Publications

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.

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

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. Program Summary: Program Title: Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) CPC Library link to program files: https://doi.org/10.17632/cxbxs9btsv.1 Developer's repository link: https://github.com/lammps/lammps Licensing provisions: GPLv2 Programming language: C++, Python, C, Fortran Supplementary material: https://www.lammps.org Nature of problem: Many science applications in physics, chemistry, materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from atomic to mesoscale to macroscopic. Solution method: The LAMMPS code uses parallel spatial decomposition, distributed neighbor lists, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Størmer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addition, LAMMPS supports a wide range of interatomic potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features. Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the LAMMPS code. References: [1] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117 (1995) 1–19. [2] L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard–Jones molecules, Phys. Rev. 159 (1967) 98–103.

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.

A data-driven framework is presented for building magneto-elastic machine-learning interatomic potentials (ML-IAPs) for large-scale spin-lattice dynamics simulations. The magneto-elastic ML-IAPs are constructed by coupling a collective atomic spin model with an ML-IAP. Together they represent a potential energy surface from which the mechanical forces on the atoms and the precession dynamics of the atomic spins are computed. Both the atomic spin model and the ML-IAP are parametrized on data from first-principles calculations. We demonstrate the efficacy of our data-driven framework across magneto-structural phase transitions by generating a magneto-elastic ML-IAP for α-iron. The combined potential energy surface yields excellent agreement with first-principles magneto-elastic calculations and quantitative predictions of diverse materials properties including bulk modulus, magnetization, and specific heat across the ferromagnetic–paramagnetic phase transition.

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We present a numerical modeling workflow based on machine learning 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.

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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, cumulative molecular dynamics (MD) simulations of both high and low energy beryllium deposition in tungsten were performed. 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.

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Atomistic simulations can capture physics of free expansion into two-phase region.

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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.

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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.

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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.

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.

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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.

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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 machine learning IAPs (ML-IAPs) based on four local environment descriptors - atom-centered symmetry functions (ACSF), 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.

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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.

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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.

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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.

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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].

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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.

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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.

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We have recently shown that the final density of silicon under shock compression is anomalously enhanced by introducing voids in the initial uncompressed material. Using molecular simulation, we also demonstrated a molecular mechanism for the effect, which is seen in a growing class of other similar materials. We have shown that this mechanism involves a premature local phase transition nucleated by local shear strain. At higher shock loads we show here that this transition becomes frustrated producing amorphous silicon.We also observe local melting below the equilibrium melt line for bulk silicon. Large-scale non-equilibrium molecular dynamics (NEMD) and Hugoniostat simulations of shock compressed porous silicon are used to study the mechanism. Final stress states and strength were characterized versus initial porosity and for various porosity microstructures.

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 austen- ite 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 tech- niques 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.

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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.

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Scientific impact: The project supports the investigation of energetic materials. This work is providing fundamental insight into initiation mechanisms in energetic materials.

End of year summary including report on project milestones, project productivity, and next steps.

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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.

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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.

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Ammonium nitrate mixed with fuel oil (ANFO) is a commonly used blasting agent. In this paper we investigated the shock properties of pure ammonium nitrate (AN) and two different mixtures of ammonium nitrate and n-dodecane by characterizing their Hugoniot states. We simulated shock compression of pure AN and ANFO mixtures using the Multi-scale Shock Technique, and observed differences in chemical reaction. We also performed a large-scale explicit sub-threshold shock of AN crystal with a 10 nm void filled with 4.4 wt% of n-dodecane. We observed the formation of hotspots and enhanced reactivity at the interface region between AN and n-dodecane molecules.

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The rapidly improving compute capability of contemporary processors and accelerators is providing the opportunity for significant increases in the accuracy and fidelity of scientific calculations. In this paper we present performance studies of a new molecular dynamics (MD) potential called SNAP. The SNAP potential has shown great promise in accurately reproducing physics and chemistry not described by simpler potentials. We have developed new algorithms to exploit high single-node concurrency provided by three different classes of machine: the Titan GPU-based system operated by Oak Ridge National Laboratory, the combined Sequoia and Vulcan BlueGene/Q machines located at Lawrence Livermore National Laboratory, and the large-scale Intel Sandy Bridge system, Chama, located at Sandia. Our analysis focuses on strong scaling experiments with approximately 246,000 atoms over the range 1-122,880 nodes on Sequoia/Vulcan and 40-18,630 nodes on Titan. We compare these machine in terms of both simulation rate and power efficiency. We find that node performance correlates with power consumption across the range of machines, except for the case of extreme strong scaling, where more powerful compute nodes show greater efficiency. This study is a unique assessment of a challenging, scientifically relevant calculation running on several of the world's leading contemporary production supercomputing platforms. © 2014 Springer International Publishing.

