To the Theory of Force Constants for Multiatomic Systems in the Tight-Binding Model (Part II)
Keywords:theory of force constants, Coulomb interaction energy, energy of a multiatomic system, Gr¨uneisen law
An approximate expression for the Coulomb interaction energy in solids has been obtained in the framework of the tight-binding model. The condition of adiabatic approximation and the procedure of quantum statistical averaging for the first (static) term in the expansion of the average potential energy in small nuclear shifts are analyzed, which allowed the electron contribution to the thermal expansion of solids to be calculated. An equation of state for a solid is obtained in the harmonic approximation by analyzing the internal energy and the thermal properties of the solid. A relationship between the specific heats Cv and Cp, which agrees with the Gr¨uneisen law, is found.
M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954).
R.P. Feynman, Phys. Rev. 56, 340 (1939).
I.O. Marushko, Ukr. Fiz. Zh. (to be published).
A.A. Maradudin, E.W. Montroll, and G.H. Weiss,Theory of Lattice Dynamics in the Harmonic Approximation (Academic Press, New York, 1963).
L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (Pergamon Press, Oxford, 1980).
Ya.P. Terletsky, Statistical Physics (North-Holland, Amsterdam, 1971).
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