Session B25: Focus Session: Simulation of Matter at Extreme Conditions - Shock-Induced Chemistry

Extending DFT to Long Time-Scales: Using the Density Functional Tight Binding Approach for Materials Under Extreme Temperatures and Pressures

We report here on density functional tight binding (DFTB) simulations of covalently bonded materials over a pressure range of 10 -- 2,000 GPa and a temperature range of 300 -- 30,000 K using both standard and new interaction potentials we have created for these conditions. Density Functional Theory (DFT) has been shown to accurately reproduce the high pressure-temperature chemistry, phase boundaries, and EOS of many materials. DFT-MD simulations, though, scale poorly with computational effort and thus are generally limited to nanometer system sizes and picosecond time-scales. In contrast, chemical kinetic effects and phase changes can span up to nanosecond timescales and significantly longer length scales. The DFTB method holds promise as a high throughput simulation capability by providing orders of magnitude increase in computational efficiency while retaining most of the accuracy of Kohn-Sham DFT. We show that DFTB interaction potentials can be created by (a) fitting the DFTB repulsive energy to measured and computed compression data, and (b) using an extended basis set that includes $d$-orbital interactions, as needed. Our new potential for carbon yields accurate material properties for diamond, graphite, the BC8 phase, and simple cubic carbon, as well as for the shock Hugoniot of diamond compressed up to the conducting liquid. We also discuss simulations of the long-time scale reactivity of H$_{2}$O$_{2}$ under detonation conditions, and shock compression of astrophysical ice mixtures and the subsequent synthesis of pre-biotic materials. Our results provide a straightforward method by which DFTB can be made to provide equation of state and long-time scale chemical kinetic data at a similar accuracy to standard quantum codes. Our approach could be extended to any number of materials related to geology and planetary science, including silicon, SiO$_{2}$, and hydrocarbon systems.   

Pressure-induced Polymerization in Substituted Acetylenes

A fundamental understanding of shock-induced chemical reactions in organics is still lacking and there are limited studies devoted to determining reaction mechanisms, evolution of bonding, and effect of functional group substitutions. The fast timescale of reactions occurring during shock compression create significant experimental challenges (diagnostics) to fully quantify the mechanisms involved. Static compression provides a complementary route to investigate the equilibrium phase space and metastable intermediates during high pressure chemistry, although at a much slower timescale. In this study, we present our results from our ongoing high pressure in situ synchrotron x-ray diffraction and vibrational spectroscopy experiments on substituted acetylenes: tert-butyl acetylene [TBA: (CH3)3-C$\equiv $CH] and ethynyl trimethylsilane [ETMS: (CH3)3-SiC$\equiv $CH]. We observed that the onset pressure of chemical reactions (at room temperature) in these compounds is significantly higher in static compression (TBA: 11 GPa and ETMS: 26 GPa) when compared to shock input pressures (TBA: 6.1 GPa and ETMS: 6.6 GPa). The products were polymeric in nature, recovered to ambient conditions with little degradation and fully characterized using spectroscopy, calorimetry, and other techniques to identify reaction mechanisms.   

Non-equilibrium Molecular Dynamics Studies of Interfacial Chemistry in Shocked Ni/Al Nanolaminates

The response of Ni/Al composite materials to shock loading has been studied using non-equilibrium molecular dynamics and an EAM force field. The simulation cells consist of layered Ni and Al laminates with at least 3 million particles in a 1:1 mole ratio. The main thrust of our research is to gain a better understanding of the chemistry that occurs at the Ni/Al interface when the real material is shocked. Initial geometries were chosen so as to identify the factors important to reaction in the complex macro-scale material. Specifically, we vary the orientation of the interface with respect to the shock wave and the geometry of the interface ($i.e.$, deviation from planarity) to study how mixing and reactivity of Ni and Al are affected. Our results show a clear dependence of pressure and temperature on interface orientation, in agreement with continuum-scale simulations.   

