EFFECT OF RADIATION ON MATERIALS

J. S. Slater*

High-energy radiation, corpuscular—in the form of charged ions, electrons, and neutrons—and electromagnetic, can have a destructive effect on materials used in the construction of nuclear reactors. In the present article, the types of defects produced in solids by various kinds of radiation are considered from the standpoint of the theory of the structure of solids, and experiments that have been, or can be, carried out to investigate the destructive action of radiation are also discussed.

The destructive action of radiation is a consequence of the displacement of atoms of the solid caused by it, of the trapping of particles in the body in the form of impurities, and, finally, of the ionization produced by the radiation. To understand the phenomenon under consideration, one must know what effect atomic displacements and the appearance of impurities have on the properties of a solid, and to what extent this effect is independent of whether these changes are caused by radiation or by some other cause. We shall therefore begin with a brief review of the present state of the theory of the solid, paying special attention to the role of atomic displacements and impurities. After considering the theories of these phenomena and the experimental methods for studying them, we shall turn to the case of defects produced by radiation.

The fundamental characteristic of a solid is that, under ordinary conditions, its properties are a single-valued function of the arrangement of the atoms, regardless of how the atoms came to occupy these positions. A solid is formed by two constituent parts: the nuclei of the atoms and the electrons. For a given position of the nuclei, the electrons may have a large number of stationary states, but their transitions from one state to another occur so rapidly that they reach the position corresponding to thermal equilibrium in a time short in comparison with the duration of our experiments. This serves as the basis for the assertion that the properties of a solid are uniquely determined by the positions

* J. Appl. Phys. 22, No. 3, 237 (1951).

of its atoms (i.e., nuclei). The only exceptions are: first, the case when we are dealing with time intervals as short as the time of passage of a fast particle through matter. During this time the electrons may not have time to reach a state of equilibrium, despite the rapidity with which they approach that state. Second, there is the case of a very good insulator, when the electronic conductivity is so small that a nonequilibrium charge distribution can persist for measurable intervals of time. We shall make special note of these cases. Apart from the exceptions named, the statement made remains valid.

It is evident that any study of a solid containing imperfections is conveniently divided into two parts: (a) clarification of the question of how the atoms came to be in the positions in which they are, and (b) clarification of the influence of the arrangement of the atoms on the properties of the material. Common to these two questions is the problem of determining the arrangement of the atoms. Of course, unlike electrons, atoms cannot be regarded as being in a state of thermal equilibrium, for many processes of atomic displacement at low temperatures occur so slowly that the atoms may remain in unstable or metastable positions for a very long time. The most direct way of determining the positions of atoms consists in a direct study of the structure by means of diffraction of X rays, electrons, or neutrons. These methods are not as intuitive as, for example, the visual perception of visible objects; however, in the last section we shall show that these methods provide a great deal for determining the nature of atomic displacements in solids. The data of all other methods are less direct; most of them are based on observations of changes in various physical properties when atoms are displaced, and the reliability of the data thus obtained depends on how good the theories are that explain these physical properties.

Let us turn to consideration of the solid state and answer the question: what properties does a solid have for a given arrangement of atoms? Then we shall return to the other question: how do atoms change their positions as a result of the irradiation process?

I. PROPERTIES OF A SOLID WITH AN IMPERFECT CRYSTAL LATTICE

The typical properties that interest us depend on imperfections of the crystal lattice. However, it is better to begin by considering the case of a perfect crystal. Here two methods are used, based either on an atomic model or on the band picture, and representing two possible theoretical approximations that give similar results. Each of the methods is useful in its own domain.

1. Atomic and zone models of the solid body

The atomic model is especially suitable for discussing the mechanical properties of solids. In this model it is assumed that each atom interacts with its neighbors. In the case of ions these are electrostatic forces. If the atoms have electrons in common, the interaction is effected by means of covalent forces. When atoms are brought into too close contact and the electron clouds surrounding the atoms begin to penetrate into one another, electronic repulsion arises. At large distances, weak van der Waals attractive forces act between any pair of atoms. Forces of all these categories act both between two atoms in a diatomic molecule and between two colliding atoms in a gas. It cannot, however, be assumed that in a solid there is a simple superposition of the forces acting between two atoms, since the presence of atoms bonded to a given one will change the ability of the latter to act on other atoms. Saturation of valence is the most familiar example of this phenomenon: an atom whose number of bonds with its neighbors is equal to its valence cannot have additional bonds with other atoms. If the valence bonds of an atom are saturated, then its electronic structure is, in a certain sense, frozen and not capable of easy change. At the same time, if an atom has unsaturated valence bonds, it very readily forms other bonds, i.e., its electronic structure possesses a certain flexibility.

In crystals of valence compounds the valence bonds between the atoms of molecules are usually saturated, so that their electronic structures are rather rigid, and electrons cannot pass from some molecules to others. Therefore such crystals are not conductors of electricity. The molecules are bound to one another only by weak intermolecular forces (van der Waals forces). Thus these substances are insulators and, when the temperature is raised, melt and sublime into a molecular gas. In a metal, on the other hand, the valence bonds of the atoms are not saturated, molecules are not formed, and the electrons move rather freely from one valence bond to another or from one part of the crystal to another; therefore such a substance is an electrical conductor. Ionic crystals, such as NaCl or oxides like BeO or BaO, are built from ions that have closed electron shells. These ions are bound by forces of electrostatic attraction, balanced by forces of electronic repulsion; here there are no valence bonds, no mobility of the electronic structure, and no electrical conductivity.

This atomic model is suitable for considering the mechanical properties of a solid. In the simplest types of deformation, such as, for example, homogeneous compression, the atoms draw closer together,

repulsive forces begin to exceed the attractive forces and offer resistance to pressure. In a uniform elastic shear the atomic planes tend to slide one relative to another. By considering the change of the forces with distance, one can determine the resistance to shear. At considerably larger displacements, when individual atoms fall between the nodes or are torn out of the lattice, one can reason in the same way. But in all cases it is necessary to take into account the change of the simple interatomic forces and to consider the saturation of valences. Thus it is evident that if an atom in a crystal has enough neighbors to saturate its valence bonds, then the approach of an additional atom to it will produce a different result than if the given atom had a smaller number of neighbors.

As regards electrical properties, as we have already seen, the atomic picture gives a correct representation of the electrical conductivity of substances.

To a certain extent one can also explain magnetic properties: the inner electron shells of some elements are not filled and have an uncompensated magnetic moment. The incompleteness of the shells gives them a certain flexibility, manifested in the possibility of orienting the magnetic moment in various directions, which gives rise to magnetic effects. On the other hand, a number of electrical properties are difficult to explain with the aid of the atomic model. As typical examples one may mention three substances—C (diamond), Si, Ge. All three substances crystallize in one and the same diamond lattice, which is apparently typical for structures with saturated valence. Each atom forms four well-defined valence bonds with its four nearest neighbors, saturating its valences. According to what has been set forth above, one should expect these substances to be insulators; this is true for diamond, but not for silicon and germanium, which are the best-known semiconductors. To explain this and a number of other similar cases, a band model is needed.

The electronic energy level in an isolated atom is very narrow. This means that an electron situated at such a level always has one and the same energy. If two atoms are brought into contact, this level is shifted, the magnitude of the shift depending on the interatomic distance. If the two atoms are identical, so that each of them has one and the same energy level, then the interaction of the atoms will manifest itself not only in the displacement of this level, but also in its splitting into two levels, the distance between which increases as the atoms approach one another. If a multitude of atoms is brought together into a crystal, then a similar phenomenon is observed on a much larger scale. All the initially identical levels of identical atoms split in such a way that there is formed—

there are as many levels as there are identical atoms in the crystal, but the magnitude of the total splitting will be almost the same as in the case of two atoms. Thus, when there is a large number of atoms in the crystal, the group of levels will be arranged practically continuously and will form an energy zone (band). Each of the original energy levels splits into a band and, since these bands broaden as the atoms are brought closer together, it may happen that they overlap and form a continuous series of levels. On the other hand, if the splitting is small, gaps may remain between the bands.

Let us compare the number of levels in each band with the number of electrons actually present in the crystal. In valence and ionic crystals, as a rule, we find that there are just enough electrons to fill a certain number of the lowest bands, while the higher bands remain empty. By contrast, in a metal some bands are only partially filled, and above them there are unoccupied levels. In this case the material conducts electricity, and an electric field will accelerate the electrons, increasing their energy only slightly. Thus, conductivity takes place only when, as in a metal, immediately above the occupied levels there are empty levels to which electrons can pass from the occupied bands. In valence and ionic crystals, where there are gaps between the energy bands, there is no conductivity. What has been set forth corresponds to the conclusions of the atomic model, but an additional feature appears which makes it possible here to understand the case of Si and Ge. In diamond there is a very wide gap between the valence band and the next unoccupied level, and therefore the material is a good insulator. In Si and Ge this gap is very small. At high temperatures electrons can be excited by thermal motion and transferred from the occupied valence band into the upper band—the conduction band, as a result of which the material becomes a conductor. The so-called intrinsic conductivity then appears, rapidly increasing with temperature. There is also another, more important mechanism of conductivity. If the crystal contains impurity atoms, their energy levels will not be included in the main bands, since these bands arise only through the interaction of the energy levels of identical atoms. Some of these impurity levels may lie in the gap between the valence band and the conduction band. Investigation shows that there are two possibilities. In some cases a moderate rise in temperature can excite an electron from an impurity level into the upper unfilled conduction band, which leads to the appearance of conductivity. Such an impurity atom is called a donor atom. The resulting conductivity is called electronic (or n-type conductivity), since the carriers are ...

J. Slater

negatively charged electrons transferred to the upper level. In the other case the impurity level is normally unoccupied, and a moderate rise in temperature excites an electron from the lower valence band to this level, which is called an acceptor level. The resulting conductivity is called hole conductivity (or \(p\)-type conductivity), since the carriers are associated with holes in the valence band, which, as can be shown, have properties characteristic of positively charged particles.

An interesting case, intermediate between a conductor and a semiconductor, is graphite—an exceptional substance of its kind, with an unusual crystalline structure. In graphite the electrons completely fill the lower valence band, but the next band is directly adjacent to it. The density of electronic states falls to zero at the boundary between the bands and then increases again, i.e. this density is zero at only one point. As a result, graphite has electrical properties intermediate between those of a conductor and a semiconductor.

