Photoelastic trends for amorphous and crystalline solids of differing network dimensionality

Abstract

A single model is developed for the different photoelastic response of Ge-family materials and chalcogen-based molecular solids. If ${\chi }^{\prime }$ is the "Grüneisen" parameter for the electronic susceptibility, experiment shows that ${\chi }^{\prime }<0\mathrm{}$ for the former group, while ${\chi }^{\prime }>1\mathrm{}$ for the latter. In addition, several group IV-VI compounds have $0\le {\chi }^{\prime }\le 1$. 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 ${\chi }^{\prime }$ should depend linearly on $\frac{2\eta }{E_g}$, with $E_g$ the Penn-Phillips gap and dimension-less $\eta$ determined from experiment. Reliable values of ${\chi }^{\prime }$, $E_g$, 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 ${\chi }^{\prime }$ versus $\frac{2\eta }{E_g}$ exhibits the predicted linear correlations for materials with ${\chi }^{\prime }<0\mathrm{}$ and ${\chi }^{\prime }>1\mathrm{}$; 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 ${\chi }^{\prime }$ 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. ${\chi }^{\prime }>1\mathrm{}$ follows from the bonding strength dichotomy in (${\chi }^{\prime }<0\mathrm{}$ obtains for covalent 3D-network solids. It is suggested that ${\chi }^{\prime }$ can serve as an indicator of network dimensionality for these two cases.