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Elastic constants and thermodynamical quantities for crystal lattices from many-body perturbation theory

The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and isothermal) and the coefficient of thermal expansion. The perturbation expansion is developed up to third-order and diagrams corresponding to the equations are represented. The present results extend the existing ones by giving expressions for the elastic constants of arbitrary order and terms which are higher-order in the interatomic force constants that have been obtained earlier. The perturbation expansion in terms of arbitrary macroscopical parameters is considered and the similarity of expansions with respect to different parameters is emphasized. A physical interpretation of the harmonic phonon eigenvectors is considered. To the author's knowledge, no such similar interpretation of the harmonic phonon eigenvectors has been given in the literature before.