Abstract
Based on the established bond moduli of surface atoms ys and interior ones yi in a nanostructure, surface modulus Ys(D) and interior modulus Yi(D) are modeled with D being size. And then the Young's modulus Y(D) is determined through considering the volume fraction of Ys(D) and Yi(D). It is found that the variations of Ys(D), Yi(D) and Y(D) are evident, where cubooctahedron is taken as the shape of nanoparticles. In Cu and diamond nanoparticles, although their Ys(D) and Yi(D) present the decrease trend with D dropping, the increase in Y(D) of Cu nanoparticles but the decrease of Y(D) for diamond nanoparticles are existing. As expected, the contribution of Ys(D) is important, since it is Ys(D) > Y0 mainly leading to Y(D) > Y0 for Cu nanoparticles, and the similar case happens for diamond nanoparticles when D < 2.8 nm, where Ys(D) < Y0 and Y(D) < Y0 are seen with Y0 being bulk Young's modulus. However, it is also pointed out that the contribution of Yi(D) can not be ignored and it is no longer a constant with Yi(D) ≤ Y0. This can be reflected by, one hand the different change trend of Ys(D) and Y(D) in Cu nanoparticles, and the other hand the case where Ys(D) > Y0 but Y(D) < Y0 for diamond nanoparticles as D > 2.8 nm. All this implies that the reason why Y(D) greatly rely on size and have different change trend for different materials can be clarified by considering Ys(D) and Yi(D).
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