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At least 883 records · Page 49

Phase Transformation Mechanism of Amorphous Calcium Phosphate to Hydroxyapatite Investigated by Liquid-Cell Transmission Electron Microscopy

Crystallization via phase transformation of a metastable precursor is a ubiquitous and effective strategy used by living systems to direct the growth of crystalline nanomaterials with remarkable functional properties. However, determining the exact process by which transformation occurs at the nanoscale is a difficult challenge. In this work, the recrystallization process of amorphous calcium phosphate (ACP) to hydroxyapatite (HAP) is explored by liquid-cell transmission electron microscopy. The effect of confinement in the liquid-cell is found to increase the size of ACP nanoparticles. In the presence of Mg 2+ , these large ACP nanoparticles transform to HAP by first dissolving from the interior to create a hollow structure, after which HAP forms preferentially on the surface and then subsequently in the bulk solution. We propose that the preferential dissolution within ACP particles is due to a change in the structure and/or chemistry of the ACP surface, likely associated with dehydration before crystallization of HAP. These results imply an important role of the confined environment of the liquid-cell in regulating the size of ACP particles, which then affects the surface structure and the detailed dissolution–recrystallization pathway. Moreover, we stress the key role of Mg 2+ in controlling HAP formation by stabilizing ACP via reduction in ACP solubility. This work provides a better understanding of the roles of additives and confinement during the phase transformation of ACP to HAP through dissolution and recrystallization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transformation of Gibbsite to Boehmite in Caustic Aqueous Solution at Hydrothermal Conditions

Phase transformations among aluminum (oxyhydr)oxide minerals play important roles across a wide range of natural and industrial settings. In highly caustic aqueous solutions, uncertainty persists regarding whether solid-state or dissolution-reprecipitation pathways dominate. We explored transformation of gibbsite [a Al(OH)3] to boehmite (? AlOOH) in caustic NaOH solution at hydrothermal conditions as a function of temperature, Al(III) and NaOH concentrations, and reaction time. Comparison of detailed structural and morphological solids characterization by XRD, SEM/TEM, AFM, Raman spectroscopy, and high field 27Al MAS NMR to predictions from equilibrium thermodynamics calculations suggests the critical importance of dissolution-reprecipitation across our range of system conditions. The yield and physical properties of the boehmite product was found to be sensitive to the hydrothermal treatment temperature and the Al/OH- ratio, controlled by the loading of gibbsite with respect to NaOH. Experiments at lower Al/OH- ratios (e.g., 0.64) indicate that the dissolution of the gibbsite reaches an aqueous aluminate saturation state sufficient to overcome the nucleation barrier for boehmite. Higher Al/OH- ratios (e.g., 3.2) are found to slow the phase transformation, leaving residual unreacted gibbsite in the final product. Higher temperatures appear to improve the phase transformation rate, but also typically yield smaller sized boehmite particles. Particle morphological analyses compared to thermodynamic expectations suggest an important role of kinetics at mineral/solution interfaces, both in the gibbsite dissolution rate as well as the growth rate of boehmite nanocrystals.

Zhang, Xin↗

Structural Transformation and Chemical Stability of a Shock-Compressed Insensitive High Explosive Single Crystal: Time-Resolved Raman Spectroscopy

