# Frenkel, Yakov Ilyich

# Frenkel, Yakov Ilyich

(*b*. Rostov, Russia, 10 February 1894; *d*. Leningrad, U.S.S.R., 23 January 1954)

*physics*

As a child Frenkel exhibited both interest and ability in music and painting; but later, in school, he was attracted to mathematics and physics. In 1911 he completed his first independent mathematical paper, in which he created a new type of calculus—but it proved to be already known under the name calculus of finite differences. In 1912 he independently developed a physical theory which he showed to A. F. Joffe, with whom he established a close relationship. In 1913 Frenkel entered the Physics and Mathematics Faculty of St. Petersburg University, from which he graduated with honors in 1916. In 1916–1917 he participated in a seminar led by Joffe at the Petrograd Polytechnic Institute, and in 1918 he taught at the newly created Tavrida University in Simferopol. Frenkel returned to Petrograd (Leningrad) in 1921 and worked at the Physico-Technical Institute, which was directed by Joffe, fur the rest of his life; he also taught theoretical physics at Leningrad Polytechnic Institute. In 1929 Frenkel was elected an associate member of the Academy of Sciences of the U.S.S.R. He spent 1930–1931 in the United States, where he lectured at the University of Minnesota.

Frenkel published many scientific books and journal articles, and his research encompassed extremely varied fields of theoretical physics. He was one of the founders of the modern atomic theory of solids (metals, dielectrics, and semiconductors). In 1916 he conceived, on the basis of the Bohr model of the atom, the theory of the double electric layer on the surface of metals, which permitted the first evaluations of the surface tensions of metals and of the contact potential. In 1924, on the basis of virial theory, Frenkel demonstrated that during the condensation of a metal from vapor the valence electrons of the atoms must become itinerant, moving at a speed comparable to the rate of intra-atomic motion. This was a noteworthy contribution to the problem of the heat capacity of electrons in metals, which had been blocking progress of the theory.

In 1927 Frenkel became the first to attempt to construct a theory of metals based on the representations of quantum wave mechanics and was able to explain quantitatively the large mean free paths of electrons in metals. In 1928 he developed a simple, elegant deduction of the Pauli theory of the paramagnetism of electrons in metals, used in the majority of textbooks. He also offered in that year the first quantum mechanical explanation of the nature of ferromagnetism, which was independently developed somewhat later in Werner Heisenberg’s theory. He simultaneously offered the theory of coercive force in metals.

Using the virial theorem, Frenkel established the connection between the electron theory of metals, the Thomas-Fermi atomic model, as well as the theory of the nucleus and high-density stars. The general fundamental questions first raised in these works have not lost their significance. In 1930 Frenkel and J. G. Dorfman offered the first theoretical substantiation of the breakup of a ferromagnetic substance into separate domains and predicted the existence of single-domain particles.

In 1930–1931 Frenkel made a detailed study of the absorption of light in solid dielectrics and semiconductors. He pointed out the possibility of the emergence of two different forms of excitation in a crystal. When light is absorbed, an excitation state without ionization may appear. Frenkel called this excitation state “exciton,” since such a state has the properties of a quasi particle distributed inside the dielectric or semiconductor. The second type of excitation generated by light in solid bodies, according to Frenkel’s theory, is associated with ionization, i.e., with formation of a free electron and a free hole. When bound together the electron and hole form a unique neutral system that possesses a discrete energy spectrum; this system is called Frenkel’s exciton.

Frenkel’s work on the theory of electric breakdown in dielectrics and semiconductors (1938) has great significance. As early as 1926, in his work on thermal motion in solid and liquid bodies, Frenkel was the first to work out a model of a real crystal, in which a fraction of the molecules or ions oscillate around temporary equilibrium positions which are intermediate between lattice points and in which a fraction of the lattice points are correspondingly free; the vacancies thus formed (Frenkel’s defects) migrate throughout the crystal.

In distinction to the generally held representation of the closeness of the liquid state to the gaseous, Frenkel put forward the new idea of an analogy between a liquid and a solid body. He considered a liquid to be a body possessing short-range but not long-range order. Frenkel’s theory of diffusion and viscosity, which was built on this model, proved to be exceedingly fruitful. Frenkel systematically developed his thory of the liquid state in the monograph *Kineticheskaya teoria zhidkostey* (“The Kinetic Theory of Liquids,”, 1945), which earned him the firstdegree State Prize in 1947.

Frenkel paid considerable attention to the theory of the mechanical properties of solid bodies. In papers published in conjunction with T. A. Kontorova (1937, 1938) it was first demonstrated theoretically that in distortion-free lattices a special form of particle motion is possible—a gradual, mutually concordant shift from certain equilibrium positions to others, which leads to a gradual, mutual displacement of the rows of atoms. This theory permitted the explanation of several specific particulars of the plastic deformation and twinning of crystals. The theory of the elasticity of rubbery substances, developed by Frenkel and S. E. Bresler in 1939, proved to be in good agreement with experimental data.

Frenkel’s research had an essential influence on the development of electrodynamics and the theory of electrons, as well as the theory of atomic nuclei. His 1926 study served as the basis for the investigation of many questions concerning the dynamics of a spinning electron before the appearance, in 1928, of Dirac’s theory of relativistic quantum mechanics. In *Elektrodinamika*, published by Frenkel in 1928, questions of classical electrodynamics were examined from a completely new point of view. In 1936 he was the first to attempt the construction of a statistical theory of heavy nuclei, considering the nucleus as a solid body and setting aside the individual motion of nucleons. In 1939, shortly after the discovery of the splitting of heavy nuclei by Otto Hahn and Fritz Strassman, Frenkel developed (independently of Bohr and J. A. Wheeler) a theory which explains the process of splitting as the result of the electrocapillary oscillation of electrically charged drops of nucleic liquid.

Frenkel also solved many problems in meteorology and geophysics. Between 1944 and 1949 he proposed the theory of atmospheric electrification in which the close connection between the electrification of clouds and the existence of fields in cloudless atmosphere was established. In 1945 he formulated a new theory of geomagnetism.

## BIBLIOGRAPHY

1. Original Works. Frenkel’s writings include *lehrbuch der Elektrodynamik*, 2 vols. (Berlin, 1926–1928); *Kinetic Theory of Liquids* (Oxford, 1946); *Wave Mechanics. Elementary Theory* (New York, 1950); *Wave Mechanics. Advanced General Theory* (New York, 1950); *Sobranie izbrannykh trudov* (“Collection of Selected Works”), 3 vols. (Moscow–Leningrad, 1956–1958); *Prinzipien der Theorie der Atomkerne* (Berlin, 1957); and *Statistische Physik* (Berlin, 1957).

II. Secondary Literature. Articles and books on Frenkel and his work (in Russian) are A. I. Anselm, “Yakov Ilyich Frenkel”, in *Uspekhi Fizicheskikh nahk*, **47** , pt. 3 (1952), 470; J. G. Dorfman, “Yakov Ilyich Frenkel”, in Frenkel’s *Sobranie izbrannykh trudov*, II (Moscow–Leningrad, 1958), 3–15; V. Y. Frenkel, *Yakov Ilyich Frenkel* (Moscow–Leningrad, 1966); and I. E. Tamm, “Yakov Ilyich Frenkel”, in *Uspekhi fizicheskikh nauk*, **76** , pt. 3 (1962), 327.

J. G. Doreman

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