  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.
