Chronicle

Session of the Department of Physical, Mathematical and Chemical Sciences of the Academy of Sciences of the Ukrainian SSR on Problems of Physics

From February 2 to 5 of this year, a session of the Department of Physical, Mathematical and Chemical Sciences of the Academy of Sciences of the Ukrainian SSR was held at the Kiev Institute of Physics of the Academy of Sciences of the Ukrainian SSR. The session discussed some of the work carried out in the physical institutions of the Academy of Sciences of the Ukrainian SSR: the Kharkov Physico-Technical Institute (UPTI), the Kiev Institute of Physics (IFAN), and the Laboratory of Metallophysics (LMF).

A group of reports was devoted to the work of Prof. B. G. Lazarev’s laboratory (UPTI) on superconductivity.

L. S. Kan, B. G. Lazarev, and A. I. Sudovtsov, in their “Studies of Superconductivity of Indium and Tin under Hydrostatic All-Round Compression at Pressures of \(1370\ \text{kg}/\text{cm}^2\) and \(1730\ \text{kg}/\text{cm}^2\),” improved their methodology for obtaining high pressures, based on freezing water in a closed volume. Applying a method of measuring pressure with the aid of superconducting manometers, they demonstrated a high uniformity of the pressures obtained by their method.

They continued their work on measuring the displacement of the critical temperature and critical magnetic fields as a function of pressure for polycrystalline and single-crystal tin and polycrystalline indium. In all cases the displacement proved to be proportional to the pressure. In tin the effect is greater than in indium. The displacement of the critical magnetic field decreases as the temperature is lowered, both under ordinary conditions characteristic of transition curves and under pressure; it is different for single-crystal and polycrystalline specimens.

For the first time the authors succeeded in experimentally detecting, with the aid of a specially developed method, a change in volume during the superconducting transition in a magnetic field. However, these observations do not yet possess the accuracy of quantitative measurements.

Of great interest were the “Studies of Superconductivity at High Frequencies” by A. A. Galkin and B. G. Lazarev, which lead to the kinetics of the formation of the superconducting state. In these experiments the idea was used of destroying the superconducting state by a magnetic field of current. If the amplitude of the sinusoidal alternating current passed through the superconductor exceeds the critical value, then the oscillogram of the change in voltage drop across the specimen under investigation is correspondingly distorted, since during the superconducting transition the voltage drop across the specimen changes abruptly from a definite value to zero, or vice versa. It is evident that the temporal width of the jump on the voltage oscillogram corresponds to the time interval of the superconducting transition in a magnetic field.

Transferring this idea into an elegant technique of a transformer with a core made of a superconductor, the authors directly measured both the upper limit

duration of the transition of the specimen from the normal state to the superconducting one (\(\tau \ll 10^{-6}\) sec), and the minimum velocity of displacement of the boundary between the normal and superconducting phases (\(v > 10^3\) cm/sec).

Improvement of the apparatus used will undoubtedly enable the authors to refine their results considerably.

In the next paper, by B. G. Lazarev and A. A. Galkin: “Some Details of the Superconducting Transition,” the temperature dependence of the resistance of tin specimens and tantalum in the region of the transition from the normal state to the superconducting one was investigated. The experimental difficulties consist in the need to maintain the constancy of the temperature with great accuracy, since the entire temperature interval of the transition amounts to one or two thousandths of a degree.

The course of the resistance with temperature in the transition region showed a very complex “structure.” The most interesting feature in this dependence is that, after the resistance reaches zero, with a further lowering of the temperature it again returns discontinuously to its normal value and preserves it over a certain interval of \(< 5 \cdot 10^{-4}\) degree. Then there is a drop to zero, followed by regimes of oscillations with small, ever-diminishing amplitudes. This region of the “tail” is broader the more the specimen is deformed. The picture becomes the more complicated the greater the current passing through the specimen with which the measurements are made.

Measurements in a magnetic field gave a different picture, and one substantially different for cases of transverse and longitudinal fields.

