Computationally Guided Materials Discovery

Transcription

1

2 International Materials Research Congress 2017: Tutorial Computationally Guided Materials Discovery High-throughput Computations, Softwares and Databases, Experimental Feedback Prashun Gorai National Renewable Energy Laboratory Colorado School of Mines

3 High-throughput Computations: General Down-selection Approach materials search space Define search space (known materials, hypothetical structures, alloy compositions) descriptor (metric) of target property candidates detailed calculations Develop a descriptor/metric to quantify the target property (e.g. a figure of merit) Approximate but reliable Computationally tractable Perform higher accuracy or detailed calculations Phase stability, defect calculations etc. experimental realization Eureka! (hopefully) Seemingly straightforward, practical implementation non-trivial 3/42

4 Developing a Robust, Quantitative Descriptor is Challenging materials search space A descriptor is a quantitative metric for the desirable material properties descriptor (metric) of target property candidates 1. Can be a set of material properties example: transparent conducting oxides large band gap (transparent), high carrier mobility detailed calculations 2. Can be a figure of merit example: thermoelectric material thermoelectric figure of merit zt experimental realization Calculation of the descriptor should also be computationally tractable 4/42

5 Examples of Materials Discovery Enabled by HT Computations PV, topological insulators, batteries, thermoelectrics, gas storage, water splitting, REVIEW ARTICLE PUBLISHED ONLINE: 20 FEBRUARY 2013 DOI: /NMAT3568 The high-throughput highway to computational materials design Stefano Curtarolo 1,2 *, Gus L. W. Hart 2,3, Marco Buongiorno Nardelli 2,4,5, Natalio Mingo 2,6, Stefano Sanvito 2,7 and Ohad Levy 1,2,8 5/42

6 High-throughput Computations: Good, Bad and Ugly The Good Large number of materials can be rapidly screened to down select candidates Can accelerate materials discovery and learning of new structure-property relationships Computational advances (softwares, infrastructure) have been rapid to enable HT computations The Bad Developing a robust descriptor is quite challenging Results may depend on the computational method of choice - lack of prediction consistency Experimental validation may not be able keep pace with the rate at which predictions are generated The Ugly Without experimental validation, the literature is inundated with nonsensical results HT computations can lead to HT errors! Seemingly straightforward, practical implementation non-trivial 6/42

7 Example: Computationally Guided Discovery of Thermoelectric Materials 1. Urgent need to discover high-performing thermoelectric materials computations can accelerate the discovery 2. Edisonian trial-and-error approaches have resulted in limited success computationally guided discovery may be successful 3. Descriptor of TE performance is complicated due to contraindicated properties computationally guided discovery may be successful Computationally guided discovery of thermoelectric materials Prashun Gorai, Vladan Stevanović and Eric S. Toberer REVIEWS Monday August 21, 10:00 (Tulum F) Gorai, Stevanovic, Toberer, Nature Reviews Materials, 2, (2017) 7/42

8 Outline Break (2.5 min), Primer on thermoelectrics (1) Why is computational search of thermoelectric materials challenging? (2) Boltzmann transport theory (1) Descriptors of thermoelectric performance (8+break+ 6) Theory, examples, limitations, improvements Challenges: dopability (4) Break (2.5 min), Softwares for HT computations (2) Open-access databases (3) Role of data informatics (1) Role of experimental validation (1) Outlook (1), Q&A (10 min) 8/42

9 Questions? 9/42

10 Primer on Thermoelectrics T hot SOLID Thermoelectric Figure of Merit zt = 2 ( L + e ) T 1 zt V heat charge Complex function of Intrinsic material properties zt Temperature Carrier concentration (doping) Carrier concentration (cm 3 ) T cold Advantages Wide range of waste heat sources, enormous potential Solid-state, highly-scalable, reliable Challenges Device conversion efficiencies are low Discovery of new materials challenging because of contraindicating properties Materials discovery key to advancing thermoelectric technology Gorai, Stevanovic, Toberer, Nature Reviews Materials, 2, (2017) 10/42

