K. Dahmen et al., Bending of crystalline plates under the influence of surface stress - a finite element analysis, SURF SCI, 446(1-2), 2000, pp. 161-173
Changes in the surface stress Delta tau((s)) at the solid-vacuum and the: s
olid-liquid interface are typically measured via the Sending of a (thin) cr
ystalline plate. The bending is converted into Delta tau((s)) with the help
of elasticity theory. Although the conversion is trivial for the unconstra
ined bending of an elastic isotropic substrate, it becomes less straightfor
ward for single crystals. In this paper we firstly consider the analytical
solution for the free two-dimensional bending of a cubic substrate under th
e influence of a homogeneous, but anisotropic surface stress. Secondly, the
bending is calculated numerically for the experimentally mostly realized c
ase of a sample with (100) or (111) surfaces clamped along one edge. In pri
nciple, separate numerical calculations are required for each individual ma
terial and surface orientation. It is shown that a parameterized form of th
e analytical solution for the unconstrained bending can still be used in mo
st cases. The appropriate parameters are calculated for various Poisson rat
ios and crystal anisotropies. (C) 2000 Elsevier Science B.V. All rights res
erved.