Heat Capacity and Structure of Vitreous Silica and Diamond‐Like Lattices (I)

Abstract

AbstractThe phonon spectra of lattices with crystalline and glassy structures possessing skeletons of the purely covalent or ionic‐covalent type are discussed on the basis of the “one‐dimensional‐three‐dimensional model”. The upper frequency band, from ω′ to ωmax (ω′ ≪ ωmax), corresponds to a one‐dimensional frequency distribution g1(ω) in which elastic waves may propagate only in certain principal directions. In the lower band from 0 to ω′, the frequency distribution g3(ω) is three‐dimensional, as in the usual Debye‐Born‐von Karman theory. For the one‐dimensional distribution g1(ω) the exact solution is used and taken from papers by Pirenne and Renson, Deltour and Kartheuser for monoatomic and diatomic chains. The phonon spectrum for vitreous silica is discussed in terms of the present model, since its structure resembles that of β‐cristobalite. It is shown that the “chain model” applies to the thermal capacity of vitreous silica up to 900 °K.