Electro-Optic Effect in NH4Cl

The change in refractive index $n$ produced by a dc electric field, to terms linear in the field (the Pockels effect), has been calculated for solid N${\mathrm{H}}_4$Cl. This substance, which has the CsCl structure with N${\mathrm{H}}_4^{+}$ tetrahedra replacing the ${\mathrm{Cs}}^{+}$ in a cubic array of ${\mathrm{Cl}}^{-}$ ions, has a nonvanishing Pockels effect below -30.5°C, where all tetrahedra have the same orientation. For the calculation, it has been assumed that the Pockels effect arises from field-induced changes in the normal vibrations of the N${\mathrm{H}}_4^{+}$ tetrahedra, particularly in the two sets of triply degenerate, infrared-active vibrations. Electrical anharmonicity, resulting from the nonlinear behavior of the dipole moment, has been included by expanding the dipole moment to quadratic terms in the normal coordinates. Ionic contributions to nonlinear effects arising from anharmonicities of the vibrations of the ions, i.e., those due to cubic terms in the potential energy, have been calculated to first order of perturbation theory. The resulting expression for the Pockels constant, which should be valid in the infrared and perhaps part of the visible involves a sum of contributions from vibrational transitions, the terms being related to the frequency shifts and line intensities in the dc field. Suggestions are made for obtaining experimental verification of the theory.