An analytical solution shows that the maximal strain of an impurity-free metallic monatomic chain (MC), or a defect-free nanowire (NW), varies inapparently with mechanical stress but apparently with the separation between the melting point ͓T m ͑K͔͒ and the temperature of operation in terms of exp͕͓T m ͑K͒ − T͔ −1 ͖, where K is the dimension of the NW (for a MC, K = 1.5). Reconciliation of the measured data of Au-MC breaking limit suggests that the discrepancy in measurement arises from thermal and mechanical fluctuations near the T m of the MC that is ͑1 / 4.2͒-fold of the bulk value. Findings also favor the mechanism for the high extensibility of a nanograined NW and further indicate that bond unfolding of the lower-coordinated atoms dominates the grain boundary activities, particularly at temperatures approaching surface melting.
The correlation between the thermal stability and electroaffinity of a nanosolid has been explored from the perspective of surface and interface bond-order deficiency. It turns out that the coherency of an atom at the grain boundary and the portion of atoms in the skin of a nanosolid dominate the size dependence of critical temperatures ͑T C ͒ for phase transitions. The trapping potential well depression at the surface and interface not only shifts the valence density of state positively but also enlarges the electroaffinity that determines the strength of the bond. In particular, bond-nature alteration at the junction interface, or bond-nature evolution with the reduction of atomic coordination of III-or IV-A atoms, dominates the irregular T C change with the sizes of the embedded or the III-or IV-A bare nanosolids. Atoms in "superficial" or "interfacial" skins play the core role in dictating the size effect on the thermal stability and electroaffinity of a nanosolid whereas atoms in the core interior remain as they are in the bulk.
An analytical solution shows that a competition between bond order loss and the associated bond strength gain of the lower coordinated atoms near the edge of a surface dictates the mechanics of the surface and, hence, a nanosolid. Bond order loss lowers the activation energy for atomic dislocation, whereas bond strength gain enhances the energy density or mechanical strength in the region near the surface. Therefore, the surface is harder than the bulk interior at temperatures far below the melting point (T m ), and the surface becomes softer at temperatures close to the surface T m that drops because of bond order loss. Matching predictions to measurements reveals that a transition happens to the Hall-Petch relationship for a nanosolid when the effect of bond order loss becomes dominant, and the critical size of the Hall-Petch transition depends intrinsically on the bond nature of the specimen and the ratio of T/T m , where T is the temperature of operation.
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