Studying the elastic properties of nanocrystalline copper using a model of randomly packed uniform grains

Abstract

a b s t r a c tWe develop a new Voronoi protocol, which is a space tessellation method, to generate a fully dense (containing no voids) model of nanocrystalline copper with precise grain size control; we also perform uniaxial tensile tests using molecular dynamical (MD) simulations to measure the elastic moduli of the grain boundary and the grain interior components at 300 K. We find that the grain boundary deforms more locally compared with the grain core region under thermal vibrations and is elastically less stiff than the core component at finite temperature. The elastic modulus of the grain boundary is lower than 30% of that of the grain interior. Our results will aid in the development of more accurate continuum models of nanocrystalline metals.

Effects of grain size and temperature on mechanical response of nanocrystalline copper

“…6(a), the Young's modulus nearly increases with increasing grain size. This is in agreement with previous results obtained using MD simulations [14,33] because increasing grain size is associated with a larger grain core component, which supports a higher Young's modulus. In addition, at lower temperatures, the Young's modulus has larger values, except for d ¼3 nm.…”

“…This is because the grain growth occurs due to the thermal effect following the equilibration process at 300 K. Neglecting the data for d ¼3 nm, we measured the temperature dependence of Young's modulus and obtained a value of À 37 MPa/K, which is close to the experimental value ( À 40 MPa/K) reported for the same material with a grain size of 200 nm [37]. Further, in comparison with other simulation results using 3D systems [14,33,38], the Young's modulus in our system is higher by approximately þ10 GPa at 300 K. Therefore, the quasi-2D system has strong stiffness.…”

“…Therefore, the results of flow stress are not discussed. With respect to the inverse H-P relation, previous studies using MD simulations [4][5][6][7]33] and bubble raft models [8] suggest that the critical grain size may lie between 7 and 15 nm. A recent study [14] shows that nanocrystalline Cu having grain sizes between 8 and 20 nm correspond to the transition from the H-P to the inverse H-P relation, where there is no obvious relation between stress and grain size.…”

“…2(c) shows ϕ core as a function of grain size at 100 K, 300 K, and 450 K. At a large grain size and lower temperature, the system has a higher fraction of grain core. To determine the thickness of the grain boundary in a quasi-2D system, we used a method similar to the one used by Gao et al [33], which assumes that the fraction of grain core is given by the following expression:…”

Modeling the copper microstructure and elastic anisotropy and studying its impact on reliability in nanoscale interconnects

“…Reduction in the overall free energy is typically the driving force for grain growth. The presence of grain to grain variation in pressure values (or variation in strain energies) may act as a driving force to promote grain growth (Thompson 2000;Wang et al 2013;Gianola et al 2006;J. C. M. Li 2006;Zhang et al 2005;Zielinski et al 1995).…”