Session L23: High Pressure IV

On the high pressure behavior of body-centered cubic iron

The high pressure--high temperature behavior of iron is of current interest for geophysical reason, i.e., the earth's core is believed to be iron at high p and T. The value of the pressure at which the rigid lattice of body-centered-cubic ferromagnetic iron goes unstable was recalculated by newer methods. We give some thermodinamic arguments in support of our procedure, which minimizes the Gibbs free energy at constant pressure rather than internal energy at constant volume, and then finds elastic constants as second derivatives of G with respect to strains. The calculations used WIEN2k band-structure program and a minimum path program that makes a series of jumps in structure based on the local slope and curvature of G at a point in structure space. Errors are pointed out in several recent papers that found values different than ours, mainly due to neglect of the pressure correction required when elastic constants are calculated in a system under finite pressure by differentiation of the energy rather than Gibbs free energy.   

Rheology of iron under conditions of the Earth's inner core

It is well established that the solid Earth's inner core (IC) consists of an iron-rich alloy. However, low rigidity of the IC (Poisson ratio of about 0.44) remains enigmatic. Both measured at low temperature elastic properties of hexagonal (hcp) iron phase as well as the calculated properties of the various hypothetic iron phases at high pressure (above 3 Mbar) and high temperature (from 5000 to 8000 K) are inconsistent with seismological observations. The velocity of shear waves propagation in the IC is considerably lower than the measured/calculated shear velocity of iron phases. We performed ab initio as well as classical molecular dynamics (MD) simulations of iron polycrystals, grown from melt as well as obtained by the Voronoi construction. We demosntrate, that the account for grain boundaries and/or for various structural inhomogeneities allow to bring the calculated data in close agreement with the experimental seismic data.   

Recovery Studies of Shocked Iron Single Crystals

Time resolved, \textit{in-situ }X-Ray diffraction measurements indicate that the bcc-hcp transition in single crystal iron occurs at about 13 GPa. These results also show that the high pressure phase is a polycrystal with two variants. Further studies on the recovered specimens using transmission electron microscopy show that these shocked samples surprisingly reverse transform from a high pressure polycrystal to the original single crystal structure upon release. These results will be discussed in the context of the time resolved data and theoretically based transformation pathways.   

Multi-scale modeling of ferromagnetism in bcc Fe as a function of pressure and temperature

We investigate the magnetic properties of bcc Fe as functions of pressure and temperature using multi-scale modeling techniques. We employ a first-principles fitted tight-binding total-energy model in the generalized-gradient approximation to examine bcc Fe at numerous ferromagnetic, antiferromagnetic and spin spiral states, and fit the tight-binding data to a generalized Heisenberg Hamiltonian which includes both the on-site and local exchange energy to describe the magnetic energy for any arbitrary magnetic configuration. We obtain the Curie temperature, magnetization curve, and other finite-temperature magnetic properties through extensive Monte Carlo simulations, which have been further applied to examine the influence of the magnetic fluctuations on the free energy and thermal equation of state properties of bcc Fe at high temperatures. This work was supported by US Department of Energy ASCI/ASAP subcontract to Caltech, Grant DOE W-7405-ENG-48 (to REC).   

Ellipsometry Measurements of Shock-Induced Phase Transitions

{\em In situ} measurements of crystal structures and phase transitions during dynamic high-pressure experiments are complex, thus knowledge of high-pressure high-temperature phase diagrams for many materials is limited. Since typical Hugoniot EOS and sound speed experiments do not provide this information, we have developed an ellipsometric technique which allows the real-time measurement of optical constants. Coupling measured optical properties with calculations allows one to infer structural information complimentary to techniques such as x-ray diffraction. We present dynamic ellipsometry measurements of shock-induced solid-solid ($\alpha-Fe\to \epsilon-Fe$) and solid-liquid ($\beta \to liquid -Sn$) phase transitions. In addition, the time-resolution of such dynamic phenomena suggests that information on the kinetics of phase transitions as well as deformation/relaxation can be obtained. We will also discuss our efforts to incorporate multiple wavelengths into ellipsometry measurements of dynamically compressed materials.   

Symmetry breaking in a dense liquid: Why sodium melts at room temperature.

