Symmetry of the mixing Hamiltonian in lattices with a basis

To determine substitutional and injection superstructures in alloys having a complex lattice with a basis by the method of concentration waves it is necessary to know the eigenvectors of the Fourier transform matrices V_pq() of the mixing potential of a homogeneous solid solution. A technique has been developed, investigating the variations of the matrix elements V_pq() for symmetry transformations of the spatial lattice group, to solve this problem. The symmetry elements belonging to the wave vector group determine the internal structure of the matrices V_pq() for lattices with a basis. Symmetry elements not appearing in the wave vector group determine the relation between matrices belonging to different rays of the star wave vector. Restrictions on the matrix elements V_pq(), following from symmetry, are found for an h.c.p. lattice. The eigenvectors are calculated for the matrices V_pq(), whose vectors terminate in high-symmetry points, lines, and planes of the Brillouin zone. This made it possible to separate the problem of thermodynamic competition of intermediate phases in an alloy with a hexagonal lattice into symmetric and potential parts, similarly to the way this occurs in Bravais lattices.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 13–25, August, 1993.     

Application of the pseudopotential method to the calculation of the phase transition temperature

Pseudopotential formalism was used to describe the phase transition from a two-phase to a one-phase state in alloys with limited solubility. The combined use of the pseudopotential and static concentration wave methods for calculating the temperature of the order-disorder phase transition was generalized to the case of lattices with a basis. Numerical calculations were carried out for the limiting solubility curves in the system Cd-Zn and the order-disorder transition temperatures for Mg₃Cd, MgCd, and MgCd₃ superstructures.     

The pseudopotential method and the thermodynamics of alloys

The authors review their work on the use of the pseudopotential method in the thermodynamics of alloys. Treatment of the theory of phase equilibria in alloys on the basis of the pseudopotential method makes it possible to use first principles in order to set up a thermodynamics of alloys in which the energy parameters are not presumed to be phenomenological but are calculated from the electronic characteristics of the pure components. The approach developed allows a priori calculation of the phase diagrams of alloys, the effect of cubic compression on phase diagrams, and the various thermodynamic functions of alloys. A classification of phases in alloys on the basis of analysis of their thermodynamic characteristics is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 22–39, August, 1976.     

Calculation of the binding energies of complexes formed by magnesium and zinc impurity atoms with vacancies in dilute aluminum alloys

Expressions are obtained for calculating the binding energy of an arbitrary complex formed from impurity atoms and vacancies. Calculations are made for various complexes formed from magnesium and zinc impurity atoms and vacancies in aluminum. The results obtained are used to study the role of vacancies in the formation of Guinier-Preston zones. The need to allow for the lattice relaxation is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 99–104, August, 1980.     

Thermodynamic properties of lithium,sodium, and potassium at high pressure

The Gibbs thermodynamic potential is constructed for Li, Na, and K in the lattice vibration approximation with the aid of the Krasko-Gurskii model pseudopotential. The isothermal modulus of volume elasticity and its pressure derivative are calculated. Compression values are calculated from the equation of state d/d =0. The results obtained agree well with experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 91–97, February, 1978.     

Study of point defects for B2 structures with a ω-type martensitic phase

The molecular dynamics method has been used to study the effects of the inheritance from point defects in B2 structures having an -like martensitic transformation with different final reaction products. For order defects, antistructural atoms, and their simplest complexes it has been shown that in several cases the number of atoms in the defects increases sharply for martensite during the transition to austenite. Here the fraction of chemical energy accumulated by the defects grows. A certain type of defect in the B2 structure in martensite corresponds to the appearance of high-energy linear disordered chains in directions of the [111]_B2 type. This can play a substantial role in the determine the path of the reverse martensitic transformation.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 54–59, June, 1995.