The thermodynamic calculation of the debye-waller factors of potassium bromide and magnesium oxide

Experimental low temperature thermodynamic data have been applied to the calculation of the moments of the frequency distribution of potassium bromide. The corresponding maximum frequencies v D(n) of the Debye distributions having the same nth moments have been applied in calculating the temperature variation of the Debye-Waller factor θM(T, V) at very low temperatures and at high temperatures using appropriate expansions, and at intermediate temperatures using a Padé approximant. The results agree within the limits of experimental error with calculations based upon recent observations of the integrated intensities of Bragg reflections from 93 to 500°K, but from 500 to 643°K the x-ray results are slightly lower. The maximum frequencies of the corresponding Debye distributions for magnesium oxide, calculated previously, have been applied similarly, and the resulting Debye-Waller factors agree with the x-ray results over the entire range of observation, 93 to 973°K.