The next group of reports dealt with questions of phase transformations and certain questions of metal physics.

Full Member of the Academy of Sciences of the Ukrainian SSR G. V. Kurdyumov (LMP) gave a report summarizing many years of work by him and his collaborators in the field of martensitic transformations in alloys.

Studying transformations in alloys during hardening and tempering, the author and his collaborators discovered a previously unknown type of so-called diffusionless phase transformations, which proved to be one of the principal types of phase transformations in the solid state. These transformations were called martensitic, since they were first studied using the example of martensite formation.

Martensitic transformations are characterized by reversibility and by the presence of considerable hysteresis. It was established that the crystal lattice of martensite is oriented in a quite definite way with respect to the initial one. The amount of substance undergoing the martensitic transformation is determined, in the main, by temperature, and not by the time of holding or by the rate of heating (cooling). This is evidence of the process of transformation taking place at high speed and, consequently, diffusionlessly. Moreover, it was shown that in these transformations there is no exchange of places between atoms. An ordered solution remains ordered after the martensitic transformation, with the same arrangement of neighboring atoms. Therefore the mechanism of martensitic transformation must consist in a regular rearrangement of the lattice, in which neighboring atoms are displaced relative to one another by distances amounting to fractions of interatomic distances. The possibility of realizing the observed rearrangements by means of such a mechanism was demonstrated by the speaker on models.

Only from this point of view can one account for the phenomenon of structural reversibility discovered in the author’s laboratory. Thus, for example, in experiments with a single crystal of a solid solution it was shown that after transformation on cooling it consists of a large number of crystals of the martensitic phase, regularly oriented in several positions in accordance with the symmetry of the initial lattice and the character of the orientation. As a result of the reverse transformation, one, the original, orientation of the initial single crystal arises.

In the kinetics of martensitic transformations there remains one characteristic feature that has not been explained with complete conclusiveness. As a result of the indicated mechanism, the process of growth of nuclei of the new phase proceeds very rapidly, but for some reason breaks off, and the increase in the amount of substance in the new phase occurs not through the growth of nuclei, but through an increase in their number. The author sees the reason for the limitation of the growth of crystals of the new phase in the arising stresses, which break the connection between the lattices of the old and new phases.

Corresponding Member of the Academy of Sciences of the Ukrainian SSR V. I. Danilov (LPhI), in his report “On the Nucleation of Crystallization Centers in Supercooled Liquids,” summarized the results of his investigations in this field.

Here we encounter two main problems: the phenomenon of spontaneous crystallization and the influence on crystallization of insoluble impurities. Separating the two effects is a difficult experimental task. However, the author, together with collaborators, succeeded, by working with pure organic substances and metals and after their careful additional purification, in obtaining samples satisfying the criteria for the spontaneous character of the formation in them of crystallization centers, and in studying the kinetics of this formation. On the basis of numerous investigations the author divides all substances, according to the character of the dependence of the rate of nucleation in them of crystallization centers on supercooling, into three groups, each of which is named after the substance studied in greatest detail. 1) In substances of the salol group, spontaneous crystallization is absent at all temperatures. 2) The orthochloronitrobenzene group is characterized by the presence of a sharp boundary of metastability. Substances of this group, including metals, cannot be brought into the glassy state. 3) Substances of the piperine group make it possible to obtain a curve of the dependence of the rate of nucleation of crystallization centers on supercooling over a wide range of supercoolings, and for this reason are convenient objects of investigation.

Comparison of the experimental regularities obtained with the conclusions of the fluctuation theory makes it possible to evaluate the surface tension between a crystalline nucleus and the liquid, as well as the activation energy corresponding to the transition of a molecule from the liquid into the nucleus.