11 TE Materials Discovery is Complex: Well Suited for Computations Search space is chemically, structurally diverse Contraindicated transport properties Average Atomic Mass PbTe PbSe PbS Hf 0.5 Zr 0.5 NiSn Cu 2 Se Mg 2 Sn Mg 2 Si Bi 2 Te 3 Tl 9 BiTe 6 TlSbTe 2 Sb 2 Te 3 YbZn 2 Sb 2 SnSe ZnO La 3 Te 4 Mo 3 Sb 7 Sr CoSb 3 GaSb 3 3 BiCuSeO Zn 4 Sb 3 Ba SnS 8 Ga 16 Ge 30 Ca 5 Al 2 Sb 6 FeSi 2 TiO 2 NaCoO 2 CaMnO 3 Si 0.8 Ge 0.2 Mg 3 Sb 2 structural complexity MnSi 0.75 CsBi 4 Te 6 Yb14 MnSb 11 heavier atoms zt > < 0.5 HOT SOLID charge phonon q 1 k k q 3 q k q COLD Number of Atoms in Primitive Cell q 2 ~40,000 metal-non metal compounds from ICSD Computations can guide discovery of new TE materials, identify new structure-property relations 11/42

12 Where do we look for great TE in the vast chemical space? crystal structure databases alloys hypothetical materials Inorganic crystal structure database, Crystallography open database, Pearson s crystal data, Cambridge structural database Predominantly stoichiometric, ordered compounds Majority previously synthesized Varying alloy compositions between known materials Represents a continuum search space - infinite possibilities Present computational methods not efficient for alloys Exciting, unchartered chemical space Structure prediction tools are emerging Experimental validation is necessary 12/42

13 What is Needed to Predict Thermoelectric Performance? Transport properties derived within the Boltzmann transport theory = Electrical Conductivity f 0 ( )d = 1 T Seebeck Coefficient f 0 ( )( µ)d zt = 2 ( L + e ) T Electronic Thermal Conductivity 0 = 1 T f 0 ( )( µ) 2 d Lattice Thermal Conductivity L = n,q [v n (q).i] 2 n(q)c n (q) e = 0 T ( )= [v n (k).i] 2 n(k) ( (k)) n,k 2 Need to compute: dispersions (electron, phonon) and scattering relaxation times 13/42

14 HT Search Strategies and Descriptors of Thermoelectric Performance 2006 Constant relaxation time approximation (CRTA) Descriptor focuses only on electronic transport 2011 Constant mean free path approximation (CMFP) Descriptor focuses only on electronic transport 2015 Semi-empirical descriptor Descriptors accounts for both electron and phonon transport theory examples limitations improvements 14/42

15 1. Constant Relaxation Time Approximation (CRTA) Electrical Conductivity = f 0 ( )d Transport Distribution Function = 1 T Seebeck Coefficient f 0 ( )( µ)d ( )= n,k [v n (k).i] 2 n(k) ( (k)) In this approach, the relaxation time (τ) is assumed to be constant Electrical conductivity scales linearly with τ, Seebeck is τ-independent Reduced power factor (ασ 2 /τ) is the descriptor for thermoelectric performance Large power factors are desirable for good thermoelectric performance Effect of thermal conductivity is often overlooked Electronic part of zt is evaluated within CRTA 15/42

16 1. Softwares for Solving Boltzmann Transport Equations BoltzTraP. A code for calculating band-structure dependent quantities Georg K.H. Madsen a,,davidj.singh b a Department of Chemistry, University of Aarhus, DK-8000 Århus C, Denmark b Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN , USA Received 25 September 2005; accepted 3 March 2006 Available online 2 May 2006 One of the most widely used softwares for calculation of transport coefficients from first-principles DFT calculations Other similar softwares: BoltzWann (use localized Wannier functions) 1 LanTrap (within Landauer formalism) 2 ShengBTE (solves phonon Boltzmann transport equations) 3 1 Pizzi et al., Comp. Phys. Comm. 185, 422 (2014) 2 Lundstorm et al. (2014) 3 Li et al., Comp. Phys. Comm., 185, 147 (2014) 16/42

17 1. Example: Search for Antimonide Thermoelectrics Published on Web 08/25/2006 Automated Search for New Thermoelectric Materials: The Case of LiZnSb Georg K. H. Madsen Contribution from the Department of Chemistry, UniVersity of Aarhus, DK-8000 Århus C, Denmark Received April 12, 2006; One of the earliest applications of the CRTA approach to search for new TE materials Screened 570 Sb-containing compounds from the ICSD Assumed fixed values of τ and κl for all compounds LiZnSb identified as promising candidate - experiments could not confirm Interesting candidates (Zr5ZnSb3, NaZnSb) remain unverified Madsen, J. Amer. Chem. Soc., 128, (2006) 17/42

18 1. Example: XYZ2 Thermoelectrics TmAgTe2 trigonal tetragonal Search identified XYZ2 chemistry as a promising family of thermoelectric materials Assumed constant τ for all compounds Calculated minimum κl in the amorphous limit zt of ~0.35 achieved for TmAgTe2, carrier concentration tuning was challenging Zhu et al., J. Mater. Chem. C, 3, (2015) 18/42

