A. Yu. Gufan

Structure and Thermodynamic Characteristics of Small Inert Gas Clusters

The relaxation dynamics of small groups of identical atoms interacting according to the Lennard-Jones law was studied experimentally. It is shown that for a fixed number of atoms, the probabilities of the formation of clusters with different structures depend on the random initial distribution of atoms in space, i.e., on the initial total energy and geometry of the particle distribution. Probabilities of the emergence of different structures of clusters vary greatly and do not contradict classical statistics. Except in extraordinary cases (e.g., N = 13), distances between the nearest atoms in clusters are different and change with the addition of each subsequent atom. The thermodynamics is constructed from the canonical ensembles of clusters with different numbers of particles. The resulting dependence of the cluster energy on the number of particles proves to be a smooth function, since only pair interactions were taken into account.

Models of three-particle interactions and theory of nonlinear deformations of crystals

A method of accounting for the symmetry of interaction energy of N identical atoms in terms of the theory of elastic constants has been proposed. The energy symmetry group of the cluster is GN = O(3) ⊗ PN. It has been shown that the calculation of elastic characteristics of crystals, which is based on analyzing the interaction potentials of atoms with inclusion of the symmetry, is competitive with respect to the calculations performed within the models of quantum mechanics. Nine models that depend on three parameters have been considered. In each model, the third-order elastic constants have been calculated for gold, aluminum, and copper single crystals with allowance made for the interactions of triples of atoms. The dependence of the energy of the models on the invariants forming the integral rational basis of the G3 group has the form

Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics

\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}

Computing lattice sums for calculating the elastic moduli of bcc metals via cluster decomposition

, where Ij is the invariant with number j (j = 1, 2, ..., 9). The parameters of the models are specified by the second-order elastic constants. The best agreement with experiment has been achieved for Cu with n = 2, j = 4; for Au with n = 1, j = 74; and for Al with n = 1, j = 9. It has been demonstrated that, for the calculation of all independent values of the second-, third-, fourth-, and fifth-order elastic constants, it is necessary and sufficient to include interactions between the clusters containing quadruples of atoms in the theory.

An invariant form of the potential energy function used to simulate properties of condensed matter

Two models of phase transitions under pressure, accompanied by electronic structure rearrangement, are proposed. A distinctive feature of the proposed models is the consideration of pressure-induced isotropic deformations and phonons breaking the symmetry. A mutual solid solution of ions of the same element in different ionization states is assumed to be regular. The second model supplements the first one by taking into account the physical nature of deviation of the mutual solution from the ideal one. The violation of the Curie principle during phase transitions under isotropic pressure is explained within these models.

Role of interactions of triplets of atoms in the formation of elastic properties of cubic crystals

A new approach is proposed for constructing the phenomenological theory of phase transitions. The approach is based on the classical Landau theory with allowance made for the order parameter that corresponds to changes in the charge distribution probability density of a crystal and does not affect the symmetry of the high-symmetry phase. It is demonstrated that this approach makes it possible to describe phase transitions in terms of a nonequilibrium polynomial Landau potential of degree four in the components of the order parameters. The capabilities of the proposed approach are illustrated with three systems that undergo ferroelastic phase transitions.

Equations of state according to the Mott model and a description of pressure-induced phase transitions in Se, Te, AlAs, and FeBO3

The total potential energy of a crystal U({rik}) as a function of the vectors rik connecting centers of equilibrium positions of the ith and kth atoms is assumed to be represented as a sum of irreducible interaction energies in clusters containing pairs, triples, and quadruples of atoms located in sites of the crystal lattice A2: U({rik}) ≡ ΣN=14EN({rik}). The curly brackets denote the “entire set.” A complete set of invariants {Ij({rik})}N, which determine the energy of each individual cluster as a function of the vectors connecting centers of equilibrium positions of atoms in the cluster EN({rik}) ≡ EN({Ij({rik})}N), is obtained from symmetry considerations. The vectors rik are represented in the form of an expansion in the basis of the Bravais lattice. This makes it possible to represent the invariants {Ij({rik})}N in the form of polynomials of integers multiplied by τ2m. Here, τ2 is one-half of the edge of the unit cell in the A2 structure and m is a constant determined by the model of interaction energy in pairs, triples, and quadruples of atoms. The model interaction potential between atoms in the form of a sum of the Lennard-Jones interaction potential and similarly constructed interaction potentials of triples and quadruples of atoms is considered as an example. Within this model, analytical expressions for second-order and third-order elastic moduli of crystals with the A2 structure are obtained.

Theory of the structure and properties of α-paratellurite (TeO2)

The complete potential energy of a crystal