The role of isomorphous impurities has been well studied experimentally and is satisfactorily explained by the fluctuation theory of crystallization. The author paid much attention to the effect of activated impurities, the study of which led to the conclusion that activation of impurities occurs only in the case when the impurities are in contact with the crystalline phase of the substance under investigation. The rate of activation depends on temperature and, when the latter is strongly lowered, decreases to zero. The author connects the mechanism of activation with the establishment of molecular contact between the particles of the impurity and the crystals of the crystallizing substance. Deactivation of impurities, which increases with the rise of temperature above the melting point of the liquid, is connected with the destruction of the boundary layer that arose on the surface of the particles during activation.

In his report “On the Kinetics of Two-Phase (Eutectic) Crystallization,” Prof. V. Ya. Pines (PTIAN) presented a theory of the formation, in solidifying eutectics, of layered structures consisting of alternating lamellar formations of the components entering into the alloy.

Another report by V. Ya. Pines concerned the methodology of obtaining and local X-ray structural analysis of alloys of variable concentration. The task of applying X-ray diffraction investigation requires the production of condensed films of sufficient thickness (not less than several microns). To obtain thick films, the author proposes, instead of the complicated method of feeding a spherical drop according to Vekshinsky, to use conical evaporators, which make it possible at once

high loads. Such an evaporator is a cone of aluminum oxide, lowered with its apex into a conical tungsten spiral heated by current. The author gives formulas for calculating the distribution of the condensate along the condenser with allowance for the change in the level of the evaporated metal in the evaporator.

During condensation of metals on a cold surface, the film, upon reaching a certain critical thickness, is rapidly destroyed as a result of suddenly occurring recrystallization. Therefore the author recommends using hot condensers. As such condensers he most conveniently uses thin sheets of mica, heated to several hundred degrees. To obtain specimens, the required portion of the film is cut out together with the mica substrate and wound onto a glass thread 0.3–0.5 mm in diameter. Exposures in photographing with sharply focusing tubes last 15–20 min.

The most difficult task, left unresolved in this work, is the experimental control of the local concentration of the alloy.

At the session, considerations were expressed that the principal shortcoming of the method of alloys of variable composition in roentgenography is the circumstance that, in problems of studying equilibrium states, one has to use specimens with compositions that are not in equilibrium. This limits the method to exploratory investigations and, for precise measurements, requires supplementing it by the method of individual specimens of constant composition. It is true that the study of films of variable composition with nonequilibrium states may be of independent interest.

The laboratory of Prof. S. D. Gerdryken (LIP) has been much engaged in the study of diffusion phenomena in metals. In the works presented, the task was set of clarifying the principal factors characterizing the diffusion process in two-component alloys. These determining factors are the energy and entropy of activation.

In the work of S. D. Gerdryken and I. Ya. Dekhtyar, “Influence of valency and bond strength on the rate of diffusion in silver and copper alloys,” the authors turn to the study of ternary alloys. In this case a small, impurity-like content of the third component is introduced into previously studied two-component alloys in order to investigate the influence on the diffusion process of this third element.

The diffusion of Cd (12–17%) in Ag was investigated, when Zn, Al, Sn, and Sb were introduced into the alloy as an impurity (about 3% atomic), and the diffusion of Zn (about 7%) in α-brass in the presence of impurities (about 2% atomic) Mn, Ni, Au, Sn, Sb. Both the setup of the experiments and the processing of the interesting experimental material obtained were carried out from the point of view of clarifying the influence of the valency of the impurity element on the diffusion process. The difference in activation energies for the diffusing element in the pure alloy and in the alloy with impurities proved to be a linear function of the valency of the third element. A similar linear dependence is also obtained for the change in entropy.

While paying due tribute to the experimental results, the speakers polemicized with the authors on the question of their interpretation, seeing a certain arbitrariness in the attribution of valencies which, in their opinion, are as yet indeterminate parameters for the given processes.

Two reports from the laboratory of Prof. R. I. Garber (FTIAN), known for works on the study of elastic twinning phenomena, were connected with attempts to detect and study an intermediate interlayer between the original crystal and the twin.