Despite the considerable interest in insensitive high explosives (IHE) as a safer alternative to conventional high explosives, a good understanding of the low sensitivity of IHEs to shock initiation is lacking. In particular, real-time measurements to directly probe the molecular-level response of shock compressed IHE single crystals constitute an important need. To address this need, plate impact experiments were conducted to determine time-resolved changes in the Raman spectra of 1,1-diamino-2,2-dinitroethene (FOX-7) single crystals – a representative IHE crystal – shock compressed up to 20 GPa longitudinal stress. The Raman measurements examined vibrational frequencies from 800 cm-1 to 1500 cm-1 with 15 nanosecond time resolution and were conducted at several peak stresses. At 4 – 6 GPa, two new Raman peaks appeared, in addition to the original peaks, consistent with onset of the α' – ε structural transformation reported previously in static compression work. The measured spectra indicated completion of the transformation at 10 GPa. Raman data to 20 GPa showed neither additional transformations nor any indication of chemical decomposition. This finding, though consistent with recent continuum measurements, is in marked contrast to the chemical decomposition observed at lower stresses in shock compressed conventional high explosive single crystals. Our Raman results support the previous suggestion that strengthening of intra- and inter-molecular bonds, due to the α' – ε structural transformation, plays a significant role in the insensitivity of FOX-7 single crystals to shock initiation. In conclusion, the present work, in conjunction with previous static compression studies, provides the first experimental insight into the molecular-level response of a shock compressed IHE single crystal and can serve as a bench mark for theoretical studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transformation of an Embedded Five-Membered Ring in Polycyclic Aromatic Hydrocarbons via the Hydrogen-Abstraction–Acetylene-Addition Mechanism: A Theoretical Study

Five-membered rings are constituents of many polycyclic aromatic hydrocarbons (PAHs) and their presence on the edges of large PAHs has been repeatedly observed experimentally. However, modern kinetic combustion models often do not consider the growth of PAHs through the transformation of the five-membered rings. Here, in connection with the above, we carried out a theoretical study of the mechanism of Hydrogen-Abstraction-aCetylene-Addition (HACA) transformation of an embedded five-membered ring on the armchair PAH edge to a six-membered ring, considering cyclopenta[d,e,f]phenanthrene (4,5-methylenephenanthrene) as a prototype system for this process. The potential energy surface for the reactions of cyclopenta[d,e,f]phenanthrenyl radicals produced by direct H abstractions from cyclopenta[d,e,f]phenanthrene with acetylene has been compiled at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory including zero-point vibrational energy corrections. The computed energies and molecular parameters were then used to solve the Rice-Ramsperger-Kassel-Marcus Master Equation (RRKM-ME) in order to calculate reaction rate at various pressures and temperatures, which were fitted to modified Arrhenius equation for further kinetic modeling. The results show that the HACA transformation of the embedded five-membered ring to a six-membered ring is possible, albeit slow. The most viable reaction mechanism involves the R2 + C 2 H 2 reaction, where the acetylene molecules adds to a σ-radical in the six-membered ring adjacent to the five-membered ring via a low entrance barrier. The predominant product of R2 + C 2 H 2 is predicted to be 3 ethynyl 4H cyclopenta[def]phenanthrene Pr5 via immediate H elimination from the initial addition complex. Next, Pr5 undergoes H-assisted isomerization to 4aH-pentaleno[4,3,2,1-cdef]phenanthrene Pr4, and the latter adds an H atom eventually forming the 1-pyrenylmethyl radical Pr3: R2 + C 2 H 2 ⇌ 3 ethynyl 4H cyclopenta[def]phenanthrene (Pr5) + H ⇌ 4aH-pentaleno[4,3,2,1-cdef]phenanthrene (Pr4) + H Pr5 + H ⇌ Pr4 + H Pr4 + H → 1-pyrenylmethyl (Pr3) This HACA sequence may be competitive with the methyl radical addition to the R1 radical formed by H abstraction from the CH 2 group in the five-membered ring of cyclopenta[d,e,f]phenanthrene, which provides a pathway to pyrene following two H atom losses. Relative contributions of the two mechanisms of the five- to six-membered ring transformation would strongly depend on the branching ratios of the R1 and R2 radicals produced by the H abstractions and the available concentration of C 2 H 2 vs. CH 3 and hence differ in different flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomic Insight into the Layered/Spinel Phase Transformation in Charged LiNi 0.80 Co 0.15 Al 0.05 O 2 Cathode Particles

