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耐火多主元素合金（MPEAs）因其优良的力学性能而在高温应用领域引起了广泛的关注。这些合金通常由几种高熔点元素组成，尽管它们在室温下具有高屈服强度，但在高温应用中受限于低拉伸延展性和急剧的韧脆转变。探索具有更优异强度和延性组合的新组分，是提升耐火MPEAs力学性能的关键挑战，这同时也为采用计算机辅助设计探索这些材料的巨大组分空间开辟了新的机会。近年来，许多工作引入了计算方法来识别和表征具有定制性能的合金，如机器学习（ML）、基于密度泛函理论（DFT）的从头算等。针对合金的从头算模拟，常见的方法包括使用特殊的准随机结构（SQS）、相干势近似（CPA）和机器学习原子间势（MLIPs），但这些方法都存在各自的缺陷。
Fig. 1 | Flowchart of the materials design loopusing Bayesian multi-objective optimization.
来自奥地利莱奥本材料研究中心的Franco Moitzi等人，提出了一种集成先进从头算技术的贝叶斯多目标优化框架，通过一种简单的解析模型来分析趋势，成功地应用于描述难熔MPEAs的固溶强化和延展性。该框架结合了CPA和MLIPs两种方法，同时引入了一个简单模型，可以准确捕捉难熔合金整个组分空间中与强化和塑性有关所有量的浓度依赖性质。作者对三组分和四组分合金进行了强度和延性的多目标优化，并将这些结果用来验证模型，并扩展到了更大的合金。该研究为破解难熔MPEAs的传统强度-延性难题提供了重要的研究思路。
Fig. 11 | Ductility index, D, and CRSS, τy evaluated for various alloys using the VBAmodel.
Ab initio framework for deciphering trade-off relationships in multi-component alloys
Franco Moitzi, Lorenz Romaner, Andrei V. Ruban, Max Hodapp & Oleg E. Peil
While first-principles methods have been successfully applied to characterize individual properties of multi-principal element alloys (MPEA), their use in searching for optimal trade-offs between competing properties is hampered by high computational demands. In this work, we present a framework to explore Pareto-optimal compositions by integrating advanced ab initio-based techniques into a Bayesian multi-objective optimization workflow, complemented by a simple analytical model providing straightforward analysis of trends. We benchmark the framework by applying it to solid solution strengthening and ductility of refractory MPEAs, with the parameters of the strengthening and ductility models being efficiently computed using a combination of the coherent-potential approximation method, accounting for finite-temperature effects, and actively-learned moment-tensor potentials parameterized with ab initio data. Properties obtained from ab initio calculations are subsequently used to extend predictions of all relevant material properties to a large class of refractory alloys with the help of the analytical model validated by the data and relying on a few element-specific parameters and universal functions that describe bonding between elements. Our findings offer crucial insights into the traditional strength-vs-ductility dilemma of refractory MPEAs. The proposed framework is versatile and can be extended to other materials and properties of interest, enabling a predictive and tractable high-throughput screening of Pareto-optimal MPEAs over the entire composition space.