Anisotropic thermal expansion in silicates: A density functional study of β-eucryptite and related materials

Linear response density functional calculations of the structures, phonon spectra, and thermal expansion have been performed for the hexagonal silicate β-eucryptite [β-LiAlSiO₄] and related materials, extending and refining earlier work using direct diagonalization of the dynamical matrix. The temperature (T) dependence of the lattice constants of β-eucryptite agrees well with measurements, including the minimum in a(T) found at low T. Mg ions are predicted to occupy octahedral sites in Mg_0.5SiAlO₄, in agreement with neutron scattering data. We present calculations of the thermal expansion coefficients in β-quartz that are free of adjustable parameters, and we extend the earlier work to calculate the thermal expansion coefficients of the low-T form of β-eucryptite (84 atoms per unit cell).