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Artificial Intelligence Research Letter
CRYSTAL: a multi-agent AI system for automated mapping of materials’
crystal structures
Carla P. Gomes, Junwen Bai, Yexiang Xuea), Johan Björck, Brendan Rappazzo, Sebastian Ament, Richard Bernstein, and
Shufeng Kong, Department of Computer Science, Cornell University, Ithaca, NY 14853, USA
Santosh K. Suramb),Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena CA 91125, USA
R. Bruce van Dover, Department of Materials Science and Engineering, Cornell University, Ithaca, NY, USA
John M. Gregoire ,Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena CA 91125, USA
Address all correspondence to Carla P. Gomes at gomes@cs.cornell.edu and John M. Gregoire at gregoire@caltech.edu
(Received 18 January 2019; accepted 8 April 2019)
Abstract
We introduce CRYSTAL, a multi-agent AI system for crystal-structure phase mapping. CRYSTAL is the first system that can automatically
generate a portfolio of physically meaningful phase diagrams for expert-user exploration and selection. CRYSTAL outperforms previous
methods to solve the example Pd-Rh-Ta phase diagram, enabling the discovery of a mixed-intermetallic methanol oxidation electrocatalyst.
The integration of multiple data-knowledge sources and learning and reasoning algorithms, combined with the exploitation of problem decom-
positions, relaxations, and parallelism, empowers AI to supersede human scientific data interpretation capabilities and enable otherwise
inaccessible scientific discovery in materials science and beyond.
Introduction
Artificial Intelligence (AI) excels at a range of cognitive tasks,
from speech and image recognition to game playing,
[1,2]
and
holds great promise for automating scientific discovery.
[3–8]
The interpretation of scientific data remains a challenge for
AI due to both the need for intricate scientific background
knowledge and reasoning and the lack of large annotated train-
ing datasets. AI-based reasoning and learning methods are par-
ticularly critical for the field of high-throughput materials
science where automated experiments are dramatically acceler-
ating the pace of materials discovery for a variety of critical
technologies.
[4–6,9,10]
Foundational techniques in high-
throughput materials discovery include simultaneous synthesis
of hundreds to thousands of materials using co-sputtering fol-
lowed by rapid structural characterization via synchrotron
XRD [Fig. 1(a)]. For complex materials containing three or
more elements, the most common rate-limiting step in the dis-
covery process is the construction of a crystal phase diagram
from the composition and structural characterization data. We
refer to this task as the phase mapping problem, which requires
the identification of basis patterns (or factors) corresponding to
pure crystal phases, some of which may not be sampled sepa-
rately, such that all the XRD measurements can be explained
as a mixture of the basis patterns [Figs. 1(c)–1(f)]. The XRD
measurements are typically noisy, which contributes to the
challenge of separating the basis pattern “sources”from the col-
lection of patterns. Additionally, materials thermodynamics
places a set of intricate physical constraints on the solution,
and while synthesis of materials may not reach thermodynamic
equilibrium, the non-equilibrium behavior is most commonly
exhibited as the presence of non-equilibrium phases as opposed
to deviations from, e.g., the Gibbs phase rule.
Phase mapping has traditionally been a bottleneck of the
high-throughput materials discovery cycle as the synthesis
and characterization experiments [Figs. 1(a) and 1(b)] can be
performed on several libraries of materials per day while the
manual effort required to solve a given phase mapping problem
limits the throughput to only several phase diagrams per year.
Previous reports have detailed the shortcomings of existing
de-mixing algorithms,
[12]
most notably in the presence of
noise and substantial alloying, an important phenomenon in
which a range of elemental compositions crystallize into the
same phase, causing its basis pattern to shift systematically
with composition.
[13]
Non-negative matrix factorization
(NMF) techniques
[14]
have shown promise in the efficient
extraction of representative diffraction patterns from large data-
sets,
[15,16]
but their limited ability to encode physical con-
straints and prior knowledge results in routine production of
non-physical solutions. From a computational perspective,
phase mapping is an example of a challenging NP-hard prob-
lem
[17]
whose sheer number of possible combinations of
a)
Current address: Department of Computer Science, Purdue University, West
Lafayette, IN 47907, USA.
b)
Current address: Toyota Research Institute, Los Altos, CA 94022, USA.
