It has long been puzzling regarding the trends and physical origins of the size-effect on the elasticity of ZnO nanostructures. An extension of the atomic “coordination-radius” correlation premise of Pauling and Goldschmidt to energy domain has enabled us to clarify that the elastic modulus is intrinsically proportional to the sum of bond energy per unit volume and that the size-induced elastic stiffening arises from (i) the broken-bond-induced local strain and skin-depth energy pinning and (ii) the tunable fraction of bonds between the undercoordinated atoms, and therefore, the elastic modulus of ZnO nanostructures should increase with the inverse of feature size.

As a group of wonder materials, gold and silver at the nanoscale demonstrate many intriguing properties that cannot be seen from their bulk counterparts. However, consistent insight into the mechanism behind the fascinations and their interdependence given by one integrated model is highly desirable. Based on Goldschmidt-Pauling's rule of bond contraction and its extension to the local bond energy, binding energy density, and atomic cohesive energy, we have developed such a model that is able to reconcile the observed size dependence of the lattice strain, core level shift, elastic modulus, and thermal stability of Au and Ag nanostructures from the perspective of skin-depth bond order loss. Theoretical reproduction of the measured size trends confirms that the undercoordination-induced local bond contraction, bond strength gain, and the associated binding energy density gain, the cohesive energy loss and the tunable fraction of such undercoordinated atoms dictate the observed fascinations, which should shed light on the understanding of the unusual behavior of other nanostructured materials as well. V

Although the physics behind the bulk modulus, B͑T , P͒, as a function of temperature ͑T͒ and pressure ͑P͒, has been intensively investigated, an atomic scale understanding of this attribute remains a high challenge. Here, we show that the B͑T , P͒ for BaXO 3 ͑X=Ti,Zr,Nb͒ can be established by connecting the B directly to the bond length and bond energy and their response to the applied T and P in the form of binding energy density, B͓E / d 3 ͑T , P͔͒. Besides an estimation of the Debye temperature and single bond energy, outcomes clarified that the thermally softened B arises from bond expansion and bond weakening due to lattice vibration and the mechanically stiffened B results from bond compression and bond strengthening due to mechanical work hardening.