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Results for “two-step transformation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Two-step deformation-induced martensitic transformation in additively manufactured High-Si stainless steel

Deformation-induced phase transformation in the additively manufactured (AM) Fe–18Cr–8Ni-5.5Si (in wt.%) alloy was analyzed using the in-situ electron backscattered diffraction (EBSD) record during uniaxial tensile testing in a scanning electron microscope (SEM). Analysis of EBSD data was focused to investigate phase transformation behavior during deformation with consideration of mechanical interactions among phases and grains in the ultrafine AM microstructure. The initial EBSD phase map illustrated that the as-built microstructure was a duplex structure consisting of major austenite (γ) and minor ferrite phases, some of which showed non-traditional orientation relationship since the rapid solidification in the AM process has produced non-equilibrium state in phase formation. In the deformed as-built AM alloy, the two-step martensitic transformation (γ→ε→α´) was identified as the main deformation-induced transformation mechanism. Martensitic transformation steps were found to be associated with glides of Shockley partial dislocations on closed packed (111) planes under the influence of atomic disturbance in the γ and ε phases, respectively. Using the closed-packed plane pole figures and unit cell orientations, their evolutions and mechanisms accompanying with the transformation were analyzed. Finally, the results indicate that one variant of ε-martensite forms from their parent γ phase, while two variants of α´ form from their parent ε phase.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Deciphering the multiple deformation mechanisms responsible for sustained work hardening in a FeCrCoNi medium entropy alloy

Two important and desirable properties of materials for most structural applications are high tensile strength and ductility, which typically require high work hardening to delay necking. Here, in this work, we designed and tensile tested a face-centered cubic (fcc) Fe-Cr-Co-Ni medium-entropy alloy in which multiple deformation mechanisms are triggered during tensile loading at different temperatures to induce sustained work hardening. Our strategy involved control of the relative stabilities of the fcc, hcp (hexagonal close-packed), and bcc (body-centered cubic) phases in this quaternary system via high-throughput thermodynamic calculations. This alloy not only exhibits extensive deformation-induced nanotwinning at room temperature, but also displays a two-step sequential phase transformation [γ (fcc) → ε (hcp) martensite → α’ (bcc) martensite] at 77 K, which contrasts with the single-step phase transformation [γ → ε martensite] observed in many other fcc high/medium entropy alloys with a low stacking fault energy. The sequence of phase transformation at 77K was supported by first-principles density functional theory calculations. This work provides new templates for the design of alloys capable of multiple deformation mechanisms for sustained work hardening.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Decoding Li + /Na + Exchange Route Toward High-Performance Mn-Based Layered Cathodes for Li-Ion Batteries

Li + /Na + exchange has been extensively explored as an effective method to prepare high-performance Mn-based layered cathodes for Li-ion batteries, since the first report in 1996 by P. G. Bruce (Nature, 1996. 381, 499–500). Understanding the detailed structural changes during the ion-exchange process is crucial to implement the synthetic control of high-performance layered Mn-based cathodes, but less studied. Herein, in situ synchrotron X-ray diffraction, density functional theory calculations, and electrochemical tests are combined to conduct the systemic studies into the structural changes during the ion-exchange process of an Mn-only layered cathode O3-type Li 0.67 [Li 0.22 Mn 0.78 ]O 2 (LLMO) from the corresponding counterpart P3-type Na 0.67 [Li 0.22 Mn 0.78 ]O 2 (NLMO). The temperature-resolved observations combined with theoretical calculations reveal that the Li + /Na + exchange is favorable thermodynamically and composited with two tandem topotactic phase transitions: 1) from NLMO to a layered intermediate through ≈60% of Li + /Na + exchange. 2) then to the final layered product LLMO through further Li insertion. Moreover, the intermediate-dominate composite is obtained by slowing down the exchange kinetics below room temperature, showing better electrochemical performance than LLMO obtained by the traditional molten-salt method. Finally, the findings provide guides for the synthetic control of high-performance Mn-based cathodes under mild conditions.

