  Incorporating the bond-order-length-strength correlation mechanism [Sun CQ,
Prog Solid State Chem 35, 1 -159 (2007)] and Borns criterion for melting [J.
Chem. Phys. 7, 591(1939)] into the conventional Hall-Petch relationship has
turned out an analytical expression for the size and temperature dependence of
the mechanical strength of nanograins, known as the inverse Hall-Petch
relationship (IHPR), that has long been a topic under debate regarding the
possible mechanisms. Reproduction of the measured IHPR of Ni, NiP and TiO2
nanocrystals revealed that: (i) the size induced energy densification and
cohesive energy loss of nanograins originates the IHPR that could be activated
in the contact mode of plastic deformation detection; (ii) the competition
between the inhibition of atomic dislocations, via the surface energy density
gain and the strain work hardening, and the activation for dislocations through
cohesive energy loss determine the entire IHPR profile of a specimen; (iii) the
presence of a soft quasisolid phase is responsible for the size-induced
softening and the superplasticity as well of nanostructures; (iv) the bond
nature involved and the T/Tm ratio between the temperature of operating and the
temperature of melting dictate the measured strongest sizes of a given
specimen.
