Deficiencies of the Rigid-Ion Model

Besides the discrepancies between calculated and observed dispersion curves as illustrated in Fig.4.5, there are other deficiencies of the rigid-ion model. Since the model is based on central forces, it predicts the Cauchy relations which for a cubic crystal are C 2 = 44- glance at Table 3.2 shows that these relations are only approximately satisfied for the alkali halides. 

The rigid-ion model is also inconsistent with the dielectric properties of crystals (Sect.4.3.2). At optical frequencies only the electrons (and not the ions) respond to the electric field of the light. The electronic polarization gives rise to the dielectric constant which for the alkali halides have observed values between 2 and 3. Since the rigid-ion model ignores the electronic polarizabilities, it predicts = 1. 

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