Elastic modelling of lattice distortions in concentrated random alloys

Lattice distortions, i.e. small atomic displacements away from the average lattice, are linked to a number of functional and mechanical properties of concentrated metallic alloys, particularly their yield strength. Here we develop an elastic model of lattice distortions where every atom is modeled as an Eshelby inclusion in a homogeneous elastic matrix. Local environment effects are included by considering fluctuating anisotropic eigenstrain tensors associated to the inclusions. The model is tested on several concentrated alloys, face-centered cubic (FCC) AlMg and FeNiCr alloys, as well as a fictitious body-centered cubic (BCC) binary alloy to study systematically and independently the effects of a size and an elastic modulus mismatch between the constituents. The elastic model predicts lattice distortions well when the size and elastic modulus mismatches are typically less than 5% and 25%, respectively. Interestingly, we find that when the size mismatch is small, as in FeNiCr alloys, the lattice distortion is dominated by the fluctuations of the dilatational eigenstrains rather than their average value as often assumed in elastic models of concentrated alloys. Moreover, models usually assume homogeneous elastic constants, while the limit obtained here of 25% is often exceeded in concentrated alloys, particularly with a BCC structure.

Automated summary

Lattice distortions play a crucial role in determining the mechanical properties of concentrated metallic alloys. In this study, we developed an elastic model to describe lattice distortions, considering each atom as an Eshelby inclusion in a homogeneous elastic matrix. The model was tested on various alloy systems and showed good predictive performance when the size and elastic modulus mismatches were below 5% and 25%, respectively. Interestingly, we found that in certain alloys, such as FeNiCr, lattice distortions were mainly influenced by the fluctuations of dilatational eigenstrains rather than their average values.