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Reversed anisotropies and thermal contraction of fcc (110) surfaces

“…The surprise is that for these unreconstructed FCC(110) surfaces, some of these anisotropies are reversed, i.e., they violate the "common sense" expectation. For example, experiments show that in general: (i) atoms in the topmost surface layer have a bigger mean-squared displacement (MSD) in the surface plane than normal to it, whereas one might have expected the latter to be larger, since along this direction, there are no higher layers to repel the atoms in the first layer [3,4]; (ii) the MSDs normal to the surface are larger for second layer atoms than for first layer atoms, though one would expect that the MSDs should decay monotonically into the bulk [5]; (iii) a third curious fact about unreconstructed FCC (110) surfaces is that in some cases there is a thermal contraction of interlayer distances upon heating. The rule of thumb seems to be that if the first interlayer spacing d 12 expands upon heating, then the next interlayer spacing d 23 contracts [3]; however, if d 12 exhibits a thermal contraction, then d 23 expands with increasing temperature [5,6].…”