2. Mechanical properties of solids

We have already mentioned that the mechanical properties of solids are well explained by the atomic model, which makes it possible to account quite satisfactorily for such properties as compressibility. It is well known, however, that there are a number of mechanical properties, such as strength, tensile resistance, hardness, and plasticity, that are structure-sensitive. These properties cannot be understood without investigating the role of pinning points (dislocations)*) and impurities in the lattice. Apparently the most striking is their effect on resistance to shear. If one takes into account the interatomic forces and calculates the force necessary to make one atomic plane slide over another and, consequently, to produce shear in a crystal, one obtains an extremely large value. In reality the force required to produce shears in a crystal is about one thousandth of the calculated value. An explanation of this was given some time ago and is, to a certain extent, analogous to the explanation of why a piece of paper is easily torn, whereas the same paper can withstand a considerable weight suspended from it. An incipient tear propagates, since the notch proves to be the weakest point, and almost the entire tearing force can be concentrated at this single point. In a similar way it is believed that in a crystal subjected to shear the so-called pinning-

*) See the article by Cottrell, “The Theory of Pinning Points in the Crystal Lattice,” UFN 45, no. 2, 179, 1952. (Translator’s note.)

tions can produce a special type of atomic displacement that leads to the concentration of the shearing force at a single point, so that the action of the force is increased many times over, and a relatively small force can cause slip in a crystal. The catch propagates through the crystal in the same way that a tear propagates in a piece of paper.

The theory of catches explains not only the ease of slip in a crystal, but also makes it possible to understand strengthening. Anything that impedes the motion of catches can stop slip, just as strips pasted crosswise onto paper increase its strength, for the tear is stopped when it reaches these strips. The simplest form of strengthening is work hardening, which arises when the crystal lattice is distorted. It is assumed that although each catch moves through the crystal rather freely, the sliding that it produces leaves behind a trace in the form of a disturbed region. If more and more disturbed regions arise, then a moment comes when the next catch, on passing through the crystal, encounters one of these traces of disturbance and is stopped. As the number of disturbances increases, these frozen-in displacements of the lattice increasingly impede the motion of subsequent catches, as a result of which the material undergoes work hardening. By the time the catches are distributed in the lattice so densely that they begin to interfere noticeably with one another, saturation sets in and the optimum of cold working is reached, with the greatest change in physical properties and the greatest amount of energy absorbed in the lattice, as will be seen in the next paragraph. From the tensile curve as a function of time it is evident that the continuous application of force will produce deformation at an ever smaller rate, and finally so slowly that we can speak of it as creep.

Other mechanisms of strengthening are strengthening by alloying and strengthening by dispersion hardening. It is obvious that anything that disturbs the uniformity of the crystal lattice will impede the motion of catches and lead to strengthening; impurity atoms or inclusions of another material will have such an effect. In solid solutions the solute atoms usually differ appreciably in their dimensions from the dissolved atoms. When these atoms are arranged irregularly, they disturb the periodicity of the lattice, which leads to strengthening. In dispersion hardening, precipitates cause stresses in the parent medium from which they separate, which again disturbs the regularity of the lattice and leads to strengthening.

These mechanical properties depend strongly on temperature. A distorted lattice is usually thermodynamically unstable. If

atoms can move freely, they assume positions corresponding to thermodynamic equilibrium, and the lattice becomes more regular, which usually leads to a decrease in hardness. This is the phenomenon of annealing. At low temperatures the atoms cannot move freely, because each of them is held in its equilibrium position by restoring forces. But it may happen that, when displaced by a relatively short distance, these forces can change sign and push the atom into a more stable position. The energy required to overcome this barrier is called the activation energy. For an irreversible transition to a position of more stable equilibrium, the temperature must be raised so much that the thermal energy becomes comparable with the activation energy. The higher the temperature, the greater the probability that an atom will pass over the barrier, and the more often this process occurs. The activation energy can be determined by the well-known method of measuring annealing rates. In doing so it is often found that different atoms in a distorted lattice have different activation energies.

Associated with atoms in unstable positions is the energy of internal stresses accumulated by the lattice. If an atom can pass into a position of lower energy, then in this process it loses the energy which it had absorbed while in the unstable position. There are two principal ways of measuring this absorbed energy. One of them amounts to gradually heating the material. On passing through the temperature range in which atoms readily jump from unstable positions into stable ones, they release an excess quantity of heat, which can be measured by the additional rise in temperature. The other method consists in measuring the heat of dissolution. Both the cold-worked and the annealed specimens have one and the same final energy after dissolution; and since their initial energies are different, and the cold-worked specimen has the greater energy, the difference in energies can be measured from the heats of dissolution.

There is a number of other extremely important phenomena directly connected with changes in the positions of atoms in the lattice and revealing the great influence of the arrangement of atoms on the mechanical and thermal properties of a body. The transitions from an ordered to a disordered state in certain alloys are readily understood: below the transition temperature the atoms in alloys (for example, \(\mathrm{Cu_3Au}\)) form an ordered structure, whereas above this temperature thermal vibrations lead to a disordered distribution of atoms at the sites of the original crystalline structure. This can be investigated with the aid of X-rays, thermal measurements, and, in a number of cases, electrical and magnetic methods.

Another interesting phenomenon is the damping of acoustic or mechanical vibrations. Thus, for sound waves a large absorption or scattering of energy may be observed in a certain frequency region, connected, as can be shown, with various irreversible processes in crystals. Another important field of investigation is diffusion, including both self-diffusion, i.e., the diffusion of atoms in a crystal consisting of atoms of the same kind, and the diffusion proper of impurity atoms. The study of the activation energy of diffusion can shed light on the process by which atoms exchange places in the lattice.

3. Electrical Conductivity and Thermal Conductivity

Electrical conductivity depends on two quantities: on the number of current carriers (electrons—in ordinary metallic conduction—or ions in ionic conduction) and on the mobility of these carriers (or the velocity acquired by them at unit electric-field strength). Let us consider how these quantities depend on temperature and on disturbances in the lattice for various kinds of conductors.

First of all, in a metal the number of current carriers depends hardly at all either on temperature or on the physical state of the specimen, and is structurally insensitive. It has a value of the order of one electron per atom. If the conduction band is not very full, the carriers are electrons; but if it is nearly full, then the role of current carriers is played by holes, which behave like positive charges. The number of carriers and their sign can be found from the Hall effect, i.e., from the transverse potential difference that appears in a conductor when it is placed in a magnetic field perpendicular to the current. Unfortunately, the Hall coefficient for metals is very small and difficult to measure; its interpretation is complicated when some of the carriers are positively charged and others negatively charged. As a result, we do not possess as complete information about the number of free electrons in a metal as we should like.

The mobility of electrons in a pure metal is approximately inversely proportional to temperature. The reason for this is simple. Electrons in a perfect crystal, as band theory has shown, behave like waves, just as in the case of electron diffraction. If the lattice is perfectly regular, the electrons pass through the crystal without scattering—their mobility will be infinite. They are, however, scattered by inhomogeneities of the lattice that arise as a result of thermal vibrations. The number of these inhomogeneities is proportional to the temperature. The resulting frictional force, inversely proportional to the mobility of the electrons, is proportional to the temperature. In any pure metal-

in a body that is not a perfect crystal, there is an additional resistance, since additional scattering of electrons appears at lattice inhomogeneities, which reduces their mobility in the same way as an increase in temperature would. Thus, the measurement of electrical resistance is a sensitive method for determining lattice imperfection. This is especially true of the resistivity at very low temperatures, for here the dependence of resistance on temperature disappears and the residual resistance is entirely the result of lattice irregularities. Such residual resistance arises in metals under cold working. Alloys have an even greater residual resistance, caused by irregularities of the crystalline structure. It is interesting to note that in some substitutional alloys, in which at a certain definite temperature the ordered arrangement of atoms in the lattice is replaced by a disordered one, the residual resistance is much greater in the disordered than in the ordered state.

The resistance to currents of very high frequencies in the microwave region has certain interesting features not possessed by resistance to direct current. At high frequencies electromagnetic waves penetrate into a metal only to a very small depth. This phenomenon is called the skin effect. The depth of penetration decreases with increasing frequency and conductivity of the material, as a result of which the material becomes less transparent. The depth of penetration of the current in the skin effect may be of the order of \(10^{-4}\) or \(10^{-5}\) cm. Then, by measurements of conductivity with microwave methods, it is possible to determine its value in this thin layer.

It is sometimes believed that cold working of the surface of metals leads to complete distortion of the lattice in the surface layer. The microwave method will be sensitive to such a change in the state of the surface, which is difficult to investigate by other methods. From these same measurements additional interesting data are obtained which cannot be obtained by measurements at low frequencies. Thus, at low temperature the conductivity increases and the depth of penetration of the current may become smaller than the mean free path of the electron. In turn, the mean free path of the electron increases with decreasing temperature and increasing conductivity. When these two quantities become equal, the mechanism of conductivity changes and the measured conductivity will no longer increase with decreasing temperature. By observing this phenomenon, one can obtain data on the mean free path of electrons in the surface layers, and hence on their mobility. Comparing these data with the conductivity, one can determine the number of current carriers.

Let us next consider the electrical conductivity of semiconductors. It has already been indicated that the current carriers in such materials, with a moderate increase in temperature, appear from donor or acceptor impurity levels, while at higher temperatures they appear by direct excitation from the valence band into the conduction band. This leads to the typical dependence of conductivity on temperature, which is a characteristic property of semiconductors. This dependence is easily studied by means of the Hall effect, which for semiconductors is much larger than for metals. The mobility in semiconductors can be found by analogy with metals. Here there is a resistance arising from thermal vibrations and proportional to the temperature, as in metals, and also an additional resistance caused by distortions of the lattice due to the presence of impurity atoms. A careful analysis of conductivity and of the Hall effect, recently carried out by Lark-Horovitz et al., has contributed a great deal to the understanding of the band structure and conductivity of solids.

Insulators are in many respects similar to semiconductors, except that the former lack impurity atoms and have a large gap between the valence band and the conduction band. Insulators will behave like semiconductors with intrinsic conductivity if they are heated to a sufficiently high temperature to thermally excite electrons into the conduction band. But usually the required temperature is so high that the material will melt before such conductivity appears, or (if it is an ionic crystal) ionic conductivity will arise. On the other hand, any mechanism capable of exciting electrons into the conduction band leads to the appearance of conductivity; the mobility of electrons in this band in an insulator is much lower than in a conductor. Examples are photoconductivity, in which an electron is excited through the absorption of light, and conductivity excited by bombardment with fast particles, as occurs when diamond and other substances are irradiated. As we shall see below, the excitation of a large number of electrons to higher energy levels is a typical feature of the passage of fast particles through matter. In any substance except an insulator, the number of electrons excited in this way is not large enough, in comparison with the normal number of electrons in the conduction band, to produce a noticeable change in conductivity. In a good insulator under normal conditions the number of conduction electrons is practically zero; therefore the excited electrons are easy to detect.

