Dr. Jon Belof
Lawrence Livermore National Lab, Materials Science Division, Department Member
- High energy and experienced physicist taking high-impact concepts and making them reality by building world-class tea... moreHigh energy and experienced physicist taking high-impact concepts and making them reality by building world-class teams focused on innovation, effectiveness and achieving success on time and under budget. Unique perspective on best practices for developing practical solutions to grand-challenge problems, having spent >30 years in academia, corporate sector and government. Translating complex theories of material science into high-performance computing solutions, with a track record for completion of major milestones and technical leadership.edit
The classical Richtmyer-Meshkov instability (RMI) is a hydrodynamic instability characterizing the evolution of an interface following shock loading. In contrast to other hydrodynamic instabilities such as Rayleigh-Taylor, it is known for... more
The classical Richtmyer-Meshkov instability (RMI) is a hydrodynamic instability characterizing the evolution of an interface following shock loading. In contrast to other hydrodynamic instabilities such as Rayleigh-Taylor, it is known for being unconditionally unstable: regardless of the direction of shock passage, any deviations from a flat interface will be amplified. In this article, we show that for negative Atwood numbers, there exist special sequences of shocks which result in a nearly perfectly suppressed instability growth. We demonstrate this principle computationally and experimentally with stepped fliers and phase transition materials. A fascinating immediate corollary is that in specific instances, a phasetransitioning material may self-suppress RMI.
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Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression... more
Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.
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Solid-solid phase transitions are investigated in Zr thin films using shock compression induced by a short laser pulse (<1 ns). Shock wave profiles are measured at free surfaces for films of different thicknesses (a few micrometers)... more
Solid-solid phase transitions are investigated in Zr thin films using shock compression induced by a short laser pulse (<1 ns). Shock wave profiles are measured at free surfaces for films of different thicknesses (a few micrometers) using chirped-pulse line velocimetry with 10 ps time resolution. Experiments are performed at pressures up to ∼50 GPa, which is sufficient to reach the ω and β phases under equilibrium conditions. The shock wave structures are analyzed using a general Lagrangian analysis method, which allows for the calculation of stress–strain paths and assessments of phase transition behavior. In agreement with recent short laser pulse experiments using ultra-fast x-ray diffraction, we do not find any clear evidence of the α–ω transition, though this would be expected from the phase diagram. Instead, we infer a direct transformation to a metastable β-phase at lower shock pressures (<20 GPa) and equilibrium β at higher pressures. Through the velocimetry analysis, ...
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Insights from non-equilibrium statistical mechanics, highlighting the role of work and fluctuations at the microscale, are applied toward the development of a fundamental, rigorous and purely atomistic theory of nucleation. Nanoscale... more
Insights from non-equilibrium statistical mechanics, highlighting the role of work and fluctuations at the microscale, are applied toward the development of a fundamental, rigorous and purely atomistic theory of nucleation. Nanoscale fluctuations in order, density and heat influence the local nucleation rate by orders of magnitude, necessitating their inclusion through a modern approach. Coarse-graining over the underlying Hamiltonian dynamics allows derivation of a microscale expression for the nucleation rate in terms of a classical path integral over far from equilibrium trajectories and their associated work. Second law violating states at the microscale, as found from the dynamics of small critical nucleation clusters, contribute exponentially to the observable macroscale nucleation rate.
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A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust datadriven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the... more
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust datadriven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residualbased error indicator and random-subset evaluation is introduced to search for the optimal training samples on-the-fly. Further, to exploit local latent-sp...
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Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying... more
Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying nonequilibrium material behavior, such as solidification kinetics. In ramp-wave compression experiments, the input drive pressure to the experimental setup may be exerted through one of a number of different mechanisms (e.g., magnetic fields, gas-gun-driven impactors, or high-energy lasers) and is generally required for simulating such experiments. Yet, regardless of the specific mechanism, this drive pressure cannot be measured directly (measurements are generally taken at a location near the back of the experimental setup through a transparent window), leading to an inverse problem where one must determine the drive pressure at the front of the experimental setup (i.e., the input) that corresponds to the particle velocity (the output) measured near the back of the experimental setup. We solve this inverse problem using a heuristic optimization algorithm, known as differential evolution, coupled with a multiphysics, hydrodynamics code that simulates the compression of the experimental setup. By running many rounds of forward simulations of the experimental setup, our optimization process iteratively searches for a drive pressure that is optimized to closely reproduce the experimentally measured particle velocity near the back of the experimental setup. While our optimization methodology requires a significant number of hydrodynamics simulations to be conducted, many of these can be performed in parallel, which greatly reduces the time cost of our methodology. One novel aspect of our method for determining the drive pressure is that it does not require physical modeling of the drive mechanism and can thus be broadly applied to many types of ramp-compression experiments, regardless of the drive mechanism.
