Seminar given at UC Davis, Feb 2024

1. Discovering advanced materials for energy
applications: theory, high-throughput
calculations, and automated experiments
Anubhav Jain
Lawrence Berkeley National Laboratory
UC Davis seminar, Feb 2024
Slides (already) posted to hackingmaterials.lbl.gov

2. Outline
• Introduction to density functional theory
• Thermoelectric Materials Design
• Fast and accurate methods for electronic transport
• Fast and accurate methods for thermal transport
• Automated laboratories for synthesis
2

3. 3
Today, computer aided design of products is ubiquitous – but
what are the governing equations to model materials?
?

4. Materials physics is determined by quantum mechanics
4
−!2
2m
∇2
Ψ(r)+V (r)Ψ(r) = EΨ(r)
Schrödinger equation describes all the properties
of a system through the wavefunction:
Time-independent, non-relativistic Schrödinger equation
Unfortunately, it cannot be directly
solved for all but the simplest
systems

5. What is density functional theory (DFT)?
5
DFT replaces many-body interactions with a mean field interaction (non-
interacting particles) that reproduces the same charge density.
In theory, it is exact for the ground state. In practice, accuracy depends on:
• the choice of (some) parameters
• the type of material and its electronic structure
• the property to be studied
• whether the simulated system (crystal) is a good approximation of reality.
DFT resulted in the 1999 Nobel Prize for chemistry (W. Kohn). It is responsible
for 2 of the top 10 cited papers of all time, across all sciences.
e–
e–
e– e–
e– e–

6. How does one use DFT to design new materials?
6
A. Jain, Y. Shin, and K. A.
Persson, Nat. Rev. Mater.
1, 15004 (2016).

7. Outline
• Introduction to density functional theory
• Thermoelectric Materials Design
• Fast and accurate methods for electronic transport
• Fast and accurate methods for thermal transport
• Automated laboratories for synthesis
7

8. Thermoelectric materials are an interesting
application for DFT modeling
8
• A thermoelectric material
generates a voltage based on
thermal gradient
• Applications
• Heat to electricity
• Refrigeration
• Advantages include:
• Reliability
• Easy to scale to different sizes
(including compact)

9. Thermoelectric figure of merit
9
• Many materials properties are important for thermoelectrics
• Focus is usually on finding materials that possess a high “figure
of merit”, or zT, for high efficiency
• Target: zT at least 1, ideally >2
ZT = α2σT/κ
power factor
>2 mW/mK2
(PbTe=10 mW/mK2)
Seebeck coefficient
> 100 V/K
Band structure + Boltztrap
electrical conductivity
103 /(ohm-cm)
Band structure + Boltztrap
thermal conductivity
1 W/(m*K)
• e from Boltztrap
• l difficult (phonon-phonon scattering)
Very difficult to balance these properties using intuition
alone!

10. Example: Seebeck and e– conductivity
tradeoff
10
Heavy band:
ü Large DOS
(higher Seebeck and more carriers)
✗ Large effective mass
(poor mobility)
Light band:
ü Small effective mass
(improved mobility)
✗ Small DOS
(lower Seebeck, fewer carriers)
Multiple bands, off symmetry:
ü Large DOS with small effective
mass
✗ Difficult to design!
E
k

11. 11
The experimental community has been steadily
finding diverse, high zT thermoelectric materials

12. Can new computational approaches help find
better thermoelectrics even faster?
As proposed as early as 2003 by Blake and Metiu1:
12
“With the cost of computing become relatively inexpensive one can
envisage a time where one runs multiple computer test tube
reactions like these on large Beowulf clusters - as a means of
screening for new TE materials. Certainly it appears that in the
future theory may be a very competent dance partner for what has
previously been a solo experimental effort in searching for ever
better TE materials.”
1. Blake and Metiu. Can theory help in the search for better thermoelectric materials? Chemistry, Physics, and
Materials Science of Thermoelectric Materials: Beyond Bismuth Telluride, 2003

13. We calculated a large amount of transport data
under constant relaxation time approximation
13
~50,000 crystal
structures and
band structures
from Materials
Project are used as
a source
F. Ricci, et al., An ab initio electronic transport
database for inorganic materials, Sci. Data. 4
(2017) 170085.
We compute
electronic transport
properties with
BoltzTraP and
atomate
About 300GB of
electronic transport
data is generated. All
data is available free
for download
https://contribs.materialsproject.org/projects/carrier_transport/
All data is available
free for download via
Materials Project or
direct download from
journal article.

