Microelasticity model of random alloys. Part I: mean square displacements and stresses

In concentrated solid solutions, the random distribution of elements different sizes induces characteristic displacement and stress fields at root solution strengthening. The aim this two-part article is to derive statistical properties these elastic fields. present Part I focuses on variance fields, while II addresses their spatial correlations. first part, we develop two models based respectively real-space spectral methods, mean square shear stress. Both approaches hold advantages drawbacks that are discussed here. We show in particular both directly proportional atomic eigenstrains, which embodies size differences simplifies classical lattice mismatch parameter if alloy satisfies Vegard’s law. This allows clarify scaling relations between various quantities (mismatch parameter, yield stress) bridge energy-based stress-based strengthening proposed literature. predictions for mean-square stresses also successfully compared with atomistic results obtained a model Lennard-Jones system more complex Al–Mg interatomic potential.