Na Doping in PbTe: Solubility, Band Convergence, Phase Boundary Mapping, and Thermoelectric Properties.

Many monumental breakthroughs in p-type PbTe thermoelectrics are driven by optimizing a Pb0.98Na0.02Te matrix. However, recent works found that x > 0.02 in Pb1-xNaxTe further improves the thermoelectric figure of merit, zT, despite being above the expected Na solubility limit. We explain the origins of improved performance from excess Na doping through computation and experiments on Pb1-xNaxTe with 0.01 ≤ x ≤ 0.04. High temperature X-ray diffraction and Hall carrier concentration measurements show enhanced Na solubility at high temperatures when x > 0.02 but no improvement in carrier concentration, indicating that Na is entering the lattice but is electrically compensated by high intrinsic defect concentrations. The higher Na concentration leads to band convergence between the light L and heavy Σ valence bands in PbTe, suppressing bipolar conduction and increasing the Seebeck coefficient. This results in a high temperature zT nearing 2 for Pb0.96Na0.04Te, ∼25% higher than traditionally reported values for pristine PbTe-Na. Further, we apply a phase diagram approach to explain the origins of increased solubility from excess Na doping and offer strategies for repeatable synthesis of high zT Na-doped materials. A starting matrix of simple, high performing Pb0.96Na0.04Te synthesized following our guidelines may be superior to Pb0.98Na0.02Te for continued zT optimization in p-type PbTe materials.

Two-Dimensional Rectangular and Honeycomb Lattices of NbN: Emergence of Piezoelectric and Photocatalytic Properties at Nanoscale.

Using first-principles calculations, we predict that monolayered honeycomb and rectangular two-dimensional (2D) lattice forms of NbN are metastable and naturally derivable from different orientations of its rocksalt structure. While the rectangular form is shown to retain the metallic and superconducting (SC) properties of the bulk, spectacularly contrasting properties emerge in the honeycomb form of NbN: it exhibits (a) semiconducting electronic structure suitable for valleytronics and photocatalysis of water splitting, (b) piezoelectricity with a spontaneous polarization originating from a rare sd(2)-sp(2) type hybridization, and (c) a wide gap in its phonon spectrum making it suitable for use in hot carrier solar cells. Our work demonstrates how low coordination numbers and associated strong bonding stabilize 2D nanoforms of covalently bonded solids and introduce novel functionalities of technological importance.

High Thermoelectric Performance of New Rhombohedral Phase of GeSe stabilized through Alloying with AgSbSe2.

GeSe is a IV-VI semiconductor, like the excellent thermoelectric materials PbTe and SnSe. Orthorhombic GeSe has been predicted theoretically to have good thermoelectric performance but is difficult to dope experimentally. Like PbTe, rhombohedral GeTe has a multivalley band structure, which is ideal for thermoelectrics and also promotes the formation of Ge vacancies to provide enough carriers for electrical transport. Herein, we investigate the thermoelectric properties of GeSe alloyed with AgSbSe2 , which stabilizes a new rhombohedral structure with higher symmetry that leads to a multivalley Fermi surface and a dramatic increase in carrier concentration. The zT of GeAg0.2 Sb0.2 Se1.4 reaches 0.86 at 710 K, which is 18 times higher than that of pristine GeSe and over four times higher than doped orthorhombic GeSe. Our results open a new avenue towards developing novel thermoelectric materials through crystal phase engineering using a strategy of entropy stabilization of high-symmetry alloys.

Shapes of phases in isothermal phase diagrams: what is wrong with the Thermo-Calc logo.

The solubility of defects is essential to control the mechanical, electrical and thermal properties of engineering materials. The concentration of defects can be visualized on a phase diagram as providing the width to single-phase regions of compounds. Although the shape of these regions can have a tremendous impact on the maximum defect solubility achievable and guides the engineering of materials, little attention has been paid to the shape of the phase boundaries surrounding these single-phase regions. Here we examine the shape of single-phase boundaries that can be expected for dominating neutral substitutional defects. Single-phase regions in an isothermal phase diagram should be expected to be concave or star-shaped, or at least straight polygonal sides rather than be convex-like droplets. A thermodynamic justification is used to show the concave (hyperbolic cosine) shape depends on the thermodynamic stability of the compound when various substitutional defects dominate. More stable compounds have star-like phase regions, while barely stable compounds should be more polygonal shaped. The Thermo-Calc logo for example would be more physical if it contained a star-like central compound and pointed elemental regions.

Opening the Bandgap of Metallic Half-Heuslers via the Introduction of d-d Orbital Interactions.

Half-Heusler compounds with semiconducting behavior have been developed as high-performance thermoelectric materials for power generation. Many half-Heusler compounds also exhibit metallic behavior without a bandgap and thus inferior thermoelectric performance. Here, taking metallic half-Heusler MgNiSb as an example, a bandgap opening strategy is proposed by introducing the d-d orbital interactions, which enables the opening of the bandgap and the improvement of the thermoelectric performance. The width of the bandgap can be engineered by tuning the strength of the d-d orbital interactions. The conduction type and the carrier density can also be modulated in the Mg1- x Tix NiSb system. Both improved n-type and p-type thermoelectric properties are realized, which are much higher than that of the metallic MgNiSb. The proposed bandgap opening strategy can be employed to design and develop new half-Heusler semiconductors for functional and energy applications.