Layered LiNi 0.80 Co 0.15 Al 0.05 O 2 (NCA) holds great promise as a potential cathode material for high energy density lithium ion batteries. However, its high capacity is heavily dependent on the stability of its layered structure, which suffers from a severe structure degradation resulting from a not fully understood layered → spinel phase transformation. Using high-resolution transmission electron microscopy and electron diffraction, we probe the atomic structure evolution induced by the layered → spinel phase transformation in the NCA cathode. We show that the phase transformation results in the development of a particle structure with the formation of complete spinel, spinel domains, and intermediate spinel from the surface to the subsurface region. The lattice planes of the complete and intermediate spinel phases are highly interwoven in the subsurface region. The layered → spinel transformation occurs via the migration of transition metal (TM) atoms from the TM layer into the lithium layer. Incomplete migration leads to the formation of the intermediate spinel phase, which is featured by tetrahedral occupancy of TM cations in the lithium layer. Finally, the crystallographic structure of the intermediate spinel is discussed and verified by the simulation of electron diffraction patterns.

36 MATERIALS SCIENCE↗

Crystal Morphology and Phase Transformation of LiAlO 2 : Combined Experimental and First-Principles Studies

Layered α-LiAlO 2 matrix often suffers from detrimental structural and morphological changes during its lifetime, especially under H 2 containing fuel inlet environments of molten carbonate fuel cell systems. However, the underlying mechanism of this phase and morphological transformations has rarely been explored. In this study, transmission electron microscopy (TEM) techniques were used to determine the changes in structure and morphology of LiAlO 2 samples lifted by a focused ion beam (FIB). In accordance with X-ray diffraction (XRD) analysis, TEM images show that under H-rich conditions the rhombohedral α-LiAlO 2 transforms to tetragonal γ-LiAlO 2 phase with the appearance of the (101) terminated octahedral shaped γ-LiAlO 2 crystallites. We further support, and plausibly rationalize, the observed transformations using density functional theory (DFT) calculation. The DFT computed surface energies of γ-LiAlO 2 reveal that the {101} surface becomes the lowest energy surface upon H-adsorption, thus leading to formation of observed octahedral geometry. Contrary to stabilization of γ-LiAlO 2 surfaces upon H passivation, DFT revealed H-adsorption on α-LiAlO 2 surfaces to be energetically unfavorable. Furthermore, this contrasting behavior of α-LiAlO 2 and γ-LiAlO 2 under H-rich environments could be a potential driving force for the observed α-LiAlO 2 to γ-LiAlO 2 phase transformation.

36 MATERIALS SCIENCE↗

Combinatorial Exploration and Mapping of Phase Transformation in a Ni–Ti–Co Thin Film Library

Combinatorial synthesis and high-throughput characterization of a Ni–Ti–Co thin film materials library are reported for exploration of reversible martensitic transformation. The library was prepared by magnetron co-sputtering, annealed in vacuum at 500 °C without atmospheric exposure, and evaluated for shape memory behavior as an indicator of transformation. Composition, structure, and transformation behavior of the 177 pads in the library were characterized using high-throughput wavelength dispersive spectroscopy (WDS), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and four-point probe temperature-dependent resistance (R(T)) measurements. A new, expanded composition space having phase transformation with low thermal hysteresis and Co > 10 at. % is found. Unsupervised machine learning methods of hierarchical clustering were employed to streamline data processing of the large XRD and XPS data sets. Through cluster analysis of XRD data, we identified and mapped the constituent structural phases. Finally, composition–structure–property maps for the ternary system are made to correlate the functional properties to the local microstructure and composition of the Ni–Ti–Co thin film library.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reversible Phase Transformation of Colloidal 2D Lead Halide Perovskite Platelets under Photoirradiation

