Mechanistically-guided materials chemistry: synthesis of new ternary nitrides, CaZrN$_2$ and CaHfN$_2$

Recent computational studies have predicted many new ternary nitrides, revealing synthetic opportunities in this underexplored phase space. However, synthesizing new ternary nitrides is difficult, in part because intermediate and product phases often have high cohesive energies that inhibit diffusion. Here, we report the synthesis of two new phases, calcium zirconium nitride (CaZrN$_2$) and calcium hafnium nitride (CaHfN$_2$), by solid state metathesis reactions between Ca$_3$N$_2$ and $M$Cl$_4$ ($M$ = Zr, Hf). Although the reaction nominally proceeds to the target phases in a 1:1 ratio of the precursors via Ca$_3$N$_2$ + $M$Cl$_4$ $\rightarrow$ Ca$M$N$_2$ + 2 CaCl$_2$, reactions prepared this way result in Ca-poor materials (Ca$_xM_{2-x}$N$_2$, $x<1$). A small excess of Ca$_3$N$_2$ (ca. 20 mol\%) is needed to yield stoichiometric Ca$M$N$_2$, as confirmed by high-resolution synchrotron powder X-ray diffraction. In situ synchrotron X-ray diffraction studies reveal that nominally stoichiometric reactions produce Zr$^{3+}$ intermediates early in the reaction pathway, and the excess Ca$_3$N$_2$ is needed to reoxidize Zr$^{3+}$ intermediates back to the Zr$^{4+}$ oxidation state of CaZrN$_2$. Analysis of computationally-derived chemical potential diagrams rationalizes this synthetic approach and its contrast from the synthesis of MgZrN$_2$. These findings additionally highlight the utility of in situ diffraction studies and computational thermochemistry to provide mechanistic guidance for synthesis.