Keywords: equation of state, thermodynamical properties, Gruneisen, perfect crystals, particles dynamics method.

Perfect two and three dimensional crystals with simple lattice are considered. Interactions between particles via pairwise potential are assumed. The problem of the equations of state obtaining for this system is solved in accordance with the approach proposed in [1]. Long wave approximation is used to obtain the connection between microscopic and macroscopic values. In the framework of this approximation the microscopic analog of the stress tensor was taken from [2] and generalized for the case of thermal motion. Expansion of the stress tensor and the thermal energy in terms of a small thermal parameter is conducted. The equation of state in Mie-Gruneisen form is derived. Dependence of the Gruneisen function on volume is obtained. Expressions for Gruneisen constant for simplest pairwise potential such as Mie, Lennard-Jones and Morse are calculated. It allows one to calculate parameters of the potentials using experimentally determined Gruneisen constant. For metals with face center cubic lattice, good correspondence of the Gruneisen function with experimental data [3] is shown. Also comparison with classical models [4,5,6] is conducted. The results are found to be equal to the prediction of the model [6] in the case of interactions of nearest neighbors.

It is shown that in contrast with the one dimensional case, the Gruneisen function does not have a singularity point for realizable values of deformations. However for the strong tensile deformations, the Mie-Gruneisen equation became inaccurate. For such a case the new equation of state is derived.

1

A.M. Krivtsov, "From nonlinear oscillations to equation of state in simple discrete systems", Chaos, Solitons & Fractals. V.17. No. 1, 79-87, 2003. doi:10.1016/S0960-0779(02)00450-2

2

A.M. Krivtsov, "Deformation and fracture of bodies with microstructure", Nauka, Moskow, 2007 (in Russian).

3

B.L. Glushak, V.F. Kuropatenko, S.A. Novikov, "Study of Material Strength under Dynamic Stress", Nauka, Novosibirsk, 1992 (in Russian).

4

J.C. Salter, "Introduction to Chemical Physics", 1st ed.; International Series in Physics, McGraw Hill, New York, 1939.

5

J.S. Dugdale, D.K.C. MacDonald, "The Thermal Expansion of Solids", Phis. Rev., 1953.

6

V.Y. Vaschenko, V.N. Zubarev, "Concerning the Gruneisen constant", Sov. Phys.-Sol. State, 1963.

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