MRS Communications (2019),9, 600–608
© Materials Research Society, 2019
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basis patterns and activations grows exponentially with data
size, rendering monolithic solvers and traditional search meth-
ods computationally infeasible, which motivates the explora-
tion of innovative AI approaches.
CRYSTAL: a multi-agent AI system
for phase mapping
CRYSTAL is a multi-agent AI system that can run in unsuper-
vised or semi-supervised mode and that decomposes phase
mapping into smaller, more tractable sub-problems that are
tackled by nimble algorithmic bots with unique background
knowledge and reasoning capabilities (Fig. 2). Interleaved
Agile Factor Decomposition (IAFD) is CRYSTAL’s core
phase-mapping engine, which interleaves factor decomposition
(AgileFD bot) with constraint enforcement (Gibbs,Gibbs
Alloy, and Phase Connectivity bots), whose collective reason-
ing produces physically meaningful phase maps. At a high
level, IAFD relaxes and postpones the combinatorial physical
constraints and iteratively repairs and enforces them when
violations are detected.
The graph reasoning algorithms of the Gibbs,Gibbs Alloy,
and Phase Connectivity bots are applied at a local scale to
enable parallel computation and ensure scalability for large
real-world problems. The key insight is that global maintenance
of the combinatorial physical constraints is computationally
prohibitive, yet appropriate data exploitation with local con-
straint enforcement provides global constraint satisfaction at
a relatively small computational expense. While generating a
phase diagram is a confounding and time-consuming task
even for experienced materials scientists, IAFD generates a sol-
ution typically within 2 min for the dataset reported in this
paper, a groundbreaking advance in phase mapping since no
other algorithm imposes the physical constraints to reliably
yield physically meaningful solutions (see Table S1).
The capability to rapidly generate physically meaningful
solutions enables CRYSTAL’s large-scale computations to
assess solution stability, uncovering a critical and previously
Figure 1. Materials discovery cycle. (a) Synthesis of materials using sputter co-deposition from palladium (Pd), rhodium (Rh), and tantalum (Ta) sources to
form a “materials library”thin film with continuous composition variation. Collection of both elastically (XRD) and inelastically (XRF) scattered x-rays, using a
synchrotron x-ray beam, to characterize the materials’crystal structure and composition, respectively, the latter enabling a ternary composition map of the
Pd-Rh-Ta library. (b) Each library is screened for catalytic activity using an electrochemical imaging strategy in which the best catalysts are identified using a
fluorescent marker.
[11]
Materials which appear active in the absence of methanol are denoted as “unstable.”(c) The triangle-composition plot contains the 197
distilled XRD/XRF measurements that comprise the input for phase mapping. The 12 XRD patterns along the Pd-Rh composition line illustrate
composition-dependent peak shifting due to the two elements alloying in a single-crystal structure. (d) CRYSTAL’s phase map solution identifies five phases
(purple, yellow, orange, blue, and red) and six multi-phase fields; each sample’s XRD pattern is explained by either a single phase ora mixture of phases. (e) The
XRD pattern for a phase “3”sample is shown with red sticks denoting the known peak pattern of the face centered cubic (fcc) crystal structure, indicating that the
broad range of compositions in the fcc phase field crystallize into this same structure. (f) The average atomic radius varies systematically with the alloy
composition, which CRYSTAL captures by mapping the composition-dependent fcc lattice constant.
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overlooked aspect of phase mapping. Even with the imposed
physical constraints, different phase diagram solutions are
often “inadequately differentiated”by the source XRD patterns.
Inadequate differentiation in phase mapping arises in part from
the fundamental non-invertibility of an XRD pattern to obtain
its crystalline phase source(s) and is compounded by both
noise in the source data and presence of different phases with
similar basis patterns. The standard practice in phase mapping,
and more generally in data modeling, is to extract knowledge
from a single solution that sufficiently reconstructs the source
data. In contrast, CRYSTAL explores the search space by
deploying bots in parallel to produce a large number of candi-
date solutions. Using additional bots for solution analysis and
aggregation (Figs. 2–4), CRYSTAL runs unsupervised and
autonomously to generate a parsimonious portfolio of phase
diagrams that represent different interpretations of the source
data.
