Estimation of bond-bending force constants in tetrahedral semiconductors and their variation with pressure obtained from spectroscopic data

The bond-bending force constant k_θ of the Keating-Martin (KM) model for the elastic constants of tetrahedral semiconductors is related to the optical spectrum according to k_θr²=4(1-fᵢ)ΔEₘ, where r is the bond length, fᵢ is the Phillips fraction of ionic character, and ΔEₘ is the reduction in single-particle energy per valence electron resulting from the over-all band gap. As the energy to bend a directed orbital is unrelated to the energy of competing phases, there is no d-core dehybridization or bottom of the band correction. The above formula is accurate to the limit of the KM model when fᵢ≤0.5. For more ionic compounds, it seems that k_θr²=2ΔUI, where ΔUI is the change in internal energy per atom pair upon transformation to the NaCl structure. The observed variation of k_θ with pressure is indeed equal to the value found by differentiation of the above formula. An approximate relation for Keating's third-order elastic parameter is derived: ε=-3k_θ2r.