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Phosphorus has received recent attention in the context of high-capacity andhigh-rate anodes for lithium and sodium-ion batteries. Here, we present a firstprinciples structure prediction study combined with NMR calculations whichgives us insights into its lithiation/sodiation process. We report a variety ofnew phases phases found by AIRSS and the atomic species swapping methods. Ofparticular interest, a stable Na$_5$P$_4$-C2/m structure and locally stablestructures found less than 10 meV/f.u. from the convex hull, such asLi$_4$P$_3$-P2$_1$2$_1$2$_1$, NaP$_5$-Pnma and Na$_4$P$_3$-Cmcm. The mechanicalstability of Na$_5$P$_4$-C2/m and Li$_4$P$_3$-P2$_1$2$_1$2$_1$ has been studiedby first principles phonon calculations . We have calculated average voltageswhich suggests that black phosphorus (BP) can be considered as a safe anode inlithium-ion batteries due to its high lithium insertion voltage, 1.5 V;moreover, BP exhibits a relatively low theoretical volume expansion comparedwith other intercalation anodes, 216\% ($\Delta V/V$). We identify thatspecific ranges in the calculated shielding can be associated with specificionic arrangements, results which play an important role in the interpretationof NMR spectroscopy experiments. Since the lithium-phosphides are found to beinsulating even at high lithium concentrations we show that Li-P-doped phaseswith aluminium have electronic states at the Fermi level suggesting that usingaluminium as a dopant can improve the electrochemical performance of P anodes.

$\textit{Ab initio}$ study of phosphorus anodes for lithium and sodium-ion batteries