5. W. Kohn, Phys. Rev. 94, 1409 (1954).

6. J. W. Cleland, K. Lark-Horovitz, J. C. Pigg, Phys. Rev. 78, 814 (1950).

7. J. W. Cleland, K. Lark-Horovitz, J. C. Pigg, Phys. Rev. 78, 645 (1950).

8. J. H. Crawford Jr., K. Lark-Horovitz, Phys. Rev. 78, 815 (1950).

9. J. W. Cleland, J. H. Crawford, Jr., K. Lark-Horovitz, J. C. Pigg, F. W. Young, Jr., Phys. Rev. 83, 312 (1951).

10. D. K. Stevens, J. W. Cleland, J. H. Crawford, Phys. Rev. 94, 1409 (1954).

11. W. H. Brattain, G. L. Pearson, Phys. Rev. 78, 646 (1950), Phys. Rev. 80, 846 (1950).

12. J. W. Cleland, Jr., J. H. Crawford, K. Lark-Horovitz, J. C. Pigg, F. W. Young, Phys. Rev. 84, 861 (1951); C. W. Lehman, Phys. Rev. 81, 321 (1951).

13. J. H. Crawford, Jr., J. W. Cleland, Phys. Rev. 86, 641 (1952).

14. J. H. Foster, H. Y. Fan, K. Lark-Horovitz, Phys. Rev. 86, 643 (1952).

15. W. E. Taylor, Phys. Rev. 86, 642 (1952).

16. J. W. Cleland, J. H. Crawford, Phys. Rev. 94, 1410 (1954).

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

18. W. P. Binnie, A. M. Liebschutz, Phys. Rev. 94, 1410 (1954).

19. P. H. Keeson, K. Lark-Horovitz, N. Pearlman, Phys. Rev. 89, 900 (1953).

20. C. Orman, H. Y. Fan, C. J. Coldsmith, K. Lark-Horovitz, Phys. Rev. 78, 646 (1950); K. G. McKay, Phys. Rev. 84, 829* (1951).

21. R. C. Fletcher, W. L. Brown, S. Machlup, Phys. Rev. 91, 237 (1953); R. C. Fletcher, W. L. Brown, Phys. Rev. 92, 585* (1953).

22. W. L. Brown, R. C. Fletcher, Phys. Rev. 91, 237 (1953); W. L. Brown, R. C. Fletcher, K. A. Wright, Phys. Rev. 92, 591* (1953).

23. R. H. Kernohan, G. M. McCammon, Phys. Rev. 86, 641 (1952).

24. J. S. Lukesh, Phys. Rev. 97, 345 (1955).

25. J. Koch, Nature 164, 19 (1949).

26. D. Westervelt, Phys. Rev. 86, 643 (1952).

27. P. W. Levy, G. J. Dienes, Phys. Rev. 94, 1409 (1954).

28. G. A. Hatchison Jr., Phys. Rev. 75, 1769 (1949).

29. D. T. Keating, Phys. Rev. 97, 832 (1955).

1. C. W. Tucker, Jr., P. Senio, Acta Cryst. 8, 371 (1955).
2. H. D. Holland, Acta Cryst. 8, 291 (1955).
3. M. Wittels, Phys. Rev. 89, 656 (1953).
4. R. Berman, Proc. Roy. Soc. A208, 90 (1951).
5. P. G. Klemens, Proc. Roy. Soc. A208, 108 (1951).
6. W. Primak, L. H. Fuchs, P. Day, Phys. Rev. 92, 1064 (1953).
   81*. E. A. Pearlstein, Phys. Rev. 92, 881 (1953).
7. E. A. Pearlstein, Phys. Rev. 94, 1409 (1954).
   83*. C. M. Nelson, R. L. Sproull, R. S. Caswell, Phys. Rev. 90, 364 (1953).
8. D. Mapother, Phys. Rev. 89, 1231 (1953).
9. G. J. Dienes, D. A. Kleimman, Phys. Rev. 91, 238 (1953).
10. I. Broser, R. Warminsky, Zeits. Naturforsch., 6a, 85 (1951).
11. A. W. Smith, J. Turkevish, Phys. Rev. 94, 857 (1954).
12. R. Frerichs, Phys. Rev. 94, 1408 (1954).
13. V. L. Karpov, Session of the USSR Academy of Sciences on the Peaceful Use of Atomic Energy, July 1–5, 1955, Meeting of the Division of Chemical Sciences, Publishing House of the USSR Academy of Sciences, Moscow, 1955.
    90*. S. Mayburg, W. L. Lawrence, J. Appl. Phys. 23, 1006 (1952).
    91*. J. H. Coleman, D. Bohm, J. Appl. Phys. 24, 497 (1953).