Correlation between band gap, dielectric constant, Young's modulus and melting temperature of GaN nanocrystals and their size and shape dependences

With structural miniaturization down to the nanoscale, the detectable parameters of materials no longer remain constant but become tunable. For GaN nanocrystals example, the band gap increases while the dielectric constant, Young's modulus and melting temperature decrease with decreasing the solid size. Herein, we developed the models to describe the size and shape dependences of these seemingly uncorrelated parameters for GaN nanocrystals, based on our established thermodynamic model for cohesive energy of metallic nanocrystals. Consistency between our theoretical predictions and the corresponding experimental or simulated results confirms the accuracy of the developed models and indicates the essentiality of cohesive energy in describing the effects of size and shape on the physicochemical properties of different low-dimensional systems.