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Smart Metrics for High Performance Material Design

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Smart Metrics for High Performance Material Design

  1. 1. Smart Metrics for High-Performance Material-Design Kamal Choudhary, Francesca Tavazza NIST, Gaithersburg, AIMS 2019 8/1/2019 1
  2. 2. Acknowledgement and Collaboration • Kevin Garrity, Brian DeCost, Faical Y. Congo, James Hickman, Adam Biacchi, Carelyn Campbell, Andrew Reid, James Warren, Daniel Wheeler, Zachary Trautt, Irina Kalish, Lucas Hale, Marcus Newrock, Albert Davydov, Angela HeightWalker, NIST • Ruth Pachter, Air-Force Research Lab • Deyu Lu, Matthew Carbone, Brookhaven National Lab • Marnik Bercx, Dirk Lamoen, U. Antwerp, Belgium • Evan Reed, Stanford University • Ankit Agrawal, Northwestern University • Qian Zhu, U. Nevada Las Vegas • Tony Low, U. Minnesota • Richard Hennig, University of Florida • Susan Sinnott, Penn state • Materials-Project team, Lawrence Berkeley National Laboratory • Subhasish Mandal, Rutgers University • Lidia Carvalho Gomes, National University of Singapore 2& Many others
  3. 3. Motivation Materials Genome Initiative National Quantum Initiative Build a universal infrastructure to Make your scientific-dreams come true ! (Personal motivation) Needs data and resources
  4. 4. Outline • Basics: DFT, FF and ML • Overview: JARVIS-Database and Tools • Classical data: 1) Formation energy, 2) Exfoliation energy, 3) Elastic constants, 4) Surface, 5) Vacancy and 6) GB energy [ DFT, FF, and ML methods] • Quantum data: 7) Bandgaps (OptB88vdW and TBmBJ), 8) Magnetic moments, 9) Dielectric function, 10) Solar-cell efficiency (SLME) , 11) Topological materials (Spillage), 12) Thermoelectric properties, 13) Piezoelectric properties, 14) Infrared intensities, 15) Elelctrides (ELF), 16) DFT Convergence, 17) Heterostructures, 18) STM [ DFT and ML methods]
  5. 5. • Materials Science is all about: Process-Structure-Property-Performance relationship and minimization of free-energy • Computationally: Structure = lattice constants (a,b,c), angles (alpha, beta, gamma) and basis vectors ([Si,0, 0,0],[Si,0.5,0.0,0.5],…..) • To calculate property: classical physics (e.g. classical force-fields), quantum physics (e.g. density functional theory) • MGI motivated current computational databases: Materials-Project (MP), AFLOW, OQMD • Importance of screening metrics for High-performance materials design ICSD database (with experiment al lattice constant) AFLOW OQMD PBE Materials Project MIT, LBNL (67,486 materials) Duke University (1,640,245 materials) Northwestern University (471,857 materials) Others: MatStudio, MaterialWeb, NREL-MatDB etc. 5 Email: kamal.choudhary@nist.gov Basics First
  6. 6. Density Functional Theory • Schrödinger equation for electrons: wave–particle duality • Schrödinger equation of a fictitious system (the "Kohn–Sham system") of non-interacting particles (typically electrons) that generate the same density as any given system of interacting particles • Uses density vs wavefunction quantity • Although DFT is a complete theory, several approximations such as: K-points, vdW interactions, kinetic energy deriv., spin-orbit coupling (Convergence, OptB88vdW, TBmBJ, SOC topology ) https://en.wikipedia.org/wiki/Classical_mechanics http://www.psi-k.org/Update3.shtml http://www.physlink.com/Education/AskExperts/ae329.cfm ( ) ( ) ( ) ( )rrErrV m iiiEff  =      +− 2 2 2  XCeeNeEff VVVTV +++= EH = Walter Kohn Exchange-correlation Hohenberg, Pierre; Walter Kohn (1964). "Inhomogeneous electron gas". Physical Review. 136 (3B): B864–B871 6
