The thermal behaviour (e.g. heat capacity, Cv, thermal conductivity, k) of glasses is very different from that of crystals at low temperatures (<10K) where the frequencies of the dominant phonons involved would indicate that both classes of materials would be behaving as Debye-like elastic continua [1]. However, glasses invariably exhibit a peak in Cv(T), reflecting an excess mode density (relative to the Debye-like density of states), and a plateau, rather than a peak, in k(T) reflecting increased phonon scattering. The aim of this project is to develop analytical expressions for various (force-constant-disordered) lattices (e.g. f.c.c., b.c.c., h.c.p., diamond, etc) within the mean-field approach known as the coherent-potential approximation (CPA). The peak in Cv(T) should be reproduced, since we have found that CPA successfully describes the excess mode density [2], but it is not clear to what extent the plateau in k(T) can be reproduced by this approach. If time allows, Cv(T) and k(T) will also be calculated numerically from the vibrational eigenmodes that are already available for various realistic structural models (e.g. of amorphous silica [3], germania and silicon) for comparison with the theoretical results.

[1] S.R. Elliott, Physics of Amorphous Materials (Longman: 1990).

[2] S.N. Taraskin, Y.L. Loh, G. Natarajan and S.R. Elliott, Phys. Rev. Lett. 86, 1255 (2001).