25 ENERGY STORAGE↗
DOE OSTI2025

Quantum simulations of nuclear resonances with variational methods

Background: The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices. Purpose: This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator. Methods: We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform 𝜃-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray code (GC) encoding to reduce qubit requirements. Results: We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic 𝛼−𝛼 nuclear potential and compute the 𝐷- and 𝐺-wave resonance energies with a basis size of 𝑁=16, using only four qubits. The quantum simulation results closely match the classical values, demonstrating the feasibility of our approach. Conclusions: This study demonstrates, for the first time, that the complete 𝜃-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems and lays the foundation for future investigations into resonance structures in nuclear, atomic, and molecular physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Goethite and Hematite Nucleation and Growth from Ferrihydrite: Effects of Oxyanion Surface Complexes

The presence of oxyanions, such as nitrate (NO 3 – ) and phosphate (PO 4 3– ), regulates the nucleation and growth of goethite (Gt) and hematite (Hm) during the transformation of ferrihydrite (Fh). Our previous studies showed that oxyanion surface complexes control the rate and pathway of Fh transformation to Gt and Hm. However, how oxyanion surface complexes control the mechanism of Gt and Hm nucleation and growth during the Fh transformation is still unclear. Here, we used synchrotron scattering methods and cryogenic transmission electron microscopy to investigate the effects of NO 3 – outer-sphere complexes and PO 4 3– inner-sphere complexes on the mechanism of Gt and Hm formation from Fh. Our TEM results indicated that Gt particles form through a two-step model in which Fh particles first transform to Gt nanoparticles and then crystallographically align and grow to larger particles by oriented attachment (OA). In contrast, for the formation of Hm, imaging shows that Fh particles first aggregate and then transform to Hm through interface nucleation. This is consistent with our X-ray scattering results, which demonstrate that NO 3 – outer-sphere and PO 4 3– inner-sphere complexes promote the formation of Gt and Hm, respectively. These results have implications for understanding the coupled interactions of oxyanions and iron oxy-hydroxides in Earth-surface environments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

From Layered Antiferromagnet to 3D Ferromagnet: LiMnBi-to-MnBi Magneto-Structural Transformation

Here, the intermetallic compound LiMnBi was synthesized by the two-step solid-state reaction from the elements. The synthesis temperature of 850 K was selected based on in-situ high-temperature powder X-ray diffraction data. LiMnBi crystalizes in the layered-like PbClF structure type (a = 4.3131(7) Å, c = 7.096(1) Å at 100 K, P4/nmm space group, Z = 2). LiMnBi structure is built of the alternating [MnBi] and Li layers, as determined from single-crystal X-ray diffraction data. Magnetic properties measurements and solid-state 7 Li Nuclear Magnetic Resonance data collected for polycrystalline LiMnBi samples indicate the long-range antiferromagnetic ordering of Mn sublattice at ~340 K, with no superconductivity down to 5 K detected. LiMnBi is air- and water-sensitive. In aerobic conditions, Li can be extracted from LiMnBi structure to form Li 2 O/LiOH and MnBi (NiAs structure type, P6 3 /mmc). The obtained MnBi polymorph was previously reported to be one of the strongest rare-earth-free ferromagnets, yet its bulk synthesis in powder form is cumbersome. The proposed magneto-structural transformation from ternary LiMnBi to ferromagnetic MnBi involves condensation of the MnBi4 tetrahedra upon Li deintercalation and is exclusive to LiMnBi. In contrast, ferromagnetic MnBi cannot be obtained from either isostructural NaMnBi and KMnBi, or from the structurally related CaMn 2 Bi 2 . Such a distinctive transformation in the case of LiMnBi is presumed to be due to its fitting reactivity to yield MnBi and favorable interlayer distance between [MnBi] layers, while the interlayer distance in NaMnBi and KMnBi structural analogs is unfavorably long. The studies of delithiation from the layered-like LiMnBi under different chemical environments indicate that the yield of the MnBi depends on the type of solvent used and the kinetics of the reaction. A slow rate and mild reaction media lead to a high fraction of the MnBi product. The saturation magnetization of the “as-prepared” MnBi is ~50 % of the expected value of 81.3 emu/g. Overall, this study adds a missing member to the family of ternary pnictides and illustrates how soft-chemistry methods can be used to obtain “difficult-to-synthesize” compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