  7. 7. • Coulomb potential • Lennard-Jones potential • Morse-potential • Stilinger-Weber potential • EAM and MEAM potential • Bond-order/Tersoff/Brenner • Fixed charge potentials: Coulomb-Buckingham • Other FFs: ReaxFF, COMB, AMBER, CHARMM, OPLS etc. 7 ( ) ( )( ) 12 21 2211 , rr qkq rqrqV   − = One parameter to fit/optimize These potentials lack angular information hence not able to capture elastic constants well Uses electron density, for metallic systems These potentials lack charge information Uses angle but transferability problem Uses bond information, for covalent systems Berni Alder iii amF = , VF ii −= , 2 2 dt rd m dr dV i i i =− Email: kamal.choudhary@nist.gov Classical Force-Fields
  8. 8. Machine Learning 8 1557 descriptors/features for one material • Classical force-field inspired descriptors • Arithmetic operations (mean, sum, std. deviation…) of electronegativity, atomic radii, heat of fusion,…. of atoms at each site, example: Electronegativity of (Mo+Mo+S+S+S+S)/6 = 0.15 • Atomic bond distance, angle and dihedral based descriptors https://github.com/usnistgov/jarvis • Atomistic Descriptors: Coulomb matrix, Sine matrix, MBTR, SOAP, GCNN, BP, CFID • ML: Classification, Regression, Clustering • Requires: data, descriptors, algorithm • Metrics: Classification (ROC AUC, F1 score) Regression (MAE, RMSE, r2 etc.) on k-fold CV, test set etc. 𝑇𝑃𝑅 = 𝑇𝑃 𝑇𝑃 + 𝐹𝑁 = 1 − 𝐹𝑁𝑅 ML as a screening tool for DFT
  9. 9. https://www.darpa.mil/program/explainable-artificial-intelligence
  10. 10. JARVIS-DFT, FF and ML datasets and tools 11 >35000 bulk, 1000 monolayer materials, >110 FFs, ~1 million properties
  11. 11. 12 ~10000 webpages JARVIS-Project cost estimates: • ~$1.5 million • (CPU hours+staff+web-pages etc.) (Beyond conventional-DFT database) (Classical potential/FF database) (Direct ML predictions) ~35000 webpages
  12. 12. Impact 13 34 Presentations (16 invited) 9 published papers, 3 submitted, 4 in prep. “You guys are doing something really beneficial…” “I find JARVIS-DFT very useful for my research…” User-comments:
  13. 13. Formation Energy 15 Background Metric ML model • Thermodynamic measures whether a compound will form • Experimental data available in the order of 1000 • A+B • Formation enthalpy/energy 𝞓H • 𝞓H < 0 vs 𝞓H >0 • 32486 materials with DFT (OptB88vdW) • MAE of DFT data wrt Expt: 0.13 eV/atom http://www.dynamicscience.com.au/tester/solutions1/chemistry/energy/exothermic.htm Phys. Rev. B, 98, 014107 (2018), Phys. Rev. Mat., 2, 083801 (2018), Scientific Reports 9, 8534 (2019) Learning curve Feat. importance Performance on 10% set MAE (0.12 eV/atom) compared to the range (7 eV/atoms)
  14. 14. Exfoliation en., 2D mats., Lattice-constant Error 16 Background Metric ML model ICSD ICSDPBE c cc − = • Previously 50-60 2D mats. were known • Identifying low-D was not possible until 2017 • Exfolaition energy calculation is too expensive • Lattice parameter criteria (PBE vs. vdW) • Ef<200 meV/atom • Combined data-mining criteria • 1356 predicted materials, 816 Ef • Exfoliation energy MAE: 34 meV/atom • Identified materials with ML and • Verified with DFT Scientific Reports 9, 8534 (2019) Error in lattice parameters PBE (vdW) Error- driven discovery! (Good in Bad ☺)
  15. 15. 6x6 Elastic Tensors 17 Background Metric ML model • One of the most fundamental prop. • Elastic constants expt. for ~200 materials • Quest for stiff/flexible materials • Modeling 3D vs 2D Cij • Finite-difference method • Young, Bulk, Shear mod. (13492 mats.) • Poisson ratio, sound-velocity etc. • MAE: Bulk. Mod: 10.5 GPa Shear Mod.: 9.5 GPa https://civil.seu.edu.cn/mi/constants/list.htm MP: Scientific Data 2, Article number: 150009 (2015) Phys. Rev. B, 98, 014107 (2018).
