Simulating short-range order in compositionally complex materials

Quantifying chemical short-range order in metallic alloys

Metallic alloys often form phases-known as solid solutions-in which chemical elements are spread out on the same crystal lattice in an almost random manner. The tendency of certain chemical motifs to be more common than others is known as chemical short-range order (SRO), and it has received substantial consideration in alloys with multiple chemical elements present in large concentrations due to their extreme configurational complexity (e.g., high-entropy alloys). SRO renders solid solutions "slightly less random than completely random," which is a physically intuitive picture, but not easily quantifiable due to the sheer number of possible chemical motifs and their subtle spatial distribution on the lattice. Here, we present a multiscale method to predict and quantify the SRO state of an alloy with atomic resolution, incorporating machine learning techniques to bridge the gap between electronic-structure calculations and the characteristic length scale of SRO. The result is an approach capable of predicting SRO length scale in agreement with experimental measurements while comprehensively correlating SRO with fundamental quantities such as local lattice distortions. This work advances the quantitative understanding of solid-solution phases, paving the way for the rigorous incorporation of SRO length scales into predictive mechanical and thermodynamic models.

Nanoindentation into a bcc high-entropy HfNbTaTiZr alloy-an atomistic study of the effect of short-range order

The plastic response of the Senkov HfNbTaTiZr high-entropy alloy is explored by means of simulated nanoindentation tests. Both a random alloy and an alloy with chemical short-range order are investigated and compared to the well understood case of an elementary Ta crystal. Strong differences in the dislocation plasticity between the alloys and the elementary Ta crystal are found. The high-entropy alloys show only little relaxation of the indentation dislocation network after indenter retraction and only negligible dislocation emission into the sample interior. Short-range order-besides making the alloy both stiffer and harder-further increases the size of the plastic zone and the dislocation density there. These features are explained by the slow dislocation migration in these alloys. Also, the short-range-ordered alloy features no twinning plasticity in contrast to the random alloy, while elemental Ta exhibits twinning under high stress but detwins considerably under stress relief. The results are in good qualitative agreement with our current knowledge of plasticity in high-entropy alloys.

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.