Physical trends and design principles in aliovalent double half-Heusler thermoelectrics from high-throughput computational screening

We present a high-throughput investigation of all 1062 aliovalent double half-Heusler (DHH) compositions by combining ${\mathrm{r}}^{2}\mathrm{SCAN}$-based density functional theory, Boltzmann transport, and a hybrid machine learning interatomic potentials MACE-assisted Slack workflow for lattice thermal conductivity. Clear sublattice-dependent trends are identified, where $X$- and $Y$-splitting generally favor the tetragonal $I\overline{4}2d$ prototype and preserve the half-Heusler's (HH) hybridization mechanism, while $Z$-splitting tends to stabilize $Pmn{2}_{1}$ at the prototype level but strongly perturbs the $p--d$ backbone, narrows or collapses the band gap, and greatly reduces thermodynamic competitiveness. As a result, near-hull compounds are concentrated mainly in the $X$-split and $Y$-split families, whereas the $Z$-split family is largely unstable. The thermodynamic accessibility of DHHs is further shown to correlate with both the stability of the parent HH end points an