Thermal conductivity has two different mechanisms. In a good conductor, electrons can readily carry energy from one point of a crystal to another. If in one part of the crystal they have a considerably larger kinetic energy, corresponding

at a higher temperature, they will quickly carry this energy throughout the crystal. A well-known consequence of the electron theory of metals is the constancy of the ratio of thermal conductivity to electrical conductivity (the Wiedemann–Franz law). This shows that good electrical conductors also conduct heat well. The ratio of the coefficients of electrical conductivity and thermal conductivity, however, depends on temperature: at not very high temperatures the thermal conductivity is almost independent of temperature, whereas the electrical conductivity in a perfect crystal varies inversely with temperature. Lattice imperfections will scatter electrons and change their ability to carry both current and heat and, consequently, will reduce this part of the thermal conductivity. In addition to electronic thermal conductivity there is an entirely different mechanism of thermal conduction, acting simultaneously with it and appearing to the same extent both in insulators and in conductors. This is heat transfer due to vibrations of the lattice. If an atom is set into vibration, it will act on its neighbors and force them to take part in the vibrational motion, just as happens in a system of weights connected by springs. Thermal conductivity of this type is much less than electronic thermal conductivity and does not play an essential role in good conductors, whereas in insulators it wholly determines the phenomenon of heat transfer. The thermal conductivity of the lattice is due, basically, to the propagation of acoustic waves, while electronic thermal conductivity is due to the propagation of electron waves.

Just as the scattering of electron waves reduces electronic thermal conductivity, so everything that leads to the scattering of acoustic waves reduces thermal conductivity of this type. Therefore one may expect that the latter will be considerably decreased by lattice distortions.

Although a large amount of work has been done in the theory of electrical and thermal phenomena, it is insufficient. The phenomena in germanium and silicon are well understood. A quite satisfactory state has been achieved in the understanding of the properties of pure metals.

But the theory is still far from being able to use data from measurements of the dependence of conductivity on temperature, obtained for any material, to judge the nature of displacements in the lattice. This is a consequence not so much of the unsatisfactory state of the theory as of insufficient work on carrying out the necessary calculations and of the absence of experimental data needed to test the simple predictions of the theory, in order to use it with confidence for more complicated cases.

4. Methods of Experimental Investigation of Solids

In the preceding sections some experimental methods for investigating solids were mentioned, namely, mechanical tests: obtaining stress–strain curves, measurements of hardness and creep, thermal measurements of the energy of internal stresses by heating or dissolution, electrical measurements of conductivity and of the Hall effect as functions of temperature. One may add here measurements of magnetic susceptibility, which provide, for magnetic substances, certain information about the electronic state of atoms and possess unusual sensitivity for determining small quantities of ferromagnetic substances. All the methods listed make it possible to obtain only indirect indications of the positions of atoms. If there existed sufficiently well-developed theories connecting the properties under consideration with lattice defects, then these measurements could be used to determine the number and nature of such defects. Unfortunately, however, in almost all cases the theories are insufficiently well developed and have not received complete experimental verification that would make it possible to trust their conclusions without major reservations. Further substantial development of the theory of each of the phenomena is necessary, together with extensive measurements of various properties on the same specimens. If the pictures of lattice defects determined from measurements of different properties agree, then this will allow confidence in the theories of these properties. Such a comparison has been carried out, as mentioned above, for germanium and silicon. The good agreement obtained in this case gives us confidence in the correctness of the basic propositions of the theory of the solid state. Similar work should be carried out on a larger number of materials of different types.

In contrast to these properties, the study of which gives only indirect evidence of lattice defects, there exist a number of experimental methods that make it possible to obtain direct data. Chief among them is the method of X-ray diffraction, and useful auxiliary means are the methods of electron and neutron diffraction. The classical application of X-ray diffraction is the determination of the structure of crystals. But this method can also be used to study disturbances of the crystal lattice. As a result of the work of a number of investigators, this method gives significantly more accurate data on disturbances of the crystal lattice than was the case until recently. The study of X-ray diffraction by a crystal makes it possible to represent the scattering power of the latter in the form of a Fourier series. Unfortunately, this method makes it possible to determine only the amplitudes, and not the phases, of the terms

Fourier series, so that one cannot, without additional assumptions about the phases*) directly sum these terms and obtain an image of the complete structure. These assumptions require correct conceptions and physical intuition from specialists in the field of structural analysis. They must determine structures in accordance with the known interatomic distances and with certain other physical principles.

In the same way, for a distorted lattice one can obtain, from X-ray diffraction, a Fourier series that determines the displacements of atoms from their regular positions in the lattice. In this case we again have only amplitudes, but not phases. Quite recently a theory of the Fourier image of imperfections was developed. Work on the synthesis of these series, which reveal lattice imperfections, is only beginning, so that researchers working in this field do not yet have sufficient experience to make reasonable guesses about the phases and about the types of possible displacements. There are, however, sufficient grounds to hope that, as experience accumulates, it will become possible to determine displacements from the synthesis of series and to obtain a picture of imperfections in lattices almost as definite as our present ideas about the structure of undistorted crystals. When properly used, this method should become the most valuable means of investigating lattice imperfections. As was emphasized earlier, the positions of atoms are, in a certain sense, independent variables, i.e., quantities from which all the other properties of a distorted lattice can be directly calculated. The inverse process of determining the positions of atoms from such indirect data as electrical or thermal properties is less reliable.

Alongside X-ray structural analysis, which is a method of directly determining the positions of atoms and, consequently, gives an idea of the atomic model of a solid, there exists another X-ray method used for investigating the band model. This method**) is based on the study of the emission bands of soft X-rays. If one of the electrons of an atom in a crystal is knocked out by bombardment with fast electrons, then an outer electron of that same atom can fall into the vacated place. The frequency of the X-rays emitted in this process gives the difference of energies of the corresponding levels. The electron falling into the vacant place

*) Recently, major advances have been made in the theory of structural analysis, making it possible to approach closely the solution of the problem of direct phase determination. (Translator’s note.)

**) This refers to X-ray spectroscopy of the solid state. See in more detail: E. E. Vainshtein, X-ray spectra of atoms in molecules of chemical compounds and in alloys. Publishing House of the Academy of Sciences of the USSR, Moscow–Leningrad, 1950. (Translator’s note.)

from the valence band of the crystal, can come from any place in this band. Hence it follows that the distribution of the energy of the emitted X-rays over frequencies gives a characterization of the distribution of levels in the band, provided the transition probabilities are taken into account. This method, proposed in 1930 by O’Bryan and Skinner, made it possible to determine the band structure of many metals with small atomic weights, and the results obtained are in general in good agreement with theoretical ideas and confirm the correctness of the theory. This method should be applied to other metals in order to confirm and extend our knowledge in the field of the band theory of these materials. The method should also be applied to alloys and chemical compounds and to materials with disturbances in the crystal lattice. We have already mentioned that the interaction of an atom with identical neighbors leads to a broadening of the energy bands. If in a crystal some atom, for one reason or another, is surrounded by different neighbors, for example in the case of a chemical compound, a solid solution, or the presence of impurity atoms, then the broadening of the corresponding bands will probably be quite different than in a pure metal. The bands in a distorted lattice must narrow or broaden depending on the nature of the stresses. Many features of the spectral bands of soft X-rays will reveal interesting properties of alloys and cold-worked materials. These phenomena have not yet been investigated, and the application of the method under consideration may be very fruitful.

Closely related to the method of soft X-ray spectroscopy is the method of photoelectric emission. In this method, owing to the absorption of optical radiation by the surface of a material, electrons are transferred from the valence band to the conduction band. Investigation of this phenomenon reveals the distribution of levels in the valence band and determines the width of the gap between the bands. The results of the method agree well with the data of the method of soft X-ray spectroscopy. These two methods, together with measurements of optical absorption spectra and the study of the conductivity of semiconductors as a function of temperature, can give complete information on the band structure of solids. However, they have so far been applied to very few materials. Similarly, the theory has been developed only for a few materials. The development of the theory of the solid state should be greatly aided by the expansion of theoretical and experimental work in the study of energy bands. Only after the nature of the bands becomes known will it be possible, with sufficient confidence, to develop theories of electrical conductivity and thermal conductivity to such an extent that, with their help, one can predict the effect of displacements in the lattice on these properties.

II. THE NATURE OF RADIATION DAMAGE

In the preceding sections we considered some data from the theory of the solid state. In doing so, special attention was devoted to effects produced by atomic displacements. A number of properties, such as density, compressibility, and some others, are relatively little sensitive to displacements, whereas electrical conductivity (especially at low temperatures), thermal conductivity, and hardness are especially structure-sensitive. Atomic displacements affect these properties quite independently of how the displacements were produced.

The study of cold-worked materials and of their behavior during annealing makes it possible to determine the influence, on the properties of materials, of interlocks created by purely mechanical means and to provide a theory of these phenomena. When such a study, carried out by the methods described in the preceding sections, has advanced sufficiently far, the types of displacements produced by various kinds of mechanical deformation and the influence of these displacements on structure-sensitive properties will be known precisely.

Under the action of radiation, displacements arise which are, on the one hand, similar to, and on the other hand undoubtedly different from, the displacements produced by cold working. It is clear, however, that the experimental and theoretical methods for studying radiation damage must coincide with the methods used in studying cold working. Therefore any well-conceived program for investigating radiation damage must be connected with a program for investigating, by the same methods, damage produced by cold working. This will make it possible to have two independent ways of producing atomic displacements, which can be studied not only separately but also by comparing them with one another, thereby throwing deeper light on the nature of each of the phenomena. Such a combined research program should increase our knowledge not only in the field of radiation damage, but also in solid-state physics and metallurgy, which is of great importance for obtaining new materials with properties unattainable at the present time. Unfortunately, such serious work, important irrespective of the problem of the action of radiation, has not yet been carried out.

In considering damage produced by radiation, we shall see that different types of radiation exert an effect on materials which is broadly similar and differs only in details. Just as the simultaneous study of damage produced by cold working and by radiation is more fruitful than studying them separately, so too the study of damage produced by various kinds of primary particles—neutrons, protons, or deuterons accelerated in a cyclotron, and fragments

fission of nuclei may yield more than the study of defects produced by particles of only one kind.

If we confine ourselves only to the experimental study of various kinds of radiation, then comparison of the results obtained would make it possible to determine only an empirical conversion factor showing how many times greater the destructive effect of radiation of one type is than that of another. But in combination with an effective theory explaining both the differences and the similarities in the action of various kinds of radiation, one can obtain considerably more than from the study of any single kind of radiation. Such an investigation will make it possible to apply our knowledge to cases of irradiation not previously used, for example to the action of fast neutrons with flux intensities unattainable with present experimental possibilities.

Let us now turn to the description of the types of defects presumably produced by various kinds of primary radiation, and to an exposition of the theory relating to this question, as well as of the direct experimental methods which can be or have been used to confirm this theory.

5. Theory of Radiation Action

The important kinds of radiation acting on metals and semiconductors are neutrons and charged heavy particles. The other kinds of radiation, such as photons, gamma rays, and electrons, produce a very small effect, with the exception of insulators and chemical compounds. Mesons are not yet available in sufficient quantity for the effect produced by them to be of practical interest, although it will probably be intermediate between the action of protons and electrons.

