Crystal Dynamics of Gallium Arsenide

The dispersion relation for the normal modes of vibration propagating along the [$\zeta 00$], [$\zeta \zeta \zeta$], and [$0\zeta \zeta$] directions in a single crystal of pure gallium arsenide at 296°K has been determined by neutron spectrometry. The frequencies (units ${10}^{12}$ cps) of specific modes are (a) (0,0,0): $\mathrm{TP} 8.02\pm 0.08$, $\mathrm{LO} 8.55\pm 0.20$; (b) (1,0,0): $\mathrm{TO} 7.56\pm 0.08$, $\mathrm{TA} 2.36\pm 0.015$, $\mathrm{LO} 7.22\pm 0.15$, $\mathrm{LA} 6.80\pm 0.06$; (c) (0.5,0.5,0.5): $\mathrm{TO} 7.84\pm 0.12$, $\mathrm{TA} 1.86\pm 0.02$, $\mathrm{LO} 7.15\pm 0.07$, $\mathrm{LA} 6.26\pm 0.10$. The results are analysed in terms of the dipole approximation model. Although a fairly complex version of this model provides a satisfactory description of most of the data, certain significant discrepancies remain. These indicate that the neglect of quadrupole interactions is a serious weakness of the dipole approximation model.