CRYSTAL’s algorithms
As mentioned above, CRYSTAL is a collection of nimble
algorithmic bots, with different knowledge and reasoning
capabilities performing a variety of tasks outlined in Fig. 2
and described in more detail below. The IAFD bots collec-
tively solve the phase mapping problem, using an unsuper-
vised generative approach, to produce a phase map that
satisfies the physical constraints. The CRYSTAL planner
launches parallel runs of IAFD with different random initiali-
zations and parameters, in particular the number of target
phases, and each IAFD run follows the algorithm outlined
below and illustrated in Fig. 3:
Step 0: Initialization: Initialize the inner-loop (AgileFD-Gibbs)
counter CNT1, bounded above by p, together with CNT2
which counts outer-loops bounded above by q, to be 0. As dis-
cussed below, pand qare typically set to 3 and 2 respectively.
Step 1: AgileFD bot: Apply AgileFD on randomly selected N/p
“untouched”samples
Step 2: Gibbs bot: Enforce Gibbs phase constraint on these N/p
samples
Step 3: If some samples still have not been processed, namely
CNT1 is still smaller than p, increase CNT1 by 1 and go back to
step 1, otherwise, move on to step 4
Step 4: Gibbs-Alloy bot: enforce Gibbs-Alloy constraint on all
Nsamples
Step 5: Phase Connectivity bot: enforce Connectivity constraint
on all Nsamples
Step 6: If Gibbs-Alloy constraint is violated, go back to step 4,
otherwise, go to step 7
Step 7: If CNT2 hasn’t reached the upper bound q,refined solu-
tions from Step 6 are fed into step 1 as initialization and the
whole algorithm starts over again. Otherwise, the IAFD output
is taken as the phase map finalized in step 6. Further documen-
tation and source code for IAFD can be found at http://www.
udiscover.it/resources/software/.
AgileFD bot
As illustrated in Fig. 3, we formulate phase mapping as a con-
strained matrix factorization problem. Experimental XRD
measurements are represented by a matrix Aof size L × N.
Each column of Ais a vector representing the XRD pattern
sampled at Ldiffraction angles, obtained at one out of Nsample
locations. The phase mapping problem entails decomposing A
in terms of factors Wand H, satisfying physics constraints. W
encodes the characteristic patterns or structure associated with
each pure crystalline phase and Hrepresents the mixing param-
eters, such as the phases present, their proportions, and any
alloying present.
Under the assumed “isotropic”alloying model, an XRD pat-
tern measured as a function of scattering vector magnitude will
Figure 2. Outline of the CRYSTAL system. CRYSTAL incorporates a diverse collection of fast and specialized algorithms with different types of knowledge and
computational capabilities. IAFD integrates the AgileFD,Gibbs,Gibbs Alloy, and Phase Connectivity bots, constituting CRYSTAL’s core phase-mapping engine:
AgileFD performs agile factor decomposition to learn the factors or basis patterns, corresponding to pure crystal structures, and its three partner bots enforce
physical constraints. The Phase Matching bot matches the basis patterns discovered by IAFD to known crystal structure patterns from databases. The Phase
Dimension Analysis bot analyzes and validates the generated phase maps and infers the system’s maximum number of pure phases, which dictates how many
system configurations CRYSTAL explores, using parallelism and randomization, to produce a large number of candidate phase maps. The hierarchical Clustering
bot uses automated thresholding to identify a small set of representative candidate solutions, which are provided to either the CRYSTAL Planner for solution
refinement or to the Analysis & Reporting bot to generate phase diagrams and other visualizations for human-expert inspection. The Visualizer & Interface bot
enables users to interact with CRYSTAL for solution selection and fine tuning.
