Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.
The properties of electrons in matter are of fundamental importance. They give rise to virtually all material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant gas planets. Modeling and simulation of such diverse applications rely primarily on density functional theory (DFT), which has become the principal method for predicting the electronic structure of matter. While DFT calculations have proven to be very useful, their computational scaling limits them to small systems. We have developed a machine learning framework for predicting the electronic structure on any length scale. It shows up to three orders of magnitude speedup on systems where DFT is tractable and, more importantly, enables predictions on scales where DFT calculations are infeasible. Our work demonstrates how machine learning circumvents a long-standing computational bottleneck and advances materials science to frontiers intractable with any current solutions.
A series of MD and DFT simulations were performed to investigate hydrogen self-clustering and retention in tungsten. Using a newly develop machine learned interatomic potential, spontaneous formation of hydrogen platelets was observed after implanting low-energy hydrogen into tungsten at high fluxes and temperatures. The platelets formed along low miller index orientations and neighboring tetrahedral and octahedral sites and could grow to over 50 atoms in size. High temperatures above 600 K and high hydrogen concentrations were needed to observe significant platelet formation. A critical platelet size of six hydrogen atoms was needed for long term stability. Platelets smaller than this were found to be thermally unstable within a few nanoseconds. To verify these observations, characteristic platelets from the MD simulations were simulated using large-scale DFT. DFT corroborated the MD results in that large platelets were also found to be dynamically stable for five or more hydrogen atoms. The LDOS from the DFT simulated platelets indicated that hydrogen atoms, particularly at the periphery of the platelet, were found to be at least as stable as hydrogen atoms in bulk tungsten. In addition, electrons were found to be localized around hydrogen atoms in the platelet itself and that hydrogen atoms up to 4.2 Å away within the platelet were found to share charge suggesting that the hydrogen atoms are interacting across longer distances than previously suggested. These results reveal a self-clustering mechanisms for hydrogen within tungsten in the absence of radiation induced or microstructural defects that could be a precursor to blistering and potentially explain the experimentally observed high hydrogen retention particularly in the near surface region.
SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.
This paper describes the implementation of the stress-fluctuation technique into the LAMMPS code to compute the anisotropic thermal elastic constants tensor of materials. The implementation provides both methods for computing the analytical fluctuation expressions and also a generic numerical derivative method. The former makes the extension to new potentials straightforward, as it requires writing code only for the second derivatives of each energy term w.r.t. distance, angle, etc. The latter provides a generic interface to compute an accurate approximation of the elastic constants for any potential already implemented in LAMMPS. We show how both methods compare with the direct deformation computation in several test cases and discuss the implementation advantages and limitations.
Here we present a classical molecular-spin dynamics (MSD) methodology that enables accurate computations of the temperature dependence of the magnetocrystalline anisotropy as well as magnetoelastic properties of magnetic materials. The nonmagnetic interactions are accounted for by a spectral neighbor analysis potential (SNAP) machine-learned interatomic potential, whereas the magnetoelastic contributions are accounted for using a combination of an extended Heisenberg Hamiltonian and a Néel pair interaction model, representing both the exchange interaction and spin-orbit-coupling effects, respectively. All magnetoelastic potential components are parameterized using a combination of first-principles and experimental data. Our framework is applied to the α phase of iron. Initial testing of our MSD model is done using a 0 K parametrization of the Néel interaction model. After this, we examine how individual Néel parameters impact the $B$1 and $B$2 magnetostrictive coefficients using a moment-independent δ sensitivity analysis. The results from this study are then used to initialize a genetic algorithm optimization which explores the Néel parameter phase space and tries to minimize the error in the B1 and B2 magnetostrictive coefficients in the range of 0–1200 K. Our results show that while both the 0 K and genetic algorithm optimized parametrization provide good experimental agreement for $B$1 and $B$2, only the genetic algorithm optimized results can capture the second peak in the $B$1 magnetostrictive coefficient which occurs near approximately 800 K.