The melting curve of sodium measured in [1] exhibits unusual features under pressure : the melting temperature, Tm, reaches a maximum around 30 GPa followed by a sharp decline from 1000 K to 300 K in the pressure range from 30 to 120 GPa. In this study, the structural and electronic properties of molten sodium are studied using first principles theory. With increasing pressure, liquid sodium initially evolves by assuming a more compact local structure, which accounts for the maximum of Tm at 30 GPas. However, at pressure around 65 gigapascals a transition to a lower coordinated structure takes place, driven by the opening of a pseudogap at the Fermi level. Remarkably, the broken symmetry liquid phase emerges at rather elevated temperatures and above the stability region of a closed packed free electron-like metal. The theory explains the measured drop of the sodium melting temperature, down to 300 kelvin at 105 GPas. [1] Gregoryantz et al., Phys. Rev. Lett. 94, 185502 (2005).   

The breakdown of a simple-metal paradigm at high pressures

The light alkalis at one bar and room temperature are considered the paradigms of 'simple-metal' behavior. They adopt cubic structures and their valence bands are free electron-like. Under normal conditions this has been well accounted for by pseudopotential theory. It is a common expectation that the light alkalis might even be more free electron-like at higher densities, as impelled by pressure. Advances in diamond anvil cell methods have yielded new insights in the behavior of the alkalis at megabar pressures, presenting a considerable challenge to the above paradigm. Under pressure, the light alkalis adopt non-simple structures. Initial studies by Neaton and Ashcroft [Letters to Nature, Vol. 400, 141 (1999)] on lithium suggested that with increasing pressure the valence bands first broaden, but then start narrowing substantially. Corresponding to this, the valence charge density is localizing in the interstitial spaces of the lattice and the core bands are acquiring significant width. Our work focuses on showing that this behavior may be fairly general and can be explained at the one electron level as an emerging breakdown of the weak pseudopotential hypothesis.   

Melting of Sodium Under Pressure

The bcc, fcc, and liquid phases of sodium are investigated with density functional molecular dynamic (DFT-MD) simulations. We focus on the behavior of the melting curve at high pressure. Diamond anvil cell experiments have determined a melting line with a negative slope at pressures above 33GPa [1]. In the bcc phase, the melting temperature drops from around 1000K to 700K. It decreases even further to 300K in the fcc phase. We have performed simulations for sodium in a range from zero to 100 GPa, temperatures ranging from 300K to 2000K. Equations of State (EOS) for the bcc, fcc and liquid phase are obtained. To investigate the underlying principles of melting in sodium, we study ionic and electronic structure of solid and fluid. Using our EOS, we reproduce positive and negative slopes of the melting line in the proposed pressure regions for the bcc as well as for the fcc phase. [1] E. Gregorianz, O. Degtyarewa, M. Somayazulu, R.J. Hemley, H. Mao, Phys. Rev. Lett. 94, 185502 (2005)   

An Investigation of s-d promotion at high pressure with the Projector Augmented Wave method

The PAW(1) method for ab initio density functional calculations combines advantages of both pseudopotential (PP) and all-electron (AE) methods. The PAW method provides accuracy comparable to AE methods, core-sensitive calculations, and ab initio molecular dynamics with large systems. The requirement for high accuracy in the determination of s-d promotion pressures in transition metals serves as a proving ground for the accuracy of the PAW method. We present PAW, PP, and AE APW+lo results for the case of Molybdenum, for which there is significant disagreement among recent ab initio predictions above 600 GPa. 1. P.E. Blochl, Physical Review B, 50, 17953 (1994)   

Quasi-Isentropic Compression of Ta Using Graded Density Impactors

Recent advances in the fabrication of graded density impactors have enabled the production of smooth, continuous quasi-isentropes for gas gun experiments. Using these impactors, we have performed experiments on Ta in which the sample is initially shocked to 66 GPa on the Hugoniot and then quasi-isentropically compressed to over 1 Mbar. We will present the results of lagrangian analysis of the data and compare with previous Hugoniot measurements as well as the calculated isentrope of Ta. We will also discuss potential sources of error in both the data and analysis and their effect on the measured quasi-isentrope.   