CNN-Based Phase Fault Classification in Real and Simulated Power Systems Data

This study proposes a convolutional neural network (CNN)–based two-step phase fault detection and identification method to classify anomalies in the power grid signal. Specifically, the first step checks the fault’s existence and determines the need for the second step. Subsequently, in the case of anomalies in the power grid signal, the second step identifies the type of fault, including line-to-line, single-line-to-ground, double-line-to-ground, and triple-line. Accordingly, the CNN architecture is both designed for the classification layers and trained with simulated data. To provide maximum prediction accuracy with minimum processing time, this study investigates the combinations of various feature extraction (FE) techniques, such as fast Fourier transform (FFT), amplitude and phase (AP), auto-correlation function, power spectral density, and wavelet transform (WT). Consequently, simulated and real-world results demonstrate that the proposed two-step method outperforms conventional one-step techniques, with the best performance obtained by using the combination of AP-AP, AP-WT, FFT-AP, and FFT-WT–based FE methods.

Alaca, Ozgur↗
DOE OSTI2025

Print-and-Plate Architected Electrodes for Electrochemical Transformations Under Flow

Flow cell electrodes are typically composed of porous carbon materials, such as papers, felts, and cloths. However, their random architecture hinders the fundamental characterization of electrode structure-performance relationships during in situ operation of porous electrochemical flow systems. This work describes a “print-and-plate” method that combines direct ink writing of micro-periodic lattices with a two-step metal plating process that converts them into highly conductive (sheet resistance 40 mΩ sq -1 ) electrodes. Their operando performance is assessed in an anthraquinone disulfonic acid half-cell using widefield electrochemical fluorescence microscopy, where output current and fluorescence intensity are in excellent agreement. The pressure drop associated with flow through three electrode designs is determined via simulations from which the most efficient design is identified and manufactured via print-and-plate. Confocal fluorescence microscopy is then used to create a 3D map of the state of charge (SOC) inside this print-and-plate electrode. The experimental state of the charge map is in good agreement with computational predictions. The rapid design, simulation, and fabrication of print-and-plate electrodes enable fundamental investigations of how architected porosity affects electrochemical performance under flow.

3D-printing↗
DOE OSTI2024

Two-dimensional silk

Despite the promise of silk-based devices, the inherent disorder of native silk limits performance. Here, we report highly ordered two-dimensional silk fibroin (SF) films grown epitaxially on van der Waals (vdW) substrates. Using atomic force microscopy, nano–Fourier transform infrared spectroscopy, and molecular dynamics, we show that the films consist of lamellae of SF molecules that exhibit the same secondary structure as the nanocrystallites of native silk. Increasing the SF concentration results in multilayers that grow either by direct assembly of SF molecules into the lamellae or, at high concentrations, along a two-step pathway beginning with a disordered monolayer that then crystallizes. Scanning Kelvin probe measurements show that these films substantially alter the surface potential; thus, they provide a platform for silk-based electronics on vdW solids.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A one-pot synthesis of high-density biofuels through bifunctional mesoporous zeolite-encapsulated Pd catalysts

Developing a powerful bifunctional catalyst for tandem reactions is essential to the future carbon neutrality by reducing the energy consumption in chemical industries. Herein, mesoporous zeolite-encapsulated palladium (Pd) nanoparticles (Pd@meso-ZSM-5) synthesized via emulsification-demulsification followed by a dry-gel transformation method were demonstrated to have a remarkable catalytic performance for a one-pot multiple tandem reaction of cyclic ketones (cyclopentanone, cyclohexanone) to bicyclic alkanes (bicyclopentane, bicyclohexane). Compared with supported catalysts (Pd/meso-ZSM-5) and microporous zeolite-encapsulated catalysts (Pd@ZSM-5) with a primary product of monocyclic alkane (cyclopentane, cyclohexane), Pd@meso-ZSM-5 shows much higher catalytic efficiency for the bicyclic alkanes synthesis, which was previously unattainable in the conventional two-step synthesis route. Controlled experiments and detailed characterizations show that mesoporosity provides sufficient space for the generation and diffusion of large molecular intermediates, and the intimate acid-Pd interface promotes the conversion of intermediates. As a result, this work proposes a design strategy for a mesoporous zeolite-encapsulated metal catalyst, which efficiently provides cooperative acid-hydrogenation catalysis.