Tungsten (W) is a material of choice for the divertor material due to its high melting temperature, thermal conductivity, and sputtering threshold. However, W has a very high brittle-to-ductile transition temperature, and at fusion reactor temperatures (≥1000 K), it may undergo recrystallization and grain growth. Dispersion-strengthening W with zirconium carbide (ZrC) can improve ductility and limit grain growth, but much of the effects of the dispersoids on microstructural evolution and thermomechanical properties at high temperatures are still unknown. We present a machine learned Spectral Neighbor Analysis Potential for W-ZrC that can now be used to study these materials. In order to construct a potential suitable for large-scale atomistic simulations at fusion reactor temperatures, it is necessary to train on ab initio data generated for a diverse set of structures, chemical environments, and temperatures. Further accuracy and stability tests of the potential were achieved using objective functions for both material properties and high temperature stability. Validation of lattice parameters, surface energies, bulk moduli, and thermal expansion is confirmed on the optimized potential. Tensile tests of W/ZrC bicrystals show that although the W(110)-ZrC(111) C-terminated bicrystal has the highest ultimate tensile strength (UTS) at room temperature, observed strength decreases with increasing temperature. At 2500 K, the terminating C layer diffuses into the W, resulting in a weaker W-Zr interface. Meanwhile, the W(110)-ZrC(111) Zr-terminated bicrystal has the highest UTS at 2500 K.
Advances in machine learning (ML) have enabled the development of interatomic potentials that promise the accuracy of first principles methods and the low-cost, parallel efficiency of empirical potentials. However, ML-based potentials struggle to achieve transferability, i.e., provide consistent accuracy across configurations that differ from those used during training. In order to realize the promise of ML-based potentials, systematic and scalable approaches to generate diverse training sets need to be developed. This work creates a diverse training set for tungsten in an automated manner using an entropy optimization approach. Subsequently, multiple polynomial and neural network potentials are trained on the entropy-optimized dataset. A corresponding set of potentials are trained on an expert-curated dataset for tungsten for comparison. The models trained to the entropy-optimized data exhibited superior transferability compared to the expert-curated models. Furthermore, the models trained to the expert-curated set exhibited a significant decrease in performance when evaluated on out-of-sample configurations.
The long-standing problem of predicting the electronic structure of matter on ultra-large scales (beyond 100,000 atoms) is solved with machine learning.
The focus of this project is to accelerate and transform the workflow of multiscale materials modeling by developing an integrated toolchain seamlessly combining DFT, SNAP, LAMMPS, (shown in Figure 1-1) and a machine-learning (ML) model that will more efficiently extract information from a smaller set of first-principles calculations. Our ML model enables us to accelerate first-principles data generation by interpolating existing high fidelity data, and extend the simulation scale by extrapolating high fidelity data (102 atoms) to the mesoscale (104 atoms). It encodes the underlying physics of atomic interactions on the microscopic scale by adapting a variety of ML techniques such as deep neural networks (DNNs), and graph neural networks (GNNs). We developed a new surrogate model for density functional theory using deep neural networks. The developed ML surrogate is demonstrated in a workflow to generate accurate band energies, total energies, and density of the 298K and 933K Aluminum systems. Furthermore, the models can be used to predict the quantities of interest for systems with more number of atoms than the training data set. We have demonstrated that the ML model can be used to compute the quantities of interest for systems with 100,000 Al atoms. When compared with 2000 Al system the new surrogate model is as accurate as DFT, but three orders of magnitude faster. We also explored optimal experimental design techniques to choose the training data and novel Graph Neural Networks to train on smaller data sets. These are promising methods that need to be explored in the future.
Multi-phase problems have so many more unknowns, we’d like to have a tool to constrain some open questions related to microstructure and twin & dislocation behavior. We want an atomistic scale perspective on aspects of strength. Some multi-scale questions accessible to atomistic study: What lattice-specific behavior influences dislocation production/mobility and/or twinning? Do the phase transformations wipe-out, modify or preserve grain size and orientation? Does plastic strain reset at phase transition? If so under what conditions? Tin is the material chosen for the effort because it is non-hazardous and has multiple accessible solid phases at relatively low pressures.
