Anharmonicity of the Debye-Waller factor in alkali halides

Using high intensity (${\sim}70$ Ci) $\sp{183}$Ta Mossbauer sources, we have measured the elastic scattering fraction values, $\cal F$, and the relative integrated scattering intensities for several (nnn) and (h00) Bragg reflections of three alkali halides: sodium chloride, potassium chloride, and potassium bromide. The experiments were done as a function of temperature from 85 K to 900 K. The $\cal F$ values were found by Mossbauer line-shape studies (1) and were used to correct the measured integrated intensities for thermal diffuse (inelastic) scattering so that the Debye-Waller factors could be accurately measured. Measured elastic intensities were directly corrected for thermal expansion, in constrast to earlier treatments of Debye-Waller factor data. We show that this is the only consistent way to analyse this type of data, and it also significantly reduces the strong correlation between parameters. We observed $Q\sp4$ contributions to the Debye-Waller factors in all three crystal, though the evidence is marginal in the case of KBr. This contribution varies with crystallographic orientation. After separating the scattering from the two ion types within the NaCl and KBr crystals, we found that for both NaCl and KBr the cations and anions have the same Debye-Waller factor, and thus the same mean-square displacement from equilibrium along the (111) direction. We account for this by the equipartition theorem. We also found that the Debye temperature and $Q\sp2T\sp2$ term vary with crystallographic direction. We believe this to be the first direct evidence for a non-spherical thermal cloud in cubic crystals