Session J31: Focus Session: Materials at High Pressure II: Elements

Multi-Scale Shock Compression Simulations of Metals and Metallic Phase Transitions

We present a straightforward method for efficient molecular dynamics (MD) simulation of shock compression of materials that experience thermal electronic excitations at high pressure and temperature. Previous studies have shown that exclusion of the electronic temperature at extreme conditions can result in incorrect computation of dynamic and equation of state properties. The Multi-Scale Shock Technique (MSST) is a simulation methodology based on the Navier--Stokes equations for compressible flow that enables MD simulation of a shock wave with relatively small computational cost. We extend MSST to allow for changes in the electronic entropy during shock compression while conserving Hugoniot conditions. This allows for simulation of significantly higher shock velocities than previously possibly with MSST. We have used our simulation methodology in density functional tight binding simulations of shock compressed silicon. We observe that at high shock velocities inclusion of a non-zero electron temperature results in lower computed shock Hugoniot temperatures and pressures. Our methodology is well suited for shock compression simulations of any material that experiences changes in its electronic entropy under extreme thermodynamic conditions.   

Large-Scale Molecular Dynamics Simulations of Shock-Induced Plasticity in Tantalum Single Crystals

We report on large-scale non-equilibrium molecular dynamics (NEMD) simulations of shock wave compression in Ta single crystals. The atomic interactions are modeled via a recently developed and optimized embedded-atom method (EAM) potential for Ta, which reproduces the equation of state up to 200 GPa. We examined the elastic-plastic transition and shock wave structure for wave propagation along the low index directions: (100), (110) and (111). Shock waves along (100) and (111) exhibit an elastic precursor followed by a plastic wave for particle velocities below 1.1 km/s for (100) and 1.4 km/s for (111). The nature of the plastic deformation along (110) is dominated by twinning for pressures above 40 GPa.   

Transport of particulate matter from a shocked interface

We have performed a series of shock experiments to measure the evolution and transport of micron and sub-micron Tungsten particles from a 40 micron thick layer deposited on an Aluminum substrate. Densities and velocity distributions were measured using proton radiography at the Los Alamos Neutron Science Center for vacuum conditions and with contained Argon and Xenon gas atmospheres at initial pressures of 9.5 bar and room temperature. A common shock drive resulted in free surface velocities of 1.25 km/s. An analysis of the time dependence of Lithium Niobate piezo-electric pin pressure profiles is given in terms of solutions to the particulate drag equations and the evolution equation for the particulate distribution function. The spatial and temporal fore-shortening in the shocked gas can be accounted for using reasonable values for the compressed gas shear viscosities and the vacuum distributions. The detailed form of the pin pressure data for Xenon indicates particulate breakup in the hot compressed gas.   

Thermal Emission Determination of Argon under Extreme Pressure and Temperature

Argon is a common pressure-transmitting medium in diamond anvil cell (DAC) experiments, and is often used as thermal insulation in the laser heated DAC. A more thorough understanding of the thermal properties of argon under extreme conditions is essential for measuring thermal properties of materials under similar conditions. A transient heating technique was applied to a symmetric DAC up to 50 GPa and 2500 K. A 1 $\mu $m thick iridium foil positioned within a recessed gasket hole filled with argon served as a laser absorber to pump thermal energy into the sample. Pump pulses of 6 $\mu $s temporal width were provided from an electronically modulated Yb-based fiber laser. We determined the temperature of the coupler with 500 ns time resolution by applying a Planckian fit to the thermal emission spectrum. Finite element calculations were also used to simulate thermal diffusion in the DAC cavity. The experimental results show slightly larger thermal conductivity with theory, but the results converge in the limit of high temperature. This work is supported by NSF EAR 1015239, NSF-REU, Carnegie Institution of Washington, and DOE-NNSA (CDAC).   

Thermal diffusivity of metals at high pressure

Very few measurements of thermal diffusivity have been taken at high pressure. This is especially true of metals above 2 GPa. In earlier experiments, the Angstrom method has been employed for these types of measurements. However, this method is limited for high pressure because it requires a relatively large sample. We will discuss the use of sinusoidally modulated laser heating to measure thermal diffusivity in the diamond-anvil-cell.   