The photostability of lead halide perovskites is an important criterion for their utilization in light harvesting applications. Colloidal two-dimensional mixed halide perovskites offer a convenient approach to probe photoinduced transformations using spectroscopy tools. We employed suspensions of colloidal 2D methylammonium lead halide perovskite platelets with butylammonium and octylammonium as organic spacer cations. Upon irradiation of the mixed halide perovskite (BAOAMAPb 2 (Br 3.5 I 3.5 )) colloidal platelet suspension, we observe a phase transformation, as seen from the formation of bromide rich domains (BAOAMAPb 2 Br 7 ) and an iodide complex (PbI 3 – ). Unlike in the case of 3D mixed halide films, we did not observe the formation of iodide rich domains as part of the photoinduced phase segregation process. Instead, we observed the dissociation of the BAOAMAPb 2 I 7 to form an iodide complex, PbI 3 – . Interestingly, this photoinduced phase transformation was reversible, as the products which were confined in the colloidal core restored the original mixed halide phase upon storage in dark. The spectroscopic measurements that characterize excited states of different colloidal methylammonium lead halide perovskites and kinetics of photoinduced transformation and their dark recovery are presented. Furthermore, these new phototransformations of colloidal perovskite platelets provide new insights into the processes that dictate their overall photostability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Real-Time Diagnostics of 2D Crystal Transformations by Pulsed Laser Deposition: Controlled Synthesis of Janus WSSe Monolayers and Alloys

Energetic processing methods such as hyperthermal implantation hold special promise to achieve the precision synthesis of metastable two-dimensional (2D) materials such as Janus monolayers; however, they require precise control. Here, we report a feedback approach to reveal and control the transformation pathways in materials synthesis by pulsed laser deposition (PLD) and apply it to investigate the transformation kinetics of monolayer WS 2 crystals into Janus WSSe and WSe 2 by implantation of Se clusters with different maximum kinetic energies (<42 eV/Se-atom) generated by laser ablation of a Se target. Real-time Raman spectroscopy and photoluminescence are used to assess the structure, composition, and optoelectronic quality of the monolayer crystal as it is implanted with well-controlled fluxes of selenium for different kinetic energies that are regulated with in situ ICCD imaging, ion probe, and spectroscopy diagnostics. First-principles calculations, XPS, and atomic-resolution HAADF STEM imaging are used to understand the intermediate alloy compositions and their vibrational modes to identify transformation pathways. The real-time kinetics measurements reveal highly selective top-layer conversion as WS 2 transforms through WS 2(1–x) Se 2x alloys to WSe 2 and provide the means to adjust processing conditions to achieve fractional and complete Janus WSSe monolayers as metastable transition states. The general approach demonstrates a real-time feedback method to achieve Janus layers or other metastable alloys of the desired composition, and a general means to adjust the structure and quality of materials grown by PLD, addressing priority research directions for precision synthesis with real-time adaptive control.

2D materials↗

Engineering Molecular Transformations for Sustainable Energy Conversion

Future strategies for sustainable energy production will undoubtedly require processes and materials that can efficiently convert renewable resources into fuels. Nature’s enzymes can exquisitely integrate highly active catalytic centers within flexible environments that can adaptively guide reactants to products with very high activities and selectivities. They are limited, however, by their stability and ability to integrate into large scale production processes. The design of more robust heterogeneous catalytic materials that mimic the performance of enzymes, however, has been hindered by our limited understanding of how such transformations proceed. The tremendous advances in ab initio quantum mechanical methods, atomistic simulations, and high performance computing that have occurred over the past two decades, however, provide unprecedented ability to track molecular transformations and how they proceed at specific sites and within particular environments. This information together with the advances in in situ spectroscopic methods that follow such transformations can begin to enable the design of atomic surface ensembles and nanoscale reaction environments. This paper provides the author’s perspective on how theory and simulation can be used to move from current onedimensional design efforts based on catalytic descriptors to the design of two-dimensional surfaces, threedimensional reaction environments, and proton-coupled electron transfer systems that mimic enzymes in the transformation of molecules.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Utilizing Single-Crystalline Transformations for Precise Atom Placement in Multicomponent Cluster-Based Coordination Networks