A neutron has almost no effect on an atom until it approaches the nucleus so closely that nuclear forces come into play. The force of interaction between the magnetic dipole moment of the neutron and the magnetic fields present in matter is important for diffraction and scattering of neutrons, but it is too small for radiation defects. Consequently, the cross section of a neutron in collision with an atom is very small, and a neutron can pass through considerable thicknesses of material, undergoing only a few direct collisions with atoms located at considerable distances from one another. These collisions may be regarded as independent events. The theory of these collisions is very simple and easy to understand. There may be, first, elastic collisions. They are the only important type of collision with fast neutrons and are significant for any radiation defects. In such impacts the neutron transfers a significant fraction of its energy to the atom participating in the collision. This fraction

the energy is the higher, the closer the mass of the neutron is to the mass of the atom undergoing the collision (i.e., the lighter this atom is). The recoiling neutron travels on until the next collision, when it gives up approximately the same fraction of its energy (a smaller amount, therefore, in absolute value), and so on, until it is completely slowed down. In the thermal range of velocities there may be a high probability of nuclear reactions, and if the atom participating in the collision can fission, then there is also a probability of fission of the nucleus.

The action of a neutron in a collision consists either in the formation of a recoil atom with a large energy (often tens or hundreds of thousands of volts), or of a fragment atom arising in a nuclear transformation or fission. Recoil atoms in most cases will have a charge, since part of their electrons is lost in the collision. Therefore we may begin the study of radiation effects by considering the effect produced by a recoil atom, i.e., by a heavy charged particle. In such a case the action of neutron radiation is in principle no different from the effects directly produced by heavy charged particles: protons, deuterons, alpha particles from cyclotrons, or fragments of nuclei. In other words, before us is the problem of the passage of a heavy charged particle through a solid. If this question is investigated in general form, as a function of the mass, charge, and energy of the incident heavy particle, then we shall encompass all the theoretical foundations of radiation action. The phenomenon, of course, depends both on the nature of the incident particle and on the type of solid under consideration.

Apparently the most complete study of this problem was carried out and continues to be carried out by Bohr and his school. This work relates to a considerably greater degree to the action of fast particles on gases (for example, in a Wilson chamber) than on solids, but many, if not all, of the phenomena considered will be the same in a gas and in a solid, and reduce to the interaction of incident particles with individual atoms, independent of the state of aggregation. Let us consider the behavior of fast particles passing through a gas. Initially the fast particles themselves probably carry a charge, which is very large for fast particles (like nuclear fragments at the beginning of their path), but decreases as the particle is slowed down. Fast particles acquire this charge quite independently of whether they had it initially or not. It is quite evident that if a very fast particle, for example an atom, passes through a layer of matter, then the outer, most easily detachable electrons are torn away in the process.

A simple and fairly precise rule indicates which electrons will be removed and which will not: those electrons are torn away whose orbital velocity is less than the velocity of the atom. Electrons having a greater orbital velocity remain bound.

with the atom. Since the outer electrons have low orbital velocities, and the inner ones higher velocities, this means that the outer electrons will be stripped off. In this case a positive ion is formed, for which the number of removed electrons decreases as it slows down. This decrease of charge is due to the fact that, in moving through matter, the atom more readily acquires electrons than it loses them. The particle is in an equilibrium determined by the fact that the electrons at the boundary between stripping and capture have an orbital velocity almost equal to the velocity of the particle. Such an equilibrium between ionization and capture was known already at the dawn of nuclear physics in connection with the loss and capture of electrons by alpha particles as the latter pass through matter.

A fast ion passing through matter can act in two ways on the atoms with which it collides. First, it may undergo an elastic collision and transfer recoil kinetic energy to the atom. This type of collision differs in principle little from the elastic collisions of neutrons with atoms that we have already considered. Some results will be exactly the same; for example, the fraction of the energy of the incident atom transferred to the struck atom is the greater, the closer their masses are. But here, owing to the charge of the ion, another process appears, comparable in importance with the preceding one: the striking particle can ionize or excite the electrons of the struck atom, which leads to an inelastic collision, in which the greater part of the energy of the incident particle goes to the electrons stripped off, and not to recoil atoms. It can be shown that the probability of ionization, among other quantities, depends on the square of the charge of the striking particle. It is therefore clear that when the incident particle loses energy and therefore loses charge*), ionization rapidly decreases.

If one takes into account this decrease of ionization with decreasing energy, it turns out that all the energy of the fast particle (except for a few percent of scattered energy) is expended on ionization, whereas at low energies ionization is unimportant, and the remaining energy is transferred almost entirely to recoil atoms. As will be shown below, it is precisely these recoil atoms that produce radiation damage. Therefore the greatest damage will be produced by a very fast particle at the end of its range, when it has slowed to a comparatively small velocity, although the total damage produced in the early stage of the motion may also be considerable. The limiting energy at which the transition of the dominant role from the ionization process to elastic collisions takes place (for example, when the expenditure of the particle’s energy may be attributed half to one process and half to the other) depends on the kind of incident—

) More precisely, acquires electrons. (Translator’s note.*)

of a particle and for a light particle will be smaller than for a heavy one. The reason for this is that in reality this boundary is set not by the energy, but by the velocity of the incident particle; the corresponding kinetic energy is proportional to the mass of the particle. This limiting energy is less than 10,000 eV for a proton, about 100,000 eV for an atom of medium weight (for example, a carbon atom), whereas for such heavy atoms as fragments of nuclear fission it may be greater than a million electron volts. Let us note that these figures agree with the corresponding data for the electron, which is 1800 times lighter than the proton. Inelastic collisions of an electron with excitation and ionization occur at all energies exceeding a few electron volts, while elastic collisions with transfer of energy to recoil nuclei occur at lower energies.

We may now adopt the reasonable hypothesis that only the energy transferred to recoil nuclei and leading to displacements of atoms causes radiation damage. We shall return to this hypothesis later. From it one can immediately draw certain conclusions about the damage produced by different types of particles. Let us first take the neutron. A fast neutron produces along its path ionized recoil atoms with energies of tens of thousands and hundreds of thousands of electron volts. These recoil atoms have intermediate mass (with the exception of very light or very heavy elements) and therefore themselves participate in further collisions, in which they will expend half of their energy on ionization and the other half in elastic collisions, creating secondary recoil atoms. These secondary recoil atoms will have considerably smaller energy, so small that they will scarcely ionize, but they will produce tertiary, and so on, recoil atoms with ever smaller and smaller energy. In other words, a significant fraction of the energy of each neutron (at least half) will be spent on atomic displacements. We shall consider below how much damage will actually occur in this case. The damage produced by an individual neutron consists of a certain number of isolated regions, each of which arises from one collision of the neutron with an atom. Potentially, the expenditure of a significant fraction of all the neutron energy on the formation of radiation damage is possible.

Let us now consider a fragment of nuclear fission. It is a heavy atom with an initial energy of the order of hundreds of millions of electron volts. Approximately the first 97% of the energy is dissipated in ionization, and only one or two percent of the total energy goes into the formation of damage, which occurs when the energy of the atom has decreased to the order of a million electron volts. When the remaining energy reaches this value, it will be transferred to recoil atoms, which in turn will produce secondary

and tertiary recoil atoms as well, as in the case of the neutron, so that the total potential destruction produced by a fission fragment is comparable with the disturbance produced by a neutron having an energy of one or two million electron-volts. The effects of disturbance, however, are very different because, in the case of a heavy ion, they are much more concentrated. The cross section for the collision of an ion with an atom in the region of elastic scattering is much larger than the cross section for the collision of a neutron with the same atom. The reason for this is that the ion can act on the atom by electrostatic forces and by the ordinary interatomic repulsive forces. These forces act at much greater distances than the nuclear forces, which are the only forces of interaction between a neutron and an atom. Thus a fission fragment, instead of a few elastic collisions with isolated atoms and the formation of separate regions of disturbance at distances of up to several centimeters, as occurs in the case of a neutron, will produce recoil atoms at very small distances, forming a practically continuous track of disturbances, the length of which in a solid may be of the order of several hundredths of a millimeter. The difference between these two phenomena is revealed in a Wilson chamber and on photographic plates when the tracks of fast particles are recorded. The first method is a direct experimental means of studying radiation disturbances in a gas, the second—in a solid.

Light atoms accelerated in a cyclotron (such as, for example, a proton, deuteron, or alpha particle) have an initial energy of ten or twenty million electron-volts and, as we have already seen, expend the greater part of their energy on ionization until their energy reaches the order of 10,000 eV. Accordingly, only about one thousandth of the initial energy will be spent on the formation of radiation disturbances. The recoil atoms from the primary collisions will have rather small energies, considerably smaller than the recoil atoms from neutrons or from fission fragments of nuclei, and, consequently, here secondary and tertiary recoil atoms produce less destruction. The range of such an accelerated light particle is similar to the range of a fission fragment and is of the order of several hundredths of a millimeter. The fraction of energy expended by such a light particle on ionization, which, according to our hypothesis, does not cause radiation disturbances, proves to be even greater than in the case of a fission fragment. It must be recalled in this connection that, although ionization does not entail destruction, it leads to heating of the specimen, and in any experiment on the investigation of radiation disturbances this heat must be removed.

Let us develop the considerations set forth in several directions. First we shall give a critique of the modern theory, the applications of which

were set forth by us, and we shall consider ways of improving this theory, as well as experimental methods for a direct verification of the theory. We shall next discuss relative properties and compare various kinds of radiations from the standpoint of understanding the nature of radiation damage, taking into account the actually available sources of radiation. Then we shall proceed to a more detailed study of radiation damage in solids, which differs from damage in gases and isolated atoms and supports the assumption that it is only the energy of recoil atoms, and not the ionization energy, that determines the appearance of damage. In conclusion we shall consider various types of solids and compare the damage expected in them with the available experimental data.

6. Critique of the Present State of the Theory of Radiation Action

We have already pointed out that the main contribution to the theory of radiation damage was made by Bohr. There are also published materials by other authors. None of them, however, has gone beyond the framework of Bohr’s fundamental work, although they have extended it in detailed applications to solids. At present the theory of radiation action is developed fairly well for fast particles. In the area of the theory of slow particles, however, much further work is necessary.

If two nuclei, stripped of their electron shells and possessing energies of several million volts, approach one another, they will be repelled only after having come together to a distance comparable with the dimensions of nuclei. Collision theory operates with the impact parameter—the distance of closest approach in a head-on collision; this quantity is of the order of \(10^{-13}\) cm. The fact that atoms or ions are in reality surrounded by electron shells is almost immaterial. The collision time, as can be determined, is so short that the nuclei approach and move apart from one another in a time interval short in comparison with the periods of rotation of the electrons in their orbits, so that a rearrangement of the electrons does not have time to occur, and their screening action remains unchanged. Therefore such collisions will be similar to the classical collisions of alpha particles and nuclei in Rutherford’s scattering experiments. The theory of this experiment, being a well-known theory of collisions, is directly applicable to the case described earlier. This theory of collisions does indeed have a solid foundation. The recoil cross section in this energy range is a circle with a radius of the order of the impact parameter, which explains the very small cross section for elastic scattering for fast particles.

