Formation criterion for binary metal diboride solid solutions established through combinatorial methods

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 ((MxN1-x)B-2) 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 (delta), mixing enthalpy at 0 K and 0 Pa (Delta Hmix0K), doping condition (phi), and valence electron concentration (VEC), and the formation ability of (MxN1-x)B-2 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 (MxN1-x)B-2 solid solutions could be described as follows: delta > Delta Hmix0K> phi > VEC. In addition, a newly proposed parameter, beta, could well reflect the formation ability of (MxN1-x)B-2 solid solutions: when beta > 0, the single-phase (MxN1-x)B-2 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.