Pressure-Induced Structure Transitions in Europium Metal to 92 GPa

Motivated by the recent discovery of pressure-induced superconductivity in Eu for pressures above 80 GPa [1], we have carried out high pressure angle-dispersive synchrotron x-ray diffraction measurements on Eu metal in a diamond anvil cell to 92 GPa. Our experiments confirm the bcc-to-hcp transition at 12 GPa reported in previous studies and identify two further phase transitions. The predictions of two independent density functional theory calculations are compared to the experimental results.\\[4pt] [1] M. Debessai, T. Matsuoka, J. J. Hamlin, J. S. Schilling, and K. Shimizu, Phys. Rev. Lett. \textbf{102}, 197002 (2009).   

Electronic structure and dynamics of elements at high pressures

Electronic structure and dynamics information of materials under high pressure has been very scarce due to the experimental difficulties. The standard electronic probes using electron energy loss spectroscopy (EELS) is limited to vacuum pressures. The optical probes that can reach high-pressure samples through the diamond windows, on the other hand, are limited by the energy accessibility ($<$ 5 eV) and near-zero momentum transfer, $q=(4\pi /\lambda _0 )\sin \theta $. These problems can be overcome by the newly advanced, two-photon, inelastic, xray, scattering (IXS) spectroscopy which uses high energy xrays ($\sim $ 10$^{4}$ eV) to provide the atomic-level momentum transfer and to enter (with energy $E)$ and exit (with energy $E_0 )$ the pressure vessel. The electronic spectra are revealed by analyzing the xray energy loss between the two photons, $\hbar \omega =E-E_0 $. Using IXS facilities at third-generation synchrotron source, we studied electronic structure and dynamics of two elements at high pressures in a diamond-anvil cell: i.e., He, the widest-gap insulator, and Na, the archetypal free-electron metal. At 11.9-17.9 GPa in a single crystal $^{4}$He, we observed rich electron excitation spectra, including a cut-off edge above 23 eV, a sharp exciton peak showing linear volume dependence, and a series of excitations and continuum at 26 to 45 eV. We determined electronic dispersion along the 100 direction over two Brillouin zones, and provided a quantitative picture of the helium exciton beyond the simplified Wannier-Frenkel description. At 1.6-4.39 GPa in a polycrystalline Na sample, we observed the sharp plasmon peak at low $q$ and its dispersion beyond the critical $q_{c}$. The plasmon shifts to higher energy under compression and drastic reduction of $r_{s}$. \textit{Ab-initio} theoretical calculations are conducted for interpretation of the experimental results.   

Diffusion Monte Carlo calculations of Xenon melting under pressure

The slope of the melting temperature as a function of pressure yields, via the Clausius-Clapeyron equation, important information regarding the changes in density, energy, and entropy. It is therefore crucial to resolve the long-standing differences in melt lines under pressure between Diamond Anvil Cell data (low/flat melt line) and other methods, including density functional theory (DFT) simulations$^1$ (high/steep melt line). The disagreement for Ta was recently resolved$^{2}$ and although a similar situation exists in the literature on Xe,$^{3}$ the resolution may be quite different. For example, DFT with its lack of van der Waals forces is a prima facie less credible simulation method for Xe, although excellent agreement has been obtained between calculations of the Hugoniot of Xe and experiments.$^4$ We investigate whether this theoretical shortcoming is significant for the melting transition by applying diffusion Monte Carlo. The energy differences obtained in this way are compared to the DFT results in order to address any systematic errors that may be present near the melting transition. $^1$ Taioli et al. PRB {\bf 75}, 214103 (2007); $^2$ Dewaele et al. PRL {\bf 104}, 255701 (2010); $^3$ Belonoshko el al. PRB {\bf 74}, 054114 (2006); $^4$ Root et al. PRL {\bf 105}, 085501 (2010)   

Lattice dynamics at ultra-high pressures using high-resolution inelastic x-ray scattering

While our understanding of many physical properties is enhanced by the large body of neutron, the restrictions on sample size imposed by the technique relegated the achievable information to low or at most, moderate pressures ($\sim$10 GPa) and to materials readily available in reasonable large quantities. The advent of third generation synchrotron sources and the construction of beamlines dedicated for inelastic x-ray scattering experiments (IXS), these limitations have to a great degree been overcome. Over the past few years our group has focused a large experimental and theoretical effort on quantifying the vibrational energies in metals at high-pressures and high-temperatures. Most recently, we have determined the phonon dispersions across the isostructural gamma- to alpha-cerium transition. Our new data place important thermodynamical and theoretical constraints on the underlying physics of this important transition.   