Inherent Anharmonicity of Harmonic Solids.

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest-order, harmonic, approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to nonlinear, anharmonic, interactions. Here, we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter γ, which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter as γ≈3/23-4x2/1+2x2, where x=vt/vl is the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new material engineering design metrics.

Correction: The importance of phase equilibrium for doping efficiency: iodine doped PbTe.

Correction for 'The importance of phase equilibrium for doping efficiency: iodine doped PbTe' by James Male et al., Mater. Horiz., 2019, 6, 1444-1453, DOI: 10.1039/C9MH00294D.

Estimating the lower-limit of fracture toughness from ideal-strength calculations.

Fracture mechanics is a fundamental topic to materials science. Fracture toughness, in particular, is a material property of great technological importance for device design. The relatively low fracture toughness of many semiconductor materials, including electronic and energy materials, handicaps their use in applications involving large external stresses. Here, it is shown that quantum-mechanical density functional theory calculations of ideal strength, in conjunction with an integral stress-displacement method, can be used to estimate the fracture energy needed to calculate fracture toughness. Using the fracture energy associated with the weakest crystallographic direction provides an estimation for the lower-limit of the fracture toughness of a material. The lower-limit values are in good agreement with experimental single crystal measurements across several orders-of-magnitude of fracture toughness. Furthermore, the proposed methodology is useful for benchmarking experimental measurements of fracture toughness in polycrystalline materials and can serve as a starting point for the construction of more detailed fracture models and the computational design of new materials and devices.

Visualizing defect energetics.

Defect energetics impact most thermal, electrical and ionic transport phenomena in crystalline compounds. The key to chemically controlling these properties through defect engineering is understanding the stability of (a) the defect and (b) the compound itself relative to competing phases at other compositions in the system. The stability of a compound is already widely understood in the community using intuitive diagrams of formation enthalpy (ΔHf) vs. composition, in which the stable phases form the 'convex-hull'. In this work, we re-write the expression of defect formation enthalpy (ΔHdef) in terms of the ΔHf of the compound and its defective structure. We show that ΔHdef for a point defect can be simply visualized as intercepts in a two-dimensional convex-hull plot regardless of the number of components in the system and choice of chemical conditions. By plotting ΔHf of the compound and its defects all together, this visualization scheme directly links defect energetics to the compositional phase stability of the compound. Hence, we simplify application level defect thermodynamics within a widely used visual tool understandable from basic materials science knowledge. Our work will be beneficial to a wide community of experimental chemists seeking to build an intuition for appropriate choice of chemical conditions for defect engineering.

The effect of Mg3As2 alloying on the thermoelectric properties of n-type Mg3(Sb, Bi)2.

Mg3Sb2-Mg3Bi2 alloys have been heavily studied as a competitive alternative to the state-of-the-art n-type Bi2(Te,Se)3 thermoelectric alloys. Using Mg3As2 alloying, we examine another dimension of exploration in Mg3Sb2-Mg3Bi2 alloys and the possibility of further improvement of thermoelectric performance was investigated. While the crystal structure of pure Mg3As2 is different from Mg3Sb2 and Mg3Bi2, at least 15% arsenic solubility on the anion site (Mg3((Sb0.5Bi0.5)1-xAsx)2: x = 0.15) was confirmed. Density functional theory calculations showed the possibility of band convergence by alloying Mg3Sb2-Mg3Bi2 with Mg3As2. 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 Mg3Sb2-Mg3Bi2 system.

Machine Learning Chemical Guidelines for Engineering Electronic Structures in Half-Heusler Thermoelectric Materials.

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.

The importance of phase equilibrium for doping efficiency: iodine doped PbTe.

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.

Effect of anion substitution on the structural and transport properties of argyrodites Cu7PSe6-xSx.

Inspired by the good performance of argyrodites as ion conducting thermoelectrics and as solid electrolytes we investigated the effect of isovalent S2- substitution for Se2- in Cu7PSe6. At room temperature Cu7PSe6 crystallizes in the primitive cubic ß-polymorph of the argyrodite structure and transforms to the face-centered high-temperature (HT) γ-modification above 320 K. The transition for the homologous Cu7PS6 occurs at 510 K. Promising thermoelectric and ion conducting properties are observed only in the HT modification, where the cations are mobile. Using Rietveld refinements against X-ray diffraction data the effect of isovalent S2- substitution for Se2- on the structural and transport properties in Cu7PSe6-xSx was analyzed. While a step-wise incorporation of S2- showed typical behavior for a homogeneous solid solution series, the analysis of the diffraction data gave clear evidence of anion ordering due to site preference of the sulfide ions, which can be rationalized using Pearson's HSAB concept. This leads to a stabilization of the HT structure even at lower temperatures. This selective control enables new strategies for the design of argyrodite materials, as isovalent substitution not only allows an engineering of properties, but also permits the stabilization of the polymorph with the most promising properties.