The assembly of cluster or superatom building-blocks into extended solids has revolutionized materials design, enabling the synthesis of modular semiconductors with well-defined structures and tunable electronic, magnetic or optical properties. This strategy has recently advanced the synthesis of complex metal oxides with multifunctional or emergent behaviors, but precise atom placement of multiple elements with similar chemistries or preferred coordination environments remains a significant challenge. Here, in this study, we present a strategy for synthesizing polyoxometalate (POM)-based coordination networks with up to three different cations in precisely defined positions. Our approach leverages a single-crystal-to-single-crystal (SCSC) transformation in which the spatial placement of cations is governed by their availability at distinct stages of crystallization and transformation. Specifically, [ZP 5 W 30 O 110 ] (15-n)- (Z = Na + , K + , Ca 2+ , Ag + , Bi 3+ , Y 3+ , any Ln 3+ , Th 4+ ) is coordinatively assembled with various bridging metal cations (Y 3+ , any Ln 3+ , Th 4+ ). By using the encapsulated cation (Z) to "label" the POM, we track the phase-transformation and confirm the retention of single crystallinity. The integrated use of POM labeling and SCSC transformation enables rational control over cation distribution and establishes a versatile strategy for constructing multicomponent materials with high compositional and spatial precision.

Chen, Linfeng [Univ. of California, San Diego, CA ↗

Ligand Mediated Transformation of Cesium Lead Bromide Perovskite Nanocrystals to Lead Depleted Cs 4 PbBr 6 Nanocrystals

Lead halide perovskite nanocrystals (NCs) have emerged as attractive nanomaterials owing to their excellent optical and optoelectronic properties. Their intrinsic instability and soft nature enable a post-synthetic controlled chemical transformation. We studied a ligand mediated transformation of presynthesized CsPbBr 3 NCs to a new type of lead-halide depleted perovskite derivative nanocrystal, namely Cs 4 PbBr 6 . The transformation is initiated by amine addition, and the use of alkyl-thiol ligands greatly improves the size uniformity and chemical stability of the derived NCs. The thermodynamically driven transformation is governed by a two-step dissolution-recrystallization mechanism, which is monitored optically. Our results not only shed light on a decomposition pathway of CsPbBr 3 NCs but also present a method to synthesize uniform colloidal Cs 4 PbBr 6 NCs, which may actually be a common product of perovskite NCs degradation.

36 MATERIALS SCIENCE↗

Electric-field control of tri-state phase transformation with a selective dual-ion switch

Materials can be transformed from one crystalline phase to another by using an electric field to control ion transfer, in a process that can be harnessed in applications such as batteries, smart windows and fuel cells. Increasing the number of transferrable ion species and of accessible crystalline phases could in principle greatly enrich material functionality. However, studies have so far focused mainly on the evolution and control of single ionic species (for example, oxygen, hydrogen or lithium ions). In this paper, we describe the reversible and non-volatile electric-field control of dual-ion (oxygen and hydrogen) phase transformations, with associated electrochromic and magnetoelectric effects. We show that controlling the insertion and extraction of oxygen and hydrogen ions independently of each other can direct reversible phase transformations among three different material phases: the perovskite SrCoO 3-δ , the brownmillerite SrCoO 2.5 , and a hitherto-unexplored phase, HSrCoO 2.5 . By analysing the distinct optical absorption properties of these phases, we demonstrate selective manipulation of spectral transparency in the visible-light and infrared regions, revealing a dual-band electrochromic effect that could see application in smart windows. Moreover, the starkly different magnetic and electric properties of the three phases—HSrCoO 2.5 is a weakly ferromagnetic insulator, SrCoO 3-δ is a ferromagnetic metal, and SrCoO 2.5 is an antiferromagnetic insulator—enable an unusual form of magnetoelectric coupling, allowing electric-field control of three different magnetic ground states. Finally, these findings open up opportunities for the electric-field control of multistate phase transformations with rich functionalities.

36 MATERIALS SCIENCE↗

Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids

Here, we present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry-breaking structural changes of the crystal unit cell and reveals the importance of a mechanochemical spinodal, defined as the region in strain-composition space, where the free-energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechanochemical spinodal decomposition are variationally derived from a free-energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher-order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests that mechanochemical spinodal decomposition should occur in metal hydrides such as ZrH 2-2c . The rich physics that ensues is explored in several numerical examples in two and three dimensions, and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high-temperature ceramics.

