Atomistic-continuum coupling of random alloys

Random alloys are multicomponent systems where the atomic type on each lattice site is independent of the atom types on any other lattice site. The fluctuations in local atomic configurations inherent to the random alloy prevents the accurate application of standard force-based atomistic/continuum (a/c) coupling. Errors arise because the two transitions, from atomistic to continuum and from random-to-homogeneous, occur at the same location. Here, two methods for a/c coupling that mitigate errors arising in the standard method are proposed, studied, and validated. In one method, the desired atomistic domain and its nearby surroundings are fully relaxed to an equilibrium structure and then inserted into the coupled problem as the reference configuration. This reduces the effects of the random-to-homogeneous transition, and guarantees no spurious stress at zero load. In the second method, the random-to-homogeneous transition is spatially separated from the atomistic-continuum transition by introducing a small buffer zone of well-defined 'average atoms'. The random-to-homogeneous transition is then accomplished fully atomistically while the atomistic to continuum transition is accomplished in a homogeneous material. The two methods are validated through comparisons of the stresses in the coupled method versus the true atomistic system for three different solid solution alloys (Al-5%Mg, Ni-15%Al, and medium entropy FeNiCr) as described by EAM interatomic potentials. Spurious stresses for both methods and across all three materials are negligible (approximate to 5 MPa) relative to stresses arising in realistic mechanical problems of interest. These new methods thus enable the accurate study of mechanics boundary value problems in random alloys for problems where it is essential to capture atomistic phenomena in some localized region of the random alloy.