  16. 16. Surface-Energy 18 Background Metric ML model • Energy to create a surface • Computationally very challenging using DFT • MD potentials are questionable • Surface energy for Wulff-construction Elemental surface energies up to 3 miller indices MAE: 0.13 J/m2 17576 FF surface-energies J. Phys. Cond. Matt. 30, 395901(2018)
  17. 17. Vacancy-formation Energy 19 Background Metric • Most industrial materials have defects : • Point defects (vacancy, substitution, interstitials) • Line defects (dislocations) • Planar (grain boundaries, free surfaces/nanostructures, interfaces, stacking faults) • Volume defects (voids, pores) • Computationally very challenging using DFT • MD potentials questionable • Charged defects in DFT: on-going work • FF based 1000 defect formation energies
  18. 18. Grain-boundary defect-prone Materials 20 Background Metric ML model • Computationally very challenging using DFT • MD potentials are questionable • MAE: 0.04 J/m2 • Symmetric tilt GB energies (1091) • Classical force-field data • FCC: Al, Ni, Cu, Ag, Au, Pd, Pt • BCC: Fe, W, Ta, Mo • Diamond: Si • EAM and SW potentials Unpublished work https://icme.hpc.msstate.edu/mediawiki/index.php/LAMMPS_Help3
  19. 19. Metal/Non-metals 21 Background Metric ML model • Around 200 expt. bandgaps in handbooks • One of first success of quantum physics over classical • Metal (0.0),Semi-metal (Fermi-surface touch) Semiconductor (1.5-3.5), insulator (>3.5 eV) • Need DFT/QM methods • Still QM very expensive • Conventional DFT bandgap underestimation • Expensive many-body methods • Bandgap (~0-14 eV) • TBmBJ (Meta-GGA) vs OptB88vdW • Effect on dielectric function • ~35000 OptB88vdW ~10000 TBmBJ • ~20 HSE06, ~10 G0W0,G0W0+SOC • Computational-cost • Bandgap based classification • Bandgap regression • ~0-10 eV range • Scope of improvement ROC-AUC: 0.95 MAE: 0.32 eV (OptB88vdW) 0.44 (TBmBJ) • MAE of DFT data wrt Expt: OptB88vdW: 1.33 eV TBmBJ: 0.43 eV • At least 6563 Semiconductors Scientific Data 5, 180082 (2018)
  20. 20. High Refractive Index/Dielectric Materials 22 Background Metric ML model • MAE: 0.50 (OptB88vdW) 0.45 (TBmBJ) • Dielectric function/constant for capacitors to store electric charge • Diffraction grating • Solar-cell • MAE in nx (OptB88vdW) wrt expt.: 1.15 • TBmBJ: 1.03 𝜀 𝛼𝛽 2 𝐸 = 4𝜋2 𝑒2 𝛺2 lim 𝑞→0 1 𝑞2 2𝑤 𝑘 𝛿 𝜉 𝑐𝑘 − 𝜉 𝑣𝑘 − 𝐸 𝛹 𝑐𝑘+𝑒 𝛼 𝑞|𝛹 𝑣𝑘 𝛹 𝑣𝑘 |𝛹 𝑐𝑘+𝑒 𝛽 𝑞 ∗ 𝑐,𝑣,𝑘 𝜀 𝛼𝛽 1 𝐸 = 1 + 2 𝜋 𝑃 𝜀 𝛼𝛽 2 𝐸2 𝐸 𝐸2 − 𝐸2 + 𝑖𝜂 ∞ 0 𝑑𝐸 gifer.com Scientific Data 5, 180082 (2018) • Linear optics method
  21. 21. Efficient Solar-cell Materials 23 Background Metric ML model https://www.researchgate.net/publication/224922237_Inorganic_photovoltaic_cells/figures?lo=1&utm_source=google&utm_medium=organic • Very few high-eff. solar-cell materials known (~50) • Computational challenge: high-level • DFT is very expensive • Phys. Rev. Lett. 108, 068701 (2012) 𝛼 𝐸 = 2𝐸 ℏ𝑐 𝜀1 𝐸 2 + 𝜀2 𝐸 2 − 𝜀1 𝐸 2 ɳ = 𝑃𝑚𝑎𝑥 𝑃𝑖𝑛 = max 𝐽𝑠𝑐 − 𝐽0 𝑒 𝑒𝑉 𝑘𝑇 − 1 𝑉 𝑉 𝐸𝐼𝑠𝑢𝑛 𝐸 𝑑𝐸 ∞ 0 • Spectroscopic limited maximum efficiency (SLME), PCE (%) • MAD wrt expt: ~ 4-8% • 1977 high SME materials • ROC AUC: 0.90 ML screening: 1,193,972 materials to 8,970 materials Accepted, Chem. Mater. G0W0 for 10 materials: MAD: 5.2%
