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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↗

DOE OSTI2023

Step engineering for nucleation and domain orientation control in WSe 2 epitaxy on c -plane sapphire

In this study, epitaxial growth of two-dimensional transition metal dichalcogenides on sapphire has emerged as a promising route to wafer-scale single-crystal films. Steps on the sapphire act as sites for transition metal dichalcogenide nucleation and can impart a preferred domain orientation, resulting in a substantial reduction in mirror twins. Here we demonstrate control of both the nucleation site and unidirectional growth direction of WSe 2 on c-plane sapphire by metal–organic chemical vapour deposition. The unidirectional orientation is found to be intimately tied to growth conditions via changes in the sapphire surface chemistry that control the step edge location of WSe 2 nucleation, imparting either a 0° or 60° orientation relative to the underlying sapphire lattice. The results provide insight into the role of surface chemistry on transition metal dichalcogenide nucleation and domain alignment and demonstrate the ability to engineer domain orientation over wafer-scale substrates.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Analysis of multi-electron, multi-step homogeneous catalysis by rotating disc electrode voltammetry: theory, application, and obstacles

Rotating disc electrode (RDE) voltammetry has been widely adopted for the study of heterogenized molecular electrocatalysts for multi-step fuel-forming reactions but this tool has never been comprehensively applied to their homogeneous analogues. Here, the utility and limitations of RDE techniques for mechanistic and kinetic analysis of homogeneous molecular catalysts that mediate multi-electron, multi-substrate redox transformations are explored. Using the ECEC' reaction mechanism as a case study, two theoretical models are derived based on the Nernst diffusion layer model and the Hale transformation. Current–potential curves generated by these computational strategies are compared under a variety of limiting conditions to identify conditions under which the more minimalist Nernst Diffusion Layer approach can be applied. Based on this theoretical treatment, strategies for extracting kinetic information from the plateau current and the foot of the catalytic wave are derived. RDEV is applied to a cobaloxime hydrogen evolution reaction (HER) catalyst under non-aqueous conditions in order to experimentally validate this theoretical framework and explore the feasibility of RDE as a tool for studying homogeneous catalysts. Importantly, analysis of the foot-of-the-wave via this theoretical framework provides rate constants for elementary reaction steps that agree with those extracted from stationary voltammetric methods, supporting the application of RDE to study homogeneous fuel-forming catalysts. Lastly, obstacles encountered during the kinetic analysis of cobaloxime, along with the voltammetric signatures used to diagnose this reactivity, are discussed with the goal of guiding groups working to improve RDE set-ups and help researchers avoid misinterpretation of RDE data.

08 HYDROGEN↗

DOE OSTI2021

Air separation via two-step solar thermochemical cycles based on SrFeO 3-δ and (Ba,La) 0.15 Sr 0.85 FeO 3-δ perovskite reduction/oxidation reactions to produce N 2 : rate limiting mechanism(s) determination

Two-step solar thermochemical cycles based on reversible reactions of SrFeO 3–δ and (Ba,La) 0.15 Sr 0.85 FeO 3–δ perovskites were considered for air separation. The cycle steps encompass (1) the thermal reduction of SrFeO 3–δ or (Ba,La) 0.15 Sr 0.85 FeO 3–δ perovskites driven by concentrated solar irradiation and (2) oxidation in air to remove O 2 and produce N 2 . Rate limiting mechanisms were examined for both reactions using a combination of isothermal and non-isothermal thermogravimetry for temperature-swings between 673 and 1373 K, heating rates of 10, 20, and 50 K min –1 , and O 2 pressure-swings between 20% O 2 /Ar and 100% Ar at atmospheric pressure. Evolved O 2 and associated lag due to transport behavior were measured with gas chromatography and used with measured sample temperatures to predict equilibrium compositions from a compound energy formalism thermodynamic model. Measured and predicted chemical equilibrium changes in deviation from stoichiometry were compared. Rapid chemical kinetics were observed as the samples equilibrated rapidly for all conditions, indicative that heat and mass transfer were the rate limiting mechanisms. Furthermore, the effects of bulk diffusion (or gas diffusion through the bed or pellet) were examined using pelletized and loose powdered samples and determined to have no discernable impact.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Enhanced descriptor identification and mechanism understanding for catalytic activity using a data-driven framework: revealing the importance of interactions between elementary steps

