ichiro takeuchi university of marylandhelper.ipam.ucla.edu/publications/elws1/elws1_14484.pdf ·...
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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)
t s(Å)
Permanent magnet library
Ferroelectric library
Superconductor library
High-throughput Experimentation and Machine Learning for Materials Discovery
Ichiro TakeuchiUniversity of Maryland
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• Combinatorial approach to materials discovery: mapping of complex energy and property landscapes
• Search for new superconductors and supervised machine learning of experimental database
• Structural phase distribution mapping: unsupervised machine learning of diffraction data
• Active learning is the future of high-throughput experimentation
Outline
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Univ. of MarylandV. StanevT. GaoY. IwasakiR. Greene
NISTA. G. Kusne
ONR, AFOSR, DOE Support
Acknowledgement
Duke UniversityS. Curtarolo
SLACA. Mehta
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Chemical &EngineeringNews, August 2001
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Combinatorial Libraries of Inorganic Materials
Luminescent materials libraries,Science 279, 1712 (1998)
Semiconductor gas sensor library, “electronic nose”,Appl. Phys. Lett. 83, 1255 (2003)
Magnetic shape memory alloy library,Nature Materials 2, 180 (2003)
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Various combinatorial experimental designs:
discrete libraries vs composition spreadsComposition A B
B
A
C
• Composition spreads allow continuous mapping of physical properties and phase boundaries
• Run to run variation in ordinary experiments is removed
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ferromagneticcompound
ferroelectriccompound
Low symmetryFerroelectricphase
Ferromagneticphase
composition
Temperature
Exploration of Interesting Phase Boundaries
Shape memory alloys, piezoelectric materials, multiferroic materials, magnetostrictive materials, etc.
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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)
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Rapid mapping of magnetic properties:scanning SQUID
SQUID assembly inside vacuumRoom temperature samples are measured
0 13 25 38 50 63 75
80
60
40
20
0
col
ro
w
-2.50e+007 0.00e+000 2.50e+007
rho1_25
Mn
NiGa
Raw data
Nature Materials 2, 180 (2003)
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Rapid mapping of magnetic properties:scanning SQUID
0 13 25 38 50 63 75
80
60
40
20
0
col
ro
w
-2.50e+007 0.00e+000 2.50e+007
rho1_25
Mn
NiGa
GaNi 0 1 2 3 4 5 6 7 8 9 10
Mn
50 100 150 200 250M (emu/cc)
0 13 25 38 50 63 75
80
60
40
20
0
col
ro
w
-2.50e+007 0.00e+000 2.50e+007
rho1_25
Mn
NiGa
Raw data
Nature Materials 2, 180 (2003)
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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 250M (emu/cc)
Nature Materials 2, 180 (2003)
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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)
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Targeting superconductors predicted by theory
Prediction:FeB4 is a superconductor with Tc ~ 15‐20 K
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Ch 11Ch 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
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FeBx: it looks like a real superconductor
Susceptibilityshows 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)
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Mining superconducting databases
Superconductors grouped by 3 golden coordinates “Predictions of new compounds”
Based on ~ 600 superconductors (1988)
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Solution: create our owfrom 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
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Machine learning modeling of superconducting critical temperature(random forest)
Models a
Stanev, et al.arXiv preprint arXiv:1709.02727
Models are built based on 1400 entries
Random forest solves the problem of including non-superconducting materials
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Machine learning modeling of superconducting critical temperature
Overall prediction accuracy is pretty good
Different classes of superconductors can be distinguished
Experimental Tc (log)
Pre
dict
ed T
c(lo
g)
Low Tc vs cuprates Cuprates vs low Tc
Low Tc vs Fe-based Cuprates vs Fe-based
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Machine learning modeling of superconducting critical temperature Different chemical properties/trends are revealed
BCS superconductors
~√
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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. arXiv:1709.02727
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Rapid mapping of structural phase diagram
Nature Materials 2, 180 (2003)
C. Wedel and K. Itagaki,Journal of Phase Equilibria 22, 324 (2001)
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Synchrotron diffraction set up at SSRL The entire 3” wafer (300 spots) can now be measured in 2 hrs
Structural property mapping of combinatorial wafers
XRF carried out simultaneously
Each wafer produces: 300 MB to 2 GB of image data
Reflection set upTransmission set up
w/ A. Mehta
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Hundreds of XRD Patterns are difficult to analyze by hand
2 (Degrees)
Inte
nsity
(Arb
. Uni
t)
The same is true for any spectral data (Raman, FTIR, etc.)
