Simple calculation of the mean-square displacements of volume, (110) and (100) surface atoms of chromium

Abstract

We use an analytic method based on the expansion of the dynamical matrix to determine the thermal dependence of the mean-square displacements 〈u2〉 of volume, and (100) and (110) surface atoms of Cr. For the volume and (110) surface the results are in satisfactory agreement with previous X-ray and low-energy electron diffraction data. In particular, the zero-point thermal motion of Cr-volume atoms is approximately reached at temperatures as high as 170°K in accordance with experiments. A discussion about the temperature at which the atomic vibrations are strongly frozen is carried out for b.c.c. crystals. © 1973.