Near-Equivalency of Inter and Intramolecular Hydrogen Bonding Under High-Pressure

Triamino-trinitro-benzene (TATB, C$_{6}$H$_{6}$N$_{6}$O$_{6})$ exhibits unusually strong intramolecular hydrogen bonding as evidenced by the high rotational energy barrier of the nitro and amino groups. In the condensed phase, the competing intermolecular hydrogen bonding becomes pronounced at high-pressure in its graphitic-like crystal structure. We report density functional theoretical calculations of the equation of state of TATB under hydrostatic compression of up to 250 GPa. Our results show Our results show increasing bond equivalency between the intramolecular and intermolecular hydrogen bonds of the amino and nitro groups in the region 30$<$P$<$70 GPa, beyond which the difference between the two bond distances remains constant. This approximate bond equivalency is manifested by a rapid decrease of the intermolecular -NO---HN- distance along the b lattice direction from 2.6 {\AA} at the zero pressure equilibrium geometry to 1.72 {\AA} at 67 GPa, and by a decrease of the intramolecular -NO---HN- bond from 1.65 {\AA} to 1.57 {\AA} for the same pressure region. It is expected that vibrational motions involving the NO---HN modes are sensitive to the nearly equivalent hydrogen bonding, as recent spectroscopic IR analysis of the NH$_{2}$ stretches revealed.   

Modeling of electron-ion coupling in shocked materials

This work describes and implements a quasi-statistical approach to electron-ion coupling in shocked matter. By combining this approach with the multi-scale shock technique (MSST) and a tight-binding model, the magnitude and role of electronic excitations in shocked energetic materials are studied theoretically using quantum molecular dynamics simulations. Focusing on the detonating primary explosive HN3 (hydrazoic acid), this work finds that the material transiently exhibits a high level of electronic excitation characterized by carrier densities in excess of 10$^{21}$ cm$^{-3}$, or one electronic excitation for every 8 molecules. Electronic excitations enhance the kinetics of chemical decomposition by about 30\%. The electronic heat capacity has a minor impact on the temperatures exhibited, on the order of 100 K.   

Quantum-based Molecular Dynamics Simulations of Shock-induced Reactions with Time-resolved Raman Spectra

Shock-induced reactions in liquid hydrocarbons have been studied using quantum-based, self-consistent tight-binding (SC-TB) molecular dynamics simulations with an accurate and transferable model for interatomic bonding. Our SC-TB code LATTE enables explicit simulations of shock compression using the universal liquid Hugoniot. Furthermore, the effects of adiabatic shock heating are captured precisely using Niklasson's energy conserving extended Lagrangian Born-Oppenheimer Molecular Dynamics formalism. We have been able to perform relatively large-scale SC-TB simulations by either taking advantage of the sparsity of the density matrix to achieve $O(N)$ performance or by using graphics processing units to accelerate $O(N^3)$ algorithms. We have developed the capability for the on-the-fly computation of Raman spectra from the Fourier transform of the polarizability autocorrelation function via the density matrix perturbation theory of Niklasson and Challacombe. These time-resolved Raman spectra enable us compare the results of our simulations with identical diagnostics collected experimentally. We will illustrate these capabilities with a series of simulations of shock-induced reaction paths in a number of simple molecules.   

Molecular Simulation of Shock Hugoniot for Polymers

The behavior of polymers under extreme conditions (high pressure and temperature) is of interest for a variety of applications, such as polymer-bonded explosives, coatings, adhesives, and light-weight armor. Material properties and response at extreme conditions can be determined through shock experiments, which are often difficult to measure experimentally because of difficulties in traversing a large range of pressures (up to hundreds of gigapascals) and temperatures (thousands of kelvin) with available instrumentation. In addition, interesting behavior, such as observed behind a shock front, occurs at extremely short time- and length-scales (nanoscale), which poses problems in characterizing the material using current experimental capabilities. To further understand shocked systems, simulation methods such as molecular dynamics (MD) and quantum mechanics (QM) can be used to provide insight into atomic-level phenomena. Using classical MD and QM, we have calculated the principle shock Hugoniot curves for four polymers: poly[methyl methacrylate], poly[ethylene], poly[styrene], and hydroxyl-terminated poly[butadiene]. In the MD calculations, we considered both a non-reactive (i.e. PCFF) and reactive (i.e. ReaxFF) forcefield, respectively, where calculations were performed in LAMMPS. The QM calculations were performed with density functional theory (DFT) using dispersion corrections as implemented in CP2K. We have applied both atom centered pseudopotentials (DCACPs) and Grimme van der Waals corrections in our study. Overall, results obtained by QM show much better agreement with available experimental data for the range of up to 20 GPa than classical force fields. At pressures where reactions can occur the short simulation time available in MD modeling prevents us from fully exploring possible reaction pathways.   

