  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.