We report accurate identification of descriptors for catalytic activities has long been essential to the in-depth understanding of catalysis and recently to set the basis for catalyst screening. However, commonly used methods suffer from low accuracy in predictability. This study reports an enhanced approach to accurately identify the descriptors from a kinetic dataset using a machine learning (ML) surrogate model. CO hydrogenation to methanol over Cu-based catalysts was taken as a case study. Our model captures not only the contribution from individual elementary steps but also the interaction between relevant steps within a reaction network, which was found to be essential for high accuracy. As a result, six effective descriptors are identified, which are accurate enough to ensure the trained gradient boosted regression (GBR) model for good prediction of the methanol turnover frequency (TOF) over metal (M)-doped Cu(111) model surfaces (M = Au, Cu, Pd, Pt, Ni). More importantly, going beyond the purely mathematical ML model, the catalytic role of each identified descriptor can be revealed by using model-agnostic interpretation tools, which enhances the insight into the promoting effect of alloying. The trained GBR model outperforms the conventional derivative-based methods in terms of both the predictability and the mechanism understanding. It opens alternative possibilities toward accurate descriptor-based rational catalyst optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

One-step production of renewable adipic acid esters from mucic acid over an Ir–ReO x /C catalyst with low Ir loading

The production of adipic acid, a large-volume platform chemical, from biomass represents a petroleum-free route to manufacturing nylon and other polymers more sustainably. In this study, a one-step conversion of bioderived mucic acid to adipates is reported over a heterogeneous, bifunctional Ir–ReO x /C catalyst via deoxydehydration (DODH) and catalytic transfer hydrogenation (CTH) using isopropanol as a green solvent and reductant. With very low Ir content (0.05 wt%), the catalyst provides a low-cost option for the tandem DODH–CTH process, while still enabling reuse and regeneration for at least five cycles. The reported catalytic system generates adipates in good yield (63%) without the need for additives (acids or halogens) or high pressure H 2 . Through model reactions and spectroscopic analyses, a bifunctional DODH–CTH mechanism was supported, with the Re VI/IV redox pair as the active DODH species and Ir0 saturating the dialkene intermediate via CTH. Thermal treatment in catalyst preparation and regeneration was optimized to limit metal leaching while maintaining good activity. Further, the present work outlines a one-step deoxygenation of an aldaric acid substrate from biomass using a bimetallic catalyst of low noble metal content to an important monomer for the polymer industry. This system facilitates use in future syntheses of sustainable chemicals from renewable oxygenates where the catalyst is reusable and affordable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Two-step spin-coating of vacancy-ordered double perovskites enables growth of thin films for electronic devices

Vacancy-ordered double perovskites (VODPs), such as Cs 2 TeX 6 (X = Cl, Br, I), are lead-free alternatives to conventional metal-halide perovskites (MHPs). One limitation of VODPs is the lack of processes to form thin films relevant for physical characterization and electronic devices. A two-step spin-coating method was developed for synthesizing high-quality films of Cs 2 TeBr 6 . Independently depositing CsBr and TeBr 4 enables high precursor concentrations and control over crystallization kinetics. By optimizing the spin-coating parameters, conversion of precursors to phase pure films was observed using structural and surface characterization methods. The growth of mixed-halide systems was investigated using alternative salts including CsCl and CsI. The formation of halide alloys was found to depend on the existence of routes to byproducts. Lastly, single carrier diodes of Cs2TeBr6 were designed following valence band characterization with photoelectron spectroscopy. Temperature-dependent space-charge-limited current measurements revealed that transport occurs by hopping and the hole mobility is 3.2 × 10 −5 cm 2 V −1 s −1 near room temperature. As a result, the insights from the 2-step procedure provide a pathway towards making semiconducting devices from VODPs.

Kuklinski, Owen [University of California, Santa B↗

DOE OSTI2024

The DEHVILS in the details: Type Ia supernova Hubble residual comparisons and mass step analysis in the near-infrared

Measurements of type Ia supernovae (SNe Ia) in the near-infrared (NIR) have been used both as an alternate path to cosmology compared to optical measurements and as a method of constraining key systematics for the larger optical studies. With the DEHVILS sample, the largest published NIR sample with consistent NIR coverage of maximum light across three NIR bands ( Y, J , and H ), we check three key systematics: (i) the reduction in Hubble residual scatter as compared to the optical, (ii) the measurement of a “mass step” or lack thereof and its implications, and (iii) the ability to distinguish between various dust models by analyzing slopes and correlations between Hubble residuals in the NIR and optical. We produce SN Ia simulations of the DEHVILS sample and find that it is harder to differentiate between various dust models than previously understood. Additionally, we find that fitting with the current SALT3-NIR model does not yield accurate wavelength-dependent stretch-luminosity correlations, and we propose a limited solution for this problem. From the data, we see that (i) the standard deviation of Hubble residual values from NIR bands treated as standard candles are 0.007–0.042 mag smaller than those in the optical, (ii) the NIR mass step is not constrainable with the current sample size of 47 SNe Ia from DEHVILS, and (iii) Hubble residuals in the NIR and optical are correlated in the data. We test a few variations on the number and combinations of filters and data samples, and we observe that none of our findings or conclusions are significantly impacted by these modifications.

Astronomy & Astrophysics↗

DOE OSTI2021

Hydration structure of flat and stepped MgO surfaces

We investigate the solvation structure of flat and stepped MgO(001) in neutral liquid water using ab initio molecular dynamics based on a hybrid density functional with dispersion corrections. Our simulations show that the MgO surface is covered by a densely packed layer of mixed intact and dissociated adsorbed water molecules in a planar arrangement with strong intermolecular H-bonds. The water dissociation fractions in this layer are >20% and >30% on the flat and stepped surfaces, respectively. Slightly above the first water layer, we observe metastable OH groups perpendicular to the interface, similar to those reported in low temperature studies of water monolayers on MgO. Here, these species receive hydrogen bonds from four nearby water molecules in the first layer and have their hydrophobic H end directed toward bulk water, while their associated protons are bound to surface oxygens. The formation of these OH species is attributed to the strong basicity of the MgO surface and can be relevant for understanding various phenomena from morphology evolution and growth of (nano)crystalline MgO particles to heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Observation of half-integer Shapiro steps in graphene Josephson junctions

We study quantum transport and AC Josephson effect of hexagonal boron nitride encapsulated graphene (BGB) Josephson junctions (JJs). Our experiments reveal the emergence of the half-integer Shapiro steps in the n-type regime with high electron carrier densities. We attribute this observation to the gate-tunable transmission probability of the graphene junction. Furthermore, our numerical simulations are consistent with the appearance of half-integer Shapiro steps at high transparency, which suggests a skewed current phase relationship in the graphene JJ.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Nonlinear coupling of tearing modes in reversed field pinch plasmas with stepped pressure profiles

A theory of the three-wave coupling of triplets of tearing modes in toroidal pinches [i.e., either reversed field pinches (RFPs) or tokamaks] was proposed by R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)]. However, this theory only applies to toroidal pinches with negligible equilibrium plasma pressure gradients. Such a limitation is particularly inappropriate to RFPs. This paper generalizes the analysis of R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)] in order to take the equilibrium pressure gradient into account. However, for the sake of simplicity, a stepped pressure profile, rather than a continuous profile, is employed. In the limit in which the number of steps becomes very large, the results obtained from the generalized theory are presumably equivalent to those that would have been achieved using a continuous pressure profile. The generalized theory is used to investigate the formation of the characteristic toroidally localized pattern of phase-locked m = 1 and m = 0 tearing modes in RFP plasmas that is known as the “slinky” pattern. The incorporation of the equilibrium plasma pressure into the analysis is found to be of crucial importance when determining the properties of the pattern. This is the case because the plasma pressure controls the number of unstable m = 1 and m = 0 tearing modes, and also significantly affects the strength of three-wave coupling, as well as the phase relation between the phase-locked m = 1 and m = 0 modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Stepped pressure equilibrium with relaxed flow and applications in reversed-field pinch plasmas

