C1 - THE INTRINSIC INFRARED AND RAMAN LATTICE VIBRATION SPECTRA OF CUBIC DIATOMIC CRYSTALS

Abstract

The optical properties of crystals due to lattice vibrations are expressed in terms of ε(ω), the frequency dependent complex dielectric constant. The first-order absorption spectra of polar cubic diatomic crystals yield information about ωT, ωL, e*T, γT, and εs. For the alkali halides where the assumption of an effective electric field Eeff = E + (4π/3)P is reasonably valid, ε(ω) can be related to the Szigetieffective charge, e*S = (ε0 + 2) e*T/3, which includes the short-range effects of charge deformation. For ZnS type semi-conductor crystals in which the valence electrons have extended wave functions, the effective field is more nearly equal to E and ε(ω) is expressed in terms of an effective charge e*B = e*T which is made up of a local and a non-local part. For such crystals it is likely that “charge transfer” is the predominant short-range effect. The fact that values of γT for the alkali halides are much larger than those of the ZnS crystals is largely due to the greater degree of anharmonicity in the alkali halides. The higher-order absorption spectra may involve either an anharmonic mechanism or a higher-order electric moment mechanism or a combination of these. The structure of the second-order absorption spectra arises from critical points in the “combined” density of states. For the alkali halides, the subsidiary bands are attributed to the anharmonic coupling mechanism, whereas for the ZnS type crystals, they are attributed to the second- and higher-order electric moment mechanism. Selection rules which determine the allowed combinations of modes at the Γ, L, X, and W points in the reduced zone are now available for the ZnS, diamond, and NaCl structures. Attempts to account for the structure in the absorption spectra of ZnS and CC type crystals in terms of a set of phonon energies associated with the critical points have been reasonably successful.