This document summarizes research on developing autonomous experimental systems for materials characterization and phase diagram mapping. Key points discussed include: - Using active clustering algorithms and Gaussian process classification to analyze x-ray diffraction data and autonomously map phase diagrams without human labeling or supervision. - Developing infrastructure for autonomous experiments involving autonomous data analysis, selection of new experimental conditions based on analysis, and control of experimental equipment to acquire new data. - Demonstrating this approach on systems like VNbO2 and VWO2 to map phase diagrams and metal-insulator transition temperatures as a function of composition and temperature.

1. Brian DeCost1
, Heshan Yu2
, Xiaohang Zhang2
, Seunghun Lee2
, Yangang Liang2
, Ichiro Takeuchi2
, Jason Hattrick-Simpers1
, A. Gilad Kusne1
1
National Institute of Standards and Technology, 2
University of Maryland, College Park
Autonomous experimental phase diagram acquisition
2018.08.07 -- AIMS 2018 Meeting -- NIST, Gaithersburg MD
Brian DeCost

2. 2
High-Throughput Experimental Materials Collaboratory
https://mgi.nist.gov/htemc
Distributed experimental materials science platform, built on a network of member institutes.
Realization of the HPC paradigm for experimental materials science?
Contact: martin.green@nist.gov Look for a forthcoming white paper

3. 3
Active clustering for phase diagram acquisition

4. 4
Autonomous science systems
Tabor, Daniel P., et al. "Accelerating the discovery of materials for clean energy in the era of smart automation." Nat. Rev. Mater. 3 (2018): 5-20
https://doi.org/10.1038/s41578-018-0005-z

5. 5
Parallel synthesis, serial characterization
Co-sputtering scheme Ni
Mn
Al
3” spread wafer
Ni Al
Mn
Phase diagram
Gregoire, J. M., et al. "High-throughput synchrotron X-ray diffraction for combinatorial phase mapping." Journal of synchrotron radiation 21.6 (2014): 1262-1268.
Bi
Fe V
XRD

6. 6
Unsupervised phase diagram estimation is hard
Hattrick-Simpers, Jason R., John M. Gregoire, and A. Gilad Kusne.
"Perspective: Composition–structure–property mapping in high-throughput experiments: Turning data into knowledge." APL Materials 4.5 (2016): 053211.
https://doi.org/10.1063/1.4950995
What you really want:
- multi-phase: linear unmixing
- single-phase: invariance to peak shift
- infer the number of regions...
- respect thermodynamics
- leverage archival data
- deal with missing reflections
- fast!
Compromises we can live with
How to discover e.g. line compounds with this approach?

7. 7
Simultaneous phase and property mapping
Kusne, Aaron Gilad, et al. "On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets." Scientific reports 4 (2014): 6367. 10.1038/srep06367
Finding novel rare-earth-free
permanent magnets

8. 8
GRENDEL: Iterative piecewise matrix factorization
Alternate between:
- clustering
- matrix factorization
Kusne, Aaron G., et al. "High-throughput determination of structural phase diagram and constituent phases using GRENDEL." Nanotechnology 26.44 (2015): 444002.
Include archival data from
- ICSD
- AFLOW

9. 9
Amdahl's law in materials science
Speedup (innovation) is limited by the serial portion of the process!
parallel synthesis
MnNiGe: 535 'samples'
serial characterization
Lab diffractometer
30min per composition
2 weeks per ternary!
fast (serial) characterization
Synchrotron (SLAC)
30s per composition
4.5 hours per ternary
Exploit the structure of materials data to scale up

10. 10
Autonomous run: cluster, extrapolate, select
Fe
Fe0.4Pd0.6
Fe0.4Ga0.6
Fe Fe0.4Ga0.6
Fe0.4Pd0.6

11. VO2
11
Metal Insulator transition: VNbO2, VWO2, etc.
100 150 200 250 300 350 400
10
2
10
3
10
4
10
5
R(W)
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%
Mixed
Tetragonal
We'd like to efficiently determine metal-insulator transition temperatures experimentally in a variety of systems
9mm composition spread chip
Metal-insulator transition temperature
decreases with doping
Monoclinic
By Original PNGs by Daniel Mayer, traced in Inkscape by User:Stannered - Crystal stucture
CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1735636

