MEETINGS AND CONFERENCES

AT THE GENERAL MEETINGS

OF THE ACADEMY OF SCIENCES OF THE UKRAINIAN SSR

AND ITS DIVISION OF PHYSICAL, MATHEMATICAL

AND CHEMICAL SCIENCES

In the period from May 17 to 23, general meetings of the Academy of Sciences of the Ukrainian SSR and of all its divisions were held. At these meetings elections were conducted for new full members and corresponding members of the Academy. In physics, the following vacancies were announced for election: full members of the Academy in the specialty “experimental physics”—3; corresponding members: in the specialty “theoretical physics”—1, and in the specialty “metallophysics”—1.

By the general meeting of the Division of Physical, Mathematical and Chemical Sciences and by the general meeting of the Academy, Professor A. K. Walter, Corresponding Member of the Academy of Sciences of the Ukrainian SSR B. G. Lazarev, and Corresponding Member of the Academy of Sciences of the Ukrainian SSR V. I. Danilov were elected full members of the Academy.

Anton Karlovich Walter is well known to all generations of Soviet physicists, and, thanks to his brilliant popular-science books, to wide circles of the Soviet intelligentsia as well. The beginning of his scientific activity dates to 1923. During the first decade, it was devoted to the development of the physics of dielectrics. In his numerous investigations, phenomena of electrical conductivity, high-voltage polarization, and breakdown of crystalline and amorphous dielectrics were studied. In particular, from this cycle one should note a series of works devoted to a new “electrolytic” type of breakdown of dielectrics. In these same works, the possibility of the penetration of electrons from electrodes into the interior of a crystal was shown for the first time.

A. K. Walter belongs to that core group of physicists who created and developed the Physico-Technical Institute of the Academy of Sciences of the Ukrainian SSR. Even at the present time, Anton Karlovich carries out extensive scientific-organizational work, serving as deputy director for scientific affairs of the Physico-Technical Institute of the Academy of Sciences of the Ukrainian SSR. His scientific erudition and personal qualities attract young people to him, and he has numerous pupils who have been awarded scientific degrees and titles.

Vitalii Ivanovich Danilov, in the first period of his scientific activity, was known in physics as a pioneer in the field of research

of the formation of an ordered structure of a liquid, in particular liquid metals and their alloys. These investigations led to the conclusion that the intermolecular forces determining the structure of a crystal also determine the mutual arrangement of molecules in the liquid phase. The logical extension of scientific interests to the circle of phenomena connected with the transition of a substance from the liquid state to the solid characterizes the second period of his activity.

Together with his co-workers, V. I. Danilov carried out systematic investigations of crystallization phenomena, studied the laws governing the formation of crystallization centers in the volume of supercooled liquids and on particles of mechanical impurities, and studied the influence on crystallization of impurities dissolved in a liquid. These works serve as the basis for creating a physical theory of the formation of the structure of a metallic ingot. From research on the crystallization of supercooled organic liquids and low-melting metals, V. I. Danilov went on to questions of the crystallization of refractory metals and, in particular, steel.

As is known, V. I. Danilov’s work in the field of crystallization was recognized in 1950 by the award to him of the Stalin Prize.

Lazarev Boris Georgievich, while still a young physicist, headed a large low-temperature laboratory of the then Physico-Technical Institute of the Academy of Sciences of the Ukrainian SSR. He went his own way in the field of low-temperature physics, created his own school, which achieved outstanding successes, recognized by the award in 1951 of the Stalin Prize to B. G. Lazarev.

In the laboratory headed by B. G. Lazarev, broad comprehensive study is being conducted of the properties of matter at low and ultralow temperatures. Here, for metals, the commonality was established of galvanomagnetic phenomena consisting in the periodic dependence of the magnetic susceptibility and the stepwise character of the change in electrical resistance with a change in the magnetic field, which earlier had been regarded as an exclusive peculiarity of bismuth. The question of the transition to the superconducting state, the kinetics of this transition, and its dependence on various factors, including various kinds of deformations, is being studied with great completeness. By this elegant method B. G. Lazarev succeeded in discovering a change in the volume of a metal during the superconducting transition. These and a number of other fundamental data obtained in B. G. Lazarev’s laboratory provide an experimental basis for the creation of a new theory of metals.

B. G. Lazarev used an original method for an exceptionally effective separation of helium isotopes and obtained, in large quantities, liquid helium highly enriched with the light isotope, which made it possible to carry out investigations of the influence of impurities on the behavior of a “quantum liquid.”

