Among the superconducting hydrides under high pressure, a number of studies concentrate on the ternary compounds to explore unique superconductors, which are capable of reducing the stable pressure and maintain superconductivity. In this work, to verify our proposed strategy of ternary composition lines (TCLs) to explore ternary compounds, we combined the first-principles calculations and crystal structure predictions to study the ternary compounds Li-$X$-B ($X=\mathrm{Mo}$, W) under high pressure. After calculations along five and four TCLs in Li-W-B and Li-Mo-B, respectively, five Li-W-B compounds and four Li-Mo-B compounds were predicted. The compositions of ${\mathrm{LiWB}}_4, {\mathrm{Li}}_4{\mathrm{MoB}}_2$ and ${\mathrm{LiMo}}_2{\mathrm{B}}_2$ could be thermodynamically stable under high pressure, and ${\mathrm{Li}}_2{\mathrm{WB}}_6$ is around 0.02 eV/atom above the convex hull at 0 GPa, which has potential for synthesizing. Both of the predicted ${\mathrm{Li}}_2{\mathrm{WB}}_6 P6$/mmm and ${\mathrm{Li}}_2{\mathrm{WB}}_4 R\text{−}3m$ are superconducting and their $T_{\mathrm{c}}$ are around 11 K, which are similar to the $T_{\mathrm{c}}$ of ${\mathrm{WB}}_2 P6$/mmm around 100 GPa. An anomalous increase of $T_{\mathrm{c}}$ was found in ${\mathrm{Li}}_4{\mathrm{MoB}}_2 C2/m$ upon compression. We carried out full ternary search to evaluate the validity of the TCLs strategy in the Li-W-B system at 0 GPa. Our results are helpful for understanding the phase diagram of Li-$X$-B ($\mathit{X}=\mathrm{Mo}$, W) under high pressure and the introducing of Li atoms provide candidate structures to reduce the measured stable pressure from $\sim 100$ GPa in ${\mathrm{WB}}_2 P6$/mmm to 0 GPa. Meanwhile, we preliminarily validate the strategy of TCLs in structure predictions and we expect to improve this strategy in the future, shedding light on the studies of ternary compounds.

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• Crystal structure
• High-pressure studies
• Superconductivity
• Borides
• First-principles calculations