Ichiro Takeuchi, University of Maryland

1. No impurity Ti (3 Å) Ti (6 Å) Ti (9 Å) Cu (3 Å) Cu (6Å) Cu (9 Å)
5 Å
10 Å
15 Å
20 Å
25 Å
35Å
45 Å
55 Å
ti(Å)
ts(Å)
Permanent magnet library
Ferroelectric library
Superconductor library
Combinatorial Experimentation and Machine
Learning for Materials Discovery
Ichiro Takeuchi
University of Maryland

2. - Combinatorial search of superconductors
- Active learning for directing high-throughput
experiments
Outline
Supported by NIST, ONR, and AFOSR
University of Maryland
V. Stanev
X.-H. Zhang
H. Yu
S. Lee
Y. Liang
J.P. Paglione
NIST
A. G. Kusne
B. DeCost
J. Hattrick-Simpers
Duke Univ.
S. Curtarolo
C. Oses
SLAC
A. Mehta

3. Composition Spreads of
Ternary Metallic Alloy Systems
Co-sputtering scheme Ni
Mn
Al
3” spread wafer
Al Ni
Mn
Phase diagram
Composition is mapped using an electron probe (WDS)
Review article: Green et al., JAP 113, 231101 (2013)

4. Rapid mapping of magnetic properties:
scanning SQUID
SQUID assembly
inside vacuum
Room temperature samples are measured
0 13 25 38 50 63 75
80
60
40
20
0
col
row
-2.50e+007 0.00e+000 2.50e+007
rho1_25
Mn
Ni
Ga
Raw data
Nature Materials 2, 180 (2003)

5. Rapid mapping of magnetic properties:
scanning SQUID
0 13 25 38 50 63 75
80
60
40
20
0
col
row
-2.50e+007 0.00e+000 2.50e+007
rho1_25
Mn
Ni
Ga
GaNi 0 1 2 3 4 5 6 7 8 9 10
Mn
50 100 150 200 250
M (emu/cc)
0 13 25 38 50 63 75
80
60
40
20
0
col
row
-2.50e+007 0.00e+000 2.50e+007
rho1_25
Mn
Ni
Ga
Raw data
Nature Materials 2, 180 (2003)

6. Rapid mapping of magnetic properties:
constructing functional phase diagram
GaNi 0 1 2 3 4 5 6 7 8 9 10
Mn
50 100 150 200 250
M (emu/cc)
Nature Materials 2, 180 (2003)

7. Rapid mapping of magnetic properties:
comparison with phase diagram
Nature Materials 2, 180 (2003)
C. Wedel and K. Itagaki,
Journal of Phase Equilibria 22, 324 (2001)

8. Targeting superconductors predicted by theory
Prediction:
FeB4 is a
superconductor
with Tc ~ 15‐20 K

9. Ch 11
Ch 3
Ch 13
Middle region:
FeB2 – FeB4
more Bmore Fe
temperature
resistance
4.2 K 300 K
Fe-B composition spread: FeBx(x =2-4), 16 spots on one 1 cm2 chip

10. FeBx: it looks like a real superconductor
Susceptibility
shows diamagnetism
Bc2(T)= Bc2(0)[1-(T/Tc)2]/ [1+(T/Tc)2]
gives Bc2(0) = 2 T
-> Type II BCS superconductor
Partial R drop
~ 10 K?
Superconducting phase was detected in 2 spread wafers
APL Materials 1, 042101 (2013)

11. Mining superconducting databases
Superconductors grouped by 3 golden coordinates “Predictions of new
compounds”
Based on ~ 600 superconductors (1988)

12. Solution: create our ow
from literature
29000 entries in MatNavi (2014)
Visualization and mining of NIMS SuperCon database
29000 entries
(Cuprates: more than 10000)
Data mining via supervised machine
learning using Magpie descriptors
Removing misentries, duplicates,
etc. results in 14000 entries
Magpie descriptors developed
by Wolverton et al

13. Machine learning modeling of superconducting critical temperature
(random forest)
Models a
Models are built based on 14000 entries
Random forest solves the
problem of including non-
superconducting materials
Stanev, et al.
npj Computational Materials 4, 29 (2018)

14. Machine learning modeling of superconducting critical temperature
Overall prediction accuracy is pretty good
Different classes of superconductors
can be distinguished
Low Tc vs cuprates Cuprates vs low Tc
npj Computational Materials 4, 29 (2018)
Experimental Tc (log)
PredictedTc(log)
Low Tc vs Fe-based Cuprates vs Fe-based

15. Machine learning modeling of superconducting critical temperature
Different chemical properties/trends are revealed
BCS superconductors Curprates
~
√
Expected behavior: phonon frequency
falls out as the key descriptor
Cuprates: Max Tc scales as #
unfilled orbitals (?)
Stanev, et al., npj Computational Materials 4, 29 (2018)

