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Machine-Learned Committor Functions for Reactive Molecular Dynamics

Reactive molecular dynamics (MD) is a powerful tool for atomistic-scale modeling of a diverse range of chemical processes. However, scaling these simulations to large systems and long times scales remains a challenge because of the complexity of the potential energy function required. The authors previously developed a heuristic approach, called REACTER, that incorporates reactivity in MD simulations in a less general but much more computationally efficient manner. REACTER uses standard, fixed valence force fields as the underlying potentialenergy surface for describing all interatomic interactions but adds a procedure for enforcing user-defined reactions that occur when certain geometric constraints on relative atomic positions are satisfied. Further, these bonding changes can be accepted or rejected with a probability related tothe local thermal energy. This work seeks to generalize this approach by replacing the set of user defined geometric constraints and energetic criteria with a committor function that specifies the probability of a reaction occurring on the basis of the local atomic configuration. The committor function is a useful mathematical tool for modeling rare events but, unfortunately, is very difficult to compute for realistic systems in a general way. This work describes a method for approximating the committor function using a machine learning approach, specifically a deep neural network trained with data from reactive MD and DFT-based dynamics simulations. This network is coupled to the existing REACTER protocol, as implemented in the LAMMPS MD package, and used to make on-the-fly predictions of reaction probabilities without the more extensive user input previously required. The new method is demonstrated using the polymerization of polystyrene as a case study. Although very dependent on the quality and quantity of training data, machine-learned committor functions show promise as a method for incorporating reaction probability from higher level calculations into highly scalable MD simulations.

polymer simulations↗
DOE OSTI2026

Investigating shock-induced chemical reactions in Ni+Al multilayers: A continuum-based mesoscale approach with Arrhenius kinetics and artificial thermal conduction

A new continuum-based mesoscale modeling approach for shock-induced chemical reactions (SICRs) in Ni+Al multilayers is demonstrated in Sandia’s shock physics hydrocode, CTH. The approach utilizes Arrhenius-type kinetics and artificial thermal conduction. Our work builds upon previous efforts to parameterize equations of state for Ni x Al y [J. Appl. Phys. 137, 075102 (2025)], as well as simulations of inert shocks in realistic 2D microstructures [J. Appl. Phys. 137, 225301 (2025)]. To calibrate the reaction kinetics, pairs of the reaction coordinate, R′, vs time are extracted from the molecular dynamics (MD) literature. Here, the MD-informed kinetics are used to simulate the dynamic evolution of pressure and temperature in 2D mesoscale simulations. Overall, the MD-informed kinetics obtained for planar interfaces are too slow, as initial reaction is not observed on a nanosecond time scale. Even with quasi-periodic shock focusing leading to the formation of so-called “hot-spots,” the hot spots are unable to grow and coalesce using the fitted Arrhenius rate constants. However, by increasing the rate constants by two orders of magnitude, SICRs are observed at a shock pressure near 30 GPa, which is supported by experiments. Consequently, these mesoscale simulations suggest that unresolved shear-based mechanical mixing might possibly account for the discrepancies in kinetic rates, with shock-generated intense perturbations, interfacial vortical flows, and elevated temperatures serving as favorable reaction conditions. Future work will calibrate a shear-dependent reaction rate from the MD simulations with realistic interfaces that are wavy, diffuse, and disordered.

Kittell, David E. [Sandia National Laboratories (S↗
DOE OSTI2026

Machine Learning Interatomic Potentials for Modeling Framework Flexibility and Water Uptake in NbOFFIVE-1-Ni Metal–Organic Framework

Metal–organic frameworks (MOFs), with their distinctive porous structures and tunable chemical properties, have shown immense promise in the separation and storage of gases. Currently, the accurate simulation of their adsorptive properties remains challenging, especially for systems where the molecules fit very tightly into the pores. Traditional simulation methods often approximate the frameworks as rigid and do not account for the framework flexibility seen in materials such as NbOFFIVE-1-Ni. First-principles molecular dynamics (FPMD) simulations offer the desired accuracy in modeling this flexibility but are limited by their extensive computational demands, rendering them impractical for long simulations. Conversely, classical force field-based simulations offer computational efficiency but lack the necessary accuracy. Here, to break this accuracy-efficiency trade-off, we have developed machine learning interatomic potentials trained on energies and forces from FPMD to model the framework flexibility of NbOFFIVE-1-Ni in the presence of water over nanosecond time scales. Furthermore, by integrating MLIP-driven molecular dynamics (MLIP-MD) with grand canonical Monte Carlo (GCMC) simulations, we further incorporated framework flexibility into adsorption predictions, yielding water adsorption isotherms that better align with experimental data compared to those of conventional GCMC simulations. These advances offer new opportunities for the design and optimization of MOFs in gas storage and separation applications.