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shift multiplicatively, with, for example, a 1% lattice contrac-
tion causing peaks to shift by a factor of 1.01. We convert
the multiplicative shift to an additive constant by performing
the factorization of logarithmically transformed patterns, mak-
ing Aa convolutive mixture of the bases in W. W and Hare
naturally non-negative, leading to a convolutive non-negative
matrix factorization (CNMF) problem,
[18]
which AgileFD
performs using lightweight multiplicative coordinate gradient-
descent updating rules applied to the logarithmically transformed
XRD data.
[19,20]
Gibbs and Gibbs-Alloy bots
For a physical system where lelements are deposited, Gibbs’
phase rule implies that at most lphases are present at each sam-
ple location. Mathematically, this is equivalent to constraining
the number of non-zero elements in the vector
m
Hm
∗,nfor any
sample location nto be no more than l.
The Gibbs bot uses a Mixed Integer Programming (MIP)
approach to find the best activation matrix Hthat activates no
more than lphases per sample point and minimize the recon-
struction loss, while holding the phases in Wfixed.
[21]
Notice
that when Wis fixed, the columns of matrix Hare independent
which leads to a decomposition into a smaller MIP program per
violated sample point, which finds the best lphases that mini-
mize the reconstruction loss of sample location n, as described
further in the Supplementary Information.
The Gibbs Alloy bot extends the Gibbs constraint by reduc-
ing the allowed number of coexisting phases allowed by one
when alloying is detected, i.e., for those sample locations
with varying mean shift parameters compared with nearby
locations. This is motivated by the thermodynamic degree of
freedom associated with alloying, although instead of identify-
ing details of the alloying behavior, the bot identifies where
alloying is taking place and lowers the number of allowable
phases by 1 at those composition points.
Phase and Phase Field Connectivity
bot
The Connectivity constraint requires that both (i) the sample
points where a specific phase is present and (ii) the sample
points where each unique set of phases is present form a con-
nected component in composition space, which is determined
using the activations of each phase for each composition sam-
ple. Specifically, we define a graph Gin which sample points
are nodes and two nearby sample points in composition
space are connected with an edge based on the Delaunay
Figure 3. Solving phase mapping using an unsupervised generative approach. The IAFD bot network solves phase mapping as a constrained matrix factorization
problem in which the input XRD pattern matrix (A) is decomposed into factors Wand Hsuch that W×Happroximates Awhile satisfying physical constraints. W
encodes the characteristic patterns of pure crystal phases (including shifted versions) and Htheir activations, which dictate both the amount and the pattern
shifting extent of each pure phase in each XRD measurement. IAFD starts with p(typically three) rounds of interactions between the AgileFD and Gibbs bots
followed by rounds of iterations between the Gibbs Alloy and Phase Connectivity bots, until all the constraints are satisfied. AgileFD performs matrix factorization
using light-weight multiplicative updating rules, without enforcing the combinatorial physical constraints. The AgileFD solution’s violations of the connectivity
constraint and the constraints based on Gibbs’phase rule are repaired by the corresponding bots in an interleaved manner using efficient algorithms (red circles
highlight repaired activations of H). The entire procedure is repeated for solution refinement (typically q= 2), and the resulting generated basis patterns are
passed to the Phase Matching bot to identify the crystal structures by comparison with ICDD and/or determine if the solution potentially contains a new phase.
The figure illustrates a representative XRD pattern of the Pd-Rh-Ta system (#69) that is decomposed into shifted versions of two different basis patterns (0.16
and 0.84 of each, respectively).
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Triangulation. The Connectivity constraint states that the sam-
ple locations nfor which
m
Hm
n,kis larger than zero must form a
connected component in graph G, and that phase fields consist-
ing of a unique combination of phases must similarly form a con-
nected component. The Phase and Phase Field Connectivity bot
rectifies the connectivity constraints in a lazy and iterative
manner. See also Supplementary Information.