16. Machine learning modeling of superconducting critical temperature
DOS of predicted superconductors show unusual structure
Combining SuperCon (experimental database),
machine learning, ICSD, and AFLOW, we predict
possible new superconductors
Stanev, et al. npj Computational Materials 4, 29 (2018)

17. BCC Fe
Hexagonal FeGa
FCC FePd
Not in Database
FCC Fe
Not in Database
Orthorhombic Fe
and Pd Silicides
Structural phase mapping using libraries
Long et al.,
Rev. Sci. Instrum. 80,
103902 (2009)
Stanev et al.,
npj Computational Mat
(2018) 4:43
Fe
Ga
Pd
3” spread wafer

18. Kusne, et al. Scientific Reports 4, 6367 (2014)

19. Phase mapping based on active learning
• Semi‐Supervised Learning: Propagate knowledge
from measured/known samples to unmeasured samples
• Quantify Certainty of Prediction
• Graph‐based phase separation algorithm used
Not Measured
Coarse Measurement
Measured (Active)
Sample to Query
Certainty of Cluster Label (0‐1)
Ni
Mn
Ge Ni
Mn
Ge
Runs Live at SLAC X‐Ray Beam Line!

20. Combinatorial
Library
Measure
Composition
Graph
Coarse Structure
Measurement
Machine
Learning:
Phase Diagram
Determination
Active
Learning:
Optimal
QueryMeasured
Samples
(black)
Active Learning: Flow Chart
Active Learning Implementation:
• Select query that minimizes ‘risk’
• Risk : estimated expected classification error

21. Not Measured
Coarse Measurement
Measured (Active)
Sample to Query
Certainty of Cluster Label (0‐1)
Ternary Spread
Demonstration : Fe‐Ga‐Pd
Active Learning: Example
Fe
Fe0.6Pd0.4
Fe0.6Ga0.4
Previous results:
non‐negative matrix
factorization:
Rev. Sci. Instrum. 80,
103902 (2009)
Hierarchical clustering:
Rev. Sci. Instrum. 78,
072217 (2007)

22. Active learning: algorithm finds the boundaries
for you
Iteration
Risk: Estimated
expected
classification
error

23. Live Active Learning Phase Mapping
Ni‐Mn‐Ge
Ni
Mn
Ge
Final
mapping
‐ F‐measure used for accuracy
‐ 10% of samples required for measurements
to get 80% accuracy for the whole
SLAC Beamline 1-5, July 2017

24. Pure
VO2
Autonomous mapping of composition‐
temperature phase diagram
100 150 200 250 300 350 400
10
2
10
3
10
4
10
5
R()
T (K)
0.33
0.96
1.36
1.68
2.27
2.61
2.86
3.44
c-Al
2
O
3
substrate
W%Nb%
W – substituted VO2
Metal-insulator transition
temperature shifts to lower
temperature with doping
3%W-
VO2
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
%W substitution
Temperature(○C)
20
40
60
70
Expected phase diagram
Tetragonal
Monoclinic
Mixed
Clustering + active learning for
autonomous control
Monoclinic
Tetragonal

25. 27.00 27.75 28.50
10
1
10
4
10
7
Intensity
2
V1-x
Wx
O2
VO2
Autonomous mapping of composition‐
temperature phase diagram
V1-xWxO2
Room temperature diffraction
Composition spread chip
9 mm wide
VO2 V1-xWxO2
DeCost, et al. (2018)
Bruker C2
software
Anton-Parr
temperature
stage
Both controlled
by active
learning
algorithm
https://www.youtube.com/watch?v=GSsAykESATM

26. Procedures for active learning of
autonomous phase diagram mapping

27. Procedures for active learning of
autonomous phase diagram mapping
# of all possible
measurements:
12 x 9 = 108
Start measurements
at room temperature
“Project” to higher
temperatures
Move to higher
temperatures once
enough confidence is
established
Need to measure less
and less points at
higher temperatures

28. Autonomous mapping of composition‐
temperature phase diagram

29. Evolution of the combinatorial strategy
(and a future forecast)
Circa 1990 2000 2010 2017 and beyond
Challenges:
How to make
hundreds of samples
fast
How to measure
large number of
samples: speed,
number and
quantitative accuracy
How to quickly
analyze large
amount of data
Machine learning
to control and
reduce number
of samples# of samples:
x 100-1000
# of samples: x 0.1 – 0.2
# of samples: x 0.1 – 0.2 Reducing the number of data points

30. Summary
Machine learning can greatly enhance combinatorial experimentation
Active learning can be used to effectively control combinatorial
experimentation and reduce the number of individual runs
3rd Annual Machine Learning for Materials Research Workshop and Summer Camp, Univ. of Maryland
Sponsored by NIST, Moore Foundation, and UMD
https://www.nanocenter.umd.edu/events/mlmr/
August, 2018