In the report “Investigation of secondary cleavage,” R. I. Garber reported on new experiments carried out with calcite crystals. It turned out that secondary cleavage (cleavage along the twinning plane) is found only in some cases. Only with great difficulty

it is possible to split the crystal along this plane, especially after repeated operations of formation and destruction of the elastic twin. This leads the author to the conclusion that the hardening observed during twinning is connected with the hardening of the crystal at fracture along the faces of secondary cleavage.

The interferometric study of the split surface showed the presence of a general curvature of the surface with a deflection arrow of the order of tenths of a micron, in the absence of terraces and steps characteristic of a fracture surface along a face of ordinary cleavage. These observations give the author grounds for concluding that between the twinning interlayer and the original crystal an amorphous transition region is formed, of thickness not exceeding several tenths of a micron.

Certain doubts of the opponents as to the sufficient substantiation of the author’s conclusions were based on the fact that the presence of a general curvature of the surface is not excluded, because of the nonideality of the crystal, also on an ordinary face of it. If the optical method did not reveal the crystalline microstructure of the fracture surface, this still does not mean that it will be absent when revealed by a more delicate technique, say, electron microscopy.

In the work of R. I. Garber and G. B. Rais, “A Crystal-Optical Study of a Twinned Calcite Crystal,” theoretical calculations were carried out of the coefficients of reflection of light at the interface of separation with a twinned uniaxial crystal for various states of polarization of the incident light. The results of the calculations were used for comparison with the results of measurements carried out in the range of angles from 64° to 90°. The agreement obtained between the experimental and theoretical data should testify to the absence of an intermediate layer between the twin and the original crystal. However, owing to the considerable error of the measurements, amounting to 5%, the question cannot be considered finally settled.

At the Institute of Physics of the Academy of Sciences a series of works was carried out on electronic phenomena in nonmetallic solids.

In the report of Full Member of the Academy of Sciences of the Ukrainian SSR V. E. Lashkarev, “Photoelectromotive Forces in Semiconductors,” the results of work jointly carried out with K. M. Kosonogov were presented—experimental investigations in this field, completed by the speaker with the creation of a theory that satisfactorily explains from a single point of view a large group of diverse phenomena.

The authors showed that on ordinary copper oxide there may be obtained both a barrier photoeffect (a “minus” effect) and a crystal photoeffect of the opposite sign (a “plus” effect). It has been shown experimentally and theoretically that the sign of the photoeffect is wholly determined by the sign of the contact field at the illuminated electrode. The blocking layer in hole semiconductors gives a “minus” effect, the anti-blocking layer a “plus” effect. The latter, in contrast to the barrier effect, is very sensitive to the volume properties of the semiconductor (the concentration of capture levels for photoelectrons).

Spectral investigations of both signs of effects led to the discovery of an increased sensitivity of “plus” elements in the ultraviolet, which finds a natural explanation within the framework of the proposed theory of the origin of photo-emf. The latter, owing to the extremely short residence time of photoelectrons in states with increased energy, reduces the problem to the study of the diffusion of free charges in an electric field.

It was shown that the photoconductivity of copper-oxide specimens giving a “plus” effect can be divided into parts: one depending on the electric field and one not depending on it. The relative weight of the second increases with increasing wavelength of the light used.

It has been theoretically shown that the part of the photoconductivity not controlled by the field is connected with the photoeffect directly at local levels.

The controlled part, however, is associated with the transition of electrons into the mobile state. The concentration of excess holes may be much greater than the concentration of photoelectrons, since the holes must compensate the volume charge of electrons not only in the free band, but also of those that have settled out of it onto local trapping levels. Therefore the conditional quantum yield may be greater than unity, which indeed was also shown by measurements of saturation currents in the photoconductivity of “plus elements.”

It proved possible to determine a number of parameters of the theory, in particular the diffusion-displacement length of the electrons, which turned out to be equal to 30 microns, and the lifetime of the electron in the free state—\(0.5 \cdot 10^{-5}\) sec.

Prof. S. I. Pekar, further developing the theory of the polaron that he is elaborating, presented a report, “The Polaron Theory of Electrical Conductivity.”