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Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied... more
Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied to a model face-centered cubic (fcc) metal that undergoes phase transitions to the body-centered cubic (bcc) as well as the hexagonal close-packed phases at high temperatures and pressures. Large-scale molecular dynamics simulations of ultrarapid freezing show that bcc nucleates and grows well outside of the region of its thermodynamic stability. An extensive study of crystal–liquid equilibria confirms that at any given pressure, there is a multitude of metastable solid phases that can coexist with the liquid phase. We define for every crystal phase, a solid cluster in liquid (SCL) basin, which contains all solid clusters of that phase coexisting with the liquid. A rigorous methodology is developed that allows for practical calculations of nucleatio...
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The interaction of actinides and actinide alloys such as the δ-stabilized Pu-Ga alloy with iron is of interest to understand the impurity effects on phase stability. A newly developed and self-consistent CALPHAD thermodynamic database is... more
The interaction of actinides and actinide alloys such as the δ-stabilized Pu-Ga alloy with iron is of interest to understand the impurity effects on phase stability. A newly developed and self-consistent CALPHAD thermodynamic database is presented which covers the elements: Pu, U, Fe, Ga across their whole composition and temperature ranges. The phase diagram and thermodynamic properties of plutonium-iron (Pu-Fe) and uranium-iron (U-Fe) systems are successfully reassessed, with emphasis on the actinide rich side. Density functional theory (DFT) calculations are performed to validate the stability of the stoichiometric (Pu,U)6Fe and (Pu,U)Fe2 compounds by computing their formation enthalpies. These data are combined to construct the Pu-U-Fe ternary phase diagram. The thermodynamic assessment of Fe-Ga is presented for the first time and application to the quaternary Pu-U-Fe-Ga system is discussed.
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As theoretically hypothesized for several decades in group IV transition metals, we have discovered a dynamically stabilized body-centered cubic (bcc) intermediate state in Zr under uniaxial loading at sub-nanosecond timescales. Under... more
As theoretically hypothesized for several decades in group IV transition metals, we have discovered a dynamically stabilized body-centered cubic (bcc) intermediate state in Zr under uniaxial loading at sub-nanosecond timescales. Under ultrafast shock wave compression, rather than the transformation from α-Zr to the more disordered hex-3 equilibrium ω-Zr phase, in its place we find the formation of a previously unobserved nonequilibrium bcc metastable intermediate. We probe the compression-induced phase transition pathway in zirconium using time-resolved sub-picosecond x-ray diffraction analysis at the Linac Coherent Light Source. We also present molecular dynamics simulations using a potential derived from first-principles methods which independently predict this intermediate phase under ultrafast shock conditions. In contrast with experiments on longer timescale (> 10 ns) where the phase diagram alone is an adequate predictor of the crystalline structure of a material, our recent study highlights the importance of metastability and time dependence in the kinetics of phase transformations.
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Classical nucleation theory (CNT) is a promising way to predictively model the submicrosecond kinetics of phase transitions that occur under dynamic compression, such as the suite of experiments performed over the past two decades on the... more
Classical nucleation theory (CNT) is a promising way to predictively model the submicrosecond kinetics of phase transitions that occur under dynamic compression, such as the suite of experiments performed over the past two decades on the solidification of liquid water to the high-pressure ice VII phase. Myint et al. [Phys. Rev. Lett. 121, 155701 (2018)] presented the first CNT-based model for these types of rapid phase transitions, but relied on an empirical scaling parameter in their transient induction model to simulate the lag time that occurs prior to the onset of significant formation of ice VII clusters in the system. To build on that study, we model the liquid water-ice VII phase transformation using a numerical discretization scheme to solve the Zel'dovich-Frenkel partial differential equation, which is a fundamental CNT-based kinetic equation that describes the statistical time-dependent behavior of solid cluster formation. The Zel'dovich-Frenkel equation inherently accounts for transience in the nucleation kinetics and eliminates the need for the empirical scaling factor used by Myint et al. One major result of this research is that transience is found to play a relatively small role in the nucleation process for the dynamic-compression time scales of the liquid water-ice VII experiments being simulated. Instead, we show that it is possible to properly model the lag time using steady-state CNT by making small refinements to the interfacial free energy value. We have also developed a new dimensionless parameter that may be applied a priori to predict whether or not transient nucleation will be important in a given dynamic-compression experiment.
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Understanding the behavior of materials at extreme pressures is a central issue in fields like aerodynamics, astronomy, and geology, as well as for advancing technological grand challenges such as inertial confinement fusion. Dynamic... more
Understanding the behavior of materials at extreme pressures is a central issue in fields like aerodynamics, astronomy, and geology, as well as for advancing technological grand challenges such as inertial confinement fusion. Dynamic compression experiments to probe high-pressure states often encounter rapid phase transitions that may cause the materials to behave in unexpected ways, and understanding the kinetics of these phase transitions remains an area of great interest. In this review, we examine experimental and theoretical/computational efforts to study the freezing kinetics of water to a high-pressure solid phase known as ice VII. We first present a detailed analysis of dynamic compression experiments in which water has been observed to freeze on sub-microsecond time scales to ice VII. This is followed by a discussion of the limitations of currently available molecular and continuum simulation methods in modeling these experiments. We then describe how our phase transition kinetics models, which are based on classical nucleation theory, provide a more physics-based framework that overcomes some of these limitations. Finally, we give suggestions on future experimental and modeling work on the liquid-ice VII transition, including an outline of the development of a predictive multiscale model in which molecular and continuum simulations are intimately coupled.
