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 e(ω) , the frequency dependent complex dielectric constant. The first-order absorption spectra of polar cubic diatomic crystals yield information about ω T , ω L , e * T , γ T , and e s . For the alkali halides where the assumption of an effective electric field E eff = E + (4 π /3) P is reasonably valid, e (ω) can be related to the Szigetieffective charge, e * S = (e 0 + 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 e ( 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 γ T 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. A first-order Raman effect occurs only for crystals with ZnS and CC structures. The Raman spectra of zinc blende exhibits lines due to the TO ( q ≈ 0) and the LO ( q ≈ 0) vibration modes, whose intensities and depolarization factors are reasonably well understood. A second-order Raman effect occurs for all of the cubic diatomic crystals and may involve either a second-order electronic polarizability mechanism or an anharmonic mechanism or a combination of these. The second-order spectra, which have thus far only been investigated in diamond and the alkali halides, are continuous in character and have an appreciable number of prominent peaks. As in the case of the infrared absorption spectra, the structure arises from critical points in the combined density of phonon pair states. Selection rules have also been established for the combination of modes at Γ, X, L and W points in the reduced zone which can take part in Raman scattering in ZnS, CC, and NaCl type crystals. The intensity of the second-order Raman spectra of the alkali halide increases with increasing polarizability of the ions. The spectra of NaCl, NaBr, KBr, and KI are polarized except for the most prominant peak which is depolarized. The spectra of KCl and RbBr, which have a mass ratio of the ions close to unity, are apparently everywhere polarized. In CsCl type crystals, on the other hand, the spectra are everywhere depolarized. The theory of the depolarization effects in second-order Raman spectra has not yet been worked out in detail.