19 1. Limitations of Constant Relaxation Time Approximation Constant relaxation time is a very crude approximation Scattering relaxation time (~ 1/rate) is highly energy- and temperature-dependent In general, power factors are overestimated Thermal conductivity is ignored! Liu et al., Phys. Rev. B, 95, (2017), Chen et al., J. Mater. Chem. C, 4, 4414 (2016) 19/42

20 2. Constant Mean Free Path Approximation (CMFPA) Electrical Conductivity = f 0 ( )d Transport Distribution Function = 1 T Seebeck Coefficient f 0 ( )( µ)d ( )= n,k [v n (k).i] 2 n(k) ( (k)) v(e) (E) = In this approach, the relaxation time (τ) is now energy-dependent Materials have to be nanostructured to ensure λ is limited by grain size Reduced power factor (ασ 2 /λ) is the descriptor for thermoelectric performance Effect of thermal conductivity is overlooked Electronic part of zt is evaluated within CMFPA 20/42

21 2. Example and Limitations a 10 3 n-doped Power factor Seebeck 10 3 P/L (µw cm 1 K 2 nm 1 ) P/L (µw cm 1 K 2 nm 1 ) b Nb 2 O 6 Zn 1 (#36290) Ce 1 O 6 Se 2 (#60778) Cl 12 Ta 2 Te 4 (#401907) Mo 1 O 7 P 2 (#202810) Ca 1 Nb 2 O 6 (#15208) Ce 1 O 7 P 2 (#160452) B 2 Cs 3 Li 2 Na 1 O 6 (#36531) O18 Ti 10 (#31399) p-doped Lu 2 O 3 (#33659) F 6 O 2 Sb 1 (#78849) Gd 2 O 3 (#27996) Ce 2 O 3 (#96202) Br 2 Hg 2 O 6 (#31925) B 2 Cs 3 Li 2 Na 1 O 6 (#36531) O18 Ti 10 (#31399) Ba 1 N 2 O 6 (#35495) B 2 Ce 3 Cl 3 O 6 (#413237) O5 Ti 1 Y 2 (#34692) Al 6 Ca 4 O 16 S 1 (#28480) F 6 Na 1 Sb 1 (#25538) Cd 3 Na 2 O 10 Si 3 (#28416) O5 Si 1 Sr 3 (#18151) Ce 1 I 4 O 12 (#16665) B 2 Na 1 O 5 Sc 1 (#409522) O6 W 1 Y 2 (#20955) Ba 1 N 2 O 6 (#34902) N2 O 6 Pb 1 (#52350) Power factor Seebeck La 2 O 3 (#96201) Cl 6 Cs 2 Sn 1 (#9023) F 1 Na 3 O 4 W 1 (#417289) O7 P 2 Sn 1 (#30583) Ce 1 O 3 Sr 1 (#71352) Br 1 F 4 N 1 O 2 (#412427) N2 O 6 Sr 1 (#35494) C3 N 4 (#83263) O3 Sr 1 Zr 1 (#41083) F 6 Te 1 (#67609) Cl 12 Ta 2 Te 4 (#401907) O7 P 2 W 1 (#904390) O3 Y 2 (#16394) S (µv K 1 ) S (µv K 1 ) HT screening of ~2500 materials from the ICSD TiO2 Magneli phases and Cs3Li2NaB2O6 identified as promising candidates Candidates remain experimentally unverified Well-known thermoelectrics not identified Limitations: mean free path assumed constant for all materials Some materials have to be nanostructured below 5 nm Thermal stability of nanostructured materials is an issue 21/42

22 Questions? PERSPECTIVE FOCUS Fishing the Fermi sea PAUL C. CANFIELD is at Ames Laboratory, and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA. The scientist who is skilled in the art of new materials design and discovery will develop a variety of strategies for identifying promising spots to fish for new materials and ground states. P. C. Canfield, Nature Physics 4, 167 (2008) 22/42

23 3. Semi-empirical Thermoelectric Quality Factor constant core T-dep zt = 2 T ( L + e ) zt = u (v + 1) Lattice thermal conductivity Charge carrier mobility L = A 1 Mv y s T 2 V z n x + 3k B 2 6 1/3 v s V z 1 1 n 2/3 Modeled κl (Wm -1 K -1 ) Ca 5 In 2 Sb 6 PbTe Ga 2 O 3 Mg 2 Si AlP Si GaP GaAs SiC BP AlN d-c ZnGeP 2 InI SrTiO 3 1 SrIn 2 O 4 MoTe 2 Cu 3 TaTe 4 Bi 2 O Experimental κ L (Wm -1 K -1 ) Miller, Gorai, Stevanovic, Toberer et al, Chem. Mat. 29, 2494 (2017) Yan, Gorai, Stevanovic, Toberer et al, Energy Environ. Sci. 8, 983 (2015) 23/42

