Session X02: Theory and Simulations of Materials at Extreme Conditions

Modeling and experimental studies of neat and metal-doped stishovite, coesite, and quartz under high pressure.

The results of a comparative study of neat and doped silicon dioxide polymorphs (Fe, Ni or Cu) obtained by density functional theory (DFT) at 0 K and at ambient pressure, 10 GPa, and 20 GPa are presented. The metal atoms are introduced at substitutional and octahedral interstitial sites of the crystal, and the relaxed structures are analyzed and ranked according to total energy. Changes in the enthalpy of the neat and doped crystals are estimated at selected temperatures using quantum mechanics molecular dynamics (DFT-MD). We report the modeled enthalpy of the neat and doped crystals, as well as the dependency of the unit-cell parameters, band gaps, and Raman-active modes on pressure, and compare some of these results to those obtained experimentally using a diamond anvil cell. In addition, we present our search results of the high-pressure phases of silicon dioxide using DFT-based evolutionary simulations and report on the stability of the silica phases, as evaluated by convex-hull construction.   

Dynamics of the High-Pressure Phase Transition in 2,4,6-triamino-1,3,5-trinitrobenzene (TATB)

Understanding the sensitivity and performance of energetic materials (EMs) requires information on how they respond under extreme conditions. TATB is an insensitive crystalline EM with graphitic-like layers and a resilient 2D intermolecular hydrogen bonded network. Recent static compression diamond anvil cell experiments combined with first-principles calculations found evidence it undergoes a high-pressure phase transition that involves sliding of its graphitic layers. Layer sliding alters the stacking motif and leads to a transition from a triclinic to monoclinic unit cell. In this work, the dynamics of the phase transition under pressure are investigated using density functional theory and a classical force field. Assessments of the thermodynamic drivers and kinetic barriers for the transition are discussed.   

Pseudopotentials for simulations of materials at extreme conditions

The ONCVPSP approach [1] has been extended to permit deep core electrons to be active and to accurately reproduce atomic scattering properties to high energies. The basic principles of generalized norm conservation and systematic convergence optimization have been preserved. The original algorithms have been revised to permit consistent optimization of multiple pseudo wave functions for each angular momentum. Ground-state benchmark performance with active deep levels is comparable to that for the original 1 and 2 projector valence plus shallow-core potentials. A confined-atom model has been developed to compare pseudo and all-electron atoms at extreme temperatures and pressures, and verifies the accuracy of the extended potentials up to temperatures which ionize deep core electrons. The open-source oncvpsp-4.0.1 code incorporating these advances for scalar- and fully-relativistic treatments is now available.
1. D. R. Hamann, Phys. Rev. B 88, 085117 (2013).   

Chemical Potential of Nitrogen at High Pressure and High Temperature: Application to Phase Diagram Calculations of Nitrogen-Rich Compounds

High-pressure research of nitrogen-rich compounds is driven by a quest for hard materials and compounds with high energy density, but also has implications for planetary science. To predict the formation of nitrogen-rich compounds at high pressure and high temperature, knowledge of the chemical potential of nitrogen at extreme conditions is an indispensible ingredient. Here, we provide models together with intelligible data for the chemical potential of molecular nitrogen at temperature and pressure conditions relevant for experiments in the diamond anvil cell. In combination with first-principles calculations, we derive pressure−temperature phase diagrams readily accessible to guide experimental efforts. We demonstrate the validity of our approach for characteristic systems, including pure nitrogen and nitrogen-rich metal nitrogen phases that have already been discovered at pressures above 50 GPa. We then provide predictions for new metal-nitrogen compounds awaiting their synthesis at high pressure and high temperature.   

Finite-Temperature Dynamics of Elemental Electrides Under Extreme Conditions

Crystalline alkali metals generally exhibit near free-electron behavior at ambient conditions. For sodium at high pressures of above 200GPa, a deviation from such a metallic behavior was found in the insulator hP4 electride phase[1]. We investigated the temperature-induced changes in such systems using density functional theory. For the solid phase, the closure of the band gap with increasing temperature was explored through a comparison between the time scales for electron–phonon and phonon–phonon interactions. However, the more-intriguing aspect has been the observation of a metallic state, upon melting of Na-hP4, with coalescent dynamic electron bubbles rather than a conventional uniform electron gas. In essence, the emphasis of this work is to highlight the differences between the dynamics of the electride phases of pure elements, e.g., Na-hP4, vis-à-vis non-electride phases, e.g. Na-tI19, under thermal effects.

[1] Y. Ma et al., Nature 458, 182 (2009).   

A first-principles study on the phase stability of Mg1-xFexN alloys: the unconventional rock-salt occurrence under high pressure

Due to the large atomic radius difference of Mg and Fe, alloys between them cannot be synthesized at ambient pressure. However, using a combination of high pressure and nitrogen incorporation, Serghiou et al [1] reported a rock-salt (RS) solid solution formation between MgN and FeN. The potential of these materials for applications in spintronics and their structural analog condition to Mg_1-xFe_xO, one of the most abundant phases of the Earth's interior, require knowledge of their properties. Therefore, we employ ab initio electronic structure calculations based on density functional theory (DFT) to investigate the field stability, structural and magnetic properties of bulk Mg_1-xFe_xN. Our results provide insights to understand the interplay between pressure and composition to stabilize the RS structure and the rise/suppression of magnetism in the solid solution.

[1] G. Serghiou, et al., Angew. Chem. Int. Ed. 54, 15109-15112 (2015).