36 MATERIALS SCIENCE↗

Universal linear intensity transformations using spatially incoherent diffractive processors

Abstract Under spatially coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number ( N ) of optimizable phase-only diffractive features is ≥~2 N i N o , where N i and N o refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially incoherent monochromatic light, the spatially varying intensity point spread function ( H ) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H ( m , n ; m ′, n ′) = | h ( m , n ; m ′, n ′)| 2 , where h is the spatially coherent point spread function of the same diffractive network, and ( m , n ) and ( m ′, n ′) define the coordinates of the output and input FOVs, respectively. Using numerical simulations and deep learning, supervised through examples of input-output profiles, we demonstrate that a spatially incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N ≥ ~2 N i N o . We also report the design of spatially incoherent diffractive networks for linear processing of intensity information at multiple illumination wavelengths, operating simultaneously. Finally, we numerically demonstrate a diffractive network design that performs all-optical classification of handwritten digits under spatially incoherent illumination, achieving a test accuracy of >95%. Spatially incoherent diffractive networks will be broadly useful for designing all-optical visual processors that can work under natural light.

36 MATERIALS SCIENCE↗

The self-healing of defects induced by the hydriding phase transformation in palladium nanoparticles

Nanosizing can dramatically alter material properties by enhancing surface thermodynamic contributions, shortening diffusion lengths, and increasing the number of catalytically active sites per unit volume. These mechanisms have been used to explain the improved properties of catalysts, battery materials, plasmonic materials, etc. Here we show that Pd nanoparticles also have the ability to self-heal defects in their crystal structures. Using Bragg coherent diffractive imaging, we image dislocations nucleated deep in a Pd nanoparticle during the forward hydriding phase transformation that heal during the reverse transformation, despite the region surrounding the dislocations remaining in the hydrogen-poor phase. We show that defective Pd nanoparticles exhibit sloped isotherms, indicating that defects act as additional barriers to the phase transformation. Our results resolve the formation and healing of structural defects during phase transformations at the single nanoparticle level and offer an additional perspective as to how and why nanoparticles differ from their bulk counterparts.

36 MATERIALS SCIENCE↗

High-performance photonic transformers for DC voltage conversion

Abstract Direct current (DC) converters play an essential role in electronic circuits. Conventional high-efficiency DC voltage converters, especially step-up type, rely on switching operation, where energy is periodically stored within and released from inductors and/or capacitors connected in a variety of circuit topologies. Since these energy storage components, especially inductors, are fundamentally difficult to scale down, miniaturization of switching converters proves challenging. Furthermore, the resulting switching currents produce significant electromagnetic noise. To overcome the limitations of switching converters, photonic transformers, where voltage conversion is achieved through light emission and detection processes, have been demonstrated. However, the demonstrated efficiency is significantly below that of the switching converter. Here we perform a detailed balance analysis and show that with a monolithically integrated design that enables efficient photon transport, the photonic transformer can operate with a near-unity conversion efficiency and high voltage conversion ratio. We validate the theory with a transformer constructed with off-the-shelf discrete components. Our experiment showcases near noiseless operation and a voltage conversion ratio that is significantly higher than obtained in previous photonic transformers. Our findings point to the possibility of a high-performance optical solution to miniaturizing DC power converters and improving the electromagnetic compatibility and quality of electrical power.

42 ENGINEERING↗

Learning stochastic dynamics and predicting emergent behavior using transformers

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior under conditions not observed during training. We consider a lattice model of active matter undergoing continuous-time Monte Carlo dynamics, simulated at a density at which its steady state comprises small, dispersed clusters. We train a neural network called a transformer on a single trajectory of the model. The transformer, which we show has the capacity to represent dynamical rules that are numerous and nonlocal, learns that the dynamics of this model consists of a small number of processes. Forward-propagated trajectories of the trained transformer, at densities not encountered during training, exhibit motility-induced phase separation and so predict the existence of a nonequilibrium phase transition. Transformers have the flexibility to learn dynamical rules from observation without explicit enumeration of rates or coarse-graining of configuration space, and so the procedure used here can be applied to a wide range of physical systems, including those with large and complex dynamical generators.

97 MATHEMATICS AND COMPUTING↗