Metal Physics

(or physical metallurgy), a branch of physics that deals with the structure and properties of metals. Like dielectric physics and semiconductor physics, metal physics is a subdivision of solid-state physics. Modern metal physics represents a synthesis of microscopic theory, which explains the properties of metals by the distinctive features of the atomic structure of the metals, and metal science, which uses the methods of thermodynamics, continuum mechanics, and other fields to investigate the structure and properties of real metallic materials. The primary physical and chemical properties of metals were studied as early as the 19th century because metals were used so extensively. The nature of these properties could not be understood, however, without developing the concepts of the atomic structure of matter.

Microscopic theory of metals. The microscopic theory of metals was first developed in the 20th century. In 1900, P. Drude proposed a model of a metal in which the electrical conductivity was due to the flow of an “electron gas” that fills the interatomic space. By assuming that the electron gas is in thermal equilibrium and that electrons “drift” under the action of an applied electric field and collide with atoms, Drude obtained the correct value for the electrical conductivity of metals at room temperature and also explained the relation between electrical and thermal conductivities (the Wiedemann-Franz law). H. Lorentz developed Drude’s idea by applying the kinetic theory of gases to the electron gas. However, the rigorous Drude-Lorentz theory, which was constructed by application of the laws of classical mechanics and statistics, was even less effective in explaining the experimental data than the primitive ideas that preceded it. In addition to the fact that this theory did not yield the correct temperature dependence of the electrical conductivity, it could not explain why the electron gas does not affect the specific heat of metals. (The specific heat of metals does not deviate appreciably from the Dulong and Petit law, which is valid for both metals and nonmetals.) This theory was also unable to explain (1) the value obtained for the paramagnetic susceptibility of metals, which was much less than that predicted by theoretical arguments, and (2) the lack of temperature dependence of this quantity.

In 1927–28, W. Pauli and A. Sommerfeld explained the “anomalies” of paramagnetic susceptibility and specific heat by assuming that only a very small fraction of the total number of electrons participates in the transfer of electric charge and heat and is responsible for spin paramagnetism. At ordinary temperatures, most of the electron gas is in a degenerate state, in which it is not affected by a change in temperature. The works of Pauli and Sommerfeld form the foundation of the modern electron theory of metals. In 1930, L. Landau showed that the diamagnetism of metals is due to the orbital motion of these very electrons and is one-third of the spin paramagnetism. In magnetic fields and at low temperatures, the diamagnetism may be manifested in the form of a complex periodic dependence of the magnetic moment on the field. Quantum oscillations of magnetic susceptibility and electrical resistance in a magnetic field were later observed experimentally.

In 1929–30, F. Bloch and L. Brillouin examined the effect of the periodic field of a crystal lattice on an electron gas. Their work made it possible to explain, for example, the mean free path of electrons in a metal, which greatly exceeds the mean distance between atoms, and led to the development of the band theory of solids. For a metal, the decisive factor is whether or not the Fermi surface passes through an unfilled energy band. Thermal conductivity, electrical conductivity, and many other properties of metals are determined by the electrons in this band (conduction electrons). A dispersion law (the dependence of energy on momentum) for electrons is found by investigating the behavior of a metal in static and variable electric and magnetic fields; phenomena such as quantum oscillations, galvanomagnetic phenomena, the magnetoacoustic effect, and cyclotron resonance may be used for these investigations. Combined with data on the energy spectrum of electrons (which may be obtained, for example, from X-ray emission spectra), the dispersion law provides quite comprehensive information on electrons in a metal.

The study of the lattice itself is also important since its features determine such properties of metals as specific heat and electrical conductivity. The methods of electron diffraction, X-ray diffraction, and neutron diffraction have made it possible to determine the atomic and magnetic structures of metals and to investigate the thermal vibrations of the crystal lattice. Resonance methods, such as electron paramagnetic resonance, nuclear magnetic resonance, and the Mossbauer effect, have made it possible to study local magnetic and electric crystalline fields in metals.

The application of the theory of exchange interaction to electrons in a metal (W. Heisenberg and P. Dirac, 1927) made it possible to understand the nature of ferromagnetism and to detect new magnetically ordered states of a metal: antiferromagnetism (L. Néel, 1932) and ferrimagnetism. The investigation by J. Bardeen, L. Cooper, and J. Schrieffer in 1957 of the interaction of electrons with each other and with the lattice made it possible to elucidate the nature of superconductivity. Normal, superconducting, and magnetically ordered (ferromagnetic, antiferromagnetic, and ferrimagnetic) metals are three important subjects studied in metal physics.

