The X-ray scattering from epitaxially grown films of Nb on sapphire was measured as a function of the thickness of Nb. For thicknesses, d, greater than 8nm, the mean-square displacements perpendicular to the growth planes increased as dn, where n was equal to about 0.68. The correlation length for these displacements increased as dm, where m was equal to about 0.51. The results were explained in terms of the strains which existed when the film thickness was greater than the distance between misfit dislocations.

The Structure of Epitaxially Grown Thin Films: a Study of Niobium on Sapphire. A.R.Wildes, R.A.Cowley, R.C.C.Ward, M.R.Wells, C.Jansen, L.Wireen, J.P.Hill: Journal of Physics - Condensed Matter, 1998, 10[36], L631-7