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.