Photoelastic trends for amorphous and crystalline solids of differing network dimensionality

A single model is developed for the different photoelastic response of Ge-family materials and chalcogen-based molecular solids. If χ^' is the "Gr\"uneisen" parameter for the electronic susceptibility, experiment shows that χ^'<0 for the former group, while χ^'>1 for the latter. In addition, several group IV-VI compounds have 0≤χ^'≤1. In our model the dielectric constant is calculated, within the Drude formalism, using one Penn-Phillips oscillator for Ge-family solids and two for molecular chalcogenides. The model predicts that χ^' should depend linearly on 2ηEg, with Eg the Penn-Phillips gap and dimension-less η determined from experiment. Reliable values of χ^', Eg, and other relevant parameters are tabulated for a large number of materials. New experimental results are also presented for ZnTe. The experimental evidence provides support for the model. A plot of χ^' versus 2ηEg exhibits the predicted linear correlations for materials with χ^'<0 and χ^'>1; the slopes are in excellent agreement with measured band-gap volume derivatives. These correlations pertain to amorphous and crystalline solids alike. For the molecular chalcogenides, it is concluded that band-broadening influences χ^' through a uniform "red shift" of the lower-energy oscillator with respect to the stationary upper oscillator. The observed photoelastic trends are related to bonding topology by analogy with arguments previously applied to phonons. χ^'>1 follows from the bonding strength dichotomy in (3D)-network structures, whereas χ^'0 obtains for covalent 3D-network solids. It is suggested that χ^' can serve as an indicator of network dimensionality for these two cases.