As a corresponding member in the specialty “theoretical physics,” the department elected and the general meeting of the Academy of Sciences confirmed Doctor of Physico-Mathematical Sciences, Deputy Director for Scientific Affairs of the Kiev Institute of Physics of the Academy of Sciences, A. S. Davydov.

Davydov Alexander Sergeevich is a graduate of Moscow University and a pupil of I. E. Tamm. At first his interest was directed toward the field of the theory of elementary particles, to which his Candidate’s dissertation also belongs. Among these investigations one should note the theory of a particle with spin \( \frac{3}{2} \).

During the period of the Patriotic War, A. S. Davydov headed a large factory laboratory, and from 1945 he has worked at the Institute of Physics of the Academy of Sciences of the Ukrainian SSR. Here his scientific interest begins to be attracted by the complex problem of spectroscopy of the solid state, which is in the very initial stage of theoretical study. Proceeding from the exciton, A. S. Davydov, thanks to his ability in every problem to discern the main ...

and, choosing the needed approximation, quickly advances and lays the foundations of a new branch of theoretical physics—the physical optics of molecular crystals—and already in 1949, at the Lebedev Physical Institute, brilliantly defends his doctoral dissertation. Thus, in the person of A. S. Davydov, the Academy of Sciences of the Ukrainian SSR has a major, rapidly growing scientist. He succeeded not only in creating, for the first time, the internal-neutron foundations of the molecular theory of dispersion and pleochroism of crystals, and in explaining remarkable features in the electronic spectra of crystals, but also in predicting many of these features, the correctness of which was only subsequently confirmed by experiment.

In the specialty “metal physics,” Prof. A. A. Smirnov was elected a corresponding member.

Smirnov Adrian Anatolievich, in his research, has covered a wide range of questions relating to the theory of metals and metallic alloys. This includes work on the construction of the electron theory of alloys, work on the study of violations of the regularity of the crystal lattice of alloys and on the construction of a theory of diffusion, work on the theory of resistance of pure metals and alloys, and others. In these works A. A. Smirnov constructed a general theory of electron motion in the crystal lattice of ordered alloys, and, on its basis, studied the question of electrical resistance and galvanomagnetic effects in alloys of the indicated type.

Alongside the general meeting of the Academy and the meetings of the departments, scientific sessions of the departments also took place. At the Department of Physico-Mathematical and Chemical Sciences, the physics section worked. Below are given brief abstracts of the reports.

1. D. I. Blokhintsev, “Elementary Particles and Fields.”
In quantum mechanics, the sharp boundary between particles and the medium, somewhat violated even at the very beginning, has been somewhat further violated. The conception of particles as material points is incompatible with quantum mechanics. However, in quantum mechanics there still remain many analogies with classical mechanics. These analogies come to an end in the transition to high energies, when we are dealing with the multiplication of particles. In the mathematical interpretation this is reflected as an increase in the number of degrees of freedom of the system under consideration. The concept of a field, from the very beginning, presupposes an infinitely large number of degrees of freedom. In this lies its greater generality, but in this also lies the difficulty. A field can be decomposed into normal oscillations, the energies and momenta of which prove to be quantized. Fields can exchange with other fields energy and momentum in finite portions. Thus, a transition takes place from fields to particles. Particles arise as excitations of a field. From this point of view the field is primary and the particles secondary. An analogy to this may be a solid body and the phonons arising in it.

The question of excitations of a field without particles remains unclear.

Characteristic of the quantum theory of the field is the presence of “zero” oscillations of the field, which are experimentally detected in the splitting of the electronic level of the hydrogen atom. Analogously, polarization oscillations (the well-known “background”) of the positron-electron field are obtained.

Together with the phenomenon of vacuum polarization, all this leads to a remarkable analogy with a solid body. The difference between the field and a dielectric is that the number of degrees of freedom remains infinite. This is the greatest modern theory.

A. I. Akhiezer expressed the view that everything said by D. I. Blokhintsev relates to two fields: the electron and photon fields. In the latter

In this case we artificially break the connection between the two fields, for which the only basis is the relation:

\[ \frac{e^{2}}{\hbar c}=\frac{1}{137}. \]

In meson fields, however, we do not have a small constant. Therefore Akhiezer believes that in reality both fields and particles will remain in the theory. But with regard to the photon field, perhaps it is better to speak not of the primacy and secondary nature, but of the interrelation between the quantum and the field.

I. M. Lifshitz also expressed his negative attitude toward the idea of the “primacy” of the field. Since, with respect to noninteracting particles, the conclusions of statistics and thermodynamics would be incorrect, one must always speak of interacting particles, and in the field conception the very presence of interaction already violates the concept of a particle. Therefore the very posing of the question of the primacy of one or the other is illegitimate.