The multi-region relaxed magnetohydrodynamics (MRxMHD) has been successful in the construction of equilibria in three-dimensional (3D) configurations. In MRxMHD, the plasma is sliced into sub-volumes separated by ideal interfaces, each undergoing relaxation, allowing the formation of islands and chaos. The resulting equilibrium has a stepped pressure profile across sub-volumes. The stepped pressure equilibrium code (SPEC) was developed to calculate MRxMHD equilibria numerically. In this work, we have extended the SPEC code to compute MRxMHD equilibria with field-aligned flow and rotation, following the theoretical development to incorporate cross-helicity and angular momentum constraints. The code has been verified for convergence and compared to a Grad–Shafranov solver in 2D. We apply our new tool to study the flow profile change before and after the sawtooth crash of a reversed-field pinch discharge, in which data of the parallel flow is available. We find the promising result that under the constraints of cross-helicity and angular momentum, the parallel flow profile in post-crash SPEC equilibrium is flat in the plasma core and the amplitude of the flow matches experimental observations. Lastly, we provide an example equilibrium with a 3D helical field structure as the favored lower energy state. This will be the first 3D numerical equilibrium in which the flow effects are self-consistently calculated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

On the non-existence of stepped-pressure equilibria far from symmetry

The Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502) has been successful in the construction of equilibria in 3D configurations that contain a mixture of flux surfaces, islands and chaotic magnetic field lines. In this model, the plasma is sliced into sub-volumes separated by ideal interfaces, and in each volume the magnetic field is a Beltrami field. In the cases where the system is far from possessing a continuous symmetry, such as in stellarators, the existence of solutions to a stepped-pressure equilibrium with given constraints, such as a multi-region relaxed MHD minimum energy state, is not guaranteed but is often taken for granted. Using SPEC, we have studied two different scenarios in which a solution fails to exist in a slab with analytic boundary perturbations. Here we found that with a large boundary perturbation, a certain interface becomes fractal, corresponding to the break up of a Kolmogorov–Arnold–Moser (KAM) surface. Moreover, an interface can only support a maximum pressure jump while a solution of the magnetic field consistent with the force balance condition can be found. An interface closer to break-up can support a smaller pressure jump. We discovered that the pressure jump can push the interface closer to being non-smooth through force balance, thus significantly decreasing the maximum pressure it can support. Our work shows that a convergence study must be performed on a SPEC equilibrium with interfaces close to break-up. These results may also provide insights into the choice of interfaces and have applications in finding out the maximum pressure a machine can support.

3D equilibrium↗

DOE OSTI2021

Success of digital adiabatic simulation with large Trotter step

The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. Here we show that with additional conditions, the circuit depth can be linear in simulation time T. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Two-step charge density wave transition and hidden transient phase in 1 T – TiSe 2

Using variable temperature atomic pair distribution function analysis, we study the emergence of charge density wave (CDW) order in 1T-TiSe 2 and find that it takes place via a two-step transition. First, upon decreasing temperature to about 235(3) K, CDW related lattice distortions emerge in the individual TiSe 2 layers alone. Then, upon further decreasing the temperature, the two-dimensional distortions in the layers couple and the widely recognized three-dimensional 2a o x 2a o x 2c o superstructure emerges at about 205(3) K. Because two different band gaps are known to emerge at the same temperatures, the finding indicates the presence of strong electron-phonon coupling. The transient phase between the two steps lacks inversion symmetry and may serve as a precursor of the debated chiral 1T-TiSe 2 phase. Finally, our findings are important for the understanding of the enigmatic CDW transition in 1T-TiSe 2 and CDW instabilities in van der Waals materials in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Cooperative mechanisms behind nanoscale smoothing on metal surfaces: From adatom diffusion to step nucleation

