Ab initio calculation of the thermodynamic properties and atomic temperature factors of ${\mathrm{SiO}}_2$ α-quartz and stishovite

The constant-volume specific heat, the entropy, the phonon contributions to internal energy and Helmholtz free energy, and the atomic temperature factors of α-quartz and stishovite, two allotropic forms of ${\mathrm{SiO}}_2$, are calculated as a function of temperature from ab initio phonon band structures. Available experimental data agree with our calculated values over a wide range of temperature. α-quartz has more accessible phonon states at low temperatures, while stishovite has larger contributions to the thermodynamic functions from the zero-point motion.