Phase Matching and Phase
Dimensionality Analysis bots
The Phase Matching bot matches the basis patterns produced
by the IAFD module, as part of each solution, to known crystal
structure patterns from the ICDD. Fitting an ICDD-derived pat-
tern to each basis pattern (see Supplementary Information for
details) provides the additional opportunity to threshold the
loss such that if no ICDD-derived pattern sufficiently matches
the basis pattern, then the basis pattern may be describing a new
phase. The matching of a single ICDD entry to multiple basis
patterns in a single solution is an indication that the K(number
of phases) of the solution is too large and thus the solution is
invalid. Based on this concept, the CRYSTAL planner
monitors Phase Dimensionality Analysis results to determine
the maximum number of phases to consider for the given sys-
tem. The CRYSTAL planner runs IAFD configurations with an
increasing number of phases until the resulting phase diagrams
have an ICDD entry assigned to more than one basis pattern or
the valid solution rate becomes vanishingly small, providing
automatic determination of the upper bound on the number of
phases (basis patterns).
Phase Diagram Clustering and Analysis
& Reporting bots
The IAFD bot produces physically meaningful phase diagrams,
whose phases are labeled using the ICDD, for the known
phases. CRYSTAL runs the IAFD module in parallel (in this
paper we report 500 runs for a given number of phases but in
general 100 or fewer runs is sufficient) to produce candidate
phase diagrams that require automated phase diagram analysis
and consolidation. The Clustering bot takes as input the set of
solutions produced by parallel runs of the IAFD module and
outputs a small set of representative candidate solutions. This
bot uses hierarchical agglomerative clustering based on
Figure 4. CRYSTAL’s solution to the Pd-Rh-Ta catalyst system. (a) CRYSTAL automatically generates 2500 phase diagrams in parallel from which the Phase
Dimension Analysis bot identifies 1639 valid solutions and the Clustering bot identifies 100 representative solutions for additional refinement. (b) From the 100
refined phase diagrams, CRYSTAL automatically identifies the span of solutionswith different physical meaning, which is 20 phase diagrams in this case. (c) The
selected 20 phase diagrams that represent their respective clusters. (d) The final solution resulting from expert consideration of CRYSTAL’s report. The expert
user also provided minor manual refinement of the phase diagram, in particular small phase field boundary adjustments in composition regions with sparse
measurement data. (e) Color scheme for the phase fields where the single-phase fields are labeled and phase combinations are denoted by linkages. The 11
phase fields marked with a black circle appear in the final solution. (f) The basis patterns for the final solution with stick patterns from the International Center for
Diffraction Data shown in red. Composition mapsof the relative lattice constant for each phase reveal alloying-based shifts due to the different atomic radii of the
elements (Ta > Pd > Rh). The dot size denotes the phase concentration. (g) The methanol oxidation onset potential for the ternary and binary composition spaces
where Rh-Ta is the only binary to exhibit catalytic activity. The overlay of the final solution’s phase field boundaries reveals that the best activity (lowest onset
potential) is observed in the mixed orth-Rh
2
Ta + hex-Pd
3
Ta phase field.
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pair-wise phase diagram dissimilarity with automated thresh-
olding. A distance metric between phase diagrams is defined
as the across-sample average of the dissimilarity of the pair
of phase fields in which the sample resides in the pair of
phase diagrams. The phase field for a given sample is defined
as the set of basis patterns activated for that sample, which is
labeled according to the ICDD phase matching results, and
the comparison of the resulting pair of ICDD phase sets is per-
formed under consideration that multiple ICDD patterns may
match a given basis pattern within a predefined tolerance.
Hierarchical clustering of phase diagram solutions provides
(i) 100 representative solutions from the initial runs of IAFD
and (ii) a portfolio of unique phase diagrams from the 100
refined solutions where the number of clusters is determined
through automated thresholding based on unique sets of
ICDD patterns. The set of representative candidate solutions
identified by the clustering bot are provided to either the
CRYSTAL Planner for solution refinement by the IAFD mod-
ule, as initial solutions, or to the Analysis & Reporting bot to
generate phase diagrams and other visualizations for
human-expert inspection.
Pd-Rh-Ta experiments
The Pd-Rh-Ta system was chosen for investigation based on
the use of Pd in catalysts for alcohol oxidation in alkaline elec-
trolytes
[22]
and recent success improving the methanol oxida-
tion reactivity of Pt by combining it with Ta, where surface
sub-oxides of Ta appeared to lower the adsorption of CO and
thus mitigate catalyst poisoning.
