An Empirical Potential of Interatomic Interaction

A potential of interatomic interaction for simulating complex structural states of solids (grain boundaries and heterogeneous equilibrium states) is put forward. In simulating heterogeneous states of systems, the potential must simultaneously provide for stability conditions for several phases in equilibrium and correct values of a number of macroscopic parameters such as lattice constants, elastic moduli, internal energy, heat capacity, and stability parameters. The existing empirical potentials of interatomic interaction fail to provide agreement of the calculated and experimentally obtained parameters determining the structure of the system and structural transformations due to changes in the external parameters. The potential under discussion is a polynomial representing a solution to the problem of interpolation of functions and their derivatives to the nth order prescribed on a finite system of points (Hermit interpolation problem). The relation for a general solution to the foregoing problem is so complicated that it is virtually inapplicable. A new polynomial is constructed on the basis of the Lagrangian interpolation polynomial. The interpolation of the known interatomic potentials with allowance for the fourth-order derivatives by the polynomial is achieved with high accuracy where three to four interpolation nodes are specified. Local changes can easily be introduced to the polynomial. In doing so, the values of the potential and its derivatives in other regions of space are retained. This allows mechanical stability for stable and metastable phases to be ensured.     

Phonon anomalies and martensitic transitions in bcc materials

The general systematics of phonon spectral anomalies are considered for materials with bcc and B2 structures. In a model of central pair-wise interactions, it is shown that anomalies on the TA₂ branch at =1/3 (211), the LA phonon branch at =2/3 (111), and on the TA branch at =1/2 (111) arise simultaneously with the softening of the shear elastic moduli C' and C₄₄. The TA phonon anomaly at =1/3 (110) is not due to softening of the elastic moduli, but rather is due to the long range nature of the pair-wise or multiparticle interaction. A model is proposed for the nucleation of the martensitic phase for B2 compounds, the distinctive feature of which is a consideration of the softening of the shear moduli, which is modulated by lattice relaxation around ordering defects, along with the possibility of additional defect ordering near the transition.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 10, pp. 31–39, October, 1993.     

Dimensional Hume-Rothery factor and shear stability of bcc solid solutions

The relation between the elastic shear constants and the dimensional Hume-Rothery factor is traced on the basis of the pseudopotential method for a number of bcc solid solutions AB. It is clarified that in the case of a substantial difference between the atomic volumes _A and _B, the constant c=(c₁₁-c₁₂)/2 takes on anomalously low values and even vanishes. The conclusion is hence made that the explanation of the 15% Hume-Rothery rule is possible from the aspect of stability of the crystalline lattice to shear. The presence of lattice distortion is not needed here in principle, as had been assumed earlier. It is shown that ordering of atoms according to the CsCl type can result in an abrupt increase in the value of c, i.e., in stabilizing the lattice of the initial disordered solid solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 97–102, March, 1980.     

A Model of Regular Nanostructure

Using the methods of statistical physics, the properties of nanostructured elements produced by breaking a large system of internal interfaces are investigated. Taking into account the resulting dependences, a quantum model of nanostructured state is formulated in approximations of Kroning–Penney, and electronic properties are calculated as a function of grain size.     

Molecular-dynamics study of the effect of simple defects on B2 lattice stability

The molecular-dynamics method is used in conjunction with the Parinelli-Rahman Lagrangian to investigate the influence of simple defects on the stability of the B2 lattice of the model alloy TiNi. Common defect types associated with deviation from stoichiometry and atomic disorder are considered. Under conditions of small elastic moduli, the displacement fields around the defects have a long-range nature, leading to a cooperative interaction of the defects and a lowering of the energy of the system when the defects are ordered. Depending on the symmetry of the displacement fields that are formed, the defects may either stabilize the B2 structure or tend to make it unstable and facilitate a martensite transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–8, January, 1992.     

Spall fracture of coarse- and ultrafine-grained FCC metals under nanosecond high-current relativistic beam irradiation

Experimental data are presented on the fracture mechanism and plastic deformation and thickness of the spalled layer obtained on irradiation of targets made from coarse- and fine-grained fcc metals (copper and aluminum) by a nanosecond high-current relativistic beam. The general and special features inherent in the modification of the microstructure of the spalled layer and near the surface of the spall fracture are discussed for the coarse- and fine-grained materials of the targets. Possible reasons for the varying extent to which the characteristics of the spall fracture of the copper and aluminum targets are affected by the grain size are suggested. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 20–24, March, 2009.     

Octahedrally coordinated cation superlattices in spinels

Static concentration waves have been used to determine all physically nonequivalent superlattices for octahedrally coordinated cations in spinels related to Lifshits (000) and {(100), (010), (001)} stars. These superlattices exhaust the types of cation ordering in the octahedral sublattice for spinels at present known. The nature of the order-disorder transition has been determined for these superlattices, and equilibrium equations have been derived that define the temperature dependence of the degree of long-range order.Translated from Izvestiya Vusshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 57–62, November, 1982.     

Ordering of body-centered cubic ternary alloys with three types of site. I

The ordering theory of A-B-D alloys with body-centered cubic (bcc) lattices and three types of site is examined by the Gorskii-Bragg-Williams approximation. It is shown that under certain conditions there can be two critical temperatures (T₀) for the order-disorder phase transition. The case of alloys with a quasi-binary BA-BD section is examined in detail.