24 3. Example: Search for New Binary A1B1 Thermoelectric Materials ztmax SnSe(Cmcm) ZnSb SnS GeTe PbSe InSe MnTe rocksalt PbTe PbS SnTe n-type InSe PbO GaTe CdSb SnSe PbS PbSe ZnSb PbTe bubble radius scales with β SnTe PbS AlSb MnSe p-type InI AgBr PbS AgI PbSe SnSe CdSb SnTe GeTe GeTe GeSe PbS PbSe PbTe LaN Space Group Number Count ,1 1,2 1,3 2,3 3,4 1,1,2 1,2,2 1,3,3 1,2,3 1,3,4 1,3,7 1,4,6 2,5,6 1,1,1,1 1,1,11,14 4,9,9 Stoichiometry space group orthorhombic Nearly 30% of known thermoelectric materials are A1B1 compounds Known thermoelectric materials are correctly identified with β Identified new candidate materials; independent re-discovery (n-type SnSe, zt = 2.2) Gorai, Toberer, Stevanovic et al., Chem. Mater. 18, 6213 (2015), Cho et al. Nature Comm. 7, (2016) 24/42

25 3. Example: Computational Identification of Quasi-2D TE Materials 3 Quasi Low-dimensional Materials Screening of 427 binary quasi-2d layered materials ztmax BiCuSeO InSe Sr 3 GaSb 3 CsBi 4 Te 6 Bi 2 Te 3 SnSe Ca 3 AlSb 3 Sb 2 Te 3 CaZn 2 Sb Lattice Therm. Conduc (Wm -1 K -1 ) Quasi low-dimensional structures are abundant among TE materials (cm 2 V-1s -1 ) ZrTe 5 TlI SnI 2 valence band Sb 2 Te 3 (12) Sb 2 Te 3 (166) Bi2 Te 3 HgI 2 In 2 Te 5 Bulk modulus (GPa) PbSe 1 10 L (Wm -1 K -1 ) PbS (36) SnS (63) SnSe (63) conduction band Sb 2 Te 3 (12) GeAs 2 PbSe (62) PbS (39) InSe In 2 Se 3 ZrTe BiI 5 3 GaTe(194) 1 10 SnSe (62) SbTe L (Wm -1 K -1 ) >50 Bi 2 Te 3 Gorai, Toberer and Stevanovic, J. Mater. Chem. A 4, (2016) 25/42

26 3. Semi-empirical Descriptor: Limitations By design, semi-empirical models will not capture phenomena not represented in the learning dataset Can be improved by including more experimental data in learning dataset Assumption: transport is isotropic Assumption: phonon-phonon interactions are harmonic (lattice thermal conductivity) Fermi surface: PbTe a k z Σ k y k x L valence band (orange), conduction band (blue) Pei et al., Nature Lett. 473, 66 (2011) 26/42

27 3. Descriptor Improvements: Incorporating Anharmonicity in κl Original Model Improved Model Modeled κl (Wm -1 K -1 ) factor of 5 SrTiO 3 PbTe InI SiC GaN GaP GaAs d-c Modeled κl (Wm -1 K -1 ) factor of 2 Mg 2 Si PbTe InI SrTiO 3 SiC GaN GaP GaAs d-c Cu 3 TaTe Experimental κ L (Wm -1 K -1 ) Cu 3 TaTe Experimental κ L (Wm -1 K -1 ) L = A 1 Mv y s T 2 V z n x + 3k B 2 6 1/3 v s V z 1 1 n 2/3 Incorporating coordination as a measure of anharmonicity, improves prediction Miller, Gorai, Stevanovic, Toberer et al., Chem. Mater., 29, 2494 (2017) 27/42

28 Something Missing in Descriptors: Dopability Thermoelectric Figure of Merit zt = 2 ( L + e ) T 1 zt Complex function of zt 0.5 Intrinsic material properties Temperature Carrier concentration (doping) Carrier concentration (cm 3 ) Rapid a priori prediction of material dopability is difficult 28/42