D. I. Blokhintsev, replying to the remarks on the question of “primacy,” noted that the question is: what is the most general? In such a general formulation, the field conception is the more general one, since from the very beginning we are dealing with an infinitely large number of degrees of freedom and with the creation of particles at the expense of excitations of the field.

Despite the difficulties, with respect to mesons as well the field conception can be preserved

\[ \left(\Gamma \ll \frac{mc^{2}}{\hbar}\right). \]

In the case of strong interaction we do not yet know how one should proceed.

1. S. I. Pekar, “On the Foundations of the Theory of Electrical, Photoelectric, and Optical Phenomena in Ionic Crystals.” The theory of semiconductors is divided into: 1) the phenomenological, or macrotheory (the theory of rectification, the dependence of the concentration of current carriers on temperature, the consideration of recombination, etc.), and 2) the microtheory. The phenomenological theory is insensitive to the model of the object, since the number of parameters with the aid of which the conclusions of the theory can be brought into agreement with experimental data is very large. The calculation of the coefficients of the macrotheory must be the subject of the microtheory.

The microtheory, in contrast to the macrotheory, is in an unsatisfactory state. This includes band theory, which is not capable of explaining many phenomena. Another variant of the microtheory—the adiabatic treatment—is possible and justified only for a limited discrete spectrum of particle states.

Since 1943 the author has been concerned with the consideration of electrons in an ionic crystal, which led to polaron self-consistent states. The motion of a polaron is considered as the propagation of polarization waves, leading to translation of the polarization pit. One may speak of a quasiparticle and of its effective mass, which was calculated by the author, jointly with Landau, in 1948. It turns out that polarons are energetically more favorable than band electrons. Band states cannot even be regarded as metastable states.

N. N. Bogolyubov raised an objection against the introduction of approximate operators. However, the introduction of exact operators and the calculations of Bogolyubov himself led to the same results.

The mobility of the polaron proved to be of the same order as the mobility of the hole. In the case of concentrated excess polarons, they will annihilate in the conductivity. On the basis of the polaron theory a theory of centers was developed and the effective mass \(\mu\)—the only parameter—was determined. The theory makes it possible to calculate the mobility of the polaron and its dependence on temperature, to calculate the recombination coefficients, the “shifts” of the centers and their temperature dependence.

1. A. I. Akhiezer, “Kinetics of the magnetization of a Fermi gas.” An effective method for obtaining ultralow temperatures is the magnetic method. In this case, between the final temperature \(T_f\) and the initial \(T_i\) there is the relation

\[ T_f = T_i \frac{W}{\mu H}. \]

The problem of using nuclear paramagnetism acquires tempting prospects both for obtaining ultralow temperatures and for other, more theoretical, problems. When nuclear magnetism is used,

\[ W \sim \frac{\mu^3}{a^3} \]

and \(T_f \sim \mu\). In this connection the question arises of the time for the establishment of equilibrium, which is determined by the energy of interaction between the spins and the lattice.

A mixture of \(\mathrm{He}^3\) and \(\mathrm{He}^4\), which may be regarded as a weak solution of \(\mathrm{He}^3\) in \(\mathrm{He}^4\), is directly relevant to the question raised here. This, in its purest form, is the case of a Fermi gas. Consideration of the kinetics of magnetization of a degenerate Fermi–Dirac gas shows that the relaxation time is proportional to the square of the temperature and does not depend on the density of particles. Application of the results obtained to a weak solution of \(\mathrm{He}^3\) in \(\mathrm{He}^4\) shows that at \(T = 1^\circ\mathrm{K}\) the magnetization time of \(\mathrm{He}^3\) is 18 hours. At \(T = 2^\circ\mathrm{K}\) the magnetization time is already \(\simeq 5\) hours. By introducing a diamagnetic impurity into the paramagnetic gas one can regulate the rate of change of state in a magnetic field. If an impurity with a concentration relative to \(\mathrm{He}^3\) of \(\simeq 10^{-6}\) were introduced into our solution, the magnetization time would be reduced from 18 hours to several seconds. The susceptibility would not change in this case. Diamagnetic walls may play the role of the impurity.

For the purpose of clarifying the question of the energy spectrum, it is important to study paramagnetism at low temperatures.

I. M. Lifshits noted that what is involved here may be a method for obtaining negative temperatures, since precisely in partial equilibrium, for magnetic equilibrium, one may, following Landau, speak of a negative temperature. (Negative temperatures follow from consideration of a system of particles with energy levels bounded from above.)