The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.
Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials.
We present a numerical modeling workflow based on machine learning (ML) which reproduces the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.
Erosion of the beryllium first wall material in tokamak reactors has been shown to result in transport and deposition on the tungsten divertor. Experimental studies of beryllium implantation in tungsten indicate that mixed W–Be intermetallic deposits can form, which have lower melting temperatures than tungsten and can trap tritium at higher rates. To better understand the formation and growth rate of these intermetallics, we performed cumulative molecular dynamics (MD) simulations of both high and low energy beryllium deposition in tungsten. In both cases, a W–Be mixed material layer (MML) emerged at the surface within several nanoseconds, either through energetic implantation or a thermally-activated exchange mechanism, respectively. While some ordering of the material into intermetallics occurred, fully ordered structures did not emerge from the deposition simulations. Targeted MD simulations of the MML to further study the rate of Be diffusion and intermetallic growth rates indicate that for both cases, the gradual re-structuring of the material into an ordered intermetallic layer is beyond accessible MD time scales(≤1 μs). However, the rapid formation of the MML within nanoseconds indicates that beryllium deposition can influence other plasma species interactions at the surface and begin to alter the tungsten material properties. Therefore, beryllium deposition on the divertor surface, even in small amounts, is likely to cause significant changes in plasma-surface interactions and will need to be considered in future studies.
The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.
This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.
One of the most severe obstacles to increasing the longevity of tungsten-based plasma facing components, such as divertor tiles, is the surface deterioration driven by sub-surface helium bubble formation and rupture. Supported by experimental observations at PISCES, this work uses molecular dynamics simulations to identify the microscopic mechanisms underlying suppression of helium bubble formation by the introduction of plasma-borne beryllium. Simulations of the initial surface material (crystalline W), early-time Be exposure (amorphous W-Be) and final WBe2 intermetallic surfaces were used to highlight the effect of Be. Significant differences in He retention, depth distribution and cluster size were observed in the cases with beryllium present. Helium resided much closer to the surface in the Be cases with nearly 80% of the total helium inventory located within the first 2 nm. Moreover, coarsening of the He depth profile due to bubble formation is suppressed due to a one-hundred fold decrease in He mobility in WBe2, relative to crystalline W. This is further evidenced by the drastic reduction in He cluster sizes even when it was observed that both the amorphous W-Be and WBe2 intermetallic phases retain nearly twice as much He during cumulative implantation studies.
Here, we describe recent efforts to improve our predictive modeling of rate-dependent behavior at, or near, a phase transition using molecular dynamics simulations. Cadmium sulfide (CdS) is a well-studied material that undergoes a solid-solid phase transition from wurtzite to rock salt structures between 3 and 9 GPa. Atomistic simulations are used to investigate the dominant transition mechanisms as a function of orientation, size and rate. We found that the final rock salt orientations were determined relative to the initial wurtzite orientation, and that these orientations were different for the two orientations and two pressure regimes studied. The CdS solid-solid phase transition is studied, for both a bulk single crystal and for polymer-encapsulated spherical nanoparticles of various sizes.
We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.
In this project, we investigate the use of neural networks for the prediction of molecular properties, namely the interatomic potential. We use the machine learning package Tensorflow to build a variety of neural networks and compare performance with a popular Fortran package - Atomic Energy Networks (aenet). There are two primary goals for this work: 1) use the wide availability of different optimization techniques in Tensorflow to outperform aenet and 2) use new descriptors that can outperform Behler descriptors.
