Photoelastic trends from halides to pnictides by a bond-orbital method

Abstract

The photoelastic effect, or the strain dependence of refractive index n0, essentially controls the details of light scattering in liquids, glasses, and crystals. Some knowledge of its behavior as a function of structure and chemical composition is therefore extremely valuable in a search for devices which seek to maximize or minimize such light scattering mechanisms. This paper derives a bond-orbital theory for the hydrostatic photoelastic effect (or the dependence of n0 on density ρ) for three-dimensionally coordinated crystalline structures (for which density fluctuations are directly related to primary bond length fluctuations) including four-, six-, and eightfold coordinated cations. The theory sets out the manner in which ∂n0/∂ρ depends on such fundamentals as valence, ionic radii, and degree of covalence, and highlights a term not previously derived in any prior theories of linear dielectric response. This term, involving relative anion to cation size, while not inconsequential in an evaluation of n0 itself, is absolutely essential for any understanding of ∂n0/∂ρ and completely dominates the latter in many more-ionic crystals. The final theory contains two parameters which are determined from experiment (essentially in the ionic and fully covalent limits, respectively). When complete it is tested on more than thirty halides, oxides, chalcogenides, and pnictides, for which reliable photoelastic data have been found in the literature. The agreement of theory with experiment is within experimental error for all except the tetrahedrally bonded halides for which direct interband activity by shallow-core d electrons places them outside the theory as presently constituted.