A multi-scale, atomistic-based strength model for tantalum and molybdenum

For the description of bcc tantalum and molybdenum strength at the continuum level, we have combined several extensive sets of quantum-based, atomistic calculations into a new parameterization of the Steinberg-Lund (SL) and mechanical threshold stress (MTS) strength models. This model is then used to simulate recent gas-gun shock experiments. The atomistic calculations that determine the parameters of these model were derived from two disparate methods but both based on quantum-based model generalized pseudopotential theory (MGPT) for the ion-ion interactions. In one method, Green's function boundary conditions are used to relax dynamically the boundary forces in molecular dynamics simulations of the kink-pair activation enthalpy and Peierls stress for $(a/2)<111>$ screw dislocations. The other method combines MGPT Monte Carlo simulations with full potential linear muffin-tin orbital (FP-LMTO) method of density functional theory to determine the temperature and pressure dependence of the shear modulus. We discuss the new parameterization of the models and hydrodynamic simulation results.   

Osmium under high pressure: a fully relativistic first-principles study of the structural and electronic properties.

Recently, there has been much interest in the high-pressure properties of Os after that the first bulk modulus measurement was made only four years ago. It is important to mention that to date, the phase diagram of Os is unknown. In the present work, we have studied the structural and electronic properties of Os using the full-potential LAPW method and the GGA for the exchange-correlation functional. The calculations were performed including the spin-orbit coupling which is important for heavy metals like Os. The total-energy as a function of the cell volume was computed assuming the hcp, fcc, and $\omega $ structures, for compressions up to 65{\%} of the equilibrium volume. In contradiction with the previous non-relativistic LDA-calculation, we find that Os in the hcp phase have lower energy than the fcc and $\omega $ structures. The hcp structure remains stable for pressures up to 400 GPa and not structural transition to the fcc or $\omega $ phase was found. Nevertheless, from the analysis of the band structure, we find an electronic topological transition induced by pressure at the high-symmetry point L, where three bands cross the Fermi level upon compression.   

Difference Frequency Generation Measurements of Phase Transitions in Gallium

We recently measured the vibrational excitation spectra of solid and liquid gallium with ultrafast terahertz difference frequency generation (DFG) spectroscopy. The two phases had clearly different DFG spectra, with a 250 cm$^{-1}$ phonon feature visible in the solid phase and a 50 cm$^{-1}$ excitation feature seen in the liquid phase. Prospects for using this technique to measure phase transitions of shocked systems \textit{in situ} will be discussed.   

First The motion and mobility of screw and edge dislocation in bcc tantalum

Strength in bcc metals is, surprisingly, not well understood; it is thought to be dominated at low temperature by the motion of 1/2$<$111$>$ screw dislocations. The motion of these screw dislocations is thought to be controlled by nucleation and propagation of kinks along the dislocation line, which can at high stress result in the formation of debris (vacancies, interstitials, loops, etc) in the dislocation wake. We studied the motion of screw and edge dislocations in bcc tantalum by performing large-scale molecular-dynamics simulations using both Finnis-Sinclair potentials, and model-generalized-pseudopotential-theory (MGPT) potentials [1]. We present here simulation predictions for dislocation motion, mobility, and debris formation with respect to pressure, temperature, and strain rate. [1] J. A. Moriarty, Phys. Rev. B 42, 1609 (1990).; J. A. Moriarty, Phys. Rev. B 49, 12431 (1994).   

Material Strength on Quasi-isentropes

We have recently performed experiments to study strength properties of aluminum on quasi-isentropes. The aluminum samples were initially shocked to a fixed state on the Hugoniot, then quasi-isentropically compressed and released isentropically. In these experiments, the strain rates on compression and release isentropes are nearly equivalent. We will discuss the details of the experiments and data and error analysis in deriving strength of aluminum. Recent advances in the functionally graded density impactor technology have made it possible for us to carry out these experiments with significantly reduced uncertainties. We will discuss these advances including reproducibility and planarity of the impactors. Methods to characterize these advances will be discussed. [1] Work performed under the auspices of the U.S. DOE at the University of California/Lawrence Livermore National Laboratory under contract W-7405-ENG-48.