Conclusion

Abstract

This century has seen enormous advance in our knowledge and understanding of the condensed state. The foundations of lattice dynamics were laid by Debye, Born and von Kármán early in the century, and extended later through Brillouin, Peierls and the neutron spectroscopists. They pointed out one of the tasks ahead: to unravel the meaning of the harmonic or approximately harmonic properties of solids, including the heat capacity. And yet notwithstanding the help of high speed computers, the experimental data on crystals and glasses — even the simpler cubic crystals — are not as explicable or predictable as we might like; and despite a century of measurements, precise data is still lacking for many systems of interest. This monograph includes a brief coverage of existing data on various crystal systems, and draws attention to gaps in the understanding of much of the available information at a quantitative and sometimes even a qualitative level. The gaps are greater for the anharmonic property of thermal expansion, born from the efforts of Mie and Griineisen, also early in the century. In particular, the difficulties of inelastic neutron scattering at high pressures have largely prevented the acquisition of data on the volume dependence of dispersion curves (which show the phonon frequency-wave number dependence ω(q,s)). Apart from some optical zone center frequencies obtainable from spectroscopic measurements, it is usually only at the low frequency limit that we have experimental mode Griineisen parameters, as obtained from measurements of elastic moduli under pressure.