Size-induced elastic stiffening of ZnO nanostructures: skin-depth energy pinning

It has long been puzzling regarding the trends and physical origins of the size-effect on the elasticity of ZnO nanostructures. An extension of the atomic “coordination-radius” correlation premise of Pauling and Goldschmidt to energy domain has enabled us to clarify that the elastic modulus is intrinsically proportional to the sum of bond energy per unit volume and that the size-induced elastic stiffening arises from (i) the broken-bond-induced local strain and skin-depth energy pinning and (ii) the tunable fraction of bonds between the under-coordinated atoms, and therefore, the elastic modulus of ZnO nanostructures should increase with the inverse of feature size.