First-principles demonstration of band filling-induced significant improvement in thermodynamic stability and mechanical properties of Sc$$_{1-x}$$Ta$$_{x}$$B$$_{2}$$ solid solutions

Abstract

Mixtures of different metal diborides in the form of solid solutions are promising materials for hard-coating applications. Herein, we study the mixing thermodynamics and the mechanical properties of AlB$$_{2}$$ 2 -structured Sc$$_{1-x}$$ 1 - x Ta$$_{x}$$ x B$$_{2}$$ 2 solid solutions using the first-principles method, based on the density functional theory, and the cluster-expansion formalism. Our thermodynamic investigation reveals that the two diborides readily mix with one another to form a continuous series of stable solid solutions in the pseudo-binary TaB$$_{2}$$ 2 $$-$$ - ScB$$_{2}$$ 2 system even at absolute zero. Interestingly, the elastic moduli as well as the hardness of the solid solutions show significant positive deviations from the linear Vegard’s rule evaluated between those of ScB$$_{2}$$ 2 and TaB$$_{2}$$ 2 . In case of Sc$$_{1-x}$$ 1 - x Ta$$_{x}$$ x B$$_{2}$$ 2 , the degrees of deviation from such linear trends can be as large as 25, 20, and 40% for the shear modulus, the Young’s modulus, and the hardness, respectively. The improvement in the stability as well as the mechanical properties of Sc$$_{1-x}$$ 1 - x Ta$$_{x}$$ x B$$_{2}$$ 2 solid solutions relative to their constituent compounds is found to be related to the effect of electronic band filling, induced upon mixing TaB$$_{2}$$ 2 with ScB$$_{2}$$ 2 . These findings not only demonstrate the prominent role of band filling in enhancing the stability and the mechanical properties of Sc$$_{1-x}$$ 1 - x Ta$$_{x}$$ x B$$_{2}$$ 2 , but also it can potentially open up a possibility for designing stable/metastable metal diboride-based solid solutions with superior and widely tunable mechanical properties for hard-coating applications.