Amorphous Polymeric Nitrogen from Dynamic Shock Simulation

In recent years there has been significant interest in polymeric phases of nitrogen at low pressure for potential application as an energetic material. This interest was bolstered by experimental evidence of metastable amorphous polymeric nitrogen at low pressure.\footnote{Goncharov, A. F. {\it et al}., Phys. Rev. Lett. {\bf 85}, 1262 (2000)}$^,$\footnote{Eremets, M. I. {\it et al}., Nature {\bf 411}, 170 (2001)} While considerable theoretical work has been done on many crystal phases of nitrogen, simulating amorphous polymeric nitrogen has been more challenging. Starting from first principles dynamic shock simulation of cubic-gauche nitrogen\footnote{Mattson, William D. and Balu, Radhakrishnan, Phys. Rev. B {\bf 83}, 174105 (2011)} we demonstrate a form of polymeric nitrogen at low pressure that may be directly related to amorphous polymeric nitrogen.   

Ethane and Xenon mixing: density functional theory (DFT) simulations and experiments on Sandia's Z machine

The combination of ethane and xenon is one of the simplest binary mixtures in which bond breaking is expected to play a role under shock conditions. At cryogenic conditions, xenon is often understood to mix with alkanes such as Ethane as if it were also an alkane, but this model is expected to break down at higher temperatures and pressures. To investigate the breakdown, we have performed density functional theory (DFT) calculations on several xenon/ethane mixtures. Additionally, we have performed shock compression experiments on Xenon-Ethane using the Sandia Z - accelerator. The DFT and experimental results are compared to hydrodynamic simulations using different mixing models in the equation of state. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of the Lockheed Martin company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Dynamic Response of a Carbon Fiber -- Epoxy Composite

The dynamic response of carbon fiber reinforced epoxy composite materials was investigated under planar impact loading. The samples were unidirectional (all carbon fibers oriented in a single direction) with fiber fill volumes from 62 to 68\%. Gun driven planar impact tests with impact velocities of 0.1-2.0 km/s were conducted allowing samples to be compressed up to about 15 GPa. Velocity interferometry was used to measure particle velocities from which the compressed state of the samples was determined. Wave speeds for shocks traveling along the carbon fibers are significantly higher than for those traveling transverse to the fibers or through the bulk epoxy. As a result, the dynamic material response is dependent on the relative shock - fiber orientation. Shocks traveling along the fiber direction exhibit both elastic and plastic characteristics over the stress range tested. Shocks traveling transverse to the fibers show only a single wave response similar to but slightly stiffer than the bulk response of the epoxy. Results will be presented detailing these findings which provide a basis for modeling this class of directional composite materials.   

Calculation of Transport Coefficients in Binary Yukawa Mixtures

We employ classical molecular dynamics (MD) to estimate species diffusivity and viscosity in binary Yukawa Mixtures. The Yukawa potential is used to describe the screened Coulomb interaction between the ions, providing the basis for models of dense stellar materials, inertial confined plasmas, and colloidal particles in electrolytes. We calculate transport coefficients in equilibrium simulations using the Green-Kubo relation over a range of thermodynamic conditions including the viscosity and the self-diffusivity for each component of the mixture. The inter-diffusivity (or mutual diffusivity) can then be related to the self-diffusivities by using a generalization of the Darken equation. We have also employed non-equilibrium MD to estimate inter-diffusivity during the broadening of the interface between two regions each with a high concentration of either species. The main motivation in this work is to build a model that describes the transport coefficients in binary Yukawa mixtures over a broad range of thermodynamic conditions.   

Fracture of Constructional Materials with the Covering at Shock-Wave Loadings

The behavior of constructional materials with a covering subjected to shock load is numerically modeled. The covering on a material is applied by the method of high velocity oxygen fuel. The materials created by a similar method, are widely applied in aerospace branch, both for creation of engines and for creation of details of cases. Possibility of application of multilayered coverings essentially expands the spectrum of researches for the analysis of separate layer influence on behavior of a design as a whole. Features of behavior of this sort of materials is an actual problem as well as construction of authentic models of behavior of materials with coverings as a whole. Influence of a material of a covering, quantity of layers and their geometrical parameters on fracture and shock-wave processes in a material is investigated. The range of velocities of interaction from 50 to 2000m/sec is considered. As projectiles steel cylinders and spheres were used.