External collaborators and funding This work was supported by the U.S. Department of Energy, Basic Energy Sciences, Early Career Program. Collaborators: Northwestern University (Snyder lab), Universite Catholique de Louvain (Hautier Lab), Dalhousie University (White Lab), and UC Berkeley / LBNL (Ceder, Asta, and Persson labs). Targeted Band Structure Design and Thermoelectric Materials Discovery Using High-Throughput Computation Anubhav Jain, Energy Technologies Area, Berkeley Lab High-throughput calculation engine and electronic transport database Data mining thermoelectrics and band structure engineering Benchmarking and accuracy Seebeck coefficient vs. electrical conductivity (colored by power factor) over the transport database (50,000+ compounds) computed with DFT / GGA band structures & BoltzTraP under a constant relaxation time approximation. We have developed a state-of-the-art, open- source calculation engine for performing high- throughput calculations: • FireWorks workflow software • MatMethods automatic calculation recipes All software is available open-source at www.github.com / hackingmaterials We computed a database of electronic transport properties (50,000 compounds) using BoltzTraP (cRTA) and applied it to thermoelectrics discovery. The complete transport database results will soon be disseminated publicly. Potential sources of error in the calculations include well-known problems with DFT/GGA band gaps, band curvature and DOS inaccuracies, and the use of a constant relaxation time approximation (cRTA). We compared our computations with available experimental data to determine that: • DFT underestimation of small band gaps is a major component of Seebeck coefficient errors; a “scissor” operation improves results but requires knowledge of the band gap or use of higher-order computational techniques. • Errors in power factor likely stem from a constant relaxation time approximation. For small gap compounds, band curvature differences also contribute. A collaborative effort examined the electronic transport database for novel thermoelectrics candidates. We targeted YCuTe 2 due to (i) reasonable calculated thermoelectric figure-of-merit, (ii) generally low thermal conductivities of copper chalcogenides and potential for liquid-like Cu phonon scattering mechanisms, and (iii) a good match to the synthesis capabilities of the Snyder research group. New thermoelectric materials screening: the case of YCuTe 2 (zT ~ 0.75) Future work – beyond constant relaxation time We are developing a new method for electronic transport from first- principles that includes multiple scattering mechanisms and shows much better agreement with experiment than BoltzTraP cRTA. A software implementation, AMSET, will be made available in 2017. Future work – chemical substitution strategy The current library of ~50,000 compounds is derived from compounds contained in the Materials Project (MP) database. Next, we will initiate chemical substitutions into MP compounds to generate completely novel materials for thermoelectrics and other applications. Future work – relating structure and band structure We are building a set of compositional, structural, and band structure descriptors that will serve as physically-motivated “features” for machine learning algorithms. The overall goal is to build data-driven models that provide mechanistic insights into band structure formation. Comparisons of calculated versus experimental values for Seebeck coefficient (top) and power factor (bottom). Data set includes undoped (filled) and doped (open) compounds; red circles indicate that the sign of computation and experiment differ. Low- and high-temperature (>440K) crystal structures of YCuTe 2 . Cu positions are disordered in the HT phase. Projected GGA band structure (top-left) and spin-orbit band structure (bottom- left) of YCuTe 2 . Right: Theoretical zT as a function of Fermi level. Further calculations revealed that achievable figure-of-merit (zT) is reduced by spin-orbit coupling, which removes a band degeneracy at the VBM Γ point (Te 5p character). However, a low theoretical minimum thermal conductivity of 0.43 W m -1 K -1 calculated using the Cahill-Pohl model (glassy limit) encouraged us to continue exploring this material. Experimentally measured zT of several YCuTe 2 derivatives synthesized off- stoichiometry. Performance of a previously known TmCuTe 2 phase, with a different structure but similar performance, is shown for reference. Experiments carried out by the Snyder (Northwestern) and White (Dalhousie University) groups revealed a zT reaching as high as 0.75. The moderately high zT stems from a very low measured thermal conductivity of 0.5 W m -1 K -1 , very close to the calculated minimum. Increasing the carrier concentration beyond 10 19 should further increase the zT of this material (~1.0), but our attempts to extrinsically dope this compound have thus far been unsuccessful. Computational studies are capable of generating large data sets and offer independent control over many variables. These strengths should make it possible to use calculations to extract the chemical and structural factors that lead to specific electronic properties. It is well known that oxide thermoelectrics in general exhibit lower zT than other chemistries. Possible reasons include higher thermal conductivity (due to the lower anion weight of oxygen), poor dopability of oxides (due to larger band gaps), and shorter relaxation times. Our computational database indicates that, even after controlling for all of these factors, oxides still show significantly lower zT than other anions, indicating band shape as a further differentiator. We have begun building data mining models to predict the band structure features of hypothetical compounds. One model predicts the orbital character of the VBM and CBM from the chemical components of a compound, which helps tailor chemical substitutions that retain or introduce a particular band character. Violin plots depicting the distribution of computed maximum power factor under a fixed relaxation time approximation across several thousand compounds, separated by anion type. The red lines indicate the median computed power factor for each anion. Portion of a pairwise probability diagram to predict the CBM character of compounds. Blue points indicate that the ionic orbital type on the y-axis is likely to dominate the CBM over the ionic orbital type on the x-axis; the opposite is true for red-points. As a simple example, in a compound containing both V4+ and N3-, the odds are very high that V4+ will contribute more to the CBM than N3-.
