Session T25: High Pressure: Theory

Nanoshells as a high-pressure gauge

Nanoshells, consisting of multiple spherical layers, have an extensive list of applications, usually performing the function of a probe. We add a new application to this list in the form of a high-pressure gauge in a Diamond Anvil Cell (DAC). In a DAC, where high pressures are reached by pressing two diamonds together, existing gauges fail at higher pressures because of calibration difficulties and obscuring effects in the diamonds. The nanoshell gauge does not face this issue since its optical spectrum can be engineered by altering the thickness of its layers. Furthermore their properties are measured by broad band optical transmission spectroscopy leading to a very large signal-to-noise ratio even in the multi-megabar pressure regime where ruby measurements become challenging. Theoretical calculations based on the Maxwell equations in a spherical geometry combined with the Vinet equation of state show that a three-layer geometry (SiO$_2$-Au-SiO$_2$) indeed has a measurable pressure-dependent optical response desirable for gauges.   

Pressure-induced phase transitions and superconductivity in platinum hydride

The transition metal hydrides have attracted much attention from the scientific community due to their promising properties from both fundamental and practical points of view. Here we present our recent work about platinum hydride under pressure. Structural phase transitions and superconducting properties of platinum hydride under pressure are explored through the first-principles calculations based on the density functional theory. Three new low-pressure phases (Pm-3m, Cmmm, and P4/nmm) are predicted, and all of them are metallic and stable relative to decomposed cases. Two high-pressure phases are close-packed structure with hydrogen atoms occupying the octahedral interstices. The superconducting critical temperature of two high-pressure phases correlates with the electron-phonon coupling. The presence of soft modes induced by Kohn anomalies and the hybridization between H and Pt atoms result in the strong electron-phonon coupling. Our results have great implications for other transition metal hydrides under pressure.   

The hard-disk melting transition

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte Carlo algorithm [1] allows us to thermalize systems large enough to access the thermodynamic regime. I will show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order [2]. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research. 1. Bernard, E. P.; Krauth, W. {\&} Wilson, D. B. \textit{Phys. Rev. E., }\textbf{2009}$, 80$, 056704 2. Bernard, E. P. {\&} Krauth, W. \textit{Phys. Rev. Lett., }\textbf{2011}$, 107$, 155704   

Electric Field Induced Phase Transitions

A novel theory of phase transitions that are driven by strong, symmetry-breaking electric fields is presented. The underlying mechanism is based on the formation of needle-shaped, metallic embryos that acquire strong dipole moments in the applied field. It is shown that the electrostatic contribution to the free energy can be so significant that it dominates the nucleation process and elongated metallic particles can form even in cases where they would be otherwise unstable in the bulk. As such, the theory predicts that any insulator will eventually form metallic inclusions when immersed in a sufficient electric field. Materials can thus be synthesized by the controlled application of a dc or laser field. In this work, the general mechanism is described and closed form expressions are presented for the field-dependent nucleation barrier and the effective field range as functions of material parameters. Overall, the theory presents a new parameter space to explore phase transitions and opens the venue of Field Induced Materials Synthesis (FIMS). As a provocative example, the potential for FIMS of metallic hydrogen at standard pressure is discussed; the effective field range is estimated to be $10^7 < E\ll 10^9$ V/cm (laser intensity $10^{12}< I \ll 10^{16}$ W/cm$^2$).   

Consistent first-principles pressure scales for diffraction experiments under extreme conditions

Diamond anvil cell (DAC) diffraction experiments are fundamental in geophysics and materials science to explore the behavior of solids under very high pressures and temperatures