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Autonomous synthesis of metastable materials

Sebastian Ament, Maximilian Amsler, Duncan R. Sutherland, Ming-Chiang Chang, Dan Guevarra, Aine B. Connolly, John M. Gregoire, Michael O. Thompson, Carla P. Gomes, R. Bruce van Dover

arXiv:2101.07385v2cond-mat.mtrl-scics.AIcs.LGcs.MAphysics.comp-ph

TL;DR

Mapping non-equilibrium synthesis phase diagrams is challenging because processing spaces are too vast for exhaustive exploration. SARA combines robotic lg-LSA synthesis with nested, physics-informed active-learning cycles to map phase boundaries. In Bi2O3, it maps boundaries more than two orders of magnitude faster than random or exhaustive searches and identifies conditions that trap δ-Bi2O3 at room temperature.

  • Problem

    Non-equilibrium synthesis phase diagrams span processing spaces too vast for exhaustive exploration, limiting efficient mapping of metastable-material synthesis conditions.

    Source: §I · p. 2, §II · p. 3

  • Method

    SARA combines robotic lg-LSA synthesis and optical characterization in nested active-learning loops using physics-informed Gaussian-process models and uncertainty quantification.

    Source: §III · p. 8

  • Results

    More than two orders of magnitude faster than random or exhaustive searches, SARA maps Bi2O3 phase boundaries and identifies conditions that trap metastable δ-Bi2O3 at room temperature.

    Source: §III · p. 8

  • Takeaways & Limitations

    SARA’s phase-map construction can extend to composition spreads and additional processing degrees of freedom, while its nested architecture can incorporate agents for multi-objective optimization.

    Source: §III · p. 8

Abstract

from arXiv · show

Autonomous experimentation enabled by artificial intelligence (AI) offers a new paradigm for accelerating scientific discovery. Non-equilibrium materials synthesis is emblematic of complex, resource-intensive experimentation whose acceleration would be a watershed for materials discovery and development. The mapping of non-equilibrium synthesis phase diagrams has recently been accelerated via high throughput experimentation but still limits materials research because the parameter space is too vast to be exhaustively explored. We demonstrate accelerated synthesis and exploration of metastable materials through hierarchical autonomous experimentation governed by the Scientific Autonomous Reasoning Agent (SARA). SARA integrates robotic materials synthesis and characterization along with a hierarchy of AI methods that efficiently reveal the structure of processing phase diagrams. SARA designs lateral gradient laser spike annealing (lg-LSA) experiments for parallel materials synthesis and employs optical spectroscopy to rapidly identify phase transitions. Efficient exploration of the multi-dimensional parameter space is achieved with nested active learning (AL) cycles built upon advanced machine learning models that incorporate the underlying physics of the experiments as well as end-to-end uncertainty quantification. With this, and the coordination of AL at multiple scales, SARA embodies AI harnessing of complex scientific tasks. We demonstrate its performance by autonomously mapping synthesis phase boundaries for the Bi$_2$O$_3$ system, leading to orders-of-magnitude acceleration in establishment of a synthesis phase diagram that includes conditions for kinetically stabilizing $\delta$-Bi$_2$O$_3$ at room temperature, a critical development for electrochemical technologies such as solid oxide fuel cells.

I. INTRODUCTION

High-dimensional materials search spaces make exhaustive processing-condition exploration impractical, while conventional active learning may be inefficient without physics-informed models and uncertainty quantification. SARA addresses these challenges with coordinated robotic synthesis and specialized AI agents in nested learning loops.

I. INTRODUCTION

  • The vast range of thermal processing conditions makes exhaustive exploration untenable, leaving a vanishingly small portion of materials search space explored.Active learning can reduce the number of experiments to a more tractable scale.Source: §I · p. 1
  • Many closed-loop materials workflows still rely heavily on human intervention, while metastable-material synthesis adds difficult, often unpredictable processing conditions.Prior optical phase-change searches were limited to pre-synthesized compositions under a single processing condition.Source: §I · p. 2
  • Off-the-shelf active-learning models may be outperformed by random search using twice as many samples, and this weakness worsens with search-space dimensionality.Efficient exploration also requires physics-informed models and end-to-end uncertainty quantification across experimental workflows.Source: §I · p. 2
  • SARA coordinates specialized synthesis and probing agents with physics-based models and uncertainty estimates to automate materials representation, characterization, planning, optimization, and learning.Its nested loops coordinate low-level experiments with higher-level phase-diagram exploration.Source: §I · p. 2

II. RESULTS

The study targets metastable oxide synthesis, focusing on Bi2O3 and the challenge of mapping processing conditions efficiently. It combines lateral-gradient laser spike annealing with optical measurements to detect phase boundaries across a thermal gradient.