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Molecular dynamics simulations of an embedded atom copper system in the isobaric-isenthalpic ensemble are used to study the effective solid-liquid interfacial free energy of quasi-spherical solid crystals within a liquid. This is within... more
Molecular dynamics simulations of an embedded atom copper system in the isobaric-isenthalpic ensemble are used to study the effective solid-liquid interfacial free energy of quasi-spherical solid crystals within a liquid. This is within the larger context of molecular dynamics simulations of this system undergoing solidification, where single individually prepared crystallites of different sizes grow until they reach a thermodynamically stable final state. The resulting equilibrium shapes possess the full structural details expected for solids with weakly anisotropic surface free energies (in these cases, ∼5% radial flattening and rounded [111] octahedral faces). The simplifying assumption of sphericity and perfect isotropy leads to an effective interfacial free energy as appearing in the Gibbs-Thomson equation, which we determine to be ∼177 erg/cm2, roughly independent of crystal size for radii in the 50-250 Å range. This quantity may be used in atomistically informed models of solidification kinetics for this system.
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Grand canonical Monte Carlo simulations of H2 sorption were performed in the metal–organic framework rht-MOF-1. The binding sites were revealed by combining simulation and inelastic neutron scattering data.
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Beryllium strength has been investigated under dynamic loading conditions using platforms that span a limited range of pressure and strain-rate space. Multiple Be strength models that are ostensibly calibrated to these experiments... more
Beryllium strength has been investigated under dynamic loading conditions using platforms that span a limited range of pressure and strain-rate space. Multiple Be strength models that are ostensibly calibrated to these experiments persist, and yet they predict dierent outcomes for results beyond the limited phase space where data exist. We discuss experiments using high explosives (HE) to accelerate a solid rippled Be target quasi-isentropically. The interface between the low-density gaseous HE and the perturbed face of the solid target is Rayleigh-Taylor (RT) unstable. The amplitude of the ripples will grow with time, and the Be strength will mitigate the ripple growth. By measuring and modeling the amplitude growth, we can discriminate among various strength models for Be. Our RT designs extend the pressures up to 50 GPa and the strain-rates to 10 6 s 1 . As a part of the design process, we analyze existing plate impactor and Taylor anvil experiments using available models. We pre...
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We present a set of high explosive driven Rayleigh-Taylor strength experiments for beryllium to produce data to distinguish predictions by various strength models. Design simulations using existing strength model parameterizations from... more
We present a set of high explosive driven Rayleigh-Taylor strength experiments for beryllium to produce data to distinguish predictions by various strength models. Design simulations using existing strength model parameterizations from Steinberg-Lund and Preston-Tonks-Wallace (PTW) suggested an optimal design that would delineate between not just different strength models, but different parameters sets of the PTW model. Application of the models to the post-shot results, however, suggests growth consistent with little material strength. We focus mostly on efforts to simulate the data using published strength models as well as the more recent RING relaxation model developed at VNIIEF. The results of the strength experiments indicate weak influence of strength in mitigating the growth with the RING model coming closest to predicting the material behavior. Finally, we present shock and ramp-loading recovery experiments.
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ABSTRACT We present the results from study of tantalum material strength at high pressures and high strain rates using the Omega laser system. The Ta sample is maintained in the solid state via a quasi-isentropic ramped drive using a... more
ABSTRACT We present the results from study of tantalum material strength at high pressures and high strain rates using the Omega laser system. The Ta sample is maintained in the solid state via a quasi-isentropic ramped drive using a reservoir-gap-sample configuration at high pressures (1 Mbar) and high strain rates (10^6 - 10^8 sec-1). The strength is inferred by measurement of Rayleigh-Taylor induced growth in pre-imposed sinusoidal ripples on a Ta sample [1]. Our study of the samples with single crystal, 0.25, 15 and 90 micron average grain sizes shows that there is no obvious Hall-Petch effect under such extreme conditions. We also show that RT growth is linear as long as the RT growth is below 0.15 of the original sample thickness. We show a comparison of experimental results with the recently developed Livermore Multiscale model that integrates the atomistic scale physics to macro hydro flow simulations. The NIF experimental design will also be presented [4pt] [1] H. S. Park et al., PRL. 104, 135504 (2010).
Constitutive models for material strength are currently being tested at high pressures by comparing 2D simulations with experiments measuring the Rayleigh-Taylor (RT) instability evolution in solid-state samples of vanadium (V), tantalum... more
Constitutive models for material strength are currently being tested at high pressures by comparing 2D simulations with experiments measuring the Rayleigh-Taylor (RT) instability evolution in solid-state samples of vanadium (V), tantalum (Ta), and iron (Fe). The ...