A Theory of Phonon-Like Excitations in Non-Crystalline Solids and Liquids

Elementary excitations associated with atomic motion in non-crystalline solids and liquids are studied with particular attention paid to the dependence of their dispersion on local order. In doing this, an attempt is made to obtain an exact formal expression for an effective dy-namical matrix giving the eigenfrequencies of phonons in a non-crystalline solid in terms of "effective pair-correlation functions". A brief remark is also given on the moment method and sum rules for the dynamic structure factor to study high-frequency collective motion in liquids. It is suggested that under certain restrictions the phonon-rotan-like behavior of ex-citations as observed in liquid helium is likely to exist in almost all types of structure or topological disorder systems (amorphous and glassy solids, liquids, etc.). To substantiate this, a model one-dimensional system is chosen to show how a phonon dispersion curve in a crystal lattice is modified, as the partial disorder characterizing a structure disorder system is intro-duced. Such a local disorder is shown to give rise to a frequency gap which decreases with increasing local order and eventually vanishes in the case of complete order. This result is also in qualitative agreement with the pressure- and the temperature-dependence of the rotan minimum energy in liquid helium. Simple numerical calculations are made to compare the obtained results with experiments for collective motion in liquid argon and also in liquid helium. Fairly good agreement is obtained