29 Prediction of Dopability is a Bottleneck in TE Materials Discovery The Curious Case of LiZnSb (and many others) Published on Web 08/25/2006 Automated Search for New Thermoelectric Materials: The Case of LiZnSb Georg K. H. Madsen Contribution from the Department of Chemistry, UniVersity of Aarhus, DK-8000 Århus C, Denmark Received April 12, 2006; georg@chem.au.dk experimental assessment JOURNAL OF APPLIED PHYSICS 105, n-type Thermoelectric properties of p-type LiZnSb: Assessment of ab initio calculations Eric S. Toberer, a Andrew F. May, Cidney J. Scanlon, and G. Jeffery Snyder Materials Science, California Institute of Technology, Pasadena, California 91125, USA p-type Received 25 November 2008; accepted 27 January 2009; published online 17 March 2009 ΔHD,q (ev) defect calculations 2.5 Zn-rich/Sb-poor 2.0 Sb Zn 1.5 V Sb 1.0 p-type 0.5 Zn Sb V Zn E F (ev) Material has to be appropriately (type, concentration) doped to realize predicted TE performance 29/42

30 Defect Calculations Can Guide Doping materials search space First-principles defect calculations performed on down selected materials descriptor (metric) of target property candidates detailed calculations experimental realization 1. Computationally demanding Cannot be performed on large number of materials Analysis requires significant human intervention 2. Softwares to automate defect calculations are emerging Significantly reduces the need for human intervention 30/42

31 Example of Detailed Defect Calculations Guiding Doping Discovery of new n-type Zintl pnictides HT search for n-type Zintls 2.0 Ba is an effective donor Ba doping: n-type zt~1 realized KGaSb4 (n-type) 1.5 ΔHD,q (ev) 1.0 KGaSb4, KAlSb4 0.5 Ba K E F (ev) Ortiz, Gorai, Stevanovic, Toberer, J. Mater. Chem. A 5, 5036 (2017), Chem. Mater. 29, 4523 (2017) 31/42

32 Questions? 32/42

33 Softwares for High-throughput Computations A number of softwares designed for HT computations are now available for free PyLada github.com/pylada 1. Open source softwares Typically written in Python Highly customizable Thriving community aflowlib.org 2. Manage jobs and analyze outputs Interacts with supercomputer job schedulers Error handling Powerful tools for post-calculation analyses 33/42

34 Automated Softwares for Defect Calculations PyLada Defects github.com/pylada/pylada-defects Softwares to automate defect calculations have been developed only recently PyCDT pypi.python.org/pypi/pycdt 1. Set up defect calculations Create defect structures Create input files for running defect calculations 2. Perform post-calculation analyses Finite-size corrections Create phase stability maps Self-consistently calculate carrier concentrations 34/42

35 Role of Open-Access Databases in Accelerating Materials Discovery Several open-access databases provide computational data on: 1. Phase stability 2. Electronic properties 3. Thermal properties 4. Elastic and piezoelectric properties etc. Data visualization is an important component several databases 1. Analyze high-dimensional data 2. Identify new structure-property relations 35/42

36 Example: Thermoelectrics Design Lab Materials Visualization Resources Contribute x = 10 Gorai, Stevanovic, Toberer et al., Comp. Mat. Sci. 112A, 368 (2016) 36/42

37 Live Demonstration of TEDesignLab If the internet cooperates 37/42

38 Role of Data Informatics in Accelerating Materials Discovery UCSB Experimental Thermoelectrics Database Chemistries identified by recommendation engine Large amounts of real and reciprocal space data generated through HT computations Some parameters are experimentally unaccessible Data mining can unravel new structure-property relations To be robust, even larger amounts of data are needed Chemical and structure phase high dimensional, number of materials small Gaultois et al., Chem. Mater., 25, 2911 (2013), Gaultois et al., APL Mater., 4, (2016) 38/42

39 The Need for Experimental Validation, Feedback, and Integration new TE Current Approach to TE Materials Search detail candidates Level of Theory empirical searches search in material classes candidates high-throughput searches candidates data informatics new TE Computationally-Guided TE Materials Search Level of Theory detail empirical searches structure-property relations search in material classes feedback cand. high-throughput searches data informatics Number of Materials Considered 39/42

40 Outlook High-throughput (HT) computations can accelerate materials discovery However, HT computations also means there is a chance for HT errors! Developing computationally tractable descriptors is the most challenging task Present infrastructure is quite sophisticated to enable HT computations Experimental validation is critical to the success of computational materials discovery Funding NSF-DMREF Grant , NREL High Performance Computing (HPC) prashun.gorai@nrel.gov or pgorai@mines.edu Please download slides: