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UNIVERSITY of CALIFORNIA Los Angeles Prediction of High-Performance Thermoelectric Materials and Optimal Electronic Structures F

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UNIVERSITY of CALIFORNIA Los Angeles Prediction of High-Performance Thermoelectric Materials and Optimal Electronic Structures F UNIVERSITY OF CALIFORNIA Los Angeles Prediction of High-Performance Thermoelectric Materials and Optimal Electronic Structures for Thermoelectricity A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Materials Science and Engineering by Chun Soo Park 2019 c Copyright by Chun Soo Park 2019 ABSTRACT OF THE DISSERTATION Prediction of High-Performance Thermoelectric Materials and Optimal Electronic Structures for Thermoelectricity by Chun Soo Park Doctor of Philosophy in Materials Science and Engineering University of California, Los Angeles, 2019 Professor Vidvuds Ozoli¸nˇs,Co-Chair Professor Dwight Christopher Streit, Co-Chair The thermoelectric figures of merit of bulk materials up to date have not overcome zT = 3, and only in rare occasions have they surpassed zT = 2. Bulk thermoelectrics with zT > 3 have been desired but have not yet been theoretically predicted let alone experimen- tally realized. In this doctoral work, high-performance thermoelectric materials theoretically capable of zT > 4 are identified and characterized using state-of-the-art first-principles com- putational methods based on density-functional theory. Ba2BiAu and Sr2BiAu full-Heusler compounds in particular are predicted to deliver ultrahigh thermoelectric performances { the latter across all temperature domain from cryogenic to high: 0:3 ≤ zT ≤ 5 at 100 K ≤ T ≤ 800 K. While unfortunately the compounds look not n-dopable and their predicted zT values inaccessible, they constitute a theoretical proof of concept that zT > 4 is within reach for bulk compounds. With the lessons learned from these compounds and others, the optimal electronic structures for intrinsic thermoelectric performance are generally determined for both semiconductors and metals. Highly dispersive bands at off-symmetry points that min- imize electron-phonon scattering is optimal for semiconductors, while a flat-and-linear band crossing that leads to electron filtering and high Seebeck coefficients is optimal for metals. May these generalizations help propel discoveries of more high-performance thermoelectrics. ii The dissertation of Chun Soo Park is approved. Louis-Serge Bouchard Bruce S Dunn Jaime Marian Vidvuds Ozoli¸nˇs,Committee Co-Chair Dwight Christopher Streit, Committee Co-Chair University of California, Los Angeles 2019 iii To my wife, Seungwon Chung, and my parents, No Young Park and Ye Ok Oh iv TABLE OF CONTENTS List of Figures :::::::::::::::::::::::::::::::::::::: ix Acknowledgments :::::::::::::::::::::::::::::::::::: xvii Vita ::::::::::::::::::::::::::::::::::::::::::::: xix 1 Introduction :::::::::::::::::::::::::::::::::::::: 1 1.1 Thermoelectricity . .1 1.1.1 The Thermoelectric Effect . .1 1.1.2 The Onsager-Callen Theory . .3 1.1.3 Challenges of the Figure of Merit zT ..................6 1.2 Research Efforts on zT Improvement . .9 1.2.1 Reducing Lattice Thermal Conductivity . 10 1.2.2 Enhancing the Power Factor . 12 1.3 Research Statement . 16 2 Computational Theories & Methods :::::::::::::::::::::: 17 2.1 Transport of Electrons & Phonons . 18 2.1.1 Boltzmann Transport { Electrons . 19 2.1.2 Boltzmann Transport { Phonons . 22 2.1.3 The Lifetime Problem and Scattering . 23 2.2 Scattering of Electrons . 24 2.2.1 Electron-Phonon Scattering: Part 1 . 24 2.2.2 Electron-Phonon Scattering: Part 2 . 30 v 2.2.3 Ionized Impurity Scattering . 35 2.3 Scattering of Phonons . 37 2.3.1 Lattice Anharmonicity . 38 2.3.2 Phonon-phonon Scattering . 40 3 Preliminary Investigations ::::::::::::::::::::::::::::: 45 3.1 Chalcopyrite CuFeS2 ............................... 46 3.1.1 Crystal, Magnetic, and Electronic Structures . 47 3.1.2 Electron Transport . 49 3.1.3 Phonon Transport and Nanostructuring . 53 3.1.4 Lessons . 56 3.2 Full-Heusler Fe2TiSi . 57 3.2.1 Crystal and Electronic Structures . 58 3.2.2 Electron Transport . 61 3.2.3 Phonon Transport and Alloying . 66 3.2.4 Lessons . 69 4 Prediction of High-Performance Thermoelectrics ::::::::::::::: 71 4.1 zT = 5 in Full-Heusler Ba2BiAu . 72 4.1.1 Crystal & Electronic Structures . 72 4.1.2 Scattering and Mobility . 75 4.1.3 Thermoelectric Properties . 76 4.1.4 Lessons . 80 4.2 High-Performance at Cryogenic-to-High Temperatures in Sr2BiAu . 81 4.2.1 Electronic Structure . 81 vi 4.2.2 Scattering & Mobility . 83 4.2.3 Thermoelectric Properties . 85 4.2.4 Lessons . 87 4.3 Intermetallic, B20-type CoSi . 89 4.3.1 Crystal and Electronic Structures . 90 4.3.2 Thermoelectric Properties . 91 4.3.3 Electron-phonon Scattering . 93 4.3.4 Lessons . 95 5 Optimal Electronic Structures for Thermoelectricity :::::::::::: 96 5.1 Revisiting the Mahan-Sofo Analysis . 97 5.2 Revisiting the Role of Effective Mass . 99 5.3 Deduction of Optimal Electronic Structures . 104 5.3.1 Semiconductors . 104 5.3.2 Metals . 