  22. 22. Multi-output: density of states and dielectric func. 24 Background Metric • Many material properties are spectral/frequency dependent • Used for multiple solar-cell and transport properties characteristics • Transform different grid data to an uniform data Unpublished work • Total DOS and average dielectric function • MAE for DOS and dielectric function on an interpolated grid • Best vs worst predictions ML model DOS ℰ2 Best Worst Best
  23. 23. Magnetic/Non-magnetic 25 Background Metric ML model https://twitter.com/IUCrJ/status/931161817795256320 https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Book%3A_Inorganic_Chemistry_(Wikibook)/Chapter_06%3A_Metals_and_Alloys_- _Structure%2C_Bonding%2C_Electronic_and_Magnetic_Properties/6.7%3A_Ferro-%2C_ferri-_and_antiferromagnetism • Magnetic moment (~35000 mats.) • Spin-polarized calculations • Susceptibility • DFT, DFT+U, Heisenberg & Ising models • Broken time-reversal • One of the most interesting class of materials • Hard to predict classes of mag. Materials • 5263 magnetic materials • Still Ongoing work • ROC AUC: 0.96
  24. 24. Topological Materials 26 Background Metric • Very few expt. Topological mats. known • Complex indices (Z,Z2,Chern) • For TIs, Bulk insulating and surface conducting • Difficult for Dirac and Weyl semimetals • Nature 566, 480-485 (2019) • Spin-orbit spillage (SOC: Band-structure uncertainty) • Z, Z2, Chern index, Dirac cones, Weyl nodes etc. 30000 materials Bandgap<1 eV, atomic weight>65, non-magnetic (4835) Spillage>0.5 (1868) Wannier calc. for 289 𝜂 𝐤 = 𝑛 𝑜𝑐𝑐 𝐤 − Tr 𝑃 ෨𝑃 ; Phys. Rev. B 90, 125133 (2014) Scientific Reports 9, 8534 (2019) ML model Strong TI Weak TI CTI Dirac and Weyl
  25. 25. QSHI, QAHI and Semi-metallic Materials 27 Background Metric • Hall effect • Quantum hall effect (quantized) • Spin-Hall and Anomalous Hall effect • QAHE • 1-2 QAHE, QSHI known experimentally • Spillage, non-zero Z2/ Chern number • Surface vs edge bandstructure • Anomalous Spin-hall/Hall conductivity • Only such materials computationally found yet https://physics.aps.org/articles/v8/41 • Ongoing work Surface Bandstructure Edge Bandstructure
  26. 26. Thermoelectric Materials 28 Background Metric ML model 𝑧𝑇 = 𝑆2 𝜎 𝑘 𝑒 + 𝑘𝑙 𝑇 • Converts heat to electricity and vice-versa • Too much waste heat in power-plants etc. • Need high efficiency thermoelectrics • Computational : constant relaxation time approximation, rigid band approximation • ROC AUC> 0.80 n-&p-type PF, Seebeck, zT MAD Expt. Seebeck: 54.7 μV/K MP Seebeck: 18.8 μV/K *Gyfcat • Seebeck coefficient, power factor, zT-factor, x number of datapoints • 998 high PF 3D-materials, 148 2D materials arXiv:1903.06651
  27. 27. Piezoelectric Materials 29 Background Metric • Heckmann diagram • ~ 50 experimental values found • Piezoelectric tensors, max (eij), 138 allowed spacegroups • Stress and strain coefficient • MAD wrt expt.: 0.18 C/m2 • 1595 PZ data with DFPT method • 536 mats. with eij>0.5 C/m2 Unpublished work ML model
