A simple model for vacancy order and disorder in defective half-Heusler systems

Abstract

Defective half-Heusler systems X(1-x)YZ with large amounts of intrinsic vacancies, such as Nb(1-x)CoSb, Ti(1-x)NiSb and V(1-x)CoSb, are a group of promising thermoelectric materials. Even with high vacancy concentrations they maintain the average half-Heusler crystal structure. These systems show high electrical conductivity but low thermal conductivity arising from an ordered YZ lattice, which conducts electrons, while the large amounts of vacancies on the X sublattice effectively scatters phonons. Using electron scattering it was recently observed that in addition to Bragg diffraction from the average cubic half-Heusler structure, some of these samples show broad diffuse scattering indicating short-range vacancy order while other samples show sharp additional peaks, indicating long-range vacancy ordering. Here we show that both the short and long-range ordering can be explained using the same simple model, which assumes that vacancies on the X-sublattice avoid each other. The samples showing long-range vacancy order are in agreement with the predicted ground-state of the model, while short-range order samples are quenched high-temperature states of the system. A previous study showed that changes in sample stoichiometry affect whether the short or long-range vacancy structure is obtained, but the present model suggests that thermal treatment of samples should allow controlling the degree of vacancy order, and thereby the thermal conductivity, without changes in composition. This is important as the composition also dictates the amount of electrical carriers. Independent control of electrical carrier concentration and degree of vacancy order should allow further improvements in the thermoelectric properties of these systems.