09 BIOMASS FUELS↗
DOE OSTI2023

Robust Parameter Design on Dual Stochastic Response Models With Constrained Bayesian Optimization

In engineering system design, minimizing the variations of the quality measurements while guaranteeing their overall quality up to certain levels, namely the robust parameter design (RPD), is crucial. Recent works have dealt with the design of a system whose response-control variables relationship is a deterministic function with a complex shape and function evaluation is expensive. In this work, we propose a Bayesian optimization method for the RPD of stochastic functions. Dual stochastic response models are carefully designed for stochastic functions. The heterogeneous variance of the sample mean is addressed by the predictive mean of the log variance surrogate model in a two-step approach. We establish an acquisition function that favors exploration across the feasible and optimality-improvable regions to effectively and efficiently solve the stochastic constrained optimization problem. Further, the performance of our proposed method is demonstrated by the extensive numerical and case studies. Note to Practitioners-Many manufacturing processes involve undesirable variations, which create variations in the final products. For example, many emerging manufacturing processes, such as nanomanufacturing, involve complex physical and chemical dynamics and transformation, creating variations in the manufacturing output. In such processes, it is crucial to design the manufacturing processes or products so that they have minimum variations in their quality. Meanwhile, it is also important to maintain the overall quality of the designed processes or products. Furthermore, acquiring data from many advanced manufacturing processes is often very costly, especially in the designing stage. In this work, we propose a data-driven method that automatically finds the best setting of manufacturing processes or products with the minimum variations of quality and a given constraint on the average quality satisfied. Our proposed method is used before conducting every experiment; It analyzes the historical data from previous experiments and provides a setting to be used in the next experiment. Our proposed method efficiently utilizes the historical data, and thus finds the best robust setting by conducting only a small number of experiments.

42 ENGINEERING↗
DOE OSTI2023

Lead leaching and electrowinning in acetic acid for solar module recycling

It is imperative to recover lead (Pb) contained in end-of-life solar modules. In this paper, a two-step leaching and electrowinning process using acetic acid is investigated for Pb recovery. Acetic acid with hydrogen peroxide can dissolve Pb quickly and, under some conditions, in a matter of minutes. Pb electrowinning has been successfully demonstrated from aqueous solutions of 0.009 M lead(II) acetate with 0–10% v/v acetic acid. Pb-containing deposits are found on both the copper cathode and graphite anode. X-ray diffraction, energy-dispersive X-ray spectroscopy, and Fourier transform infrared spectroscopy confirm the presence of metallic Pb and Pb(II) oxide (PbO) co-deposits on the cathode. Further, there is also the formation of lead subacetate on the cathode under certain conditions. On the anode, the deposit consists of lead(IV) oxide and superoxide (PbO 2 and Pb 1–x O 2 ). A Pb recovery rate of 99% is achieved in 0.009 M lead(II) acetate solutions with 10% v/v acetic acid by applying a reduction potential of either –0.8 V or –1.0 V versus the silver/silver chloride reference electrode for 24h. Pb leaching with acetic acid is also demonstrated from milled silicon solar modules.