14. • Advantage – we can screen *many* materials and be quite comprehensive. ~50,000 materials can
be computed and compared.
• Some disadvantages
• Fixed relaxation time often prioritizes materials with flat bands, which is undesirable in reality
• Properties are overestimated at high temperatures and high doping
• Thermal conductivity numbers are rough estimates
• No modeling of dopability / carrier type in high-throughput
• Functionals don’t include vdW interactions
• So we can’t take theory numbers at face value!
• e.g., look at the band structure (is it flat bands?)
• does the material require high temperatures or high doping? If so, less reason to believe we can achieve it in
reality
• experimental factors taken into account
• Goal was to run higher levels of theory, doping, etc. – but never got to develop this well
14
Advantages and disadvantages of approach

15. 15
New Materials from screening – TmAgTe2
• Calculations: trigonal
p-TmAgTe2 could
have power factor up
to 8 mW/mK2
• Tetragonal form also
interesting
• Ag-Te compounds
known to have low
thermal conductivity
• BUT requires 1020/cm3
carriers of doping to hit
peak in PF
Zhu, H.; Hautier, G.; Aydemir, U.; Gibbs, Z. M.; Li, G.; Bajaj, S.; Pöhls, J.-H.; Broberg, D.; Chen, W.; Jain, A.; White, M. A.; Asta,
M.; Snyder, G. J.; Persson, K.; Ceder, G. Computational and experimental investigation of TmAgTe 2 and XYZ 2 compounds, a
new group of thermoelectric materials identified by first-principles high-throughput screening, J. Mater. Chem. C, 2015, 3

16. TmAgTe2 (experiments)
16
1. Zhu, H.; et al. Computational and experimental investigation of TmAgTe 2 and XYZ 2 compounds, a new group of
thermoelectric materials identified by first-principles high-throughput screening, J. Mater. Chem. C, 2015, 3
• Expt: p-zT only 0.35 despite
very low thermal
conductivity (~0.25 W/mK)
• Limitation: carrier
concentration (~1017/cm3)
• likely limited by TmAg
defects, as determined by
followup calculations
• Later, we achieved zT ~ 0.47
using Zn-doping
2. Pöhls, J.-H., et al. First-principles calculations and experimental studies of XYZ2 thermoelectric compounds: detailed analysis
of van der Waals interactions. J. Mater. Chem. A 6, 19502–19519. https://doi.org/10.1039/C8TA06470A

17. YCuTe2 – friendlier elements, higher zT (0.75)
17
Aydemir, U.; Pöhls, J.-H.; Zhu, H., Hautier, G.; Bajaj, S.; Gibbs, Z. M.; Chen, W.; Li, G.; Broberg, D.;
Kang, S.D.; White, M. A.; Asta, M.; Ceder, G.; Persson, K.; Jain, A.; Snyder, G. J. YCuTe2: A Member of
a New Class of Thermoelectric Materials with CuTe4-Based Layered Structure. J. Mat Chem C, 2016
experiment
computation
• Calculations: p-YCuTe2 could
only reach PF of 0.4
mW/mK2
• SOC inhibits PF
• if thermal conductivity is low
(e.g., 0.4, we get zT ~1)
• Expt: zT ~0.75 – not too far
from calculation limit
• carrier concentration of 1019
• Decent performance, but
unlikely to be improved with
further optimization

18. The data set is available on the Materials
Project
18
https://next-gen.materialsproject.org/contribs/projects/carrier_transport