A heteropolar crystal, dielectrically polarized by the field of an electron of conductivity, represents for this electron a potential well in which there exist discrete quantum energy levels. Being on the very lowest of these levels, the electron stationarily maintains the necessary polarization of the crystal. The latter, in turn, by presenting a potential well for the electron, maintains the electron in a localized state. Such a self-consistent state was called a polaron by Pekar.

The transition of the electron from the “band” state to the polaron state is accompanied by a monotonic decrease of the energy of the system by several tenths of an electron-volt. The band state is neither a minimum nor even a stationary point of the energy of the system and is therefore unstable (it passes into the polaron state in a time of \(10^{-13}\) sec.).

A polaron in an external electric field moves like a negative charge with an effective mass equal to 100–1000 electron masses, and is a current carrier. In one and the same crystal the concentration of polarons is \(10^6\)–\(10^9\) times greater than the concentration of band electrons. According to calculation, the mobility of the polaron is equal to \(3\)–\(300\ \mathrm{cm}^2/\mathrm{volt}\cdot\mathrm{sec}\), which in order of magnitude coincides precisely with the observed mobilities of current carriers in various crystals. Since the concentration of polarons overwhelmingly exceeds the concentration of band electrons, and the calculated mobility of the polaron is of the same order as the observed mobility of the dominant current carrier, the latter should be recognized as a polaron (and not as a band electron, as is assumed by the modern theory of conductivity).

With the report “Electron-Oscillatory Spectrum of Naphthalene,” delivered by Dr. of Phys.-Math. Sciences A. F. Prikhotko, the author continued her work on the study of absorption spectra of molecular crystals at low temperatures. The idea of these investigations consisted in obtaining a picture of the excited energy states of “frozen” molecules. The methodology was based on the assumption that a molecular crystal, with comparatively weak interactions between molecules, simply repeats, on a shifted energy scale, the spectrum of states of free molecules. However, experimental justifications for such an assumption were lacking.

On the other hand, on the basis of the theory—recently developed at the Institute of Physics of the Academy of Sciences of the Ukrainian SSR by A. S. Davydov—of the absorption spectra of molecular crystals, as applied to monoclinic crystals of the naphthalene and anthracene type, the energy term of a molecule in a crystal may split into terms causing the appearance of new absorption lines characteristically related to the state of polarization of the light.

A. F. Prikhotko measured the absorption spectrum of naphthalene vapor for comparison with the previously measured absorption spectrum of the crystal.

naphthalene at low temperature. From a carefully performed comparative analysis of the spectra, the author draws a number of interesting conclusions, of which the following are particularly effective. In the crystal, the electronic levels of a free molecule are in fact preserved, with some deformation of them. However, new electronic states also appear in the crystal, and the lines in the spectrum corresponding to transitions to these states prove to be sharply polarized. The fluorescence of the crystal is, in its main part, connected precisely with one of these additional levels appearing in the crystal.

These important results introduce a new aspect into the study of the absorption spectra of crystals.

Finally, in the theoretical work of Prof. I. M. Lifshits and L. N. Rozenzweig (KhPTI, Academy of Sciences), “Certain Methods in the Mechanics of Crystal Lattices and Absorbing Half-Spaces,” the problem is posed of studying the influence on the spectrum of lattice vibrations of the free surface of a crystal. The influence of the free surface is treated as a perturbation in the unperturbed problem of the vibrations of an unbounded crystal lattice, and the problem is solved by the methods of the theory of regular perturbations proposed by I. M. Lifshits.

The introduced perturbation leads to the appearance, in the spectrum of vibrations, of discrete frequencies corresponding to surface waves that decay into the depth of the crystal. The frequencies separated from the acoustic branches correspond, in the limiting case of long waves, to ordinary Rayleigh waves. However, there also exist “optical” surface waves, which have no analogue in the theory of elasticity. Equations have been obtained giving the exact law of dispersion and the form of the surface waves. A general investigation of them is possible in certain limiting cases.

P. G. Borzyak.