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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.

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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.

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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.

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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.

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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.

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Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process, relying on expert physical intuition. To address this problem, a functional programming methodology was developed that may enable automated discovery of entirely new force-field functional forms, while simultaneously fitting parameter values. The method uses a combination of genetic programming, Metropolis Monte Carlo importance sampling and parallel tempering, to efficiently search a large space of candidate functional forms and parameters. The methodology was tested using a nontrivial problem with a well-defined globally optimal solution: a small set of atomic configurations was generated and the energy of each configuration was calculated using the Lennard-Jones pair potential. Starting with a population of random functions, our fully automated, massively parallel implementation of the method reproducibly discovered the original Lennard-Jones pair potential by searching for several hours on 100 processors, sampling only a minuscule portion of the total search space. This result indicates that, with further improvement, the method may be suitable for unsupervised development of more accurate force fields with completely new functional forms. © 2007 Wiley Periodicals, Inc.

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Using molecular dynamics simulations, a constitutive model for the chemical aging of polymer networks was developed. This model incorporates the effects on the stress from the chemical crosslinks and the physical entanglements. The independent network hypothesis has been modified to account for the stress transfer between networks due to crosslinking and scission in strained states. This model was implemented in the finite element code Adagio and validated through comparison with experiment. Stress relaxation data was used to deduce crosslinking history and the resulting history was used to predict permanent set. The permanent set predictions agree quantitatively with experiment.

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Germanium telluride undergoes rapid transition between polycrystalline and amorphous states under either optical or electrical excitation. While the crystalline phases are predicted to be semiconductors, polycrystalline germanium telluride always exhibits p -type metallic conductivity. We present a study of the electronic structure and formation energies of the vacancy and antisite defects in both known crystalline phases. We show that these intrinsic defects determine the nature of free-carrier transport in crystalline germanium telluride. Germanium vacancies require roughly one-third the energy of the other three defects to form, making this by far the most favorable intrinsic defect. While the tellurium antisite and vacancy induce gap states, the germanium counterparts do not. A simple counting argument, reinforced by integration over the density of states, predicts that the germanium vacancy leads to empty states at the top of the valence band, thus giving a complete explanation of the observed p -type metallic conduction.

The Independent Network Model (INM) has proven to be a useful tool for understanding the development of permanent set in strained elastomers. Our previous work showed the applicability of the INM to our simulations of polymer systems crosslinking in strained states. This study looks at the INM applied to theoretical models incorporating entanglement effects, including Flory's constrained junction model and more recent tube models. The effect of entanglements has been treated as a separate network formed at gelation, with additional curing treated as traditional phantom contributions. Theoretical predictions are compared with large-scale molecular dynamics simulations.

Constitutive models for chemically reacting networks are formulated based on a generalization of the independent network hypothesis. These models account for the coupling between chemical reaction and strain histories, and have been tested by comparison with microscopic molecular dynamics simulations. An essential feature of these models is the introduction of stress transfer functions that describe the interdependence between crosslinks formed and broken at various strains. Efforts are underway to implement these constitutive models into the finite element code Adagio. Preliminary results are shown that illustrate the effects of changing crosslinking and scission rates and history.

We performed molecular dynamics simulations of beta-amyloid (A{beta}) protein and A{beta} fragment(31-42) in bulk water and near hydrated lipids to study the mechanism of neurotoxicity associated with the aggregation of the protein. We constructed full atomistic models using Cerius2 and ran simulations using LAMMPS. MD simulations with different conformations and positions of the protein fragment were performed. Thermodynamic properties were compared with previous literature and the results were analyzed. Longer simulations and data analyses based on the free energy profiles along the distance between the protein and the interface are ongoing.

