Kamal Choudhary, NIST

1. Smart Metrics for High-Performance
Material-Design
Kamal Choudhary, Francesca Tavazza
NIST, Gaithersburg,
AIMS 2019
8/1/2019
1

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. 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. 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. • 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. 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. • 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. 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. https://www.darpa.mil/program/explainable-artificial-intelligence

11. JARVIS-DFT, FF and ML datasets and tools
11
>35000 bulk, 1000 monolayer materials, >110 FFs, ~1 million properties

12. 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

13. 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:

15. 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)

16. 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 ☺)

17. 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).

18. 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)

19. 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

20. 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

21. 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)

22. 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

23. 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%

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. Heterostructure Materials
32
Background Metric
• Lattice mismatch
• Band-alignment
• Dangling bonds
• 2D-materials with very few dangling bonds
• Still Ongoing work

33. 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)

34. 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

35. Experimental Synthesis of Predicted Materials
35
Johns-Hopkins University, University of Delaware, NIST collaborations
(On-going work)

36. Future works
36
• Ferroelectric/multi-ferroics
• Corrosion-resistant materials
• Batteries
• Charge density wave
• Superconductors
• High-entropy alloys

37. 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 !