adsorption↗
DOE OSTI2026

Dynamics and Structure of Molten Neodymium Titanate

Binary rare earth titanates can be vitrified using levitation melt quenching, and their glasses are promising for optical applications. To better understand their thermophysical properties and dynamics, we have used molecular dynamics (MD) and empirical potential structure refinement (EPSR) to simulate molten neodymium titanate, 83TiO 2 –17Nd 2 O 3 . The models are compared with high-energy synchrotron X-ray diffraction of the melt structure over 1060–1960 K and thermophysical property measurements of electrostatically levitated droplets over 1500–2200 K. As temperature increases, the network periodicity increases and the correlation length decreases, both in monotonic trends that suggest continuous structural evolution through the melt and supercooled liquid regimes. At 1900 K, the mean Ti–O and Nd–O coordination numbers are 5.8(5) and 6.7(5), compared to the glass, 5.72(6) and 7.70(26). The equilibrium melting point is measured as 1860(20) K, over 100 K higher than previous estimates. Viscosity data from MD are in good agreement with experimental measurements. The dynamic propensity of Nd is similar to that of the network-forming Ti, suggesting that Nd does not participate as a conventional modifier. The viscosity of this fragile liquid is likely controlled by the breaking of cation–oxygen bonds and rearrangements of Ti–O polyhedra.

molecular dynamics↗
DOE OSTI2022

Coordination and thermophysical properties of select trivalent lanthanides in LiCl–KCl

The coordination chemistry of various fission and decay products, such as actinides and lanthanides, are crucial to the commercial deployment of molten salt reactors as they can affect the thermophysical properties. In this report we examined the structure, coordination environment, and physical properties such as the density and the vibrational density of states for three lanthanide species, namely Ce, Eu, and Sm in the LiCl–KCl eutectic system using a combination of quantum mechanics simulations and spectroscopic experiments. Quantum mechanics molecular dynamics (QM-MD) modelling was employed to determine the physical properties of each system resulting in accurate local coordination of each species. Then, the vibrational density of states (DOS) was determined using a two-phase thermodynamic modelling which was then compared to the experimentally obtained Raman spectra of the species in molten LiCl–KCl having the eutectic composition. We find that Ce 3+ , Eu 3+ and Sm 3+ all adopt octahedral local coordination environments in the eutectic salt composition in good agreement with experimental results. Ce3+ is found to fluctuate between an octahedral six-coordinated and a seven-coordinated structure due to the increased local proximity of Cl in the eutectic salt, resulting in a lower fluidicity/diffusivity than the other trivalent lanthanides studied. The thermophysical properties of the eutectic composition with trivalent lanthanides were not significantly different from the pure eutectic salt composition, but several changes were noted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Solid-state NMR and theoretical studies illuminate lanthanum borohydride C–H borylation catalysts confined within a zeolite

Zeolite-supported single-site lanthanum borohydride catalyzes C–H borylation of hydrocarbons, while the related silica-supported complex is inactive under comparable conditions. The identical composition of support-La(BH 4 ) 2 (THF) 2 sites in the two materials implies that the support bestows underlying structural features onto La that are required for bond activation catalysis, yet the nature of these effects, which could include confinement effects and/or electronic modulation of the site itself, remains to be identified. We used solid-state nuclear magnetic resonance (SSNMR) spectroscopy and molecular dynamics simulations with machine-learning potentials (ML-MD) to analyze the electronic and steric effects imparted by the faujasite support on the precatalyst structure to correlate with catalytic activity. ML-MD simulations show that THF dissociates from La under the influence of confinement, leading to coordinatively unsaturated sites in the zeolite pores. Then, the La complex grafts on Brønsted acid sites (La BAS ) or isolated silanols (La SiO ) or remains physisorbed in the zeolite pores. Catalytic studies comparing compounds supported on faujasite zeolites containing or lacking BAS and/or silanols show that only the former complexes lead to active sites, ruling out confinement as the sole requirement for catalysis. The DFT calculations and ML-MD simulations also reveal that the surface-lanthanum coordination number is two (bidentate) for La BAS , with the metal center forming long, flexible bonds to two oxygen atoms bridging Si and Al, but only one oxygen atom (monodentate) for La SiO . The structure–activity relationship identifies confined, BAS-grafted species as active sites and provides important guidance for the design of enhanced atom-efficient catalysts.

Cui, Jinlei [Ames Laboratory, and Iowa State Univ.↗
DOE OSTI2022

Thermal neutron scattering cross sections for amorphous carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm{sup 3}. From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical optical peak at 0.25 eV for the ideal graphite disappears for amorphous carbon, in good agreement with the expected structure. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Predicting the structural basis of targeted protein degradation by integrating molecular dynamics simulations with structural mass spectrometry

Targeted protein degradation (TPD) is a promising approach in drug discovery for degrading proteins implicated in diseases. A key step in this process is the formation of a ternary complex where a heterobifunctional molecule induces proximity of an E3 ligase to a protein of interest (POI), thus facilitating ubiquitin transfer to the POI. In this work, we characterize 3 steps in the TPD process. (1) We simulate the ternary complex formation of SMARCA2 bromodomain and VHL E3 ligase by combining hydrogen-deuterium exchange mass spectrometry with weighted ensemble molecular dynamics (MD). (2) We characterize the conformational heterogeneity of the ternary complex using Hamiltonian replica exchange simulations and small-angle X-ray scattering. (3) We assess the ubiquitination of the POI in the context of the full Cullin-RING Ligase, confirming experimental ubiquitinomics results. Differences in degradation efficiency can be explained by the proximity of lysine residues on the POI relative to ubiquitin.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Source of Processable Vitrimer Viscosities: Swap Frequencies and Steric Factors

Vitrimers exhibit high, processable viscosities, where other polymers do not, and are among the most promising polymers for closed-loop material circularity. We sought to investigate the underlying chemical kinetic factors that result in high viscosities for vitrimers, which are crucial to designing vitrimers with tunable viscosity. To interrogate these factors, we achieved the first simulated predictions of real vitrimer viscosities, using a novel kinetic Monte Carlo molecular dynamics method, overcoming the time and length scale gaps to predict experimental bulk viscosities. The vitrimer architecture investigated is based on poly(dimethylsiloxane) chains and vinylogous urethane bond swaps. We probed the effects of the extent of free swapping groups, %F, the activation energy, E A , and the steric factor, ρ. The steric factor is related to the intrinsic reaction probability for molecules with sufficient energy. All three factors were found to be significant, but the role of ρ was found to be the biggest and also the most underappreciated. The results show that the inclusion of accurate ρ is of critical importance for viscosity predictions, with the evidence suggesting that the typical assumption of ρ = 1 is not valid for vitrimers and that, indeed, very low steric factors are present in bond-swap vitrimers such that values of ρ < 10 –10 may be typical. This greatly influences the bond exchange rates and, ultimately, the viscosities. Recognition of this result is necessary for the prediction of vitrimer viscosities from molecular simulations and to make vitrimers by design from molecular dynamics. We also investigated the effects that E A , ρ, and the number of free swapping groups have upon vitreous range temperatures, TV, with respect to achieving a specific viscosity (η V = 1 × 10 8 Pa·s), as well as for a commonly reported higher viscosity extrapolation (η V = 1 × 10 12 Pa·s). The evidence suggests that vitrimers may follow universal curves for E A vs T V , as a function of ρ. Finally, this study achieves the first of these comparisons of molecular simulations to experiments and reveals critical insights toward creating vitrimers by design, while providing a route for the prediction of T V from kinetic Monte Carlo molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Dynamic Monkey Bar Mechanism of Superionic Li‐ion Transport in LiTaCl 6

Abstract The LiTaCl 6 solid electrolyte has the lowest activation energy of ionic conduction at ambient conditions (0.165 eV), with a record high ionic conductivity for a ternary compound (11 mS cm −1 ). However, the mechanism has been unclear. We train machine‐learning force fields (MLFF) on ab initio molecular dynamics (AIMD) data on‐the‐fly and perform MLFF MD simulations of AIMD quality up to the nanosecond scale at the experimental temperatures, which allows us to predict accurate activation energy for Li‐ion diffusion (at 0.164 eV). Detailed analyses of trajectories and vibrational density of states show that the large‐amplitude vibrations of Cl − ions in TaCl 6 − enable the fast Li‐ion transport by allowing dynamic breaking and reforming of Li−Cl bonds across the space in between the TaCl 6 − octahedra. We term this process the dynamic‐monkey‐bar mechanism of superionic Li + transport which could aid the development of new solid electrolytes for all‐solid‐state lithium batteries.

Lei, Ming↗
DOE OSTI2025

Local structure of zinc–indium–tin oxide films via grazing-incidence x-ray pair-distribution functions and theoretical methods

A detailed experimental and theoretical study on the local (r ≤ 4.5 Å) atomic structure of amorphous and crystalline zinc–indium–tin oxide (ZITO) thin films using grazing-incidence x-ray Pair-Distribution Functions (PDFs), ab initio Molecular Dynamics (MD), and Empirical Potential Structure Refinement (EPSR) Monte Carlo simulations is presented. High-energy synchrotron x rays, a two-dimensional detector, and different incident angles were used to probe the depth uniformity of five (ZnO) 0.15 (In 2 O 3 ) 0.70 (SnO 2 ) 0.15 films that were deposited via pulsed-laser deposition at growth temperatures (T G ) ranging from 25 to 300 °C. Films deposited at T G ≤ 150 °C were amorphous. The partially crystalline (T G = 200 °C) and fully crystalline (T G = 300 °C) films were highly textured. Both crystalline and amorphous structures were investigated using ab initio MD and EPSR Monte Carlo simulations. The density of the amorphous films determined from the experimental data agreed with MD calculations. Coordination numbers, bond lengths, and distortion for metal–oxygen and for both the edge- and corner-shared In–metal shells up to 4.5 Å obtained from PDF analysis closely agreed with MD and EPSR simulations. There is a pronounced decrease in the edge- and corner-shared In–Zn distances arising from the shorter Zn–O bond length, Zn–O tetrahedral coordination, and In–O–Zn angle in amorphous ZITO compared to its crystalline counterpart. A maximum in electrical mobility was observed for the amorphous film just before crystallization occurred. While the peak is broad, consistent with nearly unchanged overall cation–oxygen coordination in the amorphous films, ESPR results indicate that the tetrahedral coordination follows the conductivity trend.

Grazing Incidence X-ray↗
DOE OSTI2022

Thermal Neutron Scattering Cross Sections for Graphitic Amorphous Carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm 3 . From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical features and the optical graphitic peak at 0.25 eV for the ideal graphite DOS disappear for graphite-like amorphous carbon, which shows good agreement with the expected structure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Machine learning assisted prediction of tungsten heavy alloy plasma facing component performance for fusion energy applications

Tungsten and tungsten heavy alloys (WHAs), known for their remarkably high hardness, durability, and corrosion resistance, play a critical role in the thriving development of nuclear fusion reactors in recent years. However, the exploration in tungsten alloys for the nuclear-related applications has been limited by the difficulty of manufacturing and the complexity of experiments to reproduce the environment of nuclear reaction. Therefore, this project aims to utilize nanoscale simulation methods such as density functional theory (DFT) and molecular dynamics (MD) with the help of machine learning techniques to not only understand the mechanisms of tungsten alloys but also allow us to computationally predict their mechanical behaviors under extreme environments. One critical problem of the application of WHAs in nuclear reactors is the surface melting. In the current design of the SPARC reactor, the WHA, W97Ni2.1Fe0.9 or W97NiFe, is chosen to be the first wall components to confine the plasma where the particles are fiercely moving and colliding into each other to create nuclear fusion reaction. This process will generate extremely high heat flux onto these WHA tiles, leaving high surface temperature that could possibly melt the surface of the WHA tiles, As illustrated in Fig. 1(a). a laser experiment previously done illustrates that a rough surface damage would be made after the surface melting where the matrix area mainly composed of nickel and iron as shown in Fig. 1(b), will first melt and then leave vacancies between these tungsten grains. Unfortunately, these kinds of roughness on the first-wall components could be deadly to the plasma inside a Tokmak reactor because the heat that is supposed to dissipate at a designed ratio through the tiles may in turn be excessively absorbed and accumulated on any uneven area of the surface, which will eventually make the whole nuclear reaction fail. In this project, we will introduce a machine learning potential, Allegro, based on DFT calculation and then build a MD model for W-Ni-Fe alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A data-driven multiscale model for reactive wetting simulations