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External collaborators and fundingThis work was supported by the U.S. Department of Energy, Basic Energy Sciences, Early Career Program. Collaborators: Northwestern University (Snyder lab), Universite Catholique de Louvain (Hautier Lab), Dalhousie University (White Lab), and UC Berkeley / LBNL (Ceder, Asta, and Persson labs).
Targeted Band Structure Design and Thermoelectric Materials Discovery Using High-Throughput Computation
Anubhav Jain, Energy Technologies Area, Berkeley Lab
High-throughput calculation engine and electronic transport database
Data mining thermoelectrics and band structure engineering
Benchmarking and accuracy
Seebeck coefficient vs. electrical conductivity (colored by power factor) over the transport database (50,000+ compounds) computed with DFT / GGA band structures & BoltzTraP under a constant relaxation time approximation.
We have developed a state-of-the-art, open-source calculation engine for performing high-throughput calculations: • FireWorks workflow software • MatMethods automatic calculation recipes
All software is available open-source at www.github.com/hackingmaterials We computed a database of electronic transport properties (50,000 compounds) using BoltzTraP (cRTA) and applied it to thermoelectrics discovery. The complete transport database results will soon be disseminated publicly.
Potent ia l sources of error in the calculations include well-known problems with DFT/GGA band gaps, band curvature and DOS inaccuracies, and the use of a constant relaxation time approximation (cRTA). We compared our computations with available experimental data to determine that:
• DFT underestimation of small band gaps is a major component of Seebeck coefficient errors; a “scissor” operation improves results but requires knowledge of the band gap or use of higher-order computational techniques.
• Errors in power factor likely stem from a constant relaxation time approximation. For small gap compounds, band curvature differences also contribute.
A collaborative effort examined the electronic transport database for novel thermoelectrics candidates. We targeted YCuTe2 due to (i) reasonable calculated thermoelectr ic f igure-of-merit , ( i i ) generally low thermal conductivities of copper chalcogenides and potential for l iqu id- l ike Cu phonon scatter ing mechanisms, and (iii) a good match to the synthesis capabilities of the Snyder research group.
New thermoelectric materials screening: the case of YCuTe2 (zT ~ 0.75)
Future work – beyond constant relaxation timeWe are developing a new method for electronic transport from first-principles that includes multiple scattering mechanisms and shows much better agreement with experiment than BoltzTraP cRTA. A software implementation, AMSET, will be made available in 2017.
Future work – chemical substitution strategyThe current library of ~50,000 compounds is derived from compounds contained in the Materials Project (MP) database. Next, we will initiate chemical substitutions into MP compounds to generate completely novel materials for thermoelectrics and other applications.
Future work – relating structure and band structureWe are building a set of compositional, structural, and band structure descriptors that will serve as physically-motivated “features” for machine learning algorithms. The overall goal is to build data-driven models that provide mechanistic insights into band structure formation.
Comparisons of calculated versus experimental values for Seebeck coefficient (top) and power factor (bottom). Data set includes undoped (filled) and doped (open) compounds; red circles indicate that the sign of computation and experiment differ.
Low- and high-temperature (>440K) crystal structures of YCuTe2. Cu positions are disordered in the HT phase.
Projected GGA band structure (top-left) and spin-orbit band structure (bottom-left) of YCuTe2. Right: Theoretical zT as a function of Fermi level.
Further calculations revealed that achievable figure-of-merit (zT) is reduced by spin-orbit coupling, which removes a band degeneracy at the VBM Γ point (Te 5p character). However, a low theoretical minimum thermal conductivity of 0.43 W m-1 K-1 calculated using the Cahill-Pohl model (glassy limit) encouraged us to continue exploring this material.
Experimentally measured zT of several YCuTe2 derivatives synthesized off-stoichiometry. Performance of a previously known TmCuTe2 phase, with a dif ferent structure but similar performance, is shown for reference.
Experiments carried out by the Snyder (Northwestern) and White (Dalhousie University) groups revealed a zT reaching as high as 0.75. The moderately high zT stems from a very low measured thermal conductivity of 0.5 W m-1 K-1, very close to the calculated minimum. Increasing the carrier concentration beyond 1019 should further increase the zT of this material (~1.0), but our attempts to extrinsically dope this compound have thus far been unsuccessful.
Computational studies are capable of generating large data sets and offer independent control over many variables. These strengths should make it possible to use calculations to extract the chemical and structural factors that lead to specific electronic properties. It is well known that oxide thermoelectrics in general exhibit lower zT than other chemistries. Possible reasons include higher thermal conductivity (due to the lower anion weight of oxygen), poor dopability of oxides (due to larger band gaps), and shorter relaxation times. Our computational database indicates that, even after controlling for all of these factors, oxides still show significantly lower zT than other anions, indicating band shape as a further differentiator. We have begun building data mining models to predict the band structure features of hypothetical compounds. One model predicts the orbital character of the VBM and CBM from the chemical components of a compound, which helps tailor chemical substitutions that retain or introduce a particular band character.
Violin plots depicting the distribution of computed maximum power factor under a fixed relaxation time approximation across several thousand compounds, separated by anion type. The red lines indicate the median computed power factor for each anion.
Portion of a pairwise probability diagram to predict the CBM character of compounds. Blue points indicate that the ionic orbital type on the y-axis is likely to dominate the CBM over the ionic orbital type on the x-axis; the opposite is true for red-points. As a simple example, in a compound containing both V4+ and N3-, the odds are very high that V4+ will contribute more to the CBM than N3-.
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