In the very same energy range of very fast particles it is obvious that, owing to the smallness of the cross section for elastic scattering, in most collisions the colliding nuclei will not approach to-

sufficiently close for elastic scattering to occur, but instead they will pass through the electron clouds. Here again the collision will occur so rapidly that the electrons will not be able to rearrange themselves during the time of the collision. The result of such a collision will be ionization. This question is treated by expanding in a Fourier series the electric field of the incident particle, rapidly changing as the latter passes through the atom, similarly to what would take place in the superposition of monochromatic light waves, and then considering the action of these waves separately, as is done in the study of the photoelectric effect. This question, although more complicated than the scattering of $\alpha$-particles, is nevertheless quite soluble, and the corresponding solutions are exact. In this range of energies we first encounter the case where, depending on the aggregate state of the target, different action of the particles is possible. As we have already mentioned, electrons knocked out of an atom behave like photoelectrons and pass to ionized or excited energy levels. In a solid there is a band structure of levels, and therefore the arrangement of the excited energy levels differs sharply from the arrangement of levels in a gas. The probabilities of ionization in a solid and in a gas must therefore be entirely different. However, investigation shows that at mean energies of the order of ten or twenty electron-volts, acquired by an ionized or excited electron, the difference between the distributions of energy levels in a solid and in a gas is small and, consequently, in both cases the results should be similar.

Thus, one may expect that the theory will be applicable for energies of the order of several million volts. These assumptions are confirmed by the good agreement of the theory with experimental data obtained in a Wilson chamber in determining the range and the ionization per unit path for fragments from nuclear fission and other particles of high energy. A larger number of such experiments should be carried out. Experiments with solids should also be carried out, for example with stacks of thin foils. These experiments will make it possible to compare the theoretically predicted values of the range of fast particles in solids with experimental data. Here we should expect confirmation of the theory rather than any unexpected novelties.

The situation is otherwise for slower particles. Unfortunately, as we have already seen, it is precisely in this range of energies that the maximum radiation damage occurs, since the greater part of the energy of the primary particles is transferred to recoil atoms. The reason is quite clear why the theory of collisions of fast particles must give poor results in the region of slow particles. If the cross section for elastic scattering becomes larger and the cross section for ionization decreases, then this corresponds

collisions in which the nuclei do not approach one another to such small distances as in the case of collisions of particles of high energy. Here the nucleus of one atom no longer penetrates into the inner electron shells of another. In this case one cannot consider the interatomic repulsion of the nuclei alone without taking account of electronic screening. Bohr made the first attempt to consider this screening, but on the basis of a rather crude atomic model. Seitz applied a somewhat more refined method. It can be seen that in such collisions, which take place over a longer time interval than collisions of very fast particles, the inner electrons can make many revolutions during the collision and therefore are able to alter their motion, which leads, in turn, to a change in the screening and in the interatomic repulsion. In sufficiently slow collisions the distances of closest approach of the colliding atoms are comparable with the interatomic distances in solids under pressure. The duration of such collisions is comparable with the periods of rotation of the outer electrons. Under these conditions the electronic system of the atom can rearrange itself so that it will be similar to the electronic systems of atoms of a solid under pressure, or of atoms approaching one another during molecular vibrations. From the theory of interatomic interactions we know the nature of the repulsive forces that arise when atoms approach one another. Despite the possibility of considering collisions from this point of view, no complete work has been done here.

The state of the theory of slow particles is such that much work still has to be done in this field and that it must be checked experimentally. It may be expected that the action of particles of low energy in solids and in gases will be quite different. In a solid, an atom possessing sufficiently small energy, when colliding with a neighboring atom, does not turn it into a recoil atom, as happens in a gas, since the struck atom is thrown back by its neighbors, which absorb the recoil energy like a shock absorber. Here we encounter the problem of collisions in solids, which we shall discuss below. It would be desirable to study such collisions experimentally in a gas, where it is relatively easy to test the theory, which promises to be rather complicated. The experiments are in principle not difficult. It is only necessary to accelerate heavy particles to relatively low energies, of the order of several hundred thousand volts and even less, which can be accomplished in many types of accelerators, and then to study their elastic scattering in a gas and the ionization produced by them. The results of this theory and of the experiments are necessary for filling serious gaps in the theory. These gaps make doubtful all present estimates of the number of displaced atoms in radiation damage.

7. Comparison of Different Types of Radiation in Experiments on Radiation Damage

In the preceding sections we saw that the primary action of different types of radiation on solids is quite different. But in the final analysis the majority of defects are produced by secondary and tertiary recoil atoms, for the primary particles, after slowing down to sufficiently low velocities, dissipate almost all their energy in elastic collisions. This makes it possible to suppose that the radiation damage produced by different types of radiation will not differ greatly. It seems that this assumption is already confirmed by experiments that have been carried out. Further work must be done to test this assumption. If it proves correct, then the question of which type of radiation should be used for studying radiation damage will become a matter of convenience.

An essential difference in the character of radiation damage is clear from the considerations given above. The range of neutrons is large, so that they can pass through samples of ordinary dimensions and, colliding with individual atoms inside the sample, will produce separate centers of damage throughout the entire volume of the sample. Thus a sample irradiated in a reactor will exhibit a volume effect, owing to which it is convenient here to use large samples. Particles accelerated in an accelerator have a small mean free path and therefore will produce damage only near the surface of the irradiated material. In this case the effects of irradiation must be studied on a microscopic scale. Fragments of nuclear fission also have small mean free paths, and here there may be two cases, depending on the distribution of the fissionable atoms. If they are dispersed inside the sample, then the fission fragments, even with a short range, will arise everywhere in the sample and therefore the effect will be volumetric. At the same time, if the sample does not contain fissionable atoms and is placed close against a sample emitting fragments of nuclear decay, the result will be the same as in bombardment in a cyclotron or other accelerator: here the defects are concentrated near the surface. From the practical point of view, the different types of irradiation differ chiefly in the amount of energy expended on ionization (and consequently on heat) relative to the energy received by the recoil atoms.

We have seen that in neutron bombardment the greater part of the energy of the bombarding particles is carried off by recoil nuclei and leads to radiation damage. At the same time, in bombardment in a cyclotron and by fission fragments, the recoil nuclei receive only a small fraction of the energy, and therefore here the removal of heat

becomes a serious problem. This problem is especially difficult to solve when the fissile material is distributed throughout the specimen, as occurs under irradiation in a reactor, where neutrons may produce nuclear fission. The practical problem of removing heat from the interior of a massive specimen is difficult to overcome, since this removal must be accomplished by thermal conduction. The problem of heat removal during bombardment in accelerators is naturally easier to solve, since the heat is generated at the surface and, consequently, it is sufficient to place the specimen on an intensively cooled massive material. In all these cases, however, the problem of temperature control is more complicated than in direct neutron bombardment, when it is easy to keep the specimen cold. The question of temperature becomes serious if we recall that radiation damage readily disappears upon annealing. In this case the annealing rate depends strongly on temperature. Therefore experiments carried out at elevated temperature, which probably occurs with poor cooling, may give a very inaccurate idea of what will happen under low-temperature irradiation. Temperature control in irradiation experiments, both in accelerators and in reactors, is a very important technical problem.

Almost all the energy of the incident neutrons can be expended in producing radiation damage, in contrast to the small fraction of the energy expended on damage by accelerated particles. But in accelerators it is possible to obtain fluxes considerably exceeding the particle fluxes obtained in experimental reactors. Simple considerations show that radiation damage produced by irradiation in an accelerator arises at a higher rate than if the specimen were irradiated in a reactor. Thus, irradiation in an accelerator has practical advantages. These advantages are partly offset, however, by the fact that, unlike cyclotrons, a reactor operates over long periods of time. Therefore long-term irradiation is very simple to carry out in the latter. All experimental reactors also make it possible to conduct a larger number of experiments simultaneously than is possible in a cyclotron. For specimens which, for practical reasons, must be large for subsequent investigations and whose irradiation must be uniform, the advantage of using a reactor is obvious. For basic experiments, on the other hand, both types of irradiators have advantages. An obvious advantage of the accelerator is the possibility of using different types of accelerated particles, regulating their energy, and generally regulating the experimental conditions. In a reactor, where many experiments are carried out simultaneously, and where the conditions during reactor operation are relatively unknown to the experimenter, careful control of these conditions is much more difficult.

As regards the use of various particles with different energies in experiments with accelerators, much more can be done than has been done so far. Such work has been carried out only with the cyclotron. We have already seen that this is a rather unsuitable way of carrying out the experiment, since a particle accelerated in a cyclotron to an energy of ten or twenty million volts dissipates a very small fraction of its energy in radiation damage before it is slowed down to several tens of kilovolts. All the rest of the energy goes into heating and, from the point of view of radiation damage, is wasted. This heat is very difficult to remove in the experiment. For experiments of this type it seems that there are many advantages in using particles of low energies, of the order of a million volts, which can be obtained in an inexpensive Van de Graaff generator. Here almost the same number of defects is produced per particle as per particle obtained in a cyclotron, but in the former case a much smaller amount of heat to be removed is produced. In addition, in a Van de Graaff generator it is easier to pass from one type of particle to another. One should advocate the use, for investigating radiation damage, of accelerated heavy ions, for example argon ions or ions of another similar element, since we have already seen that, for heavy ions at energies of about a million volts, a much larger fraction of the energy goes into radiation damage than for a light ion. Of course, at such a low initial ion energy the range of the particles will be correspondingly smaller. That part of the range in which the particles have high energy, expended mainly on ionization, will here be absent. The experiments will then be performed on an even more microscopic scale than under irradiation in a cyclotron. But this is not an insurmountable obstacle. A heavy ion possessing an energy of a million volts, on colliding with a target, produces, with considerably less heating, almost as many defects as a fission fragment with an energy of one hundred million volts. Heavy ions are therefore, from many points of view, a desirable type of particle for the investigation of radiation damage.

In this connection it is useful to mention one more feature of radiation damage which we have so far left aside. The particles used in bombardment remain inside the specimen when they reach the end of their range. If the particle is an atom knocked out by a primary neutron, then it will be of the same kind as the atoms of the substance and will be a displaced atom, not an impurity atom. On the other hand, a fission fragment or an atom ejected from an accelerator may remain inside the specimen as an impurity atom, if this specimen is not a thin foil. Then, after prolonged irradiation, in the material

there may be enough impurity atoms to produce a noticeable change in its properties. This type of radiation damage can play a very important role. If the impurity atoms are soluble in the matrix medium, then the resulting solid solution will have increased hardness and specific electrical resistance. If there is no solubility, then the impurity atoms will form certain regions that affect hardness, electrical resistance, and other properties. In some cases this influence is so great that it is comparable with the influence of the actual displacement of atoms in the crystal. Using the methods described above, one can investigate impurity atoms and estimate the effects they produce. Striking effects from many points of view may be expected from inert-gas atoms formed in nuclear fission and completely insoluble in any solid substance. These atoms may form gas pockets, which will obviously have a very unfavorable effect on the properties of the material, especially on its mechanical strength. The application proposed above of accelerated argon atoms for the study of radiation damage makes it possible to retain argon atoms inside the substance and thus to model the action of fission fragments.