Many technologies require stable or metastable surface morphology. Here, in this paper we study the factors that control the metastability of a common feature of rough surfaces: “hillocks.” We use low energy electron microscopy to follow the evolution of the individual atomic steps in hillocks on Pd(111). We show that the uppermost island in the stack often adopts a static, metastable configuration. Modeling this result shows that the degree of the metastability depends on the configuration of steps dozens of atomic layers lower. Our model allows us to link surface metastability to the atomic processes of surface evolution.

Fernandes Cauduro, Andre Luis↗

DOE OSTI2024

Adaptive time stepping for the two-time integro-differential Kadanoff-Baym equations

The nonequilibrium Green's function gives access to one-body observables for quantum systems. Of particular interest are quantities such as density, currents, and absorption spectra which are important for interpreting experimental results in quantum transport and spectroscopy. We present an integration scheme for the Green's function's equations of motion, the Kadanoff-Baym equations (KBE), which is both adaptive in the time integrator step size and method order as well as the history integration order. We analyze the importance of solving the KBE self-consistently and show that adapting the order of history integral evaluation is important for obtaining accurate results. To examine the efficiency of our method, we compare runtimes to a state-of-the-art fixed time step integrator for several test systems and show an order of magnitude speedup at similar levels of accuracy. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Primary $\gamma$-ray intensities and $\gamma$-strength functions from discrete two-step $\gamma$-ray cascades in radiative proton-capture experiments

Background: Reaction rates of radiative capture reactions can play a crucial role in the nucleosynthesis of heavy nuclei in explosive stellar environments. These reaction rates depend strongly on $\gamma$-ray decay widths in the reaction products, which are, for nonresonant capture reactions at high excitation energies, derived from the $\gamma$-ray strength function and the nuclear level density. Recently, the ratio method was applied to primary $\gamma$ rays observed from ($\textit{d, p}$) reactions and nuclear resonance fluorescence measurements to extract the dipole strength in atomic nuclei and to test the generalized Brink-Axel hypothesis. Purpose: The purpose of this work is to apply the ratio method to primary $\gamma$-ray intensities of the 63,65 Cu($\textit{p},\gamma$) reactions to extract $\gamma$-ray strength information on the nuclei 64,66 Zn. Here, the impact of spin distribution, total $\gamma$-ray decay widths, level densities, and width fluctuations on the application of the ratio method will be discussed. Additionally, by comparing the relative $\gamma$-ray strength at different excitation energies, conclusions on the validity of the generalized Brink-Axel hypothesis can be made. Method: The radiative proton capture reaction measurements have been performed at the HORUS $\gamma$-ray spectrometer of the University of Cologne at one excitation energy for each reaction. Primary $\gamma$-ray intensities have been determined by normalizing secondary $\gamma$-ray transitions in two-step cascades using their absolute branching ratio. The ratio method was applied to the measured primary $\gamma$-ray intensities as well as to previous measurements by Erlandsson et al. at different excitation energies. Results: The relative strength function curve for 64 Zn from our measurement shows no significant deviation from the previous measurement at a different excitation energy. The same is true for 66 Zn where both measurements were at almost the same excitation energy. Absolute $\gamma$-strength function values have been obtained by normalizing the relative curves to quasiparticle random phase approximation calculations because of the absence of experimental data in the respective energy region. Conclusion: The generalized Brink-Axel hypothesis, i.e., the independence of the strength function on the excitation energy, seems to hold in the studied energy region and nuclei. The method to obtain primary $\gamma$-ray intensities from two-step cascade spectra was shown to be a valuable and sensitive tool although its uncertainties are connected to the knowledge of the low-energy level scheme of the investigated nucleus. The scaling in the ratio method should be taken with care, because the relative strength is not a simple sum of $f_{E1}$ and $f_{M1}$ but a somewhat complex linear combination dependent on the excitation energy of the nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