Electron count dictates phase separation in Heusler alloys

Phase separation---and conversely, the propensity for solid-solution formation---in half-Heusler ($XYZ$) and Heusler ($X{Y}_{2}Z$) compounds is suggested from first-principles electronic-structure-based modeling to be strongly linked to the electronic behavior of the end-members. Alloying between distinct pairs of half-Heusler and Heusler compounds is possible at accessible processing temperatures when the two end-members are either isoelectronic or metallic. The formation of a band gap in semiconducting half-Heusler compounds is associated with significant stabilization. Attempts to create solid solutions with a semiconducting half-Heusler compound would lead to phase separation across the tie line because of the energy penalty associated with filling states in the gap. The alloying between two Heusler compounds, however, is expected even when the electronic behaviors of the end-members differ---clearly demonstrating the distinction between the underlying bonding within half-Heuslers and Heuslers: Half-Heuslers are well-defined intermetallics, whereas Heuslers tend to behave in a manner more in line with conventional alloys. The simple proxy related to electronic structure developed here differentiates Heusler and half-Heusler compositions that truly alloy from those that phase separate, aiding in the pursuit of reliable first-principles materials discovery.