Modeling the lattice expansion and contraction of nanocrystals in different interface environments

The lattice strain ε(D) function of nanocrystals within different interface environments was modeled. For nanoparticles and nanocrystals embedded in incoherent interfaces, the lattice shrinks with the decrease of size, resulting in the reduction of ε(D). For nanostructure materials and the nanocrystals embedded in the coherent interfaces, ε(D) increases due to lattice expansion. These changes in interfacial lattice parameters depend on the sign of interfacial stress fss, i.e., the lattice contracts when fss > 0 and expands when fss < 0. In addition, we also give a criterion to judge the sign of fss, fss is negative when the surface stress f of the matrix is larger than that of the embedded nanocrystals, and vice versa. The variation in the sign of fss is also applicable to explain the thermal stability of the interface.