[23]
The 197 XRD and XRF
measurements were acquired on four co-sputtered thin film
composition libraries: the Pd-Rh-Ta ternary library and one
for each binary system (the edges of the composition triangle).
The XRF measurements provide the mapping from the physical
location on the substrate to the Pd-Rh-Ta ternary composition
space, with measurement details and data processing as
described in Ref. 24.
The catalytic activity of each of the four composition spread
thin films was mapped using the high-throughput fluorescence-
based screening, and the results for the Pd-Rh-Ta film are
shown in Fig. 1(b) with false-color images of fluorescence
intensity showing background-subtracted images from a
charge-coupled device camera, as previously described.
[23,25]
The N
2
-sparged aqueous electrolyte contained 3 mM quinine
(fluorescent indicator) and 0.1 M potassium triflate (supporting
electrolyte). An initial voltage sweep in this electrolyte without
methanol was used to identify any regions exhibiting fluores-
cence, which could be due to film oxidation or oxidative corro-
sion, prompting our labeling of these composition regions as
“unstable.”A solution with the addition of 5 M methanol
was then used for screening catalysis of the methanol oxidation
reaction. As standard practice, the experiment was repeated
three times with fresh electrolyte and similar results were
obtained, Figs. 1(b) and 4(g) showing the results from the
first of these voltage sweeps. In all of these experiments, the
voltage sweep was performed from 0.4 to +0.5 V versus Ag/
AgCl at a scan rate of 0.05 V/s. By setting a fluorescence inten-
sity threshold, the onset potential associated with each pixel in
the library image was determined and the XRF-based composi-
tion map was used to map the onset potential data to composi-
tion space, as shown in Fig. 4(g).
Phase mapping for catalyst discovery
in the Pd-Rh-Ta system
The Pd-Rh-Ta system poses substantial phase mapping chal-
lenges due to strongly overlapped features in its phases’XRD
patterns as well as substantial alloying-based peak shifting,
which are compounded by experimental noise in the thin-film
XRD measurements. CRYSTAL generated a total of 2500
phase maps (500 phase maps per configuration with a number
of phases K= 3, 4, 5, 6, and 7). As shown in Table I, 100% of
the composition points, phases, and phase fields meet the phys-
ical constraints imposed by the algorithmic bots. For compari-
son, an analogous 2500 runs were performed using AgileFD
and NMF, with Table I revealing some constraint satisfaction,
but not sufficient to produce any physically meaningful solu-
tions. Comparison was also made with NMF
K
, a recently
reported algorithm that involves clustering of NMF compo-
nents to identify basis patterns,
[26]
which produced a single
K= 5 solution for which the constraint satisfaction rates exceed
that of NMF and AgileFD but still do not provide a physically
meaningful phase diagram where all constraints are satisfied.
Comparison of this NMF
K
solution with that of Fig. 4 is
shown in Fig. S1, revealing a substantially different interpreta-
tion of the data.
CRYSTAL continued processing of its initial 2500 phase
diagrams via the Phase Dimension Analysis bot, which deter-
mined that the system contains no more than K= 6 phases
and passed 1639 valid solutions to the Clustering bot, which
identified 100 representative solutions using hierarchical
agglomerative clustering based on pairwise phase diagram dis-
similarity. After further refining the 100 solutions using the
IAFD bots, the hierarchical Clustering bot, using automated
thresholding, identified 20 representative phase diagrams that
represent the span of different data interpretations. These
phase diagrams were passed to the Analysis & Reporting bot
to produce phase diagram visualizations and composition
maps of the phase fields and lattice constant shifts, which are
readily interpretable by an expert [Figs. 1(d)–1(f) and 4]. The
expert user analyzed and compared the 20 candidate phase dia-
grams, eliminating 15 candidate phase diagrams since they do
not meet subtle criteria based on prior knowledge specific to the
Pd-Rh-Ta system. In this case, this prior knowledge was from a
previous analysis of the Pd-Rh binary line where a single face
centered cubic (fcc) seven-phase diagram was analyzed. While
this prior knowledge was used to screen candidate solutions in
the present work, this type of knowledge can be used to initial-
ize and/or constrain IAFD, as described previously for
AgileFD.
