The study of vibrational excitations in disordered materials (e.g. glasses) is a very active field of research [1]. The vibrational behaviour of glasses is often very different from that of crystals, e.g. an excess mode density ("boson peak") exists at low frequencies in glasses, and vibrational modes at band edges can be spatially localized by disorder. The aim of the project is to investigate the vibrational behaviour of the force-constant-disordered diamond lattice (e.g. of silicon) using a mean-field approach (the coherent potential approximation). This has already been successfully applied by our group [2], to vector (i.e. transverse and longitudinal) vibrations in disordered f.c.c. lattices containing one atom per unit cell, and hence for which only an acoustic band exists. The boson peak there was found to arise from disorder-induced level-repelling and branch-hybridization effects. There are two reasons for similarly studying the diamond lattice with two atoms per unit cell. The first is that, with different types (masses) of atom decorating the two lattice sites, optic-vibration branches appear, and hence the involvement of acoustic-optic mode hybridization in boson-peak formation in real glasses can be addressed. Furthermore, it will be extremely interesting to investigate whether complete spatial localization of the vibrational modes comprising the optic band can be achieved for sufficiently large degrees of disorder. The second reason for this study is that amorphous silicon does not appear to exhibit a (significant) boson peak in experimental data. Reasons for this behaviour will be sought in this study.
[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).