Lattice strain plays a crucial role on the properties of nanoparticles. Although the effect of lattice strain on nanoparticles has been widely studied in experimental measurements and calculations, its physical mechanism from the perfective of bond identities is still poorly understood. Herein we put forward an analytical solution of the size effect and external stimuli such as pressure and temperature dependence of lattice strain and bulk modulus of a nanoparticle from the perspective of atomistic origin. A shell–core configuration has been considered for the nanoparticle structure. It has been found that the lattice strain as well as quantum trapping and energy storage exerted by the compressive stress and thermal stress would be responsible for the mechanical behavior of nanoparticles. The theoretical predictions were well consistent with the experimental data and ab initio calculations, implying that the model could be expected to be a general approach to understand mechanical behavior in nanomaterials.

Combining the thermodynamics at the nanometer scale and the continuum mechanics, we established a universal and analytic thermodynamic model to elucidate the surface energy of nanocrystals. It was found that the surface energy decreases with decreasing the size of nanocrystals. The theoretical predictions were well consistent with the experimental data, implying that the thermodynamic model could be expected to be a general approach to understand surface energy in nanomaterials.