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First step is visualization
I. Takeuchi et al., Rev. Sci. Instrum. 76, 062223 (2005)
Martensite Phase
Austenite Phase
Ni
NiMn
Al
Al
Mn
Diffraction Intensity
Peak Angle and IntensityIntensity Cross Section
Ni Al
Mn
0 500 1000
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Fe
Fe40Pd60
Fe40Ga60
Analyze all spectra together using cluster analysis:Look for similarities between spectra
Group
To Group
Distance
XRD Spectrum Number
Dendrogram
Multi‐Dimensional Data Scaling
C. J. Long, et al.Rev. Sci. Instrum. 78,072217 (2007)
Adjust the dendrogram
Initial construction of structural phase diagram
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D=.5
D=1
D=0
Comparing XRD patterns
D = “distance”
rxy = 1
rxy = 0
rxy = -1
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Different metrics (“distance” between data points (vectors))
<Euclidean> <Manhattan>
<Pearson> D=(1‐C)/2
<fast DTW> <fast EMD>
< 1 ‐ Cos> D= 1‐C <Spearman> D=(1‐C)/2
This is often used inspeech recognition field
This is often used inimage recognition field
This is often used intext mining field
This is just transportation problembetween two data series
To find a minimum pass in the cost matrix
n
jij
m
i
n
jijij
m
i
f
fdQPEMD
1
min
1
1
min
1,
f is minimum transportation cost
22sin
ii
ii
yxyx
C
22
yyxx
yyxxC
ii
iicor
Known as normal correlation coefficient(parametric)
NN
dC i
i
spearman 3
61
This is non‐parametricindex.di is difference between ranking of data
n
kkk yxd1
n
kkk yxd 2
Iwasaki et al., npj Computational Materials 3 (1), 4
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<Euclidean> <Manhattan>
<Pearson> D=(1‐C)/2
<fast DTW> <fast EMD>
<1‐Cosine><“Correct answer”> <Spearman> D=(1‐C)/2
Different metrics calculated and clustered using hierarchical clustering: XRD patterns from Fe‐Co‐Ni composition spread
Y.K. Yoo et al. / Intermetallics 14 (2006) 241–247
Co
Fe
Nihcp
Iwasaki et al., npj Computational Materials 3 (1), 4
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Non-Negative Matrix Factorization (NMF):
Experimental Spectra
Weights Basis Spectra Residual ErrorS = W B* + E
Experimental Spectra are Deconvolved
(The Basic Idea)
Another analysis method:
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BCC Fe
Hexagonal FeGa
FCC FePd
Not in Database
FCC Fe
Not in Database
Orthorhombic Fe and Pd Silicides
Working toward a structural phase diagram using NMF
Long et al.,Rev. Sci. Instrum. 80, 103902 (2009)
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mean shift theory
Integrating ICSD with combi XRD dataMost ternary phase diagrams are not known
Each point on the ternary phase diagram is one X‐ray spectrum (expt)
Points on binary lines are simulated spectra from ICSD
They are rapidly mined/analyzed together
Scientific Reports 4, 6367 (2014)
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Integrating ICSD with combi XRD data
Fe
Fe0.6Pd0.4
Fe0.6Ga0.4mean shift theory
Most ternary phase diagrams are not known
Each point on the ternary phase diagram is one X‐ray spectrum (expt)
Points on binary lines are simulated spectra from ICSD
They are rapidly mined/analyzed together
Scientific Reports 4, 6367 (2014)
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Real time analysis of combinatorial library data (synchrotron XRD);Integration with ICSD
Diffraction data (integrated Pilatus images) plotted for different compositions as they are taken
Spectra are mapped on ternary phase diagram real time
Hierarchical clustering is used to group similar spectra together
X‐ray fluorescence data are also processed real time
Scientific Reports 4, 6367 (2014)
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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 MeasurementMeasured (Active)
Sample to QueryCertainty of Cluster Label (0‐1)
Ni
Mn
Ge Ni
Mn
Ge
Runs Live at SLAC X‐Ray Beamline
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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
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Not Measured
Coarse Measurement
Measured (Active)Sample to Query
Certainty of Cluster Label (0‐1)
Ternary SpreadDemonstration : 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)
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Active learning: algorithm finds the boundaries for you
Iteration
Risk: Estimatedexpected classificationerror
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Active Learning Phase MappingNi‐Mn‐Ge
Data from ICSD Data from AFLOW Initial measurements(16)
Combined initial information
Ni
Mn
Ge Ni
Mn
Ge Ni
Mn
Ge
Ni
Mn
Ge
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Active Learning Phase MappingNi‐Mn‐Ge
Combined initial information
Ni
Mn
Ge
Ni
Mn
Ge
Final mapping
GeNi
Mn
Manualphase mapping
‐ F‐measure used for accuracy
‐ 10% of samples required for measurementsto get 80% accuracy for the whole
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Evolution of the combinatorial strategy(and a future forecast)
Circa 1990 2000 2010 2017 and beyond
Challenges:
How to make hundreds of samplesfast
How to measurelarge 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
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Summary
Combinatorial (high‐throughput) experimentation + theory can speed up discovery of materials
Machine learning can greatly enhance combinatorial experimentation
Annual Machine Learning for Materials Research Workshop and Summer Camp, Univ. of MarylandSponsored by UMD and NISThttps://www.nanocenter.umd.edu/events/mlmr/
June, 2017