High-entropy alloys are solid solutions of multiple principal elements that are capable of reaching composition and property regimes inaccessible for dilute materials. Discovering those with valuable properties, however, too often relies on serendipity, because thermodynamic alloy design rules alone often fail in high-dimensional composition spaces. We propose an active learning strategy to accelerate the design of high-entropy Invar alloys in a practically infinite compositional space based on very sparse data. Our approach works as a closed-loop, integrating machine learning with density-functional theory, thermodynamic calculations, and experiments. After processing and characterizing 17 new alloys out of millions of possible compositions, we identified two high-entropy Invar alloys with extremely low thermal expansion coefficients around 2 × 10-6 per degree kelvin at 300 kelvin. We believe this to be a suitable pathway for the fast and automated discovery of high-entropy alloys with optimal thermal, magnetic, and electrical properties.

Using the Thermo-Calc implementation of the CALPHAD approach, high-throughput screening of the Co–Cr–Fe–Mn–Ni system was implemented to find ‘islands’ of single phase FCC structure within the compositional space in order to reduce the cost of this well-studied alloy system. The screening identified a region centred around Co₁₀Cr₁₂Fe₄₃Mn₁₈Ni₁₇, reducing the material cost compared to the equiatomic alloy by ∼40%. The alloy was experimentally investigated at room and elevated temperatures, including in-situ tensile testing. The alloy was found to possess slightly lower strength compared to the equiatomic alloy at room temperature, however, exhibited excellent thermal strength up to 873K. Deformation twinning was observed after tensile testing at room temperature, primarily attributed to the reduced stacking fault energy (SFE), which was proven by a thermodynamic model for calculating the SFE. The softening behaviour at room temperature can be explained through solid solution hardening (SSH), whereby a modified approach to Labusch's model was used to calculate the SSH in reported alloys in this study within the Co–Cr–Fe–Mn–Ni system. The modified models for SFE and SSH are proposed to be implemented into high-throughput screening algorithms for accelerated alloy design towards specific mechanical properties.

We used the Thermo-Calc High Entropy Alloy CALPHAD database to determine the stable phases of AlCrMnNbTiV, AlCrMoNbTiV, AlCrFeTiV and AlCrMnMoTi alloys from 800 to 2800 K. The concentrations of elements were varied from 1-49 atom%. A five- or six-dimensional grid is constructed, with stable phases calculated at each grid point. Thermo-Calc was used as a massive parallel tool and three million compositions were calculated, resulting in tens of thousands of compositions for which the alloys formed a single disordered body centered cubic (bcc) phase at 800 K. By filtering out alloy compositions for which a disordered single phase persists down to 800 K, composition 'islands' of high entropy alloys are determined in composition space. The sizes and shapes of such islands provide information about which element combinations have good high entropy alloy forming qualities as well as about the role of individual elements within an alloy. In most cases disordered single phases are formed most readily at low temperature when several elements are almost entirely excluded, resulting in essentially ternary alloys. We determined which compositions lie near the centers of the high entropy alloy islands and therefore remain high entropy islands under small composition changes. These island center compositions are predicted to be high entropy alloys with the greatest certainty and make good candidates for experimental verification. The search for high entropy islands can be conducted subject to constraints, e.g., requiring a minimum amount of Al and/or Cr to promote oxidation resistance. Imposing such constraints rapidly diminishes the number of high entropy alloy compositions, in some cases to zero. We find that AlCrMnNbTiV and AlCrMoNbTiV are relatively good high entropy alloy formers, AlCrFeTiV is a poor high entropy alloy former, while AlCrMnMoTi is a poor high entropy alloy former at 800 K but quickly becomes a better high entropy alloy former with increasing temperature.

We present results of MD simulations of low energy He ion bombardment of low density fuzz in bcc elements. He ions can penetrate several micrometers into sparse fuzz, which allows for a sufficient He flux through it to grow the fuzz further. He kinetic energy falls off exponentially with penetration depth. A BCA code was used to carry out the same ion bombardment on the same fuzz structures as in MD simulations, but with simpler, 10 million times faster calculations. Despite the poor theoretical basis of the BCA at low ion energies, and the use of somewhat different potentials in MD and BCA calculations, the ion penetration depths predicted by BCA are only ∼12% less than those predicted by MD. The MD-BCA differences are highly systematic and trends in the results of the two methods are very similar. We have carried out more than 200 BCA calculation runs of ion bombardment of fuzz, in which parameters in the ion bombardment process were varied. For most parameters, the results show that the ion bombardment process is quite generic. The ion species (He or H), ion mass, fuzz element (W, Ta, Mo, Fe) and fuzz element lattice parameter turned out to have a modest influence on ion penetration depths at most. An off-normal angle of incidence strongly reduces the ion penetration depth. Increasing the ion energy increases the ion penetration, but the rate by which ion energy drops off at high ion energies follows the same exponential pattern as at lower energies.

Results are presented of large-scale Molecular Dynamics simulations of low-energy He bombardment of W nanorods, or so-called 'fuzz' structures. The goal of these simulations is to see if ballistic He penetration through W fuzz offers a more realistic scenario for how He moves through fuzz layers than He diffusion through fuzz nanorods. Instead of trying to grow a fuzz layer starting from a flat piece of bulk W, a new approach of creating a fully formed fuzz structure 0.43 μm thick out of ellipsoidal pieces of W is employed. Lack of detailed experimental knowledge of the 3D structure of fuzz is dealt with by simulating He bombardment on five different structures of 15 vol% W and determining the variation in He penetration for each case. The results show that by far the most important factor determining He penetration is the amount of open channels through which He ions can travel unimpeded. For a more or less even W density distribution He penetration into fuzz falls off exponentially with distance and can thus be described by a 'half depth'. In a 15 vol% fuzz structure, the half depth can reach 0.18 μm. In the far sparser fuzz structures that were recently reported, the half depth might be 1 μm or more. This means that ballistic He penetration offers a more likely scenario than He diffusion through nanorods for how He moves through fuzz and may provide an adequate explanation for how He penetrates through the thickest fuzz layers reported so far. Furthermore, the exponential decrease in penetration with depth would follow a logarithmic dependence on fluence which is compatible with experiments. A comparison of these results and molecular dynamics calculations carried out in the recoil interaction approximation shows that results for W fuzz are qualitatively very different from conventional stopping power calculations on W with a similarly low but homogeneous density distribution.