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The goal of this Laboratory Directed Research & Development (LDRD) effort was to design, synthesize, and evaluate organic-inorganic nanocomposite membranes for solubility-based separations, such as the removal of higher hydrocarbons from air streams, using experiment and theory. We synthesized membranes by depositing alkylchlorosilanes on the nanoporous surfaces of alumina substrates, using techniques from the self-assembled monolayer literature to control the microstructure. We measured the permeability of these membranes to different gas species, in order to evaluate their performance in solubility-based separations. Membrane design goals were met by manipulating the pore size, alkyl group size, and alkyl surface density. We employed molecular dynamics simulation to gain further understanding of the relationship between membrane microstructure and separation performance.

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In the LIGA process for manufacturing microcomponents, a polymer film is exposed to an x-ray beam passed through a gold pattern. This is followed by the development stage, in which a selective solvent is used to remove the exposed polymer, reproducing the gold pattern in the polymer film. Development is essentially polymer dissolution, a physical process which is not well understood. We have used coarse-grained molecular dynamics simulation to study the early stage of polymer dissolution. In each simulation a film of non-glassy polymer was brought into contact with a layer of solvent. The mutual penetration of the two phases was tracked as a function of time. Several film thicknesses and two different chain lengths were simulated. In all cases, the penetration process conformed to ideal Fickian diffusion. We did not see the formation of a gel layer or other non-ideal effects. Variations in the Fickian diffusivities appeared to be caused primarily by differences in the bulk polymer film density.

The final report for a Laboratory Directed Research and Development project entitled, Molecular Simulation of Reacting Systems is presented. It describes efforts to incorporate chemical reaction events into the LAMMPS massively parallel molecular dynamics code. This was accomplished using a scheme in which several classes of reactions are allowed to occur in a probabilistic fashion at specified times during the MD simulation. Three classes of reaction were implemented: addition, chain transfer and scission. A fully parallel implementation was achieved using a checkerboarding scheme, which avoids conflicts due to reactions occurring on neighboring processors. The observed chemical evolution is independent of the number of processors used. The code was applied to two test applications: irreversible linear polymerization and thermal degradation chemistry.

We present the results of Molecular Dynamics and Monte Carlo simulations of n-butane and isobutane in silicalite. We begin with a comparison of the bulk adsorption and diffusion properties for two different parameterizations of the interaction potential between the hydrocarbon species, both of which have been shown to reproduce experimental gas-liquid coexistence curves. We examine diffusion as a function of the loading of the zeolite, as well as the temperature dependence of the diffusion constant at loading and for infinite dilution. Both force fields give accurate descriptions of bulk properties. We continue with simulations in which interfaces are formed between single component gases and the zeolite. After reaching equilibrium, we examine the dynamics of exchange between the bulk gas and the zeolite. In particular, we examine the average time spent in the adsorption layer by molecules as they enter the zeolite from the gas in an attempt to probe the microscopic origins of the surface barrier. The microscopic barrier is found to be insignificant for experimental systems. Finally, we calculate the permeability of the zeolite for n-butane and isobutane as a function of pressure. Our results underestimate the experimental results by an order of magnitude, indicating a strong effect from the surface barrier in these simulations. Our simulations are performed for a number of different gas temperatures and pressures, covering a wide range of state points.

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This report summarizes materials issues associated with advanced micromachines development at Sandia. The intent of this report is to provide a perspective on the scope of the issues and suggest future technical directions, with a focus on computational materials science. Materials issues in surface micromachining (SMM), Lithographic-Galvanoformung-Abformung (LIGA: lithography, electrodeposition, and molding), and meso-machining technologies were identified. Each individual issue was assessed in four categories: degree of basic understanding; amount of existing experimental data capability of existing models; and, based on the perspective of component developers, the importance of the issue to be resolved. Three broad requirements for micromachines emerged from this process. They are: (1) tribological behavior, including stiction, friction, wear, and the use of surface treatments to control these, (2) mechanical behavior at microscale, including elasticity, plasticity, and the effect of microstructural features on mechanical strength, and (3) degradation of tribological and mechanical properties in normal (including aging), abnormal and hostile environments. Resolving all the identified critical issues requires a significant cooperative and complementary effort between computational and experimental programs. The breadth of this work is greater than any single program is likely to support. This report should serve as a guide to plan micromachines development at Sandia.