  28. 28. Infrared-detector Materials 30 Background Metric • Infrared lens: Thermal imaging • Infrared astronomy • Signature of materials • Computational: phonon representation predicted easily but not intensity https://www.edmundoptics.com/resources/application-notes/optics/the-correct-material-for-infrared-applications/ • Infrared spectrum, 1595 mats., DFPT NIR (near)[14000-4000 cm-1 MWIR (mid-wave): 4000-400 cm-1 Far (FIR): 400-30 cm-1 • MAD peaks wrt expt: 6 cm-1 ML model MAE: 83 cm-1 Unpublished work NIST in space
  29. 29. Electride Materials 31 Background Metric • Electrides, with their excess electrons distributed in crystal cavities • Low work function and high carrier mobility • Analysis of the partial density of states (PDOS) around EF • Interstitial electrons occupy at least a volume ratio of 5% at the energy range of EF± 0.05 eV • 168 materials predicted • Most of them are topological Accepted, Matter
  30. 30. Heterostructure Materials 32 Background Metric • Lattice mismatch • Band-alignment • Dangling bonds • 2D-materials with very few dangling bonds • Still Ongoing work
  31. 31. High k-point/cut-off materials 33 Background Metric ML model Necessary resolution for k-point integration and cut-off • Automatic convergence • Correlation with physical properties • Regression MAE: 9.09 Angs (k-point), 85 eV (cut-off) Comp. Mat. Sci. 161, 300 (2019)
  32. 32. Scanning Tunneling Microscopy 34 Background Method • Exploits the tunneling phenomenon • Atomistic imaging, 1986 Nobel prize • Based on local density of states • Finding ground truth data for experiments is difficult • DFT could be useful • Specially 2D materials because no dangling bonds https://arxiv.org/pdf/1404.0961.pdf • Tersoff-Hamann and Bardeen method • ~1000 2D materials, bias voltage • Constant height and constant current mode • Local density of states Unpublished work
  33. 33. Experimental Synthesis of Predicted Materials 35 Johns-Hopkins University, University of Delaware, NIST collaborations (On-going work)
  34. 34. Future works 36 • Ferroelectric/multi-ferroics • Corrosion-resistant materials • Batteries • Charge density wave • Superconductors • High-entropy alloys
  35. 35. Summary 37 Thank you for your time! Email: kamal.choudhary@nist.gov • Key takeaways: 1) Unified CFID descriptors, 2) JARVIS-databases and tools • Uncertainty/error can lead to discovery • Trained 21 ML models and developed heuristic criteria for performance metrics • All the code and data are publicly available, >40000 user-views, >21000 downloads • Web-app for on-the fly prediction of properties • Contribute your expertise to extend the database • Important links: ✓ https://jarvis.nist.gov/ ✓ https://github.com/usnistgov/jarvis ✓ Slides available at: https://www.slideshare.net/KAMALCHOUDHARY4/ JARVIS for YOU !

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