Size, temperature, and bond nature dependence of elasticity and its derivatives on extensibility, Debye temperature, and heat capacity of nanostructures

With the miniaturization of a solid down to nanometer scale, the elasticity, extensibility, Debye temperature, and specific heat capacity of the solid are no longer constant but change with variation of size. These quantities also change with the temperature of the measurement and the nature of the chemical bond involved. The mechanism behind the intriguing tunability and the interdependence of these quantities remain yet a high challenge. A set of analytical solutions is presented herewith showing that the observed trends could be reproduced by taking the fact of bond order deficiency into consideration. Agreement between predictions and observations clarifies that the shortened and strengthened surface bonds dictate intrinsically the observed tunability, yet atoms in the core interior remain as they are in the bulk. The thermally softening of a specimen arises from bond expansion and bond vibration due to the internal energy increases.