14 SOLAR ENERGY↗
DOE OSTI2023

Mending cracks atom-by-atom in rutile TiO2 with electron beam radiolysis

Abstract Rich electron-matter interactions fundamentally enable electron probe studies of materials such as scanning transmission electron microscopy (STEM). Inelastic interactions often result in structural modifications of the material, ultimately limiting the quality of electron probe measurements. However, atomistic mechanisms of inelastic-scattering-driven transformations are difficult to characterize. Here, we report direct visualization of radiolysis-driven restructuring of rutile TiO 2 under electron beam irradiation. Using annular dark field imaging and electron energy-loss spectroscopy signals, STEM probes revealed the progressive filling of atomically sharp nanometer-wide cracks with striking atomic resolution detail. STEM probes of varying beam energy and precisely controlled electron dose were found to constructively restructure rutile TiO 2 according to a quantified radiolytic mechanism. Based on direct experimental observation, a “two-step rolling” model of mobile octahedral building blocks enabling radiolysis-driven atomic migration is introduced. Such controlled electron beam-induced radiolytic restructuring can be used to engineer novel nanostructures atom-by-atom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The role of amorphous ZIF in ZIF-8 crystallization kinetics and morphology

Understanding the composition and structure of amorphous precursor phases is fundamental for elucidating two-step crystallization mechanisms and designing shape- and size-controlled nanomaterials. However, that understanding is largely lacking for metal–organic framework compounds despite their growing significance as functional materials. Here, in this study, we report the crystallization of zeolite imidazolate frameworks-8 (ZIF-8, Zn(C 4 H 5 N 2 ) 2 ) via an amorphous ZIF (am-ZIF) solid precursor phase with a rough stoichiometric composition of Zn(C 4 H 5 N 2 ) 1.78 (C 4 H 6 N 2 ) 0.17 (CH 3 COO) 0.22 . The formation of am-ZIF is attributed to the incomplete deprotonation of 2-Methylimidazole (HmIm) and the involvement of the hydrogen bond between CH 3 COO– and –HN, which can further transform into the dense Dia(Zn) structure with a diamondoid crystal topology in pure water. Taking am-ZIF as a precursor, the tunable dissolution and recrystallization kinetics of am-ZIF into ZIF-8, due to the addition of EtOH and CTAB, allows the selective fabrication of dodecahedral, cubic, and hollow ZIF-8. Overall, an in-depth understanding of the differences in composition and structure of am-ZIF from ZIF-8 and the resulting crystallization kinetics suggests a novel approach to designing metal–organic frameworks with controlled crystal morphology.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Polyhalohydrins: Investigating Vicinal Functionalities by Ring-Opening of Epoxides on Polyolefins

Halohydrins are functional groups that are underexplored in polymer science. This study synthesized and examined structure–property relationships of halohydrin-functionalized polymers derived from polycyclooctene (PCOE), which was obtained via ring-opening metathesis polymerization (ROMP). The polyhalohydrins, including polychlorohydrin, polybromohydrin, and polyiodohydrin, were produced through a two-step process involving epoxidation of PCOE followed by epoxide ring-opening using hydrochloric, hydrobromic, or hydroiodic acid. These stereoirregular and regioirregular polymers are amorphous as measured by differential scanning calorimetry and X-ray scattering. Lap joint shear testing revealed an enhanced adhesive performance in polychlorohydrin and polybromohydrin, with the former demonstrating nearly three times the ultimate shear stress compared to a model polyethylene, hydrogenated PCOE. Additionally, contact angle measurements and surface free energy analysis showed an increase in hydrophilicity and polarity from iodine- to bromine- to chlorine-functionalized polyhalohydrins, aligning with trends in adhesion strength. Furthermore, these results underscore the potential of halohydrin functionalization as a versatile approach for tuning surface properties, offering new opportunities for polymer-to-polymer transformations.