1. I. M. Lifshits, “Heat capacity of thin films and crystals of small dimensions.” In the question of the heat capacity of small crystals at low temperatures, previous authors made errors. Therefore the need arose to solve the problem anew. The phonon and electron parts of the heat capacity for films and for three-dimensional formations are considered. The specific character of crystals of small dimensions in calculating the heat capacity appears in the necessity of passing to quantization of the energy. In calculating the phonon part of the heat capacity this results from the convergence of the walls; in calculating the electronic component, from the splitting of levels. The transition to quantization is determined jointly by the dimensions of the crystal and by the temperature. For linear dimensions of the crystal \(\simeq 10^{-5}\ \mathrm{cm}\), the quantization temperature \(T_{\mathrm{qv}} \simeq 1^\circ\mathrm{K}\). On passing to quantization for the phonon part of the heat capacity, instead of the Debye cubic law one obtains a dependence of the heat capacity on temperature of exponential form for crystallites and quadratic for thin films. The electronic component of the heat capacity turns out to be proportional to the temperature to the first power. The author determined the size–temperature regions for crystallites and for films in which one or another law of heat capacity is valid.

2. K. B. Tolpygo, “On the determination of the effective mass of current carriers in semiconductors from absorption of infrared rays.” The proposed method of determination…

tive mass is based on the idea that in rapidly alternating fields (optical oscillations) the inertia of the current carriers must manifest itself, and therefore the value of the effective mass must influence the optical constants of the semiconductor. The paper considers the “classical” absorption of light by free charges, which make forced oscillations under the action of the electric field of the light wave and dissipate the energy acquired from the light through collisions with the lattice. In this case the calculation is carried out under the assumption that both the kinetic energy of the carrier and the time between two successive inelastic collisions are arbitrary functions of the impulse. From the calculation there follows the possibility of determining the effective mass from data on the conductivity, Hall constant, and absorption coefficient of infrared rays of a known frequency.

As an example, the effective mass of a hole in silicon is calculated, since only for this case are all the necessary data available. The results turned out to be different from those obtained by other methods \((M = 0.3\,m_e)\). The causes of this discrepancy and the conditions of applicability of the method set forth are discussed.

1. A. F. Prikhot’ko and V. L. Broude, “Absorption spectra of benzene and hexamethylbenzene single crystals in polarized light.” The authors observed the formation of crystals in a very narrow quartz cuvette (about one micron wide), placed in a special thermostat with quartz windows. The use of a quartz micro-objective made it possible to observe on a screen, in transmitted light, the process of crystal formation. Slow cooling of benzene leads to the formation of small crystallites of various interference colors, caused by different crystallographic orientation with respect to the light beam. By varying the temperature near the melting point, it is possible to achieve a considerable enlargement of flat crystals with one of their faces strongly developed. This made it possible to select certain crystals for observation and to record their absorption spectra, which was done in polarized light at low temperatures for the three components of the spectrum of the benzene crystal associated with oscillations of the light vector parallel to the three axes of the crystal. With the aid of these spectra the question of the symmetry of the forbidden transition in benzene responsible for absorption in the region of \(2800\,\text{Å}\) is unambiguously decided. In agreement with the theory of A. S. Davydov, this sharply polarized transition (at the level of symmetry \(B_{2u}\)) in a benzene crystal has components only along the \(a\)- and \(c\)-directions in the crystal. For the \(b\)-direction the transition is forbidden, and series associated with the crystalline state of the substance are not observed. Thus, simultaneously with confirmation of Davydov’s theory, Winston’s calculations, which predict a different result, are refuted.

From the intensities of the absorption spectra it proves possible to judge the crystallographic orientations of the crystals, which, in principle, opens a prospect for optical structural analysis of crystals.

The same technique made it possible to observe directly phase transitions in hexamethylbenzene crystals at low temperatures.

1. B. I. Esel’son, B. G. Lazarev, and N. E. Alekseevskii, “Elasticity of vapor above solutions of helium isotopes.” Measurements of the vapor pressure above solutions of \(\mathrm{He}^3\) in \(\mathrm{He}^4\) were prompted by the circumstance that in some papers a deviation had been found from the well-known Raoult law, which for weak solutions establishes a proportional dependence between the lowering of the vapor pressure

solution, in comparison with the vapor pressure of the pure solvent, and the concentration of the solution. The authors of this paper discover the admission of errors in the experiments on the basis of which the above assertion was made. In the studies of the English and American authors these errors consisted in the fact that, in effect, in the measurements one could not use quantities of liquid smaller than \(10\ \mathrm{cm}^3\), whereas the deviations from Raoult’s law are connected with data obtained precisely with small quantities of a helium solution. In the other case, the Dutch authors made experimental errors in determining the vapor pressure because they failed to take into account the effect of flow along the He II film.

