Interpretation of Debye-Waller Factors

Abstract

${\Theta }^{\mathrm{DW}}\mathrm{}\left(T\right)\mathrm{}$, calculated in the quasiharmonic approximation from thermodynamic data, is compared with the results of the Mössbauer experiment on tin of Boyle et al.; the difference between the curves increases with temperature and is significant. Boyle et al. interpreted their results as showing substantial anharmonic effects and suggested that this interpretation was reasonable by appealing to a model involving a single particle in a one-dimensional well. We have applied their model to a number of other elements, especially copper, germanium and silicon, and find that the Debye-Waller data are consistent with the calorimetric data only for tin. We conclude that the very simplified model of Boyle et al. may be unreliable. The Mössbauer results of Wiedemann et al. and Yaqub and Hohenemser are considered. In view of the reliability of calorimetric data and the experimental difficulties involved in making Mössbauer measurements it is felt that Wiedemann's value of 153°K for ${{\Theta }_0}^{\mathrm{DW}}$ is too high by about 7%. The results of Yaqub and Hohenemser agree quite well with ours. They have apparently observed no evidence of vibrational anharmonicity in tin even at their highest temperature reading of 373°K.