Nanocavity hardening: impact of broken bonds at the negatively curved   surfaces
  It is expected that atomic vacancies or nanometric cavities reduce the number of chemical bonds of nearby atoms and hence the strength of a voided solid. However, the hardness of a porous specimen does not always follow this simple picture of coordination counting. An introduction of a certain amount of atomic vacancies or nanocavities could, instead, enhance the mechanical strength of the porous specimen. Understanding the mechanism behind the intriguing observations remains yet a high challenge. Here we show with analytical expressions that the shortened and strengthened bonds between the under-coordinated atoms and the associated local strain and energy trapping [Sun, Prog Solid State Chem 35, 1-159 (2007)] in the negatively curved surface skins dominate the observed nanocavity hardening. Agreement between predictions and the experimentally observed size-dependence of mechanical strength of some nanoporous materials evidences for the proposed mechanism. 
Chang Q. Sun