19. Outline
• Introduction to density functional theory
• Thermoelectric Materials Design
• Fast and accurate methods for electronic transport
• Fast and accurate methods for thermal transport
• Automated laboratories for synthesis
19

20. As mentioned, screening studies for
thermoelectrics use approximate models for zT
20
Electron mobility Thermal conductivity Figure of merit
1. Constant / uniform relaxation
time approximation
2. Semi-empirical models[1]
1. Glassy limit thermal
conductivity models[2]
2. Semi-empirical models[1]
1. Combining previous
models for electron and
thermal conductivity
(optimize for doping, T)
2. Descriptors that implicitly
optimize[1] for doping, T
!=constant
[1] Yan, J.; Gorai, P.; Ortiz, B.; Miller, S.; Barnett, S. A.; Mason, T.; Stevanović, V.; Toberer, E. S. Material
Descriptors for Predicting Thermoelectric Performance. Energy Environ. Sci. 2015, 8 (3), 983–994
[2] D. G. Cahill, S. K. Watson, R. O. Pohl, Phys. Rev. B 1992, 46, 6133-6140 ; D. G. Cahill, R. O. Pohl, Ann. Rev.
Phys. Chem. 1988, 39, 93-121.
3 fitted parameters (A0, B, s)
Band effective mass based on
DOS effective mass and valley
degeneracy
2 fitted parameters (A1, A2)
Later extended to include
coordination number effects

21. The Boltzmann transport equation
determines carrier transport properties
21
group velocity (easy)
lifetime (hard)

22. τ
...
DFPT
AMSET
∝ DOS–1 / semi-
empirical
constant lifetime
A model to explicitly calculate
scattering rates while remaining
computationally efficient
Aim: accuracy comparable to EPW at
1/100th – 1/1000th computational cost
AND with rich information content
AMSET is a new framework for calculating
transport properties including e- lifetimes

23. primary input: uniform k-mesh band structure calculation
Step 1: Band structure (probably DFT)

24. Fourier interpolation of eigenvalues and group velocities
(there is some custom resampling to get even more accurate integrations)
Step 2: Interpolation of band structure to
dense mesh

25. lifetimes calculated using scattering equations that
depend on first-principles inputs
Step 3: Use band structure and scattering
equations to determine scattering rates

26. calculate mobility, conductivity, Seebeck thermal conductivity
Step 4: Transport properties by solving BTE

27. Acoustic deformation potential (ad)
deformation potential, elastic constant
Ionized impurity (ii)
dielectric constant
Piezoelectric (pi)
dielectric constant, piezoelectric coefficient
Polar optical phonon (po)
dielectric constant, polar phonon frequency
Scattering rates determined by DFT inputs
*note: scalar equations shown, these are generalized to tensor forms

28. • All first principles inputs
• Nothing fit or tuned to
experimental data
• Rich information content
• scattering mechanisms
• E k-dependent
scattering rates
• Short runtime
• ~60 mins of DFT
calculations on 64 cores
• Plus ~40 mins of time to
run AMSET
AMSET predicts switch from
impurity to polar phonon scattering in GaN
Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.;
Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering
Rates from First Principles. Nat Commun 2021, 12 (1), 2222.

29. • Anisotropy is
also captured by
AMSET
• Allows for
analyzing non-
cubic systems
and getting
direction-
dependent
properties
AMSET can also calculate the anisotropic
transport properties of realistic materials
Crystal structure image from:
Pletikosić, Ivo et al. (2017). Band structure of a IV-
VI black phosphorus analogue, the thermoelectric
SnSe. Physical Review Letters. 120.
Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.;
Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering
Rates from First Principles. Nat Commun 2021, 12 (1), 2222.
SnSe

30. AMSET shows close agreement to experiment for the
mobility and Seebeck coefficient across many materials
Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.;
Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering
Rates from First Principles. Nat Commun 2021, 12 (1), 2222.