[19,20]
Other types of prior knowledge may also be
incorporated, which may require the development of new algo-
rithmic bots, another motivation for building CRYSTAL as a
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network of bots that can be adapted for specific research tasks
and expanded to incorporate new modes of reasoning. After
applying this filter, the expert user selected the final phase dia-
gram remaining five phase diagrams, which we note could have
also been automatically selected via a voting method since the
selected phase diagram represents the hierarchical cluster con-
taining 17 refined solutions, more than any other remaining
cluster [Fig. 4(c)].
In addition to identifying complete solubility of Pd and Rh
into the fcc structure, this phase diagram also indicates substan-
tial alloying in the intermetallic phases [Figs. 4(d)–4(f)]. For
each phase, the lattice constant variation with composition
matches expectations based on the metallic radii of the ele-
ments. For the three non-cubic phases, the observed <1% lattice
expansions are well modeled by the isometric peak shifting
model. The hex-Pd
3
Ta phase exhibits the largest alloying
extent of these phases, with up to 30 at.% of the smaller Rh
and up to 35 at.% excess of the larger Ta leading to lattice
expansions <0.7%.
CRYSTAL’s phase diagram enabled insightful interpretation
of the catalytic activity in the Pd-Rh-Ta system. Figure 4(g)
shows the result of a high-throughput screening of the
Pd-Rh-Ta libraries for methanol oxidation, a critical reaction
for direct methanol fuel cells traditionally addressed with
Pt-based catalysts.
[27]
While many of the compositions exhibit
inactivity or instability under the reaction conditions, selected
Pd-Rh-Ta compositions exhibit an activity that is on par with
the best Pt-based catalysts evaluated by this high-throughput
method. On the Rh-Ta binary line, the orth-Rh
2
Ta phase pro-
vides the highest catalytic activity. The methanol oxidation
onset potential is further lowered by 0.2 V to approximately
0.5 V versus RHE via mixing orth-Rh
2
Ta with an alloy of
hex-Pd
3
Ta at a composition Pd
0.17
Rh
0.33
Ta
0.5
. Such combina-
tions of catalyst materials have recently been proposed for over-
coming historical barriers that limit catalyst performance for
multi-step reactions,
[28,29]
and indeed the activity of this multi-
intermetallic catalyst is quite remarkable. The best thin film cat-
alysts for methanol oxidation that have been identified by this
technique include the Pt-Ta intermetallics with an onset poten-
tial of 120 mV versus Ag/AgCl,
[23]
and a family of Pt-based fcc
alloys including binary alloys with Ru, In, Sn, and Zn, which
have onset potentials between 0 and 40 mV versus Ag/
Table I. Comparison of constraint satisfaction for solutions generated by different algorithms.
K(# basis patterns) 3 4 5 6 7
CRYSTAL Gibbs 100% 100% 100% 100% 100%
Gibbs-Alloy 100% 100% 100% 100% 100%
Pure phase connectivity 100% 100% 100% 100% 100%
Phase field connectivity 100% 100% 100% 100% 100%
AgileFD Gibbs 100% 74.93% 60.20% 47.46% 37.46%
Gibbs-Alloy 52.66% 32.36% 19.05% 11.71% 7.88%
Pure phase connectivity 63.67% 49.95% 16.68% 7.03% 2.31%
Phase field connectivity 33.99% 32.29% 28.58% 34.55% 49.38%
NMF Gibbs 100% 79.01% 64.35% 55.01% 47.24%
Gibbs-Alloy 100% 79.01% 64.35% 55.01% 47.24%
Pure phase connectivity 51.60% 29.70% 23.68% 11.17% 1.94%
Phase field connectivity 28.73% 26.37% 24.73% 39.22% 56.42%
NMF
K
Gibbs NA NA 87% NA NA
Gibbs-Alloy NA NA 77% NA NA
Pure phase connectivity NA NA 40% NA NA
Phase field connectivity NA NA 50% NA NA
For each number of basis patterns (K), 500 random initializations were used to generate a set of solutions, which were then evaluated for compliance with four
physical constraints. The percentage of samples (Gibbs and Gibbs-Alloy), percentage of phases (Pure phase connectivity), and percentage of phase fields (Phase
field connectivity) are shown assuming a threshold value of 10
−6
on phase activations (values of H). While AgileFD and NMF solutions satisfy constraints for
some of the composition points despite the lack of enforcement, none of the resulting phase diagrams meet all requirements. NMF
K
produced a single K=5
solution, which satisfies constraints better than NMF and AgileFD but similarly does not provide physically meaningful phase diagrams where all constraints are
satisfied. Due to its constraint enforcement, CRYSTAL produces solutions which meet all of the physical requirements.