M. Núñez Valdez is also at the Helmholtz-Zentrum Potsdam (GFZ).   

Local Hydrodynamic Pressure for Strongly Inhomogeneous States

Continuum descriptions of complex systems, both classical and quantum, are increasingly adopted as alternatives first principles many-body analyses. The macroscopic momentum balance equation has its origin in the underlying exact conservation law, with a precisely defined operator for the associated momentum flux. Its average in a local equilibrium ensemble provides the basis for a hydrodynamic description. In particular, a local pressure is defined in terms of the trace of the average momentum flux. Other definitions for a local pressure are possible, such as a local virial pressure or a thermodynamic pressure obtained from the grand potential for local equilibrium. It is shown that all three local pressures have the same global pressure but differ locally, except for weakly inhomogeneous states. For uniform temperature, the trace of the momentum flux agrees with the local thermodynamic pressure even for strong density inhomogeneity.
This provides an important connection to density functional methods for hydrodynamic applications. For non-uniform temperatures and strong inhomogeneities there is no simple relationship among the different definitions of the local pressure, so the proper choice is that from the average momentum flux.   

32 Ages of the universe in just 2 weeks: High-speed Shock-waves in DFT

To date, the ab initio exploration of materials in extreme conditions has focused on equilibrium studies. However, this fails to capture the dynamic effects commonly seen in the shock-waves used to reach extreme conditions experimentally. In order to more accurately reproduce these mechanisms, we have developed a partially fire-and-forget approach to induce a series of independent shocks into the medium, to determine the shock response of the material.

We have also used optimisations of the Hugoniostat[1] approach tailored to ab initio calculation, so that we can use DFT-based methods to accurately calculate a complete Hugoniot in a single calculation. Using the series of isolated shocks and a predictor algorithm to approach the target pressure in uniform steps. From this, we can extract an ideal coupling parameter, reducing the calculation time, even for extreme compressions.

These two distinct improvements make it feasible to perform ab initio shock studies with high accuracy in DFT. We demonstrate these capabilities with simulations of shocks in quartz.

[1] Jean-Bernard Maillet and Stéphane Bernard. Uniaxial hugoniostat: Method and applications. In Shock Compression of Condensed Matter. American Institute of Physics, 2001   

Study of compaction, preheating and strength in shock compressed porous silica

The shock response of porous silica is investigated using molecular dynamics. We develop Hugoniot curves of amorphous SiO₂as a function of initial preheat temperature for T = 300K to T = 600K and a range of porous states ranging from full density (2.2 g/cc) down to aerogel densities (0.22 g/cc). We focus on relatively low shock pressures (under 6.0 GPa) where the compaction state changes significantly in this regime. We show peak and residual shear stress plots as a function of pressure for this system. We find that the overall strength is dependent on the compaction state of the material, which is a function of both the initial temperature and initial porosity.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.   

Accelerating the characterization of energy landscapes with swarm intelligence and machine learning

The prediction of reaction pathways for solid-solid transformations remains a key challenge. Here, we develop a pathway sampling method via swarm intelligence and graph theory and demonstrate that our PALLAS method is an effective tool to help understand phase transformations in solid-state systems. The method is capable of finding low-energy transition pathways between two minima without having to specify any details of the transition mechanism a priori. We benchmarked our PALLAS method against known phase transitions in cadmium selenide (CdSe) and silicon (Si). PALLAS readily identifies previously-reported, low-energy phase transition pathways for the wurtzite to rock-salt transition in CdSe and reveals a novel lower-energy pathway that has not yet been observed. In addition, PALLAS provides detailed information that explains the complex phase transition sequence observed during the decompression of Si from high pressure. We also introduce a computationally efficient approach based on machine learning techniques, allowing us to map the energy landscapes efficiently. The PALLAS methodology represents a promising tool for materials by design with valuable insights for novel synthesis.   

Anomalies in thermal properties of ferromagnesite (Mg1−xFex)CO3 across the spin transition

Ferromagneiste (Mg,Fe)CO₃ is considered as a major carbon carrier in the Earth’s lower mantle. Thorough knowledge of this mineral at high pressure (P) and temperature (T) can thus provide valuable insights to the Earth's deep carbon cycle. With Fe²⁺ substituting Mg²⁺ in the octahedral site, (Mg,Fe)CO₃ undergoes a spin transition from the high-spin (HS, S = 2) to the low-spin (LS, S = 0) state at 45–50 GPa. Previous static calculations [1] adopting the local density approximation + self-consistent Hubbard U (LDA+U_sc) method have succesfully explained the spin transition and accompanying volume/elastic anomlies observed in room-temperature experiments. Here, by combining LDA+U_sc with lattice dynamics, we compute the thermal properties of (Mg,Fe)CO₃ at high-(P,T) conditions. Our results indicate that nearly all thermal properties, including thermal expansion, Grüneisen parameter, heat capacity, and thus thermal conductivity, are significanlty changed by spin transition. Geophysical and geochemical consequence of spin transition in (Mg,Fe)CO₃ can thus be expected.

[1] H. Hsu and S.-C. Huang, Phys. Rev. B 94, 060404(R) (2016).   

Shock compression of dry Air

A molecular dynamics based shock compression study is presented for dry air. Dry air is modeled to consist of 78.08% of Nitrogen, 20.95% of Oxygen and 0.97% of Carbon-dioxide. Shock Hugoniot curves are developed for air under various initial temperature and pressure conditions simulating air at various mean-sea-level altitudes. Reactive potentials have been used for the simulations and possibilities of dissociation and ionization of the gaseous molecules along with chemical reactions between the gasses have been investigated. Equation of state parameters are also derived from the MD simulations for use in continuum simulations.