8. Characteristic features of radiation damage in solids

Until now, in considering radiation damage, we have used a theory that does not take into account the actual nature of the solid state. We used the simple rule that the energy of an elastic collision of atoms is converted into radiation damage, whereas energy expended on ionization does not produce such damage. In this section we shall examine this assumption in greater detail, trying to obtain a definite picture of radiation damage and hence the probable state of a material having such damage, as well as the expected types of damage.

We have already seen that the typical problem to be studied is that of a charged particle of high energy passing through a solid. At sufficiently high energies (the limiting energy is determined by the type of particle), the greater part of the energy will be spent on ionization. Let us first see why the assertion is valid that this energy is not expended on radiation damage. The first way of confirming this assumption follows from a remark made at the beginning of the review, namely that the state of a solid depends on the arrangement of atoms in the substance. This is connected with the fact that electrons can change their state so rapidly that they come almost immediately to an equilibrium configuration. Hence it may be assumed that the ionization energy of a certain number of electrons excited by the incident particle,

very rapidly spreads throughout the whole solid and decreases to a sufficiently low value per unit volume, owing to which this energy may be neglected. Another way is to compare the two mechanisms of thermal conductivity considered by us in one of the preceding sections. Let us recall that electronic thermal conductivity plays a more substantial role than the transfer of heat caused by vibrations of the lattice. The ionized electrons will in this way be able very rapidly to dissipate their energy, especially by means of electronic thermal conductivity. The same thing occurs also in an insulator, since there the ionized electrons themselves can carry thermal energy. All this takes place in a time short in comparison with the interval required for the dissipation of energy by atomic vibrations.

Of course, this argument is in a certain sense plausible. We know that the general principles of thermal equilibrium require that energy initially imparted to certain degrees of freedom in a substance, for example to electronic motion, should with time be distributed among all the other degrees of freedom. Thus, the energy of ionization will ultimately pass in part into the energy of atomic vibrations, i.e., into ordinary thermal energy. In fact, in a metal, for example, almost all the energy ultimately passes into heat, since in a metal almost all the heat capacity is contained in the atomic vibrations and there is almost no electronic heat capacity. This is essentially true also for other types of solids. We are interested, however, not in the final equilibrium, but in the kinetics of its attainment. The way in which the energy of the electrons can pass into the energy of vibrations of the nuclei is obvious. It may happen that, as the electrons move around a given atom, they are distributed in such a way that they are not equilibrated, and this corresponds to a larger charge on one side of the atomic nucleus than on the other. This will lead to an unbalanced electrostatic attraction of the nuclei, which in turn will force the nuclei to vibrate, and in this way energy will be transferred from the electrons to the nuclei. The question is only how rapidly this process proceeds in comparison with the spread of the excitation of the electrons over the entire lattice. Such a question has not been considered theoretically as thoroughly as it should be. There are indications that the exchange of energy between electrons and nuclei proceeds slowly in comparison with the propagation of the energy of the electrons, so that by the time the nuclei perceive the vibrational energy, the electronic energy will have been almost completely dissipated. Individual atoms will receive a relatively small vibrational energy, but this amount will already be sufficient for the cooling problem to arise, as we mentioned in connection with irradiation in the cyclotron. Yet this energy is still insufficient for the production of radiation damage, for, as we shall see

further, the atom must acquire much greater thermal energy before it is displaced in the lattice, and this disturbance becomes permanent.

Thus, we have considered confirmations of our proposition that the energy of electrons usually does not lead to radiation damage. The only important exception to this generalization is insulators. Here, as we already mentioned at the beginning of our review, the electronic conductivity is so small that electrons can remain in nonequilibrium states for long periods of time. We have several quite different phenomena which apparently confirm this fact. First, we may mention the case of a crystalline counter, for example a diamond counter. A particle of high energy, passing through diamond (for example, an alpha particle with an energy of the order of a million volts), will produce, chiefly, excitation of electrons into the conduction band. If the diamond is in an electric field, these electrons will be carriers of a current which can then be amplified, making it possible to use this material for counting incident particles. The electrons are collected in various parts of the crystal, being captured in “traps,” and thus produce permanent disturbances of a type that may be attributed rather to the excitation of electrons than to the displacement of nuclei. Determination of the number of electrons produced by a single incident particle in fact gives valuable confirmation of the general theory of ionization by fast heavy particles.

A similar phenomenon is also observed in certain insulating crystals, such as alkali-halide compounds, where, as is well known, electrons can be captured by definite inhomogeneities of the crystal lattice known as \(F\)-centers. Electrons in such crystals can remain for long periods of time in \(F\)-centers, which leads to darkening of the substance and to other changes in physical properties. Such capture of electrons may be caused both by excitation of electrons into the conduction band during the passage of a heavy particle and by other mechanisms: by excitation of electrons upon absorption of light, gamma rays, or incident electrons. This is the case mentioned in our introduction, when electrons and photons can produce radiation damage. Here these types of radiation produce radiation damage, although their energy, with a certain appreciable efficiency, is transferred only to electrons. Only because these substances are good insulators can the captured electrons remain for significant intervals of time without being neutralized by conduction, as would occur in an extremely short time in so good a conductor as a metal.

To a certain extent a similar exception to the general rule, which states that excitation of electrons does not produce radiation damage, is the chemical action of radiation. The properties of chemical compounds, especially covalent compounds, are similar to those of poor conductors: here an electron may be displaced from one covalent bond to another within the molecule. The probability of its return to the former bond is so small (the molecule is a poor conductor) that irreversible changes occur in the molecule, the covalent bonds change or are broken, as a result of which a chemical reaction takes place. This occurs when the time required for the electron to return to its initial position is large in comparison with the reaction time. In reality, most chemical reactions caused by radiation have this origin and are due to a greater extent to the excitation of electrons than to the appearance of recoil nuclei, although the latter also influence chemical processes. There are sufficient reasons to think that the biological action of radiation may arise in the same way, i.e. as the result of the change of one configuration of electrons into another, with the role of ionization being considerably greater than that of the appearance of recoil nuclei. In biological objects there are very large molecules possessing very poor conductivity, and consequently an extremely long time is required for the transition of a metastable configuration into an equilibrium state. Changes produced in such molecules may persist for a very long time, or even permanently.

Good insulators, in which excitation of electrons can produce irreversible radiation damage, are an exception to the cases usually considered. Most solids are fairly good conductors, and any electronic effect, as we have already seen, may dissipate before it can produce an irreversible change in the positions of the nuclei in the substance. We now approach another side of the problem: in what way the appearance of recoil nuclei can lead to irreversible displacements of atoms from their correct positions in the crystal lattice.

We have seen that by the time the energy of a heavy particle moving through a solid decreases to a certain level (within the range from \(10\,000\ \mathrm{eV}\) for a proton to a value somewhat greater than a million electron-volts for a heavy atom), the greater part of this energy will be dissipated in elastic collisions. The primary particle will transfer a significant fraction of its energy to some number of secondary particles. Each of these secondary particles, in turn, is a heavy particle of low energy moving through the crystal lattice. Each of these particles gives rise to tertiary particles, and so on.

Naturally one asks: when will this process stop? What will become of the particles—primary, secondary, tertiary, and so on? There are two ways of considering these questions, more or less complementary to one another and leading to similar results. First, we may try to trace the history of each particle: primary, secondary, tertiary, etc., and see how much energy each of them receives and how many collisions it produces in the further formation of particles. We may assume that an atom will be knocked out of its position in the lattice if it receives energy greater than a certain minimum. This minimum is probably estimated as being of the order of twenty-five electron-volts. If an atom receives energy less than the accepted minimum, then this energy will be elastic or thermal vibrational energy, and the atom will not leave its equilibrium position and will not pass into a new, less stable position. In this way we can find the total number of displaced atoms. This method was used by Seitz, James, and Brown in the theoretical consideration of this problem.

The second approximation to this problem is more statistical or thermodynamic. The kinetic energy of the nuclei is thermal energy. The process in which a fast atom collides with its neighbors and transfers its energy to them is heat conduction. What will happen if we suddenly introduce a large amount of heat into some localized point of the lattice? We ask how this heat propagates and what the rate is at which the temperature falls. The kinetic energy not only of the primary atoms, but also of the secondary, tertiary, and all those atoms whose energy exceeds twenty-five volts, is so large that it corresponds to an extremely high temperature, of the order of several hundred thousand degrees Celsius. It is then clear that a considerable region of matter around the track of the primary particle will be heated to a very high temperature. Thus, if, for example, an incident particle transfers an energy of 100,000 electron-volts to recoil atoms, then when this energy is uniformly distributed at 25 eV to each atom, we shall have 4,000 such atoms. When the average energy per particle decreases to 1 eV, then, upon exchange of this energy with neighboring atoms, we shall have \(10^5\) particles whose energy will correspond to a temperature exceeding the boiling point even of refractory substances. Therefore, around the track of the primary particle there will be a region with high temperature and vaporized material, which is often called a temperature spike. On the other hand, from such a small volume heat is transferred so rapidly, or the rate of exchange of kinetic energies is so great, that the excitation region will spread very quickly and the temperature of the material within this region will rapidly fall below the boiling point and begin to approach room temperature.

temperature. Here we have a very sharp thermal fluctuation in a small volume of the material, followed by very rapid damping.

We may further ask what the effect will be of this rapid local evaporation and softening. If the process takes place within the material, as it will in the case when the primary recoil atoms arise upon collision with neutrons from a reactor, then the result will depend to some extent on the previous state of the region where the process occurs. If this is a part of a perfect crystal lattice, then it is almost incredible that after melting and subsequent solidification this region will remain a perfect crystal. During melting the atomic order is completely disrupted, and solidification occurs so rapidly that there is no possibility of proper crystallization. The most probable result will then be aggregates of very small crystals or even of an amorphous substance, disrupting the lattice of the previously existing crystal. This disturbance will apparently remain if the surrounding temperature is sufficiently low, so that annealing proceeds very slowly, as will be the case for materials with a high melting point. The situation is different with low-melting materials. If annealing proceeds rapidly at room temperature, then the disturbed region rapidly recrystallizes and essentially disappears. Thus, in the absence of annealing we should expect, in an irradiated material, changes in properties due to trapping: hardening, increased electrical resistance, and decreased thermal conductivity. These effects are not observed if annealing takes place.

