Role of Na⁺ Interstitials and Dopants in Enhancing the Na⁺ Conductivity of the Cubic Na₃PS₄ Superionic Conductor

Abstract

In this work, we performed a first-principles investigation of the phase stability, dopant formation energy and Na⁺ conductivity of pristine and doped cubic Na₃PS₄ (c-Na₃PS₄). We show that pristine c-Na₃PS₄ is an extremely poor Na ionic conductor, and the introduction of Na⁺ excess is the key to achieving reasonable Na⁺ conductivities. We studied the effect of aliovalent doping of M⁴⁺ for P⁵⁺ in c-Na₃PS₄, yielding Na_3+<i>x</i>M_<i>x</i>P_1–<i>x</i>S₄ (M = Si, Ge, and Sn with <i>x</i> = 0.0625; M = Si with <i>x</i> = 0.125). The formation energies in all the doped structures with dopant concentration of <i>x</i> = 0.0625 are found to be relatively low. Using <i>ab initio</i> molecular dynamics simulations, we predict that 6.25% Si-doped c-Na₃PS₄ has a Na⁺ conductivity of 1.66 mS/cm, in excellent agreement with previous experimental results. Remarkably, we find that Sn⁴⁺ doping at the same concentration yields a much higher predicted Na⁺ conductivity of 10.7 mS/cm, though with a higher dopant formation energy. A higher Si⁴⁺ doping concentration of <i>x</i> = 0.125 also yields a significant increase in Na⁺ conductivity with an even higher dopant formation energy. Finally, topological and van Hove correlation function analyses suggest that the channel volume and correlation in Na⁺ motions may play important roles in enhancing Na⁺ conductivity in this structure