Phonons in SiO₂: The low-temperature heat capacity of cristobalite

Abstract

The heat capacity of cristobalite, a low-density crystalline form of SiO₂, has been measured between 2 and 20 K using a thermal relaxation technique. Except at the lowest temperatures, the temperature variation is similar to that of vitreous silica, and markedly different from that of quartz. Since the positions of the silicon atoms in cristobalite are very similar to the positions of atoms in the diamond lattice, the heat capacity is explained on the basis of a low-frequency transverse acoustic mode. A simple representation of this mode leads to quantitative agreement with experiment, with an average zone boundary frequency for the TA mode in cristobalite of 45 cm⁻¹.

The close resemblance between the heat capacities of cristobalite and vitreous silica is discussed in terms of recent calculations of the vibrational density of states in amorphous solids.