Here, we describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop’s composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material’s wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

$\mathrm{DRAGON}$: A multi-GPU orbital-free density functional theory molecular dynamics simulation package for modeling of warm dense matter

As progress in electronic structure theoretical methods is made, ab initio molecular dynamics (MD) based on orbital-free density functional theory (OF-DFT) is becoming increasingly more successful at substituting the traditional, very accurate but computationally costly Kohn–Sham (KS) approach for simulations of matter at the challenging warm dense matter (WDM) regime. However, despite the significant cost alleviation of eliminating the dependence on the KS orbitals, OF-DFT MD runs require ~10 2 to 10 3 CPU cores running for days, or even weeks, for simulations of systems comprised of 10 2 to 10 3 atoms, depending on thermodynamic conditions. Here we present DRAGON, a multi-GPU OF-DFT MD code for fast and efficient simulations of WDM. With a relatively small allocation of resources (4 to 8 GPU devices) it can provide an order of magnitude speedup for simulations containing $\mathscr{O}$(10 4 ) atoms and target systems composed of $\mathscr{O}$(10 5 ) atoms at conditions within the WDM regime, which is currently outside the capabilities of CPU codes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Modification of a force field for molecular dynamics simulations of silicon etching by chlorine atoms

Here, a modified classical molecular dynamics (MD) force field is presented for the interaction between silicon (Si) and chlorine (Cl). The original version of the force field is shown to significantly overestimate the probability of Si etching by thermal Cl atoms. However, the modified force field corrects this problem and results in generally good agreement with experimental data. Further, it is shown that while the modification of the force field improves the prediction of Si spontaneous etching with Cl atoms, it does not degrade predictions of atomic-layer etching of Si with Cl[Formula: see text] molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Dynamic Monkey Bar Mechanism of Superionic Li–ion Transport in LiTaCl 6

Here, the LiTaCl 6 solid electrolyte has the lowest activation energy of ionic conduction at ambient conditions (0.165 eV), with a record high ionic conductivity for a ternary compound (11 mS cm –1 ). However, the mechanism has been unclear. We train machine-learning force fields (MLFF) on ab initio molecular dynamics (AIMD) data on-the-fly and perform MLFF MD simulations of AIMD quality up to the nanosecond scale at the experimental temperatures, which allows us to predict accurate activation energy for Li-ion diffusion (at 0.164 eV). Detailed analyses of trajectories and vibrational density of states show that the large-amplitude vibrations of Cl – ions in TaCl 6 – enable the fast Li-ion transport by allowing dynamic breaking and reforming of Li–Cl bonds across the space in between the TaCl 6 – octahedra. We term this process the dynamic-monkey-bar mechanism of superionic Li + transport which could aid the development of new solid electrolytes for all-solid-state lithium batteries.

25 ENERGY STORAGE↗
DOE OSTI2026

High-pressure melt dynamics in shock-compressed titanium

In this work we study the high-pressure melting behavior of titanium using laser-driven shock compression with in situ femtosecond x-ray diffraction and molecular-dynamics simulations based on a machine-learned interatomic potential. The MD simulations predict the solid-liquid coexistence on the Hugoniot in the ∼111−124GPa range. Experimentally, we observe the first evidence of liquid at 86 GPa. We also observe pronounced microstructural changes with pressure, with strong grain refinement associated with the emergence of liquid, within the solid-liquid coexistence (∼110−126GPa). Above 126 GPa, we observe the persistence of residual levels of highly textured crystalline Ti to ∼180GPa, well above the expected melt completion pressure. We discuss the accuracy that current laser-shock experimental platforms have at determining the melt onset and completion pressures.

36 MATERIALS SCIENCE↗