Elastic properties lattice displacement

The obtained Ao gi = 5.7 x 10 is even larger than the value of Acr (Cu) X (= 4.7 X 10 A ), and of the hypothetical Co—Cu crystal with intermediate elastic properties than bulk cobalt and copper (4.1 x lO" A ). The derived effect of the effect of the lower coordination of the surface atoms on the mean-square relative displacement (perpendicular vs. parallel motions) is 1.4 times larger amplitude of the perpendicular vs. parallel motions, in agreement with lattice dynamics calculations. This SEXAFS study has produced a measure of the surface effect on the atomic vibrations. This has been possible due to the absence of surface or adsorbate reconstruction (i.e. no changes in bond orientations with respect to the bulk) and of intermixing. 

Our starting point for the analysis of the thermal and elastic properties of crystals is an approximation. We begin with the assertion that the motions of the i atom, will be captured kinematically through a displacement field Uj which is a measure of the deviations from the atomic positions of the perfect lattice. It is presumed that this displacement is small in comparison with the lattice parameter, uj < C qq. Though within the context of the true total energy surface of our crystal (i.e. R2,. .., Rw)) this approximation is unnecessary, we will see... 

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