Accurate modeling of disorder in lattice thermal conductivity of NbFeSb1− <i>x</i> Bi <i>x</i> half-Heusler alloys: Site-specific substitution vs virtual crystal approximation

Abstract

Accurately incorporating the disorder in lattice thermal conductivity calculations has been a very challenging problem. This work provides a combined methodological and analytical framework to evaluate lattice thermal conductivity (κL) in disordered alloys, using NbFeSb1−xBix half-Heusler systems as a prototype. First-principles density functional theory calculations are integrated with the phonon Boltzmann transport equation to obtain κL using the harmonic and anharmonic interatomic force constants (IFCs). Substitutional disorder is modeled using ordered supercells, special quasi-random structures, and the virtual crystal approximation (VCA). Phonon dispersions from supercell models are unfolded to the primitive Brillouin zone for direct comparison with VCA results, while IFC strengths are quantified using Frobenius norms. The analysis reveals that local force-constant variations are minimal, whereas mass-disorder scattering dominates phonon transport. Consequently, the VCA combined with mass-variance scattering provides an accurate and computationally efficient description of κL. A substantial reduction in lattice thermal conductivity, up to ∼ 75%, is observed with increasing Bi content in NbFeSb, highlighting the effectiveness of alloying in suppressing heat transport.