The authors of the paper carefully carried out measurements of the vapor pressure above a liquid mixture of helium isotopes for concentrations of \(\mathrm{He}^3\) from 0.1 to 2%. From the obtained values of the pressure, the concentrations of the solutions were calculated under the assumption of the validity of Raoult’s law. The results coincided with the values of the true concentration. Hence the conclusion is drawn that solutions of \(\mathrm{He}^3\) in \(\mathrm{He}^4\) behave nearly ideally within the indicated concentration limits.

In connection with A. P. Komar’s paper, a question was asked why the measurements of all the authors give values for the elasticity of helium vapor below the \(\lambda\)-point that are larger than this would be for He I (by extrapolation).

I. M. Lifshits, on the basis of a simple and convincing thermodynamic consideration, shows that in fact it should be the other way round, and the result obtained in this respect in the experiments is incomprehensible.

1. B. I. Verkhin, B. G. Lazarev, N. S. Rudenko, “Magnetic Properties of Metals at Low Temperatures.” In comparison with the paper of the same title at the previous session (see UFN 41, 556 (1950)), the present paper is characterized not so much by an expansion of the list of substances investigated as by a refinement and expansion of various data, by the collection of a large amount of factual material of a quantitative character. This material was obtained from thorough experiments carried out with the purest possible single crystals of bismuth, antimony, zinc, cadmium, beryllium, magnesium, tin, and mercury in the temperature region from room temperature down to \(1.5^\circ\mathrm{K}\) and in magnetic fields from 1500 to 15,000 oersteds. The effects of periodic variation of magnetic susceptibility in the low-temperature region as a function of the strength of the external magnetic field and as a function of the orientation of single crystals with respect to the field vector were investigated especially carefully and in detail. It is shown that the abundant quantitative experimental material obtained by the authors does not find a satisfactory explanation within the framework of existing theories.

2. L. S. Palatnik, “The Principle of Crystallogeometrical Correspondence in Epitaxy.” All phenomena of coherent bonding in crystals approximately correspond to such coordinated affine transformations of conjugate crystal lattices, of the same or different types, in which equalization of the conjugate generalized periods \(\bar A\) of the lattice is achieved.

Affine transformations may consist of uniform compression and stretching, as well as transformations of symmetry or shift, or of combinations thereof, when the difference in the unconjugated (undistorted) shortest periods of identity \((r)\) does not exceed definite limits of their initial ratios determined by the elastic properties of the mother and daughter lattices, i.e., when approximate relations of the type are satisfied

\[ \frac{|A_1|}{|A_3|}=\frac{r_1}{r_2}\ldots \]

In this case, a quasi-equilibrium state arises in the coherently conjugated system, which must correspond to a relative minimum of energy. The disruption of a coherent bond also corresponds to the requirement that the system’s energy minimum arise after the accumulation of its elastic energy exceeding the difference in surface energy at the boundaries of incoherent and coherent bonding. This determines the critical dimensions of the daughter lattice.

1. A. Z. Golik, “Structure and Viscosity of Liquid Metals and Metal Alloys.” The author’s research is conducted from the standpoint of establishing the relationship between the viscosity of liquid metals and their molecular structure. The author’s previous work was carried out with organic liquids, which are convenient objects of study. This latter circumstance made it possible to establish certain regularities and to obtain results of practical importance with respect to lubricating fluids. The principal such regularity is the dependence of the coefficient of viscosity on temperature, expressed by the formula

\[ \eta = Ae^{-\frac{B}{kT}}, \]

where, for different liquids, \(B\) proves to be a function of the liquid’s critical temperature. The critical temperature (the point of transition between the liquid and gaseous phases) is, according to the author, a significant characteristic of the intermolecular bonds in a liquid. For liquids of the same type (with the same molecular structure), as the critical temperature increases, the curves \(\eta(T)\) are regularly displaced upward. Additivity of properties is observed upon mixing: the mixing of two liquids with different critical temperatures yields a liquid whose \(\eta(T)\) characteristic lies in the interval between the characteristics of the components being mixed. This circumstance leads to the possibility of obtaining isoviscous liquids of different composition.

Turning to liquid metals, the author began his investigations with mercury, as well as with cadmium and zinc and their metallic solutions with mercury. Here, too, he obtained temperature dependences of the coefficient of viscosity analogous to that written above, and determined the value of the numerator in the exponential, which has the meaning of an activation energy.

P. Borzyak