Theory of defects. Defects in crystals affect practically all properties of metals. The influence of defects was first studied in the 1940’s in connection with the study of diffusion and plastic deformation. The concept of dislocations holds a central place in the theory of defects; the migration of these dislocations explains the plastic deformation of crystals. The above concepts were proposed by a number of researchers (L. Prandtl, 1928; U. Dehlinger, 1929; E. Orowan, M. Polanyi, and G. Taylor, 1934; la. I. Frenkel’, 1938) because the low resistance to deformation that is observed could not be explained within the frame-work of the microscopic theory of an ideal crystal. (Microscopic theory gave an estimate that was tens of thousands of times greater than the observed values.) Studies of dislocations, using such methods as electron microscopy and X-ray topography, in conjunction with theoretical research in the 1950’s and 1960’s contributed to the explanation of most mechanical properties of metals. For example, the yield point and strain aging of metals are explained by the elastic interaction between dislocations and impurity atoms; strain hardening is explained by dislocation pileups (N. F. Mott, J. Friedel, A. Seeger); and the polygonization process (the separation of deformed single crystals into blocks) is explained by the dislocation structure of the grain boundaries (W. Read, W. Shockley, F. Frank).

The production and migration of point defects in crystals lead to the formation of a dislocation and, moreover, play an independent role in the processes of diffusion, self-diffusion, and associated phenomena. Thus, the aggregate of the defects in a crystal—the defect structure—determines many properties of a real metal, including mechanical properties. The scattering of electrons and phonons by defects can play an important role in many kinetic effects in metals. The study of the effect of defects on physical properties is a rapidly developing branch of modern metal physics.

Alloys; heterophase structures. The ability of metals to form solid solutions and alloys is one of the most important properties of metals, and this property makes metals very useful. The theory of alloys is the oldest branch of metal physics, and its development has been closely connected with the problems of practical metallurgy.

The phenomenon of polymorphism is used extensively in practice to impart desirable properties to metallic materials by heat treating them. A polymorphous transformation leads to a fundamental change in all the physical properties of a metal (transformation of a metal into a nonmetal often takes place in the process). An important area of metal physics is the study of the polymorphous modifications that arise under various conditions, such as at high pressures and in superstrong magnetic fields. The investigation of the stability regions of various polymorphous phases as a function of external conditions (temperature, pressure, fields) and, in the case of alloys, as a function of concentration, makes it possible to construct phase diagrams.

The theory of phases, which was first developed in the 19th century, examines phase equilibria, phase transitions, and the structure and properties of heterophase systems. The transformation of one phase into another generally occurs by the formation, in the initial phase, of isolated crystals of the new phase, which grow, interact, and form a complex heterophase system, for example, a binary system. The shape, size, and arrangement of the crystals determine the heterophase structure of a real metal. The properties of metallic materials can be changed by adjusting the heterophase structure. In this case the properties of a heterophase system cannot be reduced to the “sum of the properties” of the individual phases. This nonadditivity of properties is due both to the presence of interphase boundaries whose specific volume in finely dispersed systems may be quite high and also to the significant distortion of phases because of elastic interaction. The influence of the elastic interaction of phases is manifested most fully during martensitic phase transformations when neither the composition nor the degree of order is changed and the phases differ only in the location of the sites of the crystal lattices. The physical nature of martensitic transformations was investigated by G. V. Kurdiumov and his colleagues.

The study of the time evolution of a heterophase system under various external conditions, that is, the study of the kinetics of the phase transformation, makes it possible to determine the intermediate states of the heterophase structure that arise during the transformation; these intermediate states may then be preserved for quite a long time if a change in external conditions “freezes” the transformation. Polycrystals, whose grain size is determined by the rate of nucleation and growth of the grains in the course of crystallization, serve as an example of such a nonequilibrium heterophase structure. Multiphase metastable states that are characterized by regular spatial arrangement of the phases are often formed as a result of elastic interaction between phases.

Thus, the structure of real metals is characterized by the presence of three structures on different scales: microscopic (atomic-crystalline) structure, defect structure, and heterophase structure. There is a close interrelationship among the different “stages” of this “hierarchy” of structures, but the difference in scales justifies the historically established difference in the methods used for their experimental and theoretical study. The existence of three directions of research in metal physics—(1) the microscopic theory of metals, (2) the investigation of defects and their influence on the properties of metals, and (3) the study of phases and heterophase metallic materials—is associated with this difference in scales. These different approaches solve from different viewpoints the general problems of metal physics—(1) the relation of the physical properties of a metal and the effects observed in the metal to its structure and (2) the dependence of the internal structure of metals on external conditions.