Theoretical study of thermo-dynamical and thermoelectric properties of novel half-Heusler alloys AlNiAs and AlNiSb

Exploring structural, mechanical, and thermoelectric properties of half-Heusler compounds RhBiX (X = Ti, Zr, Hf): A first-principles investigation

“…When the carrier concentration was 5.5 × 10 22 cm −3 , the maximum electron thermal conductivity was observed. The electronic thermal conductivity increased with the temperature from 300 to 1200 K. A similar phenomenon has been observed in other HH alloys, 35,55 thereby confirming the accuracy of our calculations.…”

“…Additionally, κ ι can be calculated using Slack’ s equation, 64 where M av , δ , n , T , and γ represent the average atomic mass in the crystal, cubic root of average atomic volume, total number of atoms in the unit cell, absolute temperature, and Grüneisen parameter, respectively. Parameter A , which depends on factor γ , can be calculated as, 55 where γ is the Grüneisen parameter, which can be calculated by Poisson's ratio, . Using the Slack equation defined, the temperature dependence of lattice thermal conductivity is calculated and plotted, as shown in Fig.…”

“…In contrast to the elastic stability conditions, 53 we can determine the mechanical stabilities of (X = Ti, Zr, Hf) compounds, which is stated as C 11 > 0, C 44 > 0, C 11 – C 12 > 0, and C 11 + 2 C 12 > 0From the elastic constants' relationship, RhBiX(X = Ti, Zr, Hf) satisfied the stability criterion. Based on the stability conditions of Born and Huang, 53 the bulk modulus ( B ), shear modulus ( G ), Young's modulus ( Y ), the Poisson's ratio ( v ), longitudinal ( υ l ), transverse ( υ s ) velocity and average sound velocity ( v m ) are defined as 54,55 …”

“…T where M av , d, n, T, and g represent the average atomic mass in the crystal, cubic root of average atomic volume, total number of atoms in the unit cell, absolute temperature, and Grüneisen parameter, respectively. Parameter A, which depends on factor g, can be calculated as, 55 A ¼…”

Effects of isotropic strain on the structure and transport properties of half-Heusler alloy BiBaK: a first-principles investigation

“…The lattice thermal conductivity ( κ ι ) of BiBaK subjected to isotropic strain was calculated using both Slack's equation and the Callaway model 62,63 as follows:where M av is the average atomic weight, δ is the cubic root of the average atomic volume, n is the number of atoms per unit cell, T is the absolute temperature, γ is the Grüneisen parameter, and A , which depends on γ , can be calculated as 64 …”