Localized Effective Charges in Diatomic Crystals

Abstract

We develop a model for simple diatomic crystals in which two effective-charge parameters are associated with the infrared-active optical-phonon mode. One of these is $e_T^{*}$, the macroscopic effective charge. The definition of the second charge, here designated as $e_l^{*}$, the localized effective charge, is model dependent and derived from a model which includes two contributions to the TO-phonon frequency. One of these is a mechanical or spring-constant contribution ${\omega }_0^2$ and the second a frequency term which provides a measure of dipole-dipole interactions. $e_l^{*}$ is computed from the experimental values of the TO-phonon frequencies and values of ${\omega }_0^2$ calculated from simple force-constant models. For the zinc-blende (ZB) and wurtzite ($W$) crystals, $e_l^{*}\simeq f_i{z}_{\mathrm{eff}}$, where $f_i$ is the fractional ionicity and $z_{\mathrm{eff}}$ is the effective chemical valence. For the rocksalt (NaCl) and CsCl crystals, $e_l^{*}$ is not proportional to $f_i$, but instead shows systematic variations with ion size parameters. For the ten-electron NaCl and CsCl crystals, $e_T^{*}\propto {\epsilon }_{\infty }^{\frac{1}{2}}$, where ${\epsilon }_{\infty }$ is the optical-frequency dielectric constant. The model calculation for $e_l^{*}$ is more reliable for the ZB and $W$ crystals than the NaCl and CsCl crystals.