Mechanical properties and phase stability of monoborides using density functional theory calculations

Abstract

We compute the structural energies, elastic constants, and stacking fault energies, and investigate the phase stability of monoborides with different compositions $\left({X}_{1\ensuremath{-}x}^{1}{X}_{x}^{2}\right)\text{B}$ $(X=\text{Ti/Fe/Mo/Nb/V})$ using density functional theory in order to search for Ti monoborides with improved mechanical properties. Our computed Young's modulus and Pugh's modulus ratio, which correlate with stiffness and toughness, agree well with predictions from Vegard's law with the exceptions of mixed monoborides containing Mo and Fe. Among all the monoborides considered in this paper, TiB has the smallest Pugh's ratio, which suggests that the addition of solutes can improve the toughness of a Ti matrix. When ${X}^{1}\mathrm{B}$ and ${X}^{2}\mathrm{B}$ are respectively most stable in the ${B}_{27}$ and ${B}_{f}$ structures, the mixed monoborides $\left({X}_{1\ensuremath{-}x}^{1}{X}_{x}^{2}\right)\text{B}$ have a lower or similar stacking fault energy than TiB and could therefore improve the ductility of the Ti matrix. Among all $\left({X}_{0.5}^{1}{X}_{0.5}^{2}\right)\text{B}$, mixed $({\mathrm{Ti}}_{0.5}{\mathrm{Mo}}_{0.5})\text{B}$ and mixed $({\mathrm{Ti}}_{0.5}{\mathrm{V}}_{0.5})\text{B}$ have a higher Young's modulus, a higher Pugh's ratio, and a smaller stacking fault energy than TiB. We also construct phase diagrams and find large solubility limits for solid solutions containing Ti compared to those containing Fe.