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Incorporating the bond–order–length–strength correlation mechanism [C. Q. Sun, Prog. Solid State Chem.35, 1 (2007)] and Born's 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). Reproduction of the measured IHPR of Ni, NiP, and TiO2 nanocrystals revealed that: (i) the competition between the size-induced energy–density gain and atomic cohesive energy loss in the surface skins of nanograins originate from the IHPR; (ii) the competition between the activation and inhibition of atomic dislocations motion activate the entire IHPR behavior; (iii) 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; (iv) a quasimolten phase present before melting determines the size-induced softening and the superplasticity of nanostructures. [ABSTRACT FROM AUTHOR]