Structure and mechanical properties of ultra-nanocrystalline diamond and nanocrystalline Cu from atomistic simulations

Abstract

Several nanocrystalline metals demonstrate the so-called “reverse Hall–Petch effect” and become softer as their average grain size, d, decreases. Using atomistic simulations, we found that ultra- nanocrystalline diamond (UNCD) shows the same behaviour. We also examined a typical metal (Cu) and found that softening at small grain sizes is not limited to hardness or yield stress, but is also evident in the cohesive energy and elastic constants of the material. The effect is attributed to the larger concentration of grain boundary atoms at smaller d. Our model, which separately considers contributions to the cohesive energy, and consequently to elastic constants, from atoms in the grains and from atoms at the grain boundaries, fits simulation results extremely well for both materials. We calculate structural properties, elastic constants and estimate the hardness to find that the two materials have several qualitative similarities, such as linear scaling of the fraction of non-crystalline atoms with respect to 1/d and similar scaling laws for cohesive energy and elastic constants. At the same time, several quantitative differences, such as broader peaks in the pair correlation function for UNCD, lead to different magnitude for the scaling coefficients. Our results compare well with experimental observations. Moreover, our theoretical analysis yields universal scaling relations for properties of nanocrystalline materials as a function of the average grain size.