12. 12
X-ray diffraction for phase diagram determination
- Dense collection
- Laboriously hand labeled by experts
- clustering can help
- scaling to more complex systems is a challenge
- higher temperatures: avoid annealing and diffusion effects
Temperature,W

13. 13
Active clustering for autonomous XRD phase mapping
Think carefully about modeling to remove researcher degrees of freedom

14. 14
Spectral clustering loosely: like kernel k-means clustering
27.00 27.25 27.50 27.75 28.00 28.25 28.50
2✓
0
50
100
Intensity(arb.units)
27.00 27.25 27.50 27.75 28.00 28.25 28.50
2✓
0
50
100
Intensity(arb.units)
1. Form the cosine similarity covariance matrix
Y
von Luxburg Tutorial on Spectral Clustering arXiv:0711.0189Zelnik-Manor and Perona, Self-Tuning Spectral Clustering, NIPS 2005
2. compute the eigendecomposition of the kernel matrix
N a = Kasolve
min
C
X
c2C
X
x2c
kx ck2
3. perform k-means clustering in the latent space
find cluster centers c:
project data onto k principal eigenvectors
Ki,j = e dcos(yi,yj )/2 i j
set to k'th nearest neighbor distance fori yi

15. 15
Gaussian process classification
p(y = 1|x) = (f(x))
(z) = 1/(1 + exp( z))
A Bayesian non-parametric generalization of logistic regression
X
0.0 0.2 0.4 0.6 0.8 1.0
X
1
0
1
y
0.0 0.2 0.4 0.6 0.8 1.0
X
1
0
1
y
0.0 0.2 0.4 0.6 0.8 1.0
X
1
0
1
y
0.0 0.2 0.4 0.6 0.8 1.0
X
1
0
1
y
0.0 0.2 0.4 0.6 0.8 1.0
X
1
0
1
y
Bayesian model selection:
gradient-based optimization of the marginal likelihood p(y|X, Hi)
0.0 0.2 0.4 0.6 0.8 1.0
X
1
0
1
y
Ki,j = e |xj xi|2
/`2
Multi-class: one-vs-all strategy
f⇤ = k(x⇤)(K + 2
I) 1
y
V[f⇤] = k(x⇤, x⇤) kT
⇤ (K + 2
I) 1
k⇤
GP prior on f:
http://gpflow.readthedocs.io
Why you should consider Bayesian non-parametric models:
principled hyperparameter tuning (without CV)
This model knows what it doesn't know!

16. 16
Active Gaussian process classification
Kapoor et al. Gaussian Processes for Object Categorization (2010)
DOI: 10.1007/s11263-009-0268-3
Classification uncertainty
Multi-class: one-vs-all strategy
arg min
xu2Xu
|fu|
p
⌃u + 2
monoclinic tetragonal
arg min
xu2Xu
|yu 0.5|
arg max
xu2Xu
⌃u
Margin
Variance
two phase

17. 17
☢
4. GET
command
f = k⇤(K + 2
nI) 1
y
V[f⇤] = k(x⇤, x⇤) kT
⇤ (K + 2
nI) 1
k⇤
0.6 0.7 0.8 0.9 1.0
composition
30
40
50
60
temperature
0.6 0.7 0.8 0.9 1.0
composition
30
40
50
60
temperature
5. POST
new data
1. GET
available data
3. POST
proposed experiment
2. (re)train and predict
Analytics client XRD client
Diffractometer
Control server
26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0
2✓
0
25
50
intensity(arb.units)
Infrastructure for autonomous experiments

18. 18
VWO2
monoclinic tetragonal

19. 19
VWO2 clustering performance
monoclinic tetragonal

20. 20
Acknowledgements
Funding sources
NIST
ONR
NRC Postdoctoral Research Associate Program
XRD setup and VNbO2 data collection by Yangang Liang
VWO2 film growth by Xiaohang Zhang
VWO2 setup by Heshan Yu
Ground truth phase labeling by Jason Hattrick-Simpers