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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. 

Half-Heusler materials are strong candidates for thermoelectric applications due to their high weighted mobilities and power factors, which is known to be correlated to valley degeneracy in the electronic band structure. However, there are over 50 known semiconducting half-Heusler phases, and it is not clear how the chemical composition affects the electronic structure. While all the n-type electronic structures have their conduction band minimum at either the Γ - or X -point, there is more diversity in the p-type electronic structures, and the valence band maximum can be at either the Γ -, L -, or W -point. Here, we use high throughput computation and machine learning to compare the valence bands of known half-Heusler compounds and discover new chemical guidelines for promoting the highly degenerate W -point to the valence band maximum. We do this by constructing an “orbital phase diagram” to cluster the variety of electronic structures expressed by these phases into groups, based on the atomic orbitals that contribute most to their valence bands. Then, with the aid of machine learning, we develop new chemical rules that predict the location of the valence band maximum in each of the phases. These rules can be used to engineer band structures with band convergence and high valley degeneracy. 

Herein we study the effect alloying Yb onto the octahedral cite of Te doped Mg 3 Sb 1.5 Bi 0.5 has on transport and the material's high temperature stability. We show that the reduction in mobility can be well explained with an alloy scattering argument due to disrupting the Mg octahedral –Mg tetrahedral interaction that is important for placing the conduction band minimum at a location with high valley degeneracy. We note this interaction likely dominates the conducting states across n-type Mg 3 Sb 2 –Mg 3 Bi 2 solid solutions and explains why alloying on the anion site with Bi isn't detrimental to Mg 3 Sb 2 's mobility. In addition to disrupting this Mg–Mg interaction, we find that alloying Yb into the Mg 3 Sb 2 structure reduces its n-type dopability, likely originating from a change in the octahedral site's vacancy formation energy. We conclude showing that while the material's figure of merit is reduced with the addition of Yb alloying, its high temperature stability is greatly improved. This study demonstrates a site-specific alloying effect that will be important in other complex thermoelectric semiconductors such as Zintl phases. 

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. 

Semiconductor engineering relies heavily on doping efficiency and dopability. Low doping efficiency may cause low mobility and failure to reach target carrier concentrations or even the desired carrier type. Semiconducting thermoelectric materials perform best with degenerate carrier concentrations, meaning high performance in new materials might not be realized experimentally without a route to optimal doping. Doping in the classic PbTe thermoelectric system has been largely successful but reported doping efficiencies can vary, raising concerns about reproducibility. Here, we stress the importance of phase equilibria considerations during synthesis to avoid undesired intrinsic defects leading to sub-optimal doping. By saturation annealing at 973 K, we decidedly fix the composition in single crystal iodine-doped PbTe samples to be Pb-rich or Te-rich without introducing impurity phases. We show that, regardless of iodine concentration, degenerate n-type carrier concentrations with ideal doping efficiency require Pb-rich compositions. Electrons in Te-rich samples are heavily compensated by charged intrinsic Pb vacancy defects. From Hall effect measurements and a simple defect model supported by modern defect calculations, we map out the 973 K ternary Pb–Te–I phase diagram to explicitly link carrier concentration and composition. Furthermore, we discuss unintentional composition changes due to loss of volatile Te during synthesis and measurements. The methods and concepts applied here may guide doping studies on other lead chalcogenide systems as well as any doped, complex semiconductor.