II. RESULTS

  • δ-Bi2O3 has the highest oxygen-ion conductivity of any known solid oxide, but its narrow 727–824°C stability window has limited industrial use.Yttrium or rare-earth substitution can stabilize it at room temperature but degrades ion conductivity.Source: §II · p. 3
  • Lateral-gradient laser spike annealing processes a stripe with spatially varying temperatures, quench rates of 10^4–10^7 K/s, and peak temperatures up to 1400°C.At one dwell time, a single experiment spans a continuous range of temperature conditions.Source: §II · p. 3
  • Because each position can be annealed only once, SARA must map processing space {x, τ, Tp} with as few synthesis experiments and property measurements as possible.The irreversible processing step makes experimental-condition selection important.Source: §II · p. 3
  • Optical-measurement gradients provide unlabeled processing phase diagrams by indicating phase boundaries without explicit crystallographic identification or expensive XRD.The approach complements XRD, whose required synchrotron access is limited.Source: §II · p. 3

A. XAI: Accelerating data acquisition and characterization

XAI accelerates reflectance mapping by combining microscopy-derived priors with physics-informed Gaussian-process models and active learning. Its stripe-specific kernel and gradient-targeted sampling reduce the measurements needed to characterize phase boundaries.

A. XAI: Accelerating data acquisition and characterization

  • Microscopy features provide stripe-specific priors, while lateral symmetry, optical-transition peaks, stripe width, and a linear component for thickness variation shape the GP kernel.The microscopy image also supports automated quality control by detecting damage or contamination that can trigger resynthesis.Source: A. XAI: Accelerating data acquisition… · pp. 4–5
  • XAI kernels reach R2 = 0.8 with as few as 16 random sampling points, compared with 25 for Matérn and 37 for RBF kernels.The XAI+LSA and XAI+RGB designs incorporate microscopy-derived priors.Source: A. XAI: Accelerating data acquisition… · p. 5
  • IGU selects measurements to reduce uncertainty in reflectance gradients, the quantity used to identify phase boundaries.XAI expands wavelength-dependent reflectance into 16 Legendre coefficients to reduce the model input dimensionality.Source: A. XAI: Accelerating data acquisition… · pp. 5–6
  • 9.7× faster acquisition and characterization than random sampling with an RBF kernel at R2 = 0.8 is achieved by XAI+RGB with IGU sampling.The XAI+RGB kernel with IGU reaches R2 scores of 0.8 and 0.9 within 9 and 15 iterations, respectively.Source: Figure 2 · p. 5, A. XAI: Accelerating data acquisition… · p. 6

B. ΣAI: Accelerating phase exploration and processing conditions

ΣAI uses uncertainty-aware models and stripe-level active learning to select synthesis conditions and map Bi2O3 phase boundaries. The learned map approaches exhaustive sampling after 25 iterations, while the acquisition strategy reaches R2_s > 0.7 within 15 iterations.