31. Timing for calculations are very reasonable and
within reach of most groups
Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.;
Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering
Rates from First Principles. Nat Commun 2021, 12 (1), 2222.
Total calculation times are ~500X faster than
DFPT+Wannier
The AMSET portion of
the calculation scales well
with system size

32. Docs: https://hackingmaterials.lbl.gov/amset/
Support: https://matsci.org/c/amset
Paper:
installation
pip install amset
usage
amset run --static-dielectric 10 ...
Can be controlled through the
command line or python interface,
integration with atomate2 for
automatic workflows
Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.; Persson, K. A.; Jain, A. Efficient Calculation
of Carrier Scattering Rates from First Principles. Nat Commun 2021, 12 (1), 2222.
AMSET is an open source python package and has
already been used in 200+ downstream studies

33. Outline
• Introduction to density functional theory
• Thermoelectric Materials Design
• Fast and accurate methods for electronic transport
• Fast and accurate methods for thermal transport
• Automated laboratories for synthesis
33

34. Goal - add automated, high-throughput thermal properties to
Materials Project – particularly 3rd + 4th order
MP Annual Meeting 2023 34

35. The problem – obtaining force constants can
require many DFT calculations
35
To obtain 2nd order IFCs
To obtain 3rd order IFCs
2 displacements in a supercell
(# of supercells needed: 1000s-10000s)
…
1 displacement in a supercell
(Usually 5 supercells needed)
Finite-displacement method IFCs extracted from HiPhive
To obtain any order of IFCs (2nd, 3rd,…) in one shot
…
displace each atom in a supercell
(Only need 5~10 supercells in total!)
• Traditionally, one performs systematic
displacements, each of which only has
a few atom movements and solves
only a small portion of the IFC matrix
• Primitive cells with reduced symmetry
and many atoms can easily require
1000 or more calculations
• The scaling goes something like:
O(Nn) where N is the number of sites
and n is the order of IFC you want. Not
scalable!

36. The solution – perform non-systematic
displacements • Instead of performing systematic
displacements, perform non-systematic
displacements in which many IFC terms are
“mixed up”
• Then, perform a best fit procedure to fit the IFC
matrix elements to the observed data
• Typically undetermined, so regularization is
important
• This method has been suggested by several
groups, for now we focus on the
implementation in the HiPhive code (Erhart
group, Chalmers University of Technology)
• Disadvantage: this method requires careful
selection of fit parameters to get correct results
36
IFCs extracted from HiPhive
To obtain any order of IFCs (2nd, 3rd,…) in one shot
…
displace each atom in a supercell
(Only need 5~10 supercells in total!)
Monte Carlo rattle penalizes displacements that lead to very small interatomic distances
Fransson, E.; Eriksson, F.; Erhart, P. Efficient Construction of Linear Models in
Materials Modeling and Applications to Force Constant Expansions. npj Comput
Mater 2020, 6 (1), 135.

37. We have been working on a workflow for lattice dynamics that
gives 100 – 1000X speedup and is automatic
37
VASP
DFT relaxation
of primitive cell
VASP
SCF on supercells
(u = 0.01-0.05 Å)
VASP
SCF on supercells
(u = 0.1-0.5 Å)
HiPhive
Fit harmonic Φ2
HiPhive
Fit anharmonic
Φ3 ,Φ4 etc
Complete Φ
Imaginary
modes?
Stable Phonon
INPUT
Bulk modulus
ShengBTE/
FourPhonon
Boltzmann
Transport
• Free Energy
• Entropy
• Heat Capacity
• Gruneisen
• Thermal Expansion • Lattice Thermal
Conductivity
No
Yes
Inner Loop
Outer Loop
No
• Quantum Covariance
• Renormalize Φ2
Imaginary
modes?
Converged free
energy?
Free Energy
Converged free
energy?
• Expand Lattice at T
Yes
Yes
No
• Phase transition
• Thermoelectric zT
Renormalization at T ≥ 0 K
Renormalization
at T ≥ 0 K
Renormalized Φ
• Corrected
Free Energy
No
Yes
100x speedup
1000x speedup