Functional groups↗
DOE OSTI2022

Investigation of twin growth mechanisms in precipitate hardened AZ91

Here, in this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) model with a dislocation-density (DD) based hardening law is employed to study the growth of a {10$\bar{1}$2} tensile twin that is blocked by basal-precipitates in precipitate-hardened AZ91 magnesium alloy. It is frequently reported that twin growth is hindered in precipitate-hardened Mg alloys; however, thick twin domains are often observed experimentally in these material systems. Detailed numerical investigation of deformation twinning starting from an early propagation stage, before twin growth, reveals that the stress fields that result from two sequentially propagated twins co-impinging on a precipitate relaxes the twin back stress locally and promotes twin growth at the twin-precipitate junction. Based on these findings, a two-step growth mechanism is proposed for twins arrested by precipitates. In the first step, the interaction of a twin tip with a precipitate develops a stress concentration on the other side of the precipitate, prompting the formation of a second twin. Subsequently, the back stresses associated with the first twin are relaxed by the formation of the second twin, allowing the first twin to grow at the twin-precipitate junction and eventually engulf the precipitate. This mechanism suggests that twin growth can be achieved locally with minimal additional external forces, explaining how relatively large twin domains can develop even in the presence of arrays of precipitates.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Computational Predictions of the Hydrolysis of 2,4,6-Trinitrotoluene (TNT) and 2,4-Dinitroanisole (DNAN)

Hydrolysis is a common transformation reaction that can affect the environmental fate of many organic compounds. In this study, three proposed mechanisms of alkaline hydrolysis of 2,4,6-trinitrotoluene (TNT) and 2,4-dinitroaniline (DNAN) were investigated with plane-wave density functional theory (DFT) combined with ab initio and classical molecular dynamics (AIMD/MM) free energy simulations, Gaussian basis set DFT calculations, and correlated molecular orbital theory calculations. Most of the computations in this study were carried out using the Arrows web based tools. For each mechanism: Meisenheimer complex formation, nucleophilic aromatic substitution, and proton abstraction reaction energies and activation barriers were calculated for the reaction at each relevant site. For TNT, it was found that the most kinetically favorable first hydrolysis steps involve Meisenheimer complex formation by attachment of OH$^{-}$ at the C1 and C3 arene carbons and proton abstraction from the methyl group. The nucleophilic aromatic substitution reactions at the C2 and C4 arene carbons were found to be thermodynamically favorable. However, the calculated activation barriers were slightly lower than previous studies, but still found to be $\Delta$G$^{\ddagger} \approx 18$ kcal/mol using PBEo AIMD/MM free energy simulations, suggesting the reactions are not kinetically significant. For DNAN, the barriers of nucleophilic aromatic substitution were even greater ($\Delta$G$^{\ddagger} > 29$ kcal/mol PBEo AIMD/MM). Further, the most favorable hydrolysis reaction for DNAN was found to be a two-step process in which the hydroxyl first attacks the C1 carbon to form a Meisenheimer complex at the C1 arene carbon C1-(OCH$_3$)OH$^{-}$, subsequently, the methoxy anion (-OCH$_3$) at the C1 arene carbon dissociates and the proton shuttles from the C1-OH to the dissociated methoxy group, resulting in methanol and an aryloxy anion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Metastability and Ostwald step rule in the crystallisation of diamond and graphite from molten carbon

Abstract Experimental challenges in determining the phase diagram of carbon at temperatures and pressures near the graphite-diamond-liquid triple point are often related to the persistence of metastable crystalline or glassy phases, superheated crystals, or supercooled liquids. A deeper understanding of the crystallisation kinetics of diamond and graphite is crucial for effectively interpreting the outcomes of these experiments. Here, we reveal the microscopic mechanisms of diamond and graphite nucleation from liquid carbon through molecular simulations with first-principles machine learning potentials. Our simulations accurately reproduce the experimental phase diagram of carbon near the triple point and show that liquid carbon crystallises spontaneously upon cooling. Metastable graphite crystallises in the domain of diamond thermodynamic stability at pressures above the triple point. Furthermore, whereas diamond crystallises through a classical nucleation pathway, graphite follows a two-step process in which low-density fluctuations forego ordering. Calculations of the nucleation rates of the two competing phases confirm this result and reveal a manifestation of Ostwald’s step rule, where the strong metastability of graphite hinders the transformation to the stable diamond phase. Our results provide a key to interpreting melting and recrystallisation experiments and shed light on nucleation kinetics in polymorphic materials with deep metastable states.

Science & Technology - Other Topics↗