Are surfaces elastically softer or stiffer?

This letter addresses the issue of surface softening versus stiffening during elastic deformation. Using a combination of molecular statics and ab initio calculations, we show that a solid surface can be either softer or stiffer elastically than the corresponding bulk. Whether a particular surface is softer or stiffer depends on the competition between atomic coordination and electron redistribution (which sometimes is referred as bond saturation) on the surface. Taking Cu as an example, we demonstrate that the Young’s modulus along 〈110〉 direction on {100} surface is larger than its bulk counterpart; meanwhile, it is smaller along 〈100〉 direction on {100} surface.