38. Results from automated workflow are promising
38
Rhombo-to-Cubic in GeTe (Tc = 650 K)
Tetragonal-to-Cubic in ZrO2 (Tc = 2650 K)
ZrO2 (cubic, Fm-3m)
GeTe (cubic, Fm-3m)
GeTe (rhombohedral, R3m)
ZrO2 (tetragonal, P42/nmc)
a b
c d
GeTe (cubic, Fm-3m)
GeTe (rhombohedral, R3m)
c d
Zr (BCC, Im-3m)
e f
Zr (HCP, P63/mmc)

39. • Expect to submit a paper on this in Feb 2024
• Workflow will be available in both the “atomate” and “atomate2”
codes
39
Next steps

40. Outline
• Introduction to density functional theory
• Thermoelectric Materials Design
• Fast and accurate methods for electronic transport
• Fast and accurate methods for thermal transport
• Automated laboratories for synthesis
40

41. Machine learning is now predicting very large
numbers of new stable compounds
0
500000
1000000
1500000
2000000
MP
stable
ICSD PDF M3GNet
stable
In a short period of time, ML algorithms can
generate potentially millions of potentially
stable compounds
M3GNet data: Chen, C., Ong, S.P. A universal graph deep learning interatomic
potential for the periodic table. Nat Comput Sci 2, 718–728 (2022).
Note that rate of new experimental deposition
into ICSD / PDF is 10K – 20K materials per year
41

42. Synthesis recipe
50 mg Li2CO3
80 mg MnO
20 mg TiO2
800 °C (air)
24 hours
50 mg
80 mg
Target
LiMnTiO4
20 mg
800 °C, 24 hours
Final
product!
There are no well-defined rules
for choosing the most effective
precursors and conditions
Experimental issues like
precursor melting, volatility, or
reactivity with the container
Initial experiments often
give zero target yield.
What to do next?
Making new materials is inherently slow and unpredictable
Even when you are successful, it is very time and labor intensive! 42

43. The A-lab aims to close the loop on rapid synthesis
Robotics
Optimization algorithms Machine learning
43

44. The A-Lab: three robotic stations work together
Precursor preparation:
Gravimetric dispenser works with a
robot arm to weigh and mix powders
Heating station:
A second robot arm operates on a rail,
transferring samples to and from box furnaces
Characterization:
A third robot arm extracts the synthesis products
and prepares them for X-ray diffraction (XRD)
The hardware team
44

45. Science use case: Synthesizing unknown (to A-lab) compounds
42,000 stable
cmpds
146 final
cmpds
“Google-stable”
Stable in air
Not in ICSD or mined literature
Of these, we selected 58 cmpds for which
precursors were readily available
No rare or unsafe elements
Objective: target some
compounds that are
computationally
predicted in Materials
Project, but not present
in that database or
several others …
And do it in 3 weeks!
45

46. Results from the A-Lab syntheses: 41/58 targets made!
Making 41 “unknown-to-system” chemical compositions in 3 weeks is a major
achievement
71% success
per target
37% success
per recipe
46
N.J. Szymanski, et al. Nature. 624 (2023).

47. Four major reasons for inability to make compounds
47

48. What’s next?
• We are working to expand automated
characterization capabilities of the A-lab,
giving greater confidence in synthesized
products closer to manual analysis
• New capabilities such as synthesis under
reducing gases as well as glove box
synthesis are being targeted
• Things are always a work in progress!
48

49. Acknowledgements
49
Thermoelectrics
• G. Jeffrey Snyder
• Jan Pohls
• Umut Aydemir
• Mary Anne White
Slides (already) posted to hackingmaterials.lbl.gov
AMSET thermal
• Alex Ganose
• Zhuoying Zhu
• Junsoo Park
• Alireza Faghininia
A-lab
• Gerbrand Ceder
• Yan Zeng
• Nate Szymanski
• Yuxing Fei
• Bernardus Rendy
Funding from the U.S. Department of Energy Toyota Research Institute