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Solid-solution alloy scattering of phonons is a demonstrated mechanism to reduce the lattice thermal conductivity. The analytical model of Klemens works well both as a predictive tool for engineering materials, particularly in the field of thermoelectrics, and as a benchmark for the rapidly advancing theory of thermal transport in complex and defective materials. This comment/review outlines the simple algorithm used to predict the thermal conductivity reduction due to alloy scattering, as to avoid common misinterpretations, which have led to a large overestimation of mass fluctuation scattering. The Klemens model for vacancy scattering predicts a nearly 10× larger scattering parameter than is typically assumed, yet this large effect has often gone undetected due to a cancellation of errors. The Klemens description is generalizable for use in ab initio calculations on complex materials with imperfections. The closeness of the analytic approximation to both experiment and theory reveals the simple phenomena that emerges from the complexity and unexplored opportunities to reduce thermal conductivity. 

The full-Heusler VFe 2 Al has emerged as an important thermoelectric material in its thin film and bulk phases. VFe 2 Al is attractive for use as a thermoelectric materials because of it contains only low-cost, non-toxic and earth abundant elements. While VFe 2 Al has often been described as a semimetal, here we show the electronic and thermal properties of VFe 2 Al can be explained by considering VFe 2 Al as a valence precise semiconductor like many other thermoelectric materials but with a very small band gap ( E g = 0.03 ± 0.01 eV). Using a two-band model for electrical transport and point-defect scattering model for thermal transport we analyze the thermoelectric properties of bulk full-Heusler VFe 2 Al. We demonstrate that a semiconductor transport model can explain the compilation of data from a variety of n and p-type VFe 2 Al compositions assuming a small band-gap between 0.02 eV and 0.04 eV. In this small E g semiconductor understanding, the model suggests that nominally undoped VFe 2 Al samples appear metallic because of intrinsic defects of the order of ∼10 20 defects per cm −3 . We rationalize the observed trends in weighted mobilities ( μ w ) with dopant atoms from a molecular orbital understanding of the electronic structure. We use a phonon-point-defect scattering model to understand the dopant-concentration (and, therefore, the carrier-concentration) dependence of thermal conductivity. The electrical and thermal models developed allow us to predict the zT versus carrier concentration curve for this material, which maps well to reported experimental investigations. 

Mg 3 Sb 2 –Mg 3 Bi 2 alloys have been heavily studied as a competitive alternative to the state-of-the-art n-type Bi 2 (Te,Se) 3 thermoelectric alloys. Using Mg 3 As 2 alloying, we examine another dimension of exploration in Mg 3 Sb 2 –Mg 3 Bi 2 alloys and the possibility of further improvement of thermoelectric performance was investigated. While the crystal structure of pure Mg 3 As 2 is different from Mg 3 Sb 2 and Mg 3 Bi 2 , at least 15% arsenic solubility on the anion site (Mg 3 ((Sb 0.5 Bi 0.5 ) 1−x As x ) 2 : x = 0.15) was confirmed. Density functional theory calculations showed the possibility of band convergence by alloying Mg 3 Sb 2 –Mg 3 Bi 2 with Mg 3 As 2 . Because of only a small detrimental effect on the charge carrier mobility compared to cation site substitution, the As 5% alloyed sample showed zT = 0.6–1.0 from 350 K to 600 K. This study shows that there is an even larger composition space to examine for the optimization of material properties by considering arsenic introduction into the Mg 3 Sb 2 –Mg 3 Bi 2 system. 

Abstract Engineering semiconductor devices requires an understanding of charge carrier mobility. Typically, mobilities are estimated using Hall effect and electrical resistivity meausrements, which are are routinely performed at room temperature and below, in materials with mobilities greater than 1 cm²V^‐1s^‐1. With the availability of combined Seebeck coefficient and electrical resistivity measurement systems, it is now easy to measure the weighted mobility (electron mobility weighted by the density of electronic states). A simple method to calculate the weighted mobility from Seebeck coefficient and electrical resistivity measurements is introduced, which gives good results at room temperature and above, and for mobilities as low as 10⁻³cm²V^‐1s^‐1,Here, μ_wis the weighted mobility, ρ is the electrical resistivity measured in mΩ cm,Tis the absolute temperature in K,Sis the Seebeck coefficient, andk_B/e = 86.3 µV K^–1. Weighted mobility analysis can elucidate the electronic structure and scattering mechanisms in materials and is particularly helpful in understanding and optimizing thermoelectric systems.