On the bending of unconstrained thin crystalline plates caused by the change in surface stress

The current technique of measuring the change in surface stress at the solid–vacuum and solid–liquid interface is typically based on the bending of a thin crystalline plate. The crucial issue is to convert the measured data such as curvature or deflection into the change in surface stress with the help of elasticity theory. In this paper, explicit relations are derived between the change in surface stress and the curvature of an unconstrained plate with arbitrary crystallographic symmetry. The result is exact in the sense that it satisfies all the relevant equations in elasticity, except the boundary conditions on the lateral edge are fulfilled on average. In addition, it is also shown that some existing results for surface stress induced bending of free isotropic and cubic plates are actually exact, although some kinetic assumptions are adopted in their derivation.