B. ΣAI: Accelerating phase exploration and processing conditions

  • ΣAI aggregates XAI reflectance-gradient data, propagates experiment-level uncertainty across the search space, and proposes new synthesis conditions.XAI transforms spatial reflectance gradients onto a temperature scale; symmetric-kernel processing requires sampling only one side of the stripe center.Source: B. ΣAI: Accelerating phase exploration… · p. 6
  • The model accounts for peak-temperature variation and temperature-profile error; at 1400°C, peak-temperature uncertainty can reach 25°C.The profile error scales with the spatial rate of temperature change; the synthesis-space Matérn kernel uses separate temperature and dwell-time length scales.Source: B. ΣAI: Accelerating phase exploration… · p. 6
  • Stripe uncertainty samples for uncertainty across the full temperature range from Tmin to Tp, improving on pointwise uncertainty sampling, which performs poorly because each stripe informs temperatures below Tp.The SU strategy reaches R2_s > 0.7 within 15 iterations.Source: B. ΣAI: Accelerating phase exploration… · p. 7
  • Exhaustive sampling of 617 lg-LSA stripes reveals connected gradient-peak ridges that delineate Bi2O3 phase-field boundaries, which selected XRD measurements then label.The labeled regions include as-deposited and densified amorphous, δ-Bi2O3, mixed δ/β, pure β-Bi2O3, and melt-quenched amorphous phases.Source: B. ΣAI: Accelerating phase exploration… · p. 7
  • At 25 iterations, the learned map qualitatively captures all major gradient boundaries, with later iterations refining their locations toward the exhaustive map.The two-phase-region onset appears by iteration 8, the phase-pure β boundary by iteration 15, and the amorphous-densification onset by iteration 25.Source: B. ΣAI: Accelerating phase exploration… · pp. 7–8
  • Approximately 14× fewer iterations reach R2_s = 0.7 than random sampling without input-uncertainty propagation; stripe uncertainty exceeds R2_s = 0.7 within 15 iterations.The reported overall AL acceleration combines the acceleration factors of the nested XAI and ΣAI cycles.Source: B. ΣAI: Accelerating phase exploration… · pp. 7–8

III. DISCUSSION

SARA combines robotic materials synthesis with automated microscopy and reflectance characterization in nested active-learning loops. In Bi2O3, it maps phase boundaries more than two orders of magnitude faster than random or exhaustive searches and identifies conditions that trap metastable δ-Bi2O3 at room temperature.

III. DISCUSSION

  • SARA combines robotic synthesis, automated microscopy and reflectance spectroscopy, and nested active-learning loops using physics-inspired Gaussian process models.The framework quantifies experimental uncertainty in both model inputs and outputs while exploring non-equilibrium synthesis phase maps with high-throughput lg-LSA.Source: §III · p. 8
  • SARA reduces the time to map Bi2O3 phase boundaries by more than two orders of magnitude versus random or exhaustive searches and identifies conditions that trap metastable δ-Bi2O3 at room temperature.The authors identify δ-Bi2O3 as a promising solid oxide electrolyte for fuel-cell applications.Source: §III · p. 8
  • The authors describe the speedup as a prerequisite for exploring additional chemical degrees of freedom, extended processing parameters, and property optimization.They also identify composition-spread mapping and added robotic measurements of target properties as possible extensions.Source: §III · p. 8
  • Proposed extensions include finding synthesis conditions for not-yet-synthesized phases, identifying solar-energy materials, and adding electrical-conductivity measurements.These examples frame synthesis phase diagrams around performance metrics for target applications.Source: §III · p. 9

A. Experiments and measurements

The experiments combine reactive sputtering of Bi2O3 films with lateral-gradient laser spike annealing and optical and X-ray characterization. The methods span film preparation, anneal conditions, microscopy, reflectance spectroscopy, and diffraction measurements.

1. Thin film deposition

  • A 170 nm Bi2O3 film with less than 10% thickness variation was deposited by RF reactive sputtering onto oxidized, highly doped p-type silicon.The substrate was rotated during deposition from a Bi target in 8 mTorr Ar and 2 mTorr O2 at 20 W.Source: §1 · p. 9

2. Lateral gradient laser spike annealing

  • The CO2-laser lg-LSA setup processed 617 stripes with peak temperatures of 400–1300°C and dwell times of 250–10,000 µs.Stripes were 5 mm long and 2 mm apart; anneal locations were randomized across the film to avoid location bias.Source: §2 · p. 9

3. Microscopy imaging

  • Microscopy used a camera with a roughly 1 mm horizontal field of view and 0.92 µm pixel spacing.The camera was aligned normal to the sample under coaxial white-light illumination.Source: §3 · p. 9

4. Reflectance spectroscopy

  • Reflectance spectra were collected from a 10 µm spot at 151 positions per stripe, spanning 340 to less than 1026 nm.The fiber scanned 1.5 mm in 10 µm increments; measurements used approximately 4500 ms integration time and dark-reference and Ag-mirror calibration.Source: §4 · p. 9

5. X-ray diffraction

  • XRD data were collected every 10 µm across each stripe using a 9.7 keV beam and 50 ms integration per frame.The beam spot was 20 µm × 40 µm at 2° incidence; detector data were integrated along χ using pyFAI.Source: §5 · p. 9

B. Computational methods

This section develops SARA’s Gaussian-process and active-learning foundations. Gaussian processes provide uncertainty-aware inference, while active learning uses that uncertainty to select informative observations.

