The need for improved functionalities is driving the search for more complicated multi-component materials. Despite the factorially increasing composition space, ordered compounds with four or more species are rare. Here, we unveil the competition between the gain in enthalpy and entropy with increasing number of species by statistical analysis of the AFLOW data repositories. A threshold in the number of species is found where entropy gain exceeds enthalpy gain. Beyond that, enthalpy can be neglected, and disorder—complete or partial—is unavoidable.

中文翻译：

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多组分系统中不可避免的无序性和熵

对功能改进的需求推动了对更复杂的多组分材料的搜索。尽管增加了组成空间，但很少有四个或更多种类的有序化合物。在这里，我们通过对AFLOW数据存储库进行统计分析，揭示了随着物种数量的增加，焓值增加和熵值增加之间的竞争。发现物种数量的阈值，其中熵增益超过焓增益。除此之外，焓可以忽略，完全或部分混乱是不可避免的。