Alternative to the Shuttleworth formulation of solid surface stress

Abstract

We examine two derivations of the Shuttleworth equation (which is a relation between surface stress $g,$ surface tension \ensuremath{\gamma}, and surface strain), and identify the flaws we perceive. Rectifying the perceived flaws leads not to the Shuttleworth equation but to $g\ensuremath{-}\ensuremath{\gamma}$ equivalence. We conclude that surface stress is merely the generalization of the concept of surface tension to an elastically anisotropic system; the surface free-energy density is one-half of the trace of the surface stress tensor, to lowest order. In our opinion, our conclusions lead to a more coherent and elegant form of surface thermodynamics which should prove useful in controlling and in understanding nanometer-scale fabrication.