Internal strain and thermal expansion of alpha -quartz below room temperature: a lattice dynamical model

Abstract

It is shown how the quasi-harmonic approximation can be applied to crystals with several varying internal strains. The quasi-harmonic theory is linear in the anharmonic parametric of lattice dynamical models, which can therefore easily be fitted to a large body of experimental data: macroscopic and internal expansion coefficients, third-order elastic constants and spectroscopically measured mode Gruneisen parameters. The method is applied to a short-range central-force model for alpha -quartz, which is fitted to experimental thermal expansion up to room temperature. For T>or approximately=90K a fair fit is obtained to both the macroscopic and the internal expansion, thus permitting a detailed examination of the roles played by tilt and by distortion of the SiO4 tetrahedra. At lower temperatures the model is in qualitative agreement with the observed behaviour, including the negative expansion along the trigonal axis. With a different set of anharmonic parameters, the model is fitted simultaneously both to the thermodynamic Gruneisen functions and to spectroscopically measured mode Gruneisen parameters. It is not possible to fit simultaneously all the available experimental data, confirming that a more sophisticated model is needed to give a complete representation of the inter-atomic forces.