Quasiharmonic approximation

Detailed analytical expressions for both external and internal strain derivatives of the Helmholtz free energy of an arbitrary perfect crystal have been derived in the quasiharmonic approximation [B38]. The model used is based on semiempirical pairwise interactions between atoms. It has been demonstrated that microscopic and macroscopic expressions for the crystal free energy coincide. The formulas obtained have been implemented in the computer code DYNAM [B39] which allows one to calculate during one run (for the given lattice vectors and positions of atoms in the unit cell) a wide range of macroscopic crystal properties, such as: thermodynamic functions, phonon dispersion curves and phonon densities of states, speed of sound waves, isothermal and adiabatic elastic constants and stiffness tensors, piezoelectric and dielectric tensors, stress tensor (and pressure), heat capacities, thermal expansion, etc. Using several types of pair potentials, a number of elastic, dielectric and thermodynamic properties of KCl and NaCl crystals have been studied for a wide range of temperatures and pressures [B39]. We showed that the quasiharmonic approximation can be successfully used almost up to half of the crystal melting temperature. The ideas developed have been used in [B52] for studying MgF₂ in collaboration with T.H.K.Barron and N.Allan (Bristol University). The method has also been generalised to include several additional phonon diagrams on the top of the quasiharmonic approximation (unpublished).

7/2/1999