Are we Beginning to Understand the Vibrational Anomalies of Glasses?

Abstract

In perfect, crystalline solids, the thermal motion of the atoms can be described through elastic waves, i.e. collective excitations. The Debye continuum model has been a good approximation in the long wavelength limit. It predicts, on the basis of a proper average of the measured speeds of sound, a low temperature specific heat proportional to the third power of the temperature, which is in excellent agreement with the experimental results in the temperature range below one percent of the Debye temperature even in rather complex crystal lattices. In all amorphous solids, however, i.e. solids lacking long range order, such an agreement has not been found. The discrepancy is, in fact, most pronounced in the low temperature range, where the specific heat is found to vary approximately as the first power of the temperature. The prefactor of the linear specific heat term lies typically in the range of 5 to 50 erg g-¹ K-², and appears to be independent of the microscopic structure of the glass or its bonding type.¹ Figs. 1 and 2 show two examples. The covalently bonded amorphous Si0₂ was slowly cooled from the melt,² while the metallically bonded amorphous Bi-Sb layer was produced by quenched condensation,³ in which process the atoms were evaporated onto a substrate which was held below 20 K. In both solids, the linear term of the specific heat anomaly has almost the same magnitude; for the amorphous Si0₂, it is 12 erg g-¹ K-² T, for the amorphous superconductor, it is 13 erg g-¹ K-² T.