Accurate knowledge of phase coexistence regions, i.e., solubility gaps (SGs), is key to the development of mixed transition metal oxides for various applications, such as thermochemical energy storage, or catalysis. However, predicting a SG from first principles in these materials is particularly challenging due to the complex interplay between several sources of entropy, the large configuration space, and the computational expense of ab initio calculations. We present an approach that yields an accurate prediction of the experimental Hausmannite-spinel SG in the case of (${\mathrm{Co}}_x{\mathrm{Mn}}_{1-x}{)}_3{\mathrm{O}}_4$. The method uses machine learning to extend an ab initio dataset of hundreds of structures, and it includes many different entropic contributions to the free energy. We demonstrate and quantify the crucial roles of phonon and paramagnetic entropy, and the importance of sampling higher-energy configurations, and correcting for finite-size limitations in the ab initio supercell configurations.

中文翻译：

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从头计算计算混合过渡金属氧化物的高温相共存区域

对相共存区域的准确了解，即溶解间隙（SGs），是开发用于各种应用（例如热化学能存储或催化）的混合过渡金属氧化物的关键。但是，由于这些熵的多个来源之间复杂的相互作用，较大的配置空间以及从头算的计算量，从这些材料的第一性原理预测SG尤其具有挑战性。我们提出了一种在以下情况下可以准确预测实验Hausmannite-spinel SG的方法：${\mathrm{有限公司}}_X{\mathrm{锰}}_{\mathrm{1个}-X}{）}_3{\mathrm{Ø}}_4$。该方法使用机器学习来扩展数百个结构的从头算数据集，并且它包括对自由能的许多不同的熵贡献。我们证明并量化了声子和顺磁熵的关键作用，以及采样高能构型以及纠正从头算起超级电池构型中有限尺寸限制的重要性。