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AgCl.
[30]
The Pd
0.17
Rh
0.33
Ta
0.5
catalyst is the only known
Pt-free catalyst with onset potential in this range. The onset
potential of 0.5 V versus RHE is also within the range of
onset overpotentials observed with Pd-based catalyst in alkaline
electrolytes,
[22]
and given the inactivity of Pd and Rh in the
weak acidic electrolyte used in our experiments, the Ta-based
intermetallics appear to enable the activity at lower pH, opening
a new direction for catalyst development and a pathway for the
further development of Pt-free catalysts.
The discovery of this multiphase catalyst highlights both the
power of high-throughput materials science and the effective-
ness of AI techniques for integrating multiple knowledge
sources to provide meaningful solutions. By teaching
CRYSTAL to reason about phase diagrams, we have for the
first time automated the generation and exploration of alterna-
tive data models, demonstrating the ability of AI systems to
accelerate phase mapping and providing a novel data-
interpretation approach for materials sciences and beyond.
Supplementary material
The supplementary material for this article can be found at
https://doi.org/10.1557/mrc.2019.50
Acknowledgments
This work was supported by NSF awards CCF-1522054 and
CNS-0832782 (Expeditions), CNS-1059284 (Infrastructure),
and IIS-1344201 (INSPIRE); ARO awards W911NF-14-1-0498
and W911NF-17-1-0187; AFOSR Multidisciplinary University
Research Initiatives (MURI) Program FA9550-18-1-0136,
Toyota Research Institute award; and US DOE Award No.
DE-SC0004993. Use of SSRL is supported by DOE Contract
No. DE-AC02-76SF00515. Use of CHESS is supported by the
NSF award DMR-1332208. The authors thank A. Mehta,
D. G. Van Campen, M. Tague, and D. Dale for assistance with
data collection.
Author contributions
The authors’contributions are as follows: C.P.G., R.B.vD., and
J.M.G. conceived and managed the project. C.P.G. conceived
CRYSTAL’S multiple knowledge source approach. J.Ba.,
JBj., C.P.G., and Y.X. designed the bots’algorithms. J.Ba.,
C.P.G., J.M.G., B.H.R., and Y.X. designed the Diagram
Rendering bot. J.Ba. implemented the IAFD bots, phase match-
ing bot, and phase analysis bot. B.H.R. implemented the dia-
gram rendering algorithm, and Analysis & Reporting and
Visualizer & Interface bots. S.K. performed the comparison
with NMF
K
. R.A.B. assisted with programming in several com-
ponents of CRYSTAL. R.B.vD. and J.M.G. acquired Pd-Rh-Ta
data, and S.K.S. and J.M.G. acquired Nb-Cu-V data with assis-
tance as noted in the Acknowledgments. S.K.S. and J.M.G.
served as human experts for both systems. C.P.G. and J.M.G.
were the primary authors of the manuscript. S.A., J.Ba., J.Bj.,
C.P.G., J.G.M., B.H.R., and Y.X. were the primary authors
of the Methods and Supplementary Information.
Data availability
The raw data for the Pd-Rh-Ta along with CRYSTAL’s results and
reports will be available at http://www.udiscover.it/resources/data/.
Further documentation and source code for IAFD can be found
at http://www.udiscover.it/resources/software/.
Author information
The authors declare no competing financial interests.
Correspondence should be addressed to gomes@cs.cornell.
edu and gregoire@caltech.edu.
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