Crystal structure and phase stability of tungsten borides*

We address the longstanding and controversial issue of ground-state structures of technically important tungsten borides using a first-principles structural search method via a particle-swarm optimization (PSO) algorithm. We have explored a large set of stable chemical compositions (convex hull) and clarified the ground-state structures for a wide range of boron concentrations, including W$_2$B, W$_3$B$_2$, WB, W$_2$B$_3$, WB$_2$, W$_2$B$_5$, WB$_3$, and WB$_4$. We further assessed relative stability of various tungsten borides and compared the calculated results with previously reported experimental data. The phase diagram predicted by the presented calculations may serve as a useful guide for synthesis of a variety of tungsten borides.