Abstract
In terms of the virial theorem for an arbitrary two-dimensional lattice a self-consistent system of equations is developed that allows its dynamics and the temperature evolution to the stability limit to be investigated in the nearest neighbour approximation. Contrary to the traditional approach the relative correlation functions of the longitudinal and transversal displacements of particles and the force constants corresponding to them are introduced. The topology of the virial surface and the evolutional trajectory of the lattice state, the temperature behaviour of the longitudinal and transversal force constants of the lattice are discussed. The irregular growth of the adiabatic elastic modulus with temperature, and the change of sign of its derivative observed experimentally in cubic crystals are explained. It is shown that there exists a temperature range where the system stability is achieved by the redistribution of the kinetic energy between the longitudinal and transversal displacements of particles. It is established that the instability of the lattice relative to its longitudinal oscillations is the main cause of its structural re-arrangement in the high temperature range in spite of the more rapid development of the transversal oscillations with temperature increase.
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Pershin, V.K., Gersht, I.S. Correlation properties and the structural instability of the twodimensional anharmonic crystal. The virial approach. Acta Physica Hungarica 57, 99–111 (1985). https://doi.org/10.1007/BF03155853
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DOI: https://doi.org/10.1007/BF03155853