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

The 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 ω max (ω′ ≪ ω max ), corresponds to a one‐dimensional frequency distribution g 1 (ω) in which elastic waves may propagate only in certain principal directions. In the lower band from 0 to ω′, the frequency distribution g 3 (ω) is three‐dimensional, as in the usual Debye‐Born‐von Karman theory. For the one‐dimensional distribution g 1 (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.