<p>The replacement of the presently used liquid electrolytes by a non-flammable solid electrolyte is an important avenue to create safer batteries. The Natrium Superionic CONductor<b> </b>(NaSiCON) Na<sub>1+x</sub>Zr<sub>2</sub>Si<sub>x</sub>P<sub>3-x</sub>O<sub>12</sub> (0 < x < 3) that displays high bulk ionic conductivity and good stability towards other NaSiCON-based electrodes is a good solid electrolyte in NaSiCON-based batteries. Despite the sizeable share of research on Na<sub>1+x</sub>Zr<sub>2</sub>Si<sub>x</sub>P<sub>3-x</sub>O<sub>12</sub>, the structural and thermodynamic properties of NaSiCON require better understanding for more efficient synthesis and optimization as a solid electrolyte, which often follows chemical intuition. Here, we analyze the thermodynamic properties of the NaSiCON electrolyte by constructing the Na<sub>1+x</sub>Zr<sub>2</sub>Si<sub>x</sub>P<sub>3-x</sub>O<sub>12</sub> phase diagram, based on density functional theory calculations, a cluster expansion framework, and Monte Carlo simulations. Specifically, we build the phase diagram as a function of temperature and composition (0 < x < 3) for the high-temperature rhombohedral structure, which has been also observed in several positive electrode materials, such as Na<sub>3</sub>Ti<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub>, Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub> and Na<sub>3</sub>Cr<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub>. Through the phase diagram, we identify the concentration domains providing the highest Na<sup>+</sup>-ion conductivity and previously unreported phase-separation behavior across three different single-phase regions. Further, we note the similarities in the phase behavior between Na<sub>1+x</sub>Zr<sub>2</sub>Si<sub>x</sub>P<sub>3-x</sub>O<sub>12</sub> and other NaSiCON-based mono-transition metal electrodes and discuss the potential competition between thermodynamics and kinetics in experimentally observed phase separation. Our work is an important addition in understanding the thermodynamics of NaSiCON-based materials and in the development of inexpensive Na-ion batteries. From our results we propose that the addition of SiO<sub>4</sub><sup>4–</sup> moieties to single-transition metal NaSiCON-phosphate-based electrodes will slow significantly the kinetics toward phase separation. </p>
Covalency, double-counting, and the metal-insulator phase diagram in transition metal oxides