Anisotropic thermal expansion in silicates: A density functional study ofβ-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 Mg0.5SiAlO₄, 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).