Establishing the formation criterion is urgent for accelerating the discovery and design of solid‐solution materials with desirable properties. The previously reported formation criterion mainly focused on solid‐solution alloys, while the formation criterion was rarely established in solid‐solution ceramics. To solve this problem, herein, we take a class of solid‐solution ceramics, namely binary metal diboride ((M_xN_1‐x)B₂) solid solutions, as a prototype. Through combinatorial methods including high‐throughput molten salt syntheses and high‐throughput first‐principles calculations combined with the machine learning approach, the correlation between influential factors, including atomic size difference (δ), mixing enthalpy at 0 K and 0 Pa (), doping condition (φ), and valence electron concentration (VEC), and the formation ability of (M_xN_1‐x)B₂ solid solutions was first studied systematically, and then their formation criterion was well established. The results showed that the influential degree of the aforementioned four factors on the formation ability of (M_xN_1‐x)B₂ solid solutions could be described as follows: δ > > φ > VEC. In addition, a newly proposed parameter, β, could well reflect the formation ability of (M_xN_1‐x)B₂ solid solutions: when β > 0, the single‐phase (M_xN_1‐x)B₂ solid solutions could be successfully synthesized in our work and vice versa. This study may provide a theoretical guidance in the discovery and design of various solid‐solution ceramics, such as the metal borides, carbides, nitrides, etc, with desirable properties.

中文翻译：

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组合法建立二元金属二硼化物固溶体的形成准则

建立形成标准对于加快发现和设计具有理想性能的固溶材料非常重要。先前报道的形成标准主要集中在固溶合金上，而很少在固溶陶瓷中建立该形成标准。为了解决这个问题，在这里，我们以一类固溶陶瓷为原型，即二元金属二硼化物（（M _x N _{1- x}）B ₂）固溶体。通过高通量熔盐合成和高通量第一性原理的组合方法与机器学习方法相结合，影响因素之间的相关性包括原子尺寸差（δ），0 K和0 Pa（）的混合焓，掺杂条件（φ）和价电子浓度（VEC）以及（M _x N _{1- x}）B ₂固溶体的形成能力首先得到系统地研究，并且那么它们的形成标准就已经确立了。结果表明，上述四个因素上的形成的能力有影响的程度（M _X Ñ _{1- X}）乙_2个固溶体可以被描述如下：δ  >  >  φ  >  VEC。此外，新提出的参数β，可以很好地反映（M _x N _{1- x}）B ₂固溶体的形成能力：当β  > 0时，在我们的工作中可以成功合成单相（M _x N _{1- x}）B ₂固溶体，并且反之亦然。这项研究可以为发现和设计各种具有理想性能的固溶陶瓷（例如金属硼化物，碳化物，氮化物等）提供理论指导。