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