Examination of the Thermal Variation of the Mean Square Atomic Displacements in Zinc and Evaluation of the Associated Debye Temperature

The two principal components of the mean square atomic displacement differences due to thermal vibrations in zinc have been measured from single-crystal x-ray diffraction intensities over a thermal range from 4.85 to 600°K. The absolute value of the components of the mean square atomic displacements parallel to the hexagonal axis and lying in the basal plane have been evaluated from the data by means of a self-consistent technique; these mean square atomic displacements are compared with existing theoretical and experimental values. The x-ray Debye temperatures ${\Theta }^M\mathrm{}\left(T\right)\mathrm{}$ have been evaluated; ${\Theta }^M\mathrm{}\left(0\right)\mathrm{}$ is found to be 219.6°K, whereas ${\Theta }^M\mathrm{}\left(600\right)\mathrm{}$ drops to 187°K. The values of ${\Theta }^M\mathrm{}\left(T\right)\mathrm{}$ are compared with theoretical calculations, as well as with other experimental results. The thermal variation of ${\Theta }^M\mathrm{}\left(T\right)\mathrm{}$ appears to be explained by volume-expansion effects over a limited thermal range ($100°\mathrm{K}<T<\mathrm{}400\mathrm{}°\mathrm{K}$). At higher temperatures, additional anharmonic effects appear to be present. An analysis of measured and calculated values of the temperature derivative of the mean square displacement has led to an evaluation of constant-volume anharmonic effects. Comparison is also made between ${\Theta }^M\mathrm{}\left(T\right)\mathrm{}$ and Debye temperatures relating to other averages over the frequency-distribution function.