Such arguments suggest that, under sufficiently prolonged irradiation, a saturation effect should appear. After all parts of the material have once undergone the process of melting and recrystallization, additional irradiation will produce no further changes. Each newly formed disturbance will occupy the place of one already existing. Maximum hardness, comparable with work hardening, will be attained; the maximum change in electrical conductivity and thermal conductivity will be observed. If we assume that the traps arising from radiation damage do not differ from the traps arising during work hardening, then such a state of saturation should be approximately the same as if the experiment were performed either with a work-hardened material or with a material that had undergone annealing. This argument suggests that irradiation will not, for example, increase the rate of creep, since it leads only to additional hardening. Such a conclusion may prove incorrect when considering creep under real irradiation conditions. Suppose that the material is in a zone of intense irradiation under load. At every moment there is formed

many small local molten regions in which the stress can decrease. The presence of local regions will make the rate of stress relaxation greater than in the absence of irradiation. This stress relaxation is another way of observing an increase in the creep rate. It is unknown, however, how significant this effect will be.

We have spoken of the action of radiation in the volume of the specimen. On the surface of the specimen, however, during bombardment in a cyclotron, or on the surface of a thin specimen (for example, foil), other phenomena will be observed under any irradiation conditions. If one of the regions with a local rise in temperature appears at the surface, then, evidently, there is a probability that some amount of material will evaporate and be lost by the specimen. This process is similar to the sputtering of material under cathode bombardment, in which the amount of sputtered material can be estimated by determining the amount of material brought to the boiling point by the action of the incident particle. This suggests that a large fraction of \(10^5\) atoms will be brought to the boiling point by an incident particle and may evaporate from the surface. This number is probably too large, since some of these atoms will be so deep inside the material that they will freeze before they can evaporate. Nevertheless, if one operates with such figures, one can conclude that, under irradiation, foil must be destroyed very rapidly. This is confirmed by cyclotron experiments showing that targets made of thin foil, placed on a backing of another material, disappear completely after one or two days, and also by certain experiments on the destruction of enriched uranium foils. The effects of which we have spoken in this section are of very great importance in the study of radiation damage, and it is precisely for them that the theory is especially insufficiently developed. Much work should be done on investigating the kinetics of the process of heating, cooling, recrystallization, and annealing of regions of local damage. Most of the theories that have hitherto been used are based on very crude assumptions: attempts are made in them to determine the numbers of secondary and tertiary particles with energy above some adopted limit, for example \(25\) ev, required to displace an atom from a lattice site. This is a very crude approximation from two points of view. First, the theory of collisions of slow particles is quite insufficiently developed. Second, the assumption that the energy threshold indicated above has any significance is not justified by anything. Apparently much closer to the truth is a picture based on a thermodynamic and statistical model, but theoretically it has not yet been developed at all. In reality the picture will be considerably more complex than we have described it.

For example, upon instantaneous heating of a small volume inside a solid, a sharp increase in pressure occurs, leading to the appearance of a shock wave that carries away part of the energy. The amplitudes of atomic motion in the shock wave are so large that they cannot be described by linear laws. In fact, it is precisely the nonlinearity of the motion that corresponds to the possibility of irreversible displacement of atoms. Such a picture will be one of the approximations. A complete consideration of these questions is a difficult task, which may be regarded as the principal unsolved problem in the theory of radiation damage.

III. RADIATION DAMAGE IN DIFFERENT TYPES OF MATERIALS

On the basis of the principles analyzed in the preceding sections, certain assumptions may be made about the expected types of damage in different materials. In most cases there are data from preliminary experiments confirming these assumptions. We shall now give a brief survey of the different types of materials, comparing the assumptions made with the experimental results, and shall consider the paths for further work. In our survey the materials are arranged in order of decreasing metallic properties: metals (including pure metals and alloys), semiconductors, insulators, and covalent molecular substances.

9. Metals

From what has been set forth above, one should expect a similarity between the radiation effect on metals and the effect of cold working, i.e., one should expect an increase in hardness, since irradiation leads to the appearance of pinning points that hinder shear deformation. These pinning points will also scatter electron and thermal waves, so that irradiation leads to an increase in electrical resistance and a decrease in thermal conductivity. The maximum change in properties under the action of radiation should, however, be comparable with the maximum effect of cold working. Thus, saturation should occur. Radiation should act to a lesser degree on a cold-worked specimen than on an annealed one, since the cold-worked specimen already has many pinning points, which are simply replaced by others during irradiation. Saturation under cold working or irradiation appears when, in essence, the entire material undergoes such deformation as it is capable of withstanding. The magnitude of these effects in a given material depends strongly on the rate of the process of annealing at room temperature. If the metal anneals, then essentially no radiation damage is observed. If the annealing rate is very small, then the action of radiation damage

will be comparable with the effect of cold working and will decrease at elevated temperatures.

These assumptions are confirmed by experimental data. The effect of radiation-induced disturbances is not observed in such metals as aluminum, in which annealing takes place at room temperature. At the same time, in copper, whose annealing takes place at a higher temperature, under the action of irradiation a strengthening is observed comparable with the maximum strengthening under cold working. Our knowledge of these phenomena will expand if serious work is carried out, by means of X-ray methods, to determine the types of pinning that arise in the metal both under irradiation and under cold working. Comparison with the relative changes in hardness and electrical resistivity will establish the validity of the assumptions that the same type of pinning always leads to the same physical consequences, irrespective of the manner in which they were formed. This will also make it possible to measure quantitatively the greatest number of pinning points that can be accumulated in a metal. This should be connected with studies of annealing and with determinations of the activation heats for annealing processes. Metals whose annealing occurs at room temperatures can be studied at lowered temperatures.

The behavior of alloys will differ from the behavior of pure metals, since irradiation may influence such processes as the disordering of an ordered structure and precipitation hardening, which occur in alloys. Little work has been done in this direction, showing the nature of the expected results, but it is quite insufficient for a full understanding of the question. Thus, with regard to disordering, it is well known that an alloy is ordered below a certain temperature and disordered above it. When an ordered alloy is irradiated below the transformation temperature, it becomes disordered, which is manifested in an increase in both hardness and electrical resistivity. The maximum hardness and resistivity are similar to the values of these quantities for the disordered alloy. These changes remain for an indefinitely long time while the alloy is below the annealing temperature. It is highly desirable, although this has not yet been done, to determine by X-ray methods the dependence of the degree of order on the irradiation dose and from this to establish a direct relationship between the degree of order and certain physical quantities—electrical resistivity, hardness, etc.

An example of an alloy with precipitation hardening is the Be-Cu system. At high temperature, more Be can be dissolved in Cu than at low temperature. Quenching from a high temperature fixes at room temperature a solid solution with composition,

corresponding to a higher temperature. Heat treatment at a certain increase in temperature leads to the precipitation of excess Be in the form of BeCu. Inclusions of the precipitated phase in the solid solution cause hardening and an increase in resistance. Irradiation of alloys at various stages of heat treatment leads to a further increase in hardness and resistance, the values of which approach limiting saturation, approximately equal to the maximum values attainable by dispersion hardening. From the results obtained so far it is not entirely clear whether this irradiation effect appears due to trapping in the lattice or because of the precipitation of a dispersed phase caused by radiation disturbances. It seems plausible that the latter should occur (at least to some degree), since under irradiation there is heating of regions which, in the presence of a supersaturated state, leads to precipitation of the dispersed phase. On the other hand, cooling of locally heated regions, as we have already indicated, corresponds to very rapid quenching; therefore it is probable that, owing to this quenching, further precipitation will not occur. Further investigation of such phenomena is necessary, including the closely related and very important case of stainless steel. This work can be combined with theoretical studies in order to try to explain the thermal state of the specimen during irradiation.

Irradiation of metals does not lead to any new striking phenomena and does not preclude their use as structural materials in reactors. The relatively small expected changes in properties are permissible during their operation. The action of radiation on metals is also manifested in a number of effects which, although more difficult to investigate theoretically, potentially have important practical significance. Under irradiation the rates of diffusion, corrosion, and creep increase. All this should be of great importance for materials used in the structures of containers holding nuclear fuel and fission products, in coolants, or in reactor communications.

From the foregoing it is clear that one should not expect an increase in the creep rate of a metal after irradiation. But there is a possibility that creep may be greater during intense irradiation, since irradiation can remove a sufficient number of atoms of the substance from the state of equilibrium and thereby allow stresses to relax faster than normal. For the same reason irradiation will naturally favor any process requiring the displacement of atoms. Such processes include diffusion and corrosion. It has not been established either theoretically or experimentally whether these effects will be sufficiently large to be of serious importance. In this case one cannot rely with sufficient confidence on

theory; therefore experiments in this field are very important for determining the further direction of the work. It should be noted that a large number of experiments are planned in this field.

A special case of radiation damage in metals arises in specimens containing fissile material. Here, for several reasons, greater damage may be expected than in solid bodies of this kind that do not contain fissile materials but are also subjected to neutron bombardment. First, the neutron causing nuclear fission releases a large amount of nuclear energy in the specimen, so that the total store of energy potentially capable of producing damage considerably exceeds the energy imparted by neutrons alone. Second, whereas the range of a neutron is rather large and it produces only a portion of the possible damage in any small volume, the range of a fission fragment is so small that the destruction produced by nuclear fission is concentrated in the immediate neighborhood of the disintegrating atom. Third, the fission fragments remain inside the specimen, acting as impurity atoms and, consequently, affecting the physical properties of the material, especially if these impurities are gaseous or other substances insoluble in the material.

Observation apparently confirms the general assumptions put forward by us in connection with radiation damage in substances containing fissile materials, commonly used as nuclear fuel in reactors. Experimental data on this question are very scanty, largely because of the extraordinary experimental difficulties of observing fissile material after irradiation owing to its strong radioactivity. Because of the experimental difficulties of the problem, at the present time research on radiation damage in fissile material will for the most part have a programmatic character and will be devoted to answering the question of whether large damage causes any special forms of nuclear-fuel elements or not. However, after such programmatic work has been carried out on various types of fuel elements, with the use, for experimental studies, of laboratories equipped with proper shielding, it will undoubtedly be possible to obtain a clearer and deeper understanding of the behavior of uranium and its alloys under irradiation.

In connection with the problems of radiation damage in metals and, in particular, in fissile materials, we must recall what was said in one of the preceding sections about the difference between damage in massive materials and in materials with a large surface-to-volume ratio (in thin foils). Let us recall that in the latter one should expect significant evaporation from the surface, leading to the destruction of the foil in a fairly short time.

10. Semiconductors

The most typical semiconductors include the elements Si, Ge, Se, and Te, as well as many chemical compounds, for example Cu₂O, which have similar properties. Among the elements, Si and Ge have been studied most thoroughly because of their extensive use in electronics as rectifiers and, more recently, transistors. We have already mentioned that the theory is splendidly confirmed by the experimentally found dependence of the number of current carriers and their mobility on temperature. These dependences provide especially good material for testing the basic ideas about the nature of radiation damage. However, in studying Si and Ge, at least two completely unexpected and as yet unexplained phenomena have been discovered. This circumstance requires that the work be continued.

