# Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline materials of cubic symmetry

## TL;DR

This paper combines atomistic simulations and a core-shell mean-field model to estimate the elastic properties of nanocrystalline cubic materials, analyzing how grain size and anisotropy influence effective stiffness.

## Contribution

It introduces a core-shell model for nanocrystalline cubic materials and validates it against atomistic simulations, highlighting the impact of grain size and anisotropy on elastic moduli.

## Key findings

- Core-shell model agrees well with atomistic simulations.
- Bulk and shear moduli vary with grain size and anisotropy.
- Elastic properties change qualitatively with Zener factor.

## Abstract

Anisotropic core-shell model of a nano-grained polycrystal, proposed recently for nanocrystalline copper, is applied to estimate elastic effective properties for a set of crystals of cubic symmetry. Materials selected for analysis differ in the lattice geometry (face-centered cubic vs. body-centered cubic) as well as the value of a Zener factor: a ratio of two shear moduli defining elastic anisotropy of a cubic crystal. The predictions are verified by means of the atomistic simulations. The dependence of the overall bulk and shear moduli on the average grain diameter is analysed. In the mean-field approach the thickness of the shell is specified by the \emph{cutoff radius} of a corresponding atomistic potential, while the grain shell is isotropic and its properties are identified by molecular simulations performed for very small grains with approximately all atoms belonging to the grain boundary zone. It is shown that the core-shell model provides predictions of satisfactory qualitative and quantitative agreement with atomistic simulations. Performed study indicates that the variation of the bulk and shear moduli with the grain size changes qualitatively when the Zener anisotropy factor is smaller or greater than one.