Knowledge Bank

The nonequilibrium configurations frozen into vitreous materials account for specific features of the phonon spectra, and these are associated with anomalies in mechanical and thermal behavior. A structure model specific for these materials is proposed. It consists of a continuous strong relatively well-ordered regime, R(Cont.), in which is dispersed a weaker, less-ordered regime, R(Disp.), in domains of nearly uniform size and spacial distribution. The optic-phonon spectrum of R(Cont.) is nearly identical with that of the crystal toward which the material transforms at $Tg$, while that of R(Disp.) is unique with respect to both position and width of the bands. The acoustic phonon spectrum is determined by elasticity and density of the composite, but its cut-off frequencies are determined by mean distances between domains of R(Disp.). These distances are evidently quite uniform. Both acoustic and optic phonon spectra display strong effects due to the acousto-optic coupling inferred from other evidence as well. For T near $0\circ K$ , the model predicts for heat capacity per mole of R(Disp.) domains: $$ C_{v}/3R = S_{1}T + C_{2}T^{2} + C_{a}(1+C_{3}T^{2}) \quad , $$ where $Ca$ is the vibrational contribution of acoustic modes. The experimentally well-documented anomalies in $Cv$ of vitreous materials are represented by $S1$, $C2$ , and $C3$ among which $S1$ is the frozen-in configuration entropy which is made T-dependent by different thermal response of R(Cont.) and R(Disp.). The effects of acousto-optic coupling are represented by $C2$ and $C3$.