Germanium can be prepared with impurities of the donor or acceptor type, i.e., it can have the properties of the \(n\)-type or the \(p\)-type. It has now been established that when germanium of any type is bombarded, additional \(p\)-centers arise. When \(n\)-type germanium is bombarded, the number of negative carriers decreases and the resistance increases. This may be interpreted in the sense that the \(n\)-type centers are neutralized by newly formed \(p\)-type centers. As the irradiation dose increases, the number of \(p\)-centers also increases, and the specimen acquires \(p\)-type conductivity. With a further increase in the irradiation dose, its resistance decreases, and it behaves in all respects like a \(p\)-type specimen. On the other hand, when \(p\)-type germanium is bombarded, it turns out that it simply acquires additional \(p\)-centers. This behavior of germanium is easily explained if one assumes that the hole left after an atom has been knocked out of a lattice site behaves like a \(p\)-type center. Such an assumption is confirmed by independent data. Owing to the properties of \(n\)-type germanium described above, it becomes possible to prepare specimens with a boundary between \(n\)- and \(p\)-parts by irradiating only one half of the specimen. Thus, a partially irradiated \(n\)-type specimen will possess rectifying properties without the need to use a point contact*).

It would seem that all these properties are in good agreement. But, as we have already mentioned, a more careful study of the data on the behavior of Si and Ge reveals two unexplained phenomena. The first phenomenon is connected with the actual number of defects. The study of unirradiated specimens made it possible to determine very accurately the number of \(n\)- and \(p\)-type impurities and their influence on the specific resistance. Hence, from the change in the specific resistance of a specimen, one can determine the number of \(p\)-type centers that arise—

*) See V. S. Vavilov, UFN 44, issue 1 (1952). (Translator’s note.)

…occurring under the action of radiation. Experiments with irradiation of samples both in the cyclotron and in the reactor led to the establishment of a remarkable fact. When a deuteron or neutron passes through a sample, only one \(p\)-type center per particle appears, instead of many centers, as one would expect from the general picture of radiation damage described earlier. Further investigation is necessary to explain such an unusual fact. It is possible that this phenomenon is connected with the fact that recovery or annealing of the defects occurs faster than expected, and that a large part of the defects disappears before measurements are made. However, such an assumption is not consistent with other observations. When germanium is bombarded with electrons, defects are found which disappear at very low temperatures. Defects produced by neutrons and deuterons disappear only upon a considerable increase in temperature. What is remarkable here is that the greater part of the changes produced in the material by the incident particle disappears at room temperature, and therefore these changes would never be observed if a high temperature were required for the disappearance of the residual effect.

Another unexplained phenomenon is found when Ge is compared with Si and other semiconductors. All the previously studied properties of Ge and Si have a considerable similarity. However, under irradiation Ge and Si behave quite differently. If Si of \(p\)- or \(n\)-type is irradiated, the resistance will increase in all cases. The same has been found for other semiconductors. This is already, in itself, a surprising phenomenon. The effect of the increase in the resistance of semiconductors upon irradiation is so significant that very good insulators can be made from them, and this may have practical importance. The effect is so large that it cannot be explained by a decrease in the mobility of the current carriers as a result of the appearance, upon irradiation, of lattice inhomogeneities, but must be attributed to a decrease in the number of the carriers themselves. Apparently, radiation creates traps in the semiconductor lattice which capture carriers—electrons or holes—and thereby reduce the electrical conductivity. Here the difference in the behavior of Ge and Si is especially incomprehensible. Although the behavior of Ge and Si under irradiation has been studied more than that of other solids, the phenomena described above show that further study of these materials is necessary. A number of research groups are actively working in this direction, but even here there remains a broad field of activity for many scientists. For example, X-ray studies of radiation damage and investigation of the absorption bands of soft X-rays will help to learn still more about the band structure and the inhomogeneities of the lattice. Silicon and germanium are such unique substances for the study of this whole range of properties that their further investigation is highly desirable, both from the standpoint of radiation damage and of other properties.

11. Ionic Compounds and Ceramics

In this section we group together insulators, including alkali-halide compounds, typical ionic crystals and metal oxides, carbides, nitrides, and such compounds as have in part the properties of ionic crystals and in part the properties of covalent compounds. Some elements, of which diamond is the typical example, are also insulators. These materials have large energy gaps between the valence band and the conduction band. They usually have no conduction electrons, and therefore their electrical conductivity is extremely low. Their thermal conductivity is effected only by lattice vibrations. They are brittle at low temperatures; on heating they become more plastic. The effect of radiation on alkali-halide compounds has attracted the attention of researchers for many years. The work was carried out chiefly with bombardment by electrons or gamma radiation. As we mentioned earlier, in insulators these types of radiation can produce radiation damage. The observed effects are very complex, and we can mention only their nature. Under irradiation, so-called color centers are formed in the substance, and the crystal becomes colored or becomes opaque. It is believed that this occurs because of the capture of electrons at vacant lattice sites that usually exist in the crystal. There is a great variety of such color centers, with different activation energies and different types of optical absorption. When a specimen is irradiated with light of various wavelengths, these centers undergo further changes and other centers appear. This is a very complex phenomenon and, although, as we have already said, it has been studied for many years, it is still not fully understood. Pringsheim’s work at Argonne showed that neutron irradiation of alkali-halide compounds produces essentially the same damage, although there is some difference in comparison with gamma or electron irradiation. Further study of these phenomena should be continued, since they are important for the foundations of the theory of ionic crystals.

The behavior of alkali-halide compounds under irradiation may give an indication of what should be expected in the case of oxides, carbides, etc., for example BeO, MgO, Be₂C, and other similar compounds of alkaline-earth and other elements that have been studied less fully. These materials are heat-resistant ceramics suitable for use at high temperatures. They will probably be used in high-temperature reactors. These materials have not been studied as fundamentally as alkali-halide compounds, and of them only BeO has been investigated under irradiation. The thermal conductivity of materials under irradiation decreases as a result of the scattering of thermal waves by the inhomogeneities of the lattice that arise.

This decrease is sufficiently large and leads to large thermal stresses under conditions of large temperature gradients, which seriously impairs the usefulness of the given material. A decrease in Young’s modulus and tensile strength is also observed, which may be the result of the presence of atoms between lattice sites, leading to weakening of the lattice. Destruction in ceramics proves to be considerably greater than in most metals. This is possibly connected with the ability of metals to undergo plastic flow, which reduces excessive internal stresses. In ceramics, because of their brittleness, internal stresses cannot be reduced in this way. However, certain reservations must be made concerning conclusions from experiments carried out on comparatively cold specimens as to the dimensions of radiation damage in such materials under high-temperature irradiation conditions. In these materials plastic flow is always possible at high temperatures, so that the mechanical properties may be better under high-temperature irradiation than at low temperatures. A large number of experiments with ceramic materials can be envisaged in order to clarify in depth their behavior under irradiation. These should include X-ray investigations, determinations of absorbed energy, specific electrical resistivity, and the Hall effect as functions of temperature over a wide range before and after annealing following irradiation. Interesting measurements of mechanical strength can be made not only at high temperatures, as we have indicated, but also at high pressures. At high pressures many ceramics, for example $\mathrm{TiO}_2$, become considerably more plastic and in tensile tests sometimes elongate by as much as 40 percent. In this connection, it is of interest to study radiation damage in such materials in the presence of hydrostatic pressure and without it. The required pressures are of the order of 20,000 or 30,000 atmospheres. Optical investigations, such as have been carried out for alkali-halide compounds, should also be performed with oxides, carbides, etc. There are preliminary indications that interesting results may be obtained here. It is desirable to combine optical investigations with studies of the dielectric constant and losses as functions of temperature and frequency. Such experiments will provide additional information on the number of vacant lattice sites arising under the action of radiation. On the other hand, irradiation of ionic crystals makes it possible to obtain specimens with a sufficient number of vacant lattice sites; therefore studies determining diffusion rates in ionic crystals can be considerably accelerated. Useful information on the band structure both of alkali-halide compounds and of ceramic materials may be obtained from investigations of their electronic bands by means of soft X-ray spectra. Interesting data may be provided by studies

changes in electrical conductivity under the action of radiation. Such experiments will in time make it possible to choose among the existing theories of this phenomenon.

In summing up, it should be said that in the field of the study of insulators much work is needed, both from the point of view of solid-state theory and with regard to radiation damage. Here one may expect more interesting and varied results than in metals.

12. Molecular Solid Compounds

We have already seen that, in molecular compounds, radiation action probably must have a nature quite different from that in most solids. Here radiation damage is rather the result of ionization or excitation of electrons produced by the radiation than of the formation of recoil nuclei. Hence, probably, there should be observed a similarity in the action both of gamma rays and electron bombardment, and of bombardment by heavy ions. The field of investigation of radiation damage in chemical substances is one of the richest and most varied, owing to the enormous number of types of chemical substances. As regards practical applications connected with the design of reactors, among molecular compounds plastics of all types and lubricating oils are of greatest importance. In general, in all these materials very serious and striking radiation damage is found, varying greatly from one material to another. The reasons for this are still not very well understood.

Leaving aside for the moment the field of solids, let us point out an important chemical problem connected with the use of water in reactors. Water dissociates under the action of radiation, which makes it much more active than in its ordinary state. Radiation can therefore accelerate chemical reactions and corrosion.

The primary mechanism of radiation damage in molecular compounds, as we have already mentioned, is the formation of ions or excited atoms in the substance. The probability of their formation constitutes part of the fundamental problem of investigating the ionizing action of particles penetrating into matter. Once these ions have been formed, the subsequent process belongs to the field of chemical kinetics, in which successive transformations of ions or excited atoms take place, the formation of free radicals, the subsequent interaction of free radicals, and the formation of new chemical substances. The study of such processes will shed light also on other problems of reaction kinetics. On the other hand, any expansion of knowledge of the kinetics of chemical reactions will help investigations of radiation damage in molecular compounds. Investigations of gaseous reactions are often carried out with the use of mass spectrometers for the purpose of observing various

reaction products. The study of gas reactions provides a very convenient way of approaching the general problem of radiation damage in molecular compounds. In liquids and solids these phenomena are complicated by the short lifetime of the free radical from the moment of its formation until it is stabilized by collision with another atom or molecule. On the basis of modern experimental work on the study of radiation damage in molecular compounds, several generalizations can be made. The first generalization concerns organic compounds. In aromatic compounds less damage is observed than in aliphatic compounds, because the benzene ring is able to absorb a considerable energy of electrons without dissociation.

There is a field in which radiation damage in chemical compounds manifests itself so clearly that it can be recommended for further study. This is the action of radiation on a photographic plate, for example of the type used to detect cosmic rays. It is well known that one can study particle tracks under a microscope, determine the number of ions produced per unit path length, etc. Usually the photographic plate is used simply as an instrument for investigating problems of high-energy particle physics. It is worth, however, reversing the process of investigation and regarding the plate as a unique solid in which visible radiation damage can be obtained. Here one can carry out delicate experiments with damage produced by particles of different masses, charges, and energies, studying, as far as possible, both the behavior of recoil nuclei and ionization.