High-pressure phases of calcium

The high-pressure phases of calcium have been investigated using a combination of density functional theory and diffusion quantum Monte Carlo calculations. Finite-temperature Gibbs free energies of several competing structures are computed at pressures near 50 GPa. The discrepancy between theory and experiment both at low and room temperature is resolved with input from diffusion quantum Monte Carlo. Furthermore, diffusion quantum Monte Carlo calculations are performed on 0 K crystalline structures up to 150 GPa. The resulting structures differ from those obtained with density functional theory.   

Lifshitz transition in \textit{cI}16 Li at high pressures: Unfolding first-principles Fermi surfaces

The Fermi surface topology of \textit{cI}16 Li is investigated using the recently developed first-principles band structure unfolding method [1]. The resulting unfolded Fermi surfaces display a clear Lifshitz transition at 47 GPa, explaining the anomalous change of superconducting transition temperature [2]. The unfolded Fermi surfaces also reveals a more complete picture of the driving force of the \textit{cI}16 phase starting at 39 GPa [3]. In addition to the previously proposed ``nesting'' effect [3] along [1$\frac{1}{2}\frac{1}{2}$], both [100] and [$\frac{1}{2}\frac{1}{2}$0] wavevectors are found to contribute significantly to the structural instability as well, due to their large phase space, a more effective effect in 3D. We expect a wide range of applications of this Fermi surface unfolding method to the study of high pressure electronic structure.\\[4pt] [1] Wei Ku et al, Phys. Rev. Lett. {\bf 104}, 216401 (2010)\\[0pt] [2] S. Deemyad and J. S. Schilling, Phys. Rev. Lett. {\bf 91}, 167001 (2003)\\[0pt] [3] M. Hanfland et al, Nature {\bf 408}, 174 (1998)   

On the role of quantum ion dynamics for the anomalous melting of lithium

Lithium has attracted a lot of interest in relation to a number of counterintuitive electronic and structural changes that it exhibits under pressure. One of the most remarkable properties of dense lithium is its anomalous melting. This behavior was first predicted theoretically based on first-principles molecular dynamics (FPMD) simulations, which treated the ions classically [1]. The lowest melting temperature was determined to be about 275~K at 65~GPa. Recent experiments measured a melting temperature about 100~K lower at the same pressure. In this talk, we will present FPMD calculations of solid and liquid lithium free energies up to 100 GPa that take into account ion quantum dynamics. We examine the significance of the quantum effects for the finite-temperature phase boundaries of lithium and, in particular, its melting curve. \\[4pt] [1] I. Tamblyn, J-Y. Raty, and S. A. Bonev, Phys. Rev. Lett. 101, 075703 (2008).\\[0pt] [2] E. Gregoryanz et al, Nature, in press.   

Graphite under high pressure

As one of the longest-known forms of carbon, graphite has been extensively studied for several decades. However, its phase diagram under high pressures is still poorly understood. Here we use both in-situ high-pressure Raman spectroscopy and synchrotron x-ray diffraction, collected on both compression and decompression, to elucidate the high-pressure behavior of highly-ordered pyrolitic graphite (HOPG) at room temperature. The Raman spectra show that G band (1580 cm$^{-1}$ at ambient pressure) of HOPG shifts to higher frequency with increased pressure, which has been attributed to pressure-induced in-plane lattice contraction. Above 19 GPa the broadening of this Raman peak indicates a reordering of the atomic structure, and is consistent with synchrotron x-ray diffraction measurements that also show a slight change in symmetry.