Abstract
Nickel-based superalloys and near-equiatomic high-entropy alloys containing molybdenum are known for higher temperature strength and corrosion resistance. Yet, complex solid-solution alloys offer a huge design space to tune for optimal properties at slightly reduced entropy. For refractory Mo-W-Ta-Ti-Zr, we showcase KKR electronic structure methods via the coherent-potential approximation to identify alloys over five-dimensional design space with improved mechanical properties and necessary global (formation enthalpy) and local (short-range order) stability. Deformation is modeled with classical molecular dynamic simulations, validated from our first-principle data. We predict complex solid-solution alloys of improved stability with greatly enhanced modulus of elasticity (3× at 300 K) over near-equiatomic cases, as validated experimentally, and with higher moduli above 500 K over commercial alloys (2.3× at 2000 K). We also show that optimal complex solid-solution alloys are not described well by classical potentials due to critical electronic effects.
Highlights
Nickel-based superalloys exhibit high-temperature strength, toughness, and oxidation resistance in harsh environments.[1]Improving existing single-crystal alloys is unlikely as melting is near 1350 °C, and, heat treatment lowers this to ~ 1270 °C
Trial and error has led to alloys with simple crystal structures, and a few with extraordinary properties,[25] e.g., formability using size disparate elements for confusion by design.[26]
For complex solidsolution alloys (CSAs) design largest, followed by Ti, Ta, and W, Mo (1.46, 1.43, and 1.37, 1.36 Å), where bandwidths and alloy hybridization determine the effect of size.[21]
Summary
Nickel-based superalloys exhibit high-temperature strength, toughness, and oxidation resistance in harsh environments.[1]. High-entropy alloys based on refractory elements may achieve higher temperature operation with superior creep strength.[3]. As for binary solid solutions, Hume-Rothery’s rules[12] for atomic size difference (δ), crystal structure, valence electron concentration (VEC), and electronegativity difference (Δχ) play a similar role in high-entropy alloy formation. Structures exhibiting enhanced high-temperature strength, ductility, fracture and creep resistance to corrosion,[7–10,13,14] and thermal stability[15] validates the concept of HEAs.[7]. Optimized CSAs offer a slightly reduced entropy with a single-phase region, or two-phase region for enhanced mechanical properties, existing in a desired operational temperature range.[16–18]. The well-established KKR-CPA predicts structural properties [e.g., Young’s (E) or bulk modulus (B)], and phase stability (ΔEform vs {cα}), as well as short-range order (SRO) via thermodynamic linear response,[18,20–23] a method, in particular, that revealed the origin for Hume-Rothery’s size-effect rule.[21,24]. Atomic size of Zr (1.60 Å) is quinary alloys and their properties are placed in context to HumeRothery-type design targets and compared to experiments
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