B. Computational methods

  • The methods section denotes input collections as X and applies a function column-wise to obtain the corresponding output collection.Source: B. Computational methods · p. 9

1. Gaussian Processes

  • Gaussian processes are distributions over functions defined by mean and covariance functions, with posterior mean and covariance available in closed form for normally distributed observation noise.Source: §1 · p. 10

2. Active Learning

  • The active-learning acquisition function uses current data to suggest the next observation, with uncertainty sampling selecting the point of maximum posterior variance.Source: §2 · p. 10
  • SARA’s active-learning backbone uses Gaussian processes for their flexibility, closed-form inference, and uncertainty quantification.Source: §2 · p. 10, §1 · p. 10

3. Input Noise

SARA accounts for uncertainty in experimental inputs as well as measured outputs, then uses a structure-informed Gaussian-process model and gradient-focused acquisition to map reflectance efficiently.

3. Input Noise

  • SARA’s input-noise correction propagates condition-dependent experimental uncertainty through a linear approximation of the Gaussian-process posterior mean.Source: §3 · p. 10

4. XAI

  • XAI compresses smooth wavelength-dependent reflectance into 10–20 Legendre-polynomial coefficients before active learning.Source: §4 · p. 10
  • The XAI kernel combines lateral symmetry, RGB-based variance scaling, and asymptotically linear behavior to incorporate structure of the stripe and thickness variation.Source: §4 · pp. 10–11
  • Integrated gradient uncertainty sampling achieves the best performance in the XAI acquisition benchmark by targeting uncertainty in reflectance gradients.Source: §4 · p. 11

5. ΣAI

The ΣAI loop estimates phase boundaries by modeling a reflectance-change signal over temperature and dwell time, while incorporating experimental uncertainty and stripe-level sampling.

5. ΣAI

  • The ΣAI target d measures spectroscopic-reflectance change over temperature and dwell time, and estimating it across those conditions supports phase-boundary estimation.Source: §5 · p. 11
  • Ignoring temperature-related input uncertainty significantly deteriorates active-learning performance in the ΣAI benchmarks.Source: §5 · p. 11
  • Temperature uncertainty combines peak-temperature and position errors; the reported standard errors are 25°C and 50 µm, respectively.Source: §5 · p. 11
  • Stripe uncertainty sampling aggregates uncertainty across the range of conditions generated by one stripe; stripe upper-confidence-bound sampling performed worse or equally well.Source: §5 · p. 12

6. Error Metrics

The section describes performance measures for the inner-loop reflectance model and the outer-loop ΣAI benchmarks, including a score adjusted for heteroscedastic errors.

6. Error Metrics

  • The inner-loop kernel and acquisition benchmarks use R², a dimensionless measure interpreted as the proportion of data variance explained by the model.Source: §6 · p. 12
  • The ΣAI benchmarks use a log-likelihood-based generalization of R² to evaluate models with heteroscedastic normal errors.Source: §6 · p. 12
  • The heteroscedastic score weights residuals from more certain observations more strongly, and reduces to R² when all noise variances are equal.Source: §6 · p. 12

VI. AUTHOR CONTRIBUTIONS

The authors divided responsibility across research leadership, SARA development, manuscript writing, and experimental and data analysis, with all authors contributing feedback.

VI. AUTHOR CONTRIBUTIONS

  • RBvD, CPG, MOT, and JMG conceived and supervised the research, while all authors provided critical feedback and helped shape the research, analysis, and manuscript.Source: §VI · p. 12
  • SA and MA developed and implemented the SARA algorithms, contributed equally, and led manuscript writing.Source: §VI · p. 12
  • DRS fabricated Bi2O3 thin-film samples and analyzed optical data; ABC performed lg-LSA; DG and JMG processed XRD data, with DRS and MCC helping analyze results.Source: §VI · p. 12
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