Number Of Pair Interactions Research Articles

Computer Experiment on Deformation of Nanocrystals of the Chromium-Niobium System. Part 2. Mechanical Properties

Molecular-dynamic simulation of the process of stretching of chromium and niobium nanocrystals and chromium-niobium bicrystals was performed to a pair-potential approximation. The authors obtained and analyzed the dependences of the potential energy, the number of pair interactions, work of deformation, stress, reduction in the cross-sectional area, and Poisson’s ratio on the strain with various orientations of nanocrystals with respect to the tensile force. They calculated the characteristics of elasticity, yielding, and strength of nanocrystals.

Computer Study of the Atomic Mechanism of Deformation and Failure of Chromium

Molecular-dynamic simulation of Cr ― Nb bicrystals subjected to stretching is carried out in a paired potential approach. Illustrations are provided for the atomic mechanism of deformation and failure, that depends on orientation of a bicrystal with respect to acting force P. In the case of a starting configuration (100)⊥P there is a mechanism of reorientation (100)⊥P → (110)⊥P, at first in niobium and then in chromium. With a starting configuration of (110)⊥P a niobium crystallite is only deformed with elastic deformation; at the same time deformation from the chromium direction is ductile-brittle in nature. With an initial configuration of (111) ⊥P purely brittle failure is observed. In all cases fracture passes through the interphase boundary. Reasons for these atomic-structural transformations are explained. The dependence of potential energy, the number of pair interactions, and the work of deformation and stress on the deformation are analyzed.

On a variational procedure for obtaining the thermodynamic properties of statistical models

AbstractA procedure is developed for obtaining approximate thermodynamic properties of statistical models, based on a well known variational principle for the free energy. The procedure involves the choice of a suitable parametrized trial Hamiltonian which contains some elementary interactions. The free trial Hamiltonian leads to the usual mean‐field approximation. When the trial Hamiltonian includes a certain number of pair interactions only, the results are regained of the constant‐coupling approximation for the Ising model if the number of interacting pairs is conveniently chosen by a comparison with the first few terms of the exact high‐temperature expansion. This procedure is simpler than existing approximations and can be easily generalized. Besides treating the Ising model, some applications are presented to the spin‐1/2 antiferromagnetic Heisenberg model, and to the spin‐1 Heisenberg model with uniaxial anisotropy.