We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the posterior variance of the MFGP, our framework naturally enables uncertainty quantification, providing estimates of confidence in the predictions. We used density functional theory as high-fidelity prediction, while a ML interatomic potential is used as low-fidelity prediction. Practical materials' design efficiency is demonstrated by reproducing the ternary composition dependence of a quantity of interest (bulk modulus) across the full aluminum-niobium-titanium ternary random alloy composition space. The MFGP is then coupled to a Bayesian optimization procedure, and the computational efficiency of this approach is demonstrated by performing an on-the-fly search for the global optimum of bulk modulus in the ternary composition space. The framework presented in this manuscript is the first application of MFGP to atomistic materials simulations fusing predictions between density functional theory and classical interatomic potential calculations.
Machine learning models, trained on data from ab initio quantum simulations, are yielding molecular dynamics potentials with unprecedented accuracy. One limiting factor is the quantity of available training data, which can be expensive to obtain. A quantum simulation often provides all atomic forces, in addition to the total energy of the system. These forces provide much more information than the energy alone. It may appear that training a model to this large quantity of force data would introduce significant computational costs. Actually, training to all available force data should only be a few times more expensive than training to energies alone. Here, we present a new algorithm for efficient force training, and benchmark its accuracy by training to forces from real-world datasets for organic chemistry and bulk aluminum.
Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of ML-IAPs based on four local environment descriptors --- Behler-Parrinello symmetry functions, smooth overlap of atomic positions (SOAP), the Spectral Neighbor Analysis Potential (SNAP) bispectrum components, and moment tensors --- using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model, and consequently computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications.
The central approximation made in classical molecular dynamics simulation of materials is the interatomic potential used to calculate the forces on the atoms. Great effort and ingenuity is required to construct viable functional forms and find accurate parametrizations for potentials using traditional approaches. Machine learning has emerged as an effective alternative approach to develop accurate and robust interatomic potentials. Starting with a very general model form, the potential is learned directly from a database of electronic structure calculations and therefore can be viewed as a multiscale link between quantum and classical atomistic simulations. Risk of inaccurate extrapolation exists outside the narrow range of time and length scales where the two methods can be directly compared. In this work, we use the spectral neighbor analysis potential (SNAP) and show how a fit can be produced with minimal interpolation errors which is also robust in extrapolating beyond training. To demonstrate the method, we have developed a tungsten-beryllium potential suitable for the full range of binary compositions. Subsequently, large-scale molecular dynamics simulations were performed of high energy Be atom implantation onto the (001) surface of solid tungsten. The machine learned W-Be potential generates a population of implantation structures consistent with quantum calculations of defect formation energies. A very shallow (<2nm) average Be implantation depth is predicted which may explain ITER diverter degradation in the presence of beryllium.
Simulating energetic materials with complex microstructure is a grand challenge, where until recently, an inherent gap in computational capabilities had existed in modelling grain-scale effects at the microscale. We have enabled a critical capability in modelling the multiscale nature of the energy release and propagation mechanisms in advanced energetic materials by implementing, in the widely used LAMMPS molecular dynamics (MD) package, several novel coarse-graining techniques that also treat chemical reactivity. Our innovative algorithmic developments rooted within the dissipative particle dynamics framework, along with performance optimisations and application of acceleration technologies, have enabled extensions in both the length and time scales far beyond those ever realised by atomistic reactive MD simulations. In this paper, we demonstrate these advances by modelling a shockwave propagating through a microstructured material and comparing performance with the state-of-the-art in atomistic reactive MD techniques. As a result of this work, unparalleled explorations in energetic materials research are now possible.
The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is proposed that includes quadratic terms in the bispectrum components. The extension is shown to provide a large increase in accuracy relative to the linear form, while incurring only a modest increase in computational cost. The mathematical structure of the quadratic SNAP form is similar to the embedded atom method (EAM), with the SNAP bispectrum components serving as counterparts to the two-body density functions in EAM. The effectiveness of the new form is demonstrated using an extensive set of training data for tantalum structures. Similar to artificial neural network potentials, the quadratic SNAP form requires substantially more training data in order to prevent overfitting. The quality of this new potential form is measured through a robust cross-validation analysis.