105 6 Summary and Outlooks :::::::::::::::::::::::::::::: 108 6.1 Conclusions . 108 6.2 Future Outlooks . 110 A Stability, Defects, and Doping of Ba2BiAu and Sr2BiAu :::::::::: 112 A.1 Computational Methods . 113 A.1.1 Defect Formation Energies . 113 A.1.2 Defect Concentration . 115 A.1.3 DFT Calculations . 116 A.2 Results & Discussions . 117 vii A.2.1 Chemical Potentials & Stability . 117 A.2.2 Defects . 117 A.3 Conclusions . 120 References ::::::::::::::::::::::::::::::::::::::::: 121 viii LIST OF FIGURES 1.1 a) Thermoelectric refrigeration induced by applied external voltage. Heat-carrying electrons flow in the direction enforced by the voltage and create temperature gra- dient. b) Thermoelectric current generation from applied temperature gradient. Charge carriers are excited at the hot end and flow to the cool end. .2 1.2 History of zT improvement in some of the highest-performing thermoelectric ma- terials to date (left) [HT17] and zT values of state-of-the-art low-temperature thermoelectrics (right) [MLZ18]. .7 1.3 Natural abundance of elements occurring in earth's crust (image taken from Wikipedia). .8 1.4 The general behaviors thermoelectric transport properties with respect to doping [ST08]. .9 1.5 A plot of the distributions that determine the magnitudes of σ, ζ, and κE, with respect to energy. The two dashed vertical lines qualitatively divide the energy- domain into four domains where Σ(E) ought to be high or low in order to max- imally benefit the n-type \electronic-part zT ". Domain (1) is the hole-regime. Domain (2) is where low-energy electrons live which contribute more to σ than ζ. Domain (3) is where the medium-energy electrons live and where the relative benefit to ζ is the largest. Domain (4) is populated by high-energy electrons that contribute mostly to κE. Domain (3) ought to be weighted with high Σ(E) for the best thermoelectric benefit. 14 2.1 A schematic of the electron and phonon Wannier functions entering the e-ph matrix elements [GCL07]. The square lattice sketches unit cells, the red curves the electron Wannier functions, and the blue curve the phonon perturbation in the Wannier representation. If any one is spatially separated from the others, gν0νλ(Re; Rph) vanishes. 34 ix 2.2 a) The interpolated electronic band structure, b) the phonon dispersion, and c) the interaction matrix elements of boron-doped diamond using Wannier interpo- lation on EPW [GLC10]. 35 2.3 a) Normal scattering. The entire scattering processes is contain within the first Brillouin zone. No thermal resistivity is experienced. b) Umklapp scattering. The interaction results in a crystal momentum that escapes the first Brillouin zone, which is essentially results in backscattering due to the periodic lattice. The reciprocal lattice translation conserves momentum. 41 3.1 a) The body-centered tetragonal unit cell of antiferromagnetic CuFeS2 belonging to the I42d space group. Fe atoms are brown, Cu atoms are blue, and S atoms are yellow. The red arrows indicate spin directions. b) The orbital-decomposed density of states of one Fe atom. c) The electronic band structure. The Fermi level (horizontal red line) is at the optimum doping level for zT at 400 K. d) The atom-decomposed electronic density of states. Cu appears nearly monovalent (3d104s0): Cu 3d contributes significantly to the upper valence bands but very little to the conduction bands. 48 3.2 (Color online) a) The Seebeck coefficient calculated with fitted τ from τ(E) / N(E)−1 scaling. b) The Seebeck coefficient calculated with constant relaxation time approximation. c) Electron conductivity from τ(E) / N −1 then scaled by the ratio with the experimental conductivity [TMI14]. The true reference lifetime is estimated to be 2 × 10−15 s as opposed to 10−14 s used by BoltzTraP. d) The power factor calculated with the scaled σ. Experimental data points from Tsujii et al are for Cu:97Zn:03FeS2 [TMI14], and those from Li et al are for Cu:97Fe1:03S2 [LZQ14]. The marker colors are associated with temperature (black for 300 K, red for 400 K). e) Average mean free paths of electrons with τ(E) = 2×10−15N −1(E) s, all of which are shorter than 1 nm. Colors indicate bands. 52 3.3 a) Phonon dispersion. b) The atom-projected phonon density of states. 54 x 3.4 a) Calculated bulk lattice thermal conductivity. The expected T −1 trend is ob- served. Experimental data points are included for comparison. b) Cumulative lattice thermal conductivity over contributions from phonon modes of increasing MFP. c) Phonon lifetimes. d) Phonon mean free paths. The horizontal red line indicates 20 nm, the target length scale of nanostructuring considered in this work. 55 3.5 a) zT with nanostructuring of 20 nm grains b) Predicted improvement of zT via ideal nanostructuring (solid blue, 20 nm grain-size and assuming it does not harm the PF) in comparison to bulk (dotted blue). The power factor (dashed red) is overlaid. At each temperature, the optimal doping concentration for maximum zT is selected. 56 3.6 a) The unit cell of a full-Heusler compound. The green atoms correspond to Fe, the purple atoms to Ti and the yellow atoms to Si.
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