Inverse Hall-Petch relationship in the nanostructured TiO₂: Skin-depth energy pinning versus surface preferential melting

The functional dependence of stress, elastic modulus, melting point, and their interdependence on the identities (bond order, nature, length, and strength) of a representative bond of the specimen has been established for deeper insight into the transition from the conventional Hall-Petch relationship (HPR) to the inverse HPR (IHPR) for nanostructured TiO₂. Theoretical reproduction of the observed inverse HPR suggests that the intrinsic competition between the energy-density gain (elastic modulus enhancement) and the cohesive-energy remnant (melting point depression) in the grain boundaries originates and the extrinsic competition between the activation and the inhibition of atomic dislocations activates the IHPR. © 2010 American Institute of Physics.