Shock wave interactions with defects, such as pores, are known to play a key role in the chemical initiation of energetic materials. The shock response of hexanitrostilbene is studied through a combination of large-scale reactive molecular dynamics and mesoscale hydrodynamic simulations. In order to extend our simulation capability at the mesoscale to include weak shock conditions (<6 GPa), atomistic simulations of pore collapse are used to define a strain-rate-dependent strength model. Comparing these simulation methods allows us to impose physically reasonable constraints on the mesoscale model parameters. In doing so, we have been able to study shock waves interacting with pores as a function of this viscoplastic material response. We find that the pore collapse behavior of weak shocks is characteristically different than that of strong shocks.
Within the EXAALT project, the SNAP [1] approach is being used to develop high accuracy potentials for use in large-scale long-time molecular dynamics simulations of materials behavior. In particular, we have developed a new SNAP potential that is suitable for describing the interplay between helium atoms and vacancies in high-temperature tungsten[2]. This model is now being used to study plasma-surface interactions in nuclear fusion reactors for energy production. The high-accuracy of SNAP potentials comes at the price of increased computational cost per atom and increased computational complexity. The increased cost is mitigated by improvements in strong scaling that can be achieved using advanced algorithms [3].
LAMMPS is a classical molecular dynamics code (lammps.sandia.gov) used to model materials science problems at Sandia National Laboratories and around the world. LAMMPS was one of three Sandia codes selected to participate in the Trinity KNL (TR2) Open Science period. During this period, three different problems of interest were investigated using LAMMPS. The first was benchmarking KNL performance using different force field models. The second was simulating void collapse in shocked HNS energetic material using an all-atom model. The third was simulating shock propagation through poly-crystalline RDX energetic material using a coarse-grain model, the results of which were used in an ACM Gordon Bell Prize submission. This report describes the results of these simulations, lessons learned, and some hardware issues found on Trinity KNL as part of this work.
The purpose of this short contribution is to report on the development of a Spectral Neighbor Analysis Potential (SNAP) for tungsten. We have focused on the characterization of elastic and defect properties of the pure material in order to support molecular dynamics simulations of plasma-facing materials in fusion reactors. A parallel genetic algorithm approach was used to efficiently search for fitting parameters optimized against a large number of objective functions. In addition, we have shown that this many-body tungsten potential can be used in conjunction with a simple helium pair potential1 to produce accurate defect formation energies for the W-He binary system.
We establish an atomistic view of the high- and low-temperature phases of iron/steel as well as some elements of the phase transition between these phases on cooling. In particular we examine the 4 most common orientation relationships between the high temperature austenite and low-temperature ferrite phases seen in experiment. With a thorough understanding of these relationships we are prepared to set up various atomistic simulations, using techniques such as Density Functional Theory and Molecular Dynamics, to further study the phase transition, in particular, quantities needed for Phase Field Modeling, such as the free energies of bulk phases and the phase transition front propagation velocity.
This report summarizes the result of LDRD project 16-0161, titled "Coarse-Grained Re- active Molecular Dynamics Simulations of Heterogeneities in Shocked Energetic Materials." The purpose of the project was to develop a coarse-grained reactive molecular dynamics capability in LAMMPS enabling simulations of initiation in energetic materials comparable in accuracy to what is currently possible using large-scale reactive molecular dynamics, but with greatly reduced computational cost. The starting point for this work was the reactive dissipative particle dynamics (DPD) approach, which has been implemented as the new USER-DPD package in LAMMPS by researchers at Army Research Laboratory. Using modified versions of the examples provided with the new package, we examined the computational efficiency of the method, as well as its ability to model energy release in energetic materials. We observed that the Shardlow splitting method provides a great speed and accuracy advantage over conventional velocity Verlet time integration. We observed that the generic model of an energetic material provided with the USER-DPD package exhibited incomplete reaction under constant volume conditions. This was caused by quenching of the internal temperature of the molecules due to a rapid build-up of repulsive interactions between product gas components under constant volume conditions. Under constant pressure conditions, complete reaction was observed, as volume expansion prevented the buildup of strong repulsive interactions. Finally, a more realistic model calibrated to reproduce the equation of state of the RDX molecular crystal was examined. This model exhibited much less quenching of the internal temperature under constant volume conditions and reacted very rapidly under constant pressure conditions.
