Thermodynamic approaches to determine the vacancy concentration in defective Nb1-CoSb half-Heusler thermoelectric materials

The defective half-Heusler compound Nb _{1- x} CoSb has been identified to be a promising thermoelectric material via modification of vacancies. Herein, we combined the experimental phase diagram with CALPHAD (CALculation PHAse Diagram) method to determine the vacancy concentration of Nb _{1- x}CoSb in the equilibrium state, which is 0.17 ≤ x ≤ 0.22 at 1173 K and 0.17 ≤ x ≤ 0.2 at 1323 K and extrapolated to the whole composition and temperature range computationally. The calculated homogeneous region of the half-Heusler phase increases first and then decreases with increasing temperature, reaching a maximum Δ x = 0.042 at ∼1123 ± 20 K. The stoichiometric NbCoSb alloy is proved to locate at the binary-phase region of Nb _{1- x}CoSb/Nb ₃Sb. This work opens a new avenue for understanding, design and preparation of thermoelectric materials.