In both continuum hydrodynamics simulations and also multimillion atom reactive molecular dynamics simulations of shockwave propagation in single crystal pentaerythritol tetranitrate (PETN) containing a cylindrical void, we observed the formation of an initial radially symmetric hot spot. By extending the simulation time to the nanosecond scale, however, we observed the transformation of the small symmetric hot spot into a longitudinally asymmetric hot region extending over a much larger volume. Performing reactive molecular dynamics shock simulations using the reactive force field (ReaxFF) as implemented in the LAMMPS molecular dynamics package, we showed that the longitudinally asymmetric hot region was formed by coalescence of the primary radially symmetric hot spot with a secondary triangular hot zone. We showed that the triangular hot zone coincided with a double-shocked region where the primary planar shockwave was overtaken by a secondary cylindrical shockwave. The secondary cylindrical shockwave originated in void collapse after the primary planar shockwave had passed over the void. A similar phenomenon was observed in continuum hydrodynamics shock simulations using the CTH hydrodynamics package. The formation and growth of extended asymmetric hot regions on nanosecond timescales has important implications for shock initiation thresholds in energetic materials.
Scientific impact: The project supports the investigation of energetic materials. This work is providing fundamental insight into initiation mechanisms in energetic materials.
We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.
The purpose of this work is to understand how defects control initiation in energetic materials used in stockpile components; Sequoia gives us the core-count to run very large-scale simulations of up to 10 million atoms and; Using an OpenMP threaded implementation of the ReaxFF package in LAMMPS, we have been able to get good parallel efficiency running on 16k nodes of Sequoia, with 1 hardware thread per core.
Building the next-generation of extreme-scale distributed systems will require overcoming several challenges related to system resilience. As the number of processors in these systems grow, the failure rate increases proportionally. One of the most common sources of failure in large-scale systems is memory. In this paper, we propose a novel runtime for transparently exploiting memory content similarity to improve system resilience by reducing the rate at which memory errors lead to node failure. We evaluate the viability of this approach by examining memory snapshots collected from eight high-performance computing (HPC) applications and two important HPC operating systems. Based on the characteristics of the similarity uncovered, we conclude that our proposed approach shows promise for addressing system resilience in large-scale systems.
Under shock compression, most porous materials exhibit lower densities for a given pressure than that of a full-dense sample of the same material. However, some porous materials exhibit an anomalous, or enhanced, densification under shock compression. We demonstrate a molecular mechanism that drives this behavior. We also present evidence from atomistic simulation that silicon belongs to this anomalous class of materials. Atomistic simulations indicate that local shear strain in the neighborhood of collapsing pores nucleates a local solid-solid phase transformation even when bulk pressures are below the thermodynamic phase transformation pressure. This metastable, local, and partial, solid-solid phase transformation, which accounts for the enhanced densification in silicon, is driven by the local stress state near the void, not equilibrium thermodynamics. This mechanism may also explain the phenomenon in other covalently bonded materials.
This report summarizes the result of LDRD project 12-0395, titled "Automated Algorithms for Quantum-level Accuracy in Atomistic Simulations." During the course of this LDRD, we have developed an interatomic potential for solids and liquids called Spectral Neighbor Analysis Poten- tial (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected on to a basis of hyperspherical harmonics in four dimensions. The SNAP coef- ficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. Global optimization methods in the DAKOTA software package are used to seek out good choices of hyperparameters that define the overall structure of the SNAP potential. FitSnap.py, a Python-based software pack- age interfacing to both LAMMPS and DAKOTA is used to formulate the linear regression problem, solve it, and analyze the accuracy of the resultant SNAP potential. We describe a SNAP potential for tantalum that accurately reproduces a variety of solid and liquid properties. Most significantly, in contrast to existing tantalum potentials, SNAP correctly predicts the Peierls barrier for screw dislocation motion. We also present results from SNAP potentials generated for indium phosphide (InP) and silica (SiO 2 ). We describe efficient algorithms for calculating SNAP forces and energies in molecular dynamics simulations using massively parallel computers and advanced processor ar- chitectures. Finally, we briefly describe the MSM method for efficient calculation of electrostatic interactions on massively parallel computers.
Density-functional theory calculations, ab-initio molecular dynamics, and the Kubo-Greenwood formula are applied to predict electrical conductivity in Ta2Ox (0 x 5) as a function of composition, phase, and temperature, where additional focus is given to various oxidation states of the O monovacancy (VOn; n=0,1+,2+). Our calculations of DC conductivity at 300K agree well with experimental measurements taken on Ta2Ox thin films and bulk Ta2O5 powder-sintered pellets, although simulation accuracy can be improved for the most insulating, stoichiometric compositions. Our conductivity calculations and further interrogation of the O-deficient Ta2O5 electronic structure provide further theoretical basis to substantiate VO0 as a donor dopant in Ta2O5 and other metal oxides. Furthermore, this dopant-like behavior appears specific to neutral VO cases in both Ta2O5 and TiO2 and was not observed in other oxidation states. This suggests that reduction and oxidation reactions may effectively act as donor activation and deactivation mechanisms, respectively, for VO0 in transition metal oxides.
Molecular dynamics simulation (MD) is an invaluable tool for studying problems sensitive to atomscale physics such as structural transitions, discontinuous interfaces, non-equilibrium dynamics, and elastic-plastic deformation. In order to apply this method to modeling of ramp-compression experiments, several challenges must be overcome: accuracy of interatomic potentials, length- and time-scales, and extraction of continuum quantities. We have completed a 3 year LDRD project with the goal of developing molecular dynamics simulation capabilities for modeling the response of materials to ramp compression. The techniques we have developed fall in to three categories (i) molecular dynamics methods (ii) interatomic potentials (iii) calculation of continuum variables. Highlights include the development of an accurate interatomic potential describing shock-melting of Beryllium, a scaling technique for modeling slow ramp compression experiments using fast ramp MD simulations, and a technique for extracting plastic strain from MD simulations. All of these methods have been implemented in Sandia's LAMMPS MD code, ensuring their widespread availability to dynamic materials research at Sandia and elsewhere.
Many of the most important and hardest-to-solve problems related to the synthesis, performance, and aging of materials involve diffusion through the material or along surfaces and interfaces. These diffusion processes are driven by motions at the atomic scale, but traditional atomistic simulation methods such as molecular dynamics are limited to very short timescales on the order of the atomic vibration period (less than a picosecond), while macroscale diffusion takes place over timescales many orders of magnitude larger. We have completed an LDRD project with the goal of developing and implementing new simulation tools to overcome this timescale problem. In particular, we have focused on two main classes of methods: accelerated molecular dynamics methods that seek to extend the timescale attainable in atomistic simulations, and so-called 'equation-free' methods that combine a fine scale atomistic description of a system with a slower, coarse scale description in order to project the system forward over long times.
We implemented two numerical simulation capabilities essential to reliably predicting the effect of non-ideal explosives (NXs). To begin to be able to treat the multiple, competing, multi-step reaction paths and slower kinetics of NXs, Sandia's CTH shock physics code was extended to include the TIGER thermochemical equilibrium solver as an in-line routine. To facilitate efficient exploration of reaction pathways that need to be identified for the CTH simulations, we implemented in Sandia's LAMMPS molecular dynamics code the MSST method, which is a reactive molecular dynamics technique for simulating steady shock wave response. Our preliminary demonstrations of these two capabilities serve several purposes: (i) they demonstrate proof-of-principle for our approach; (ii) they provide illustration of the applicability of the new functionality; and (iii) they begin to characterize the use of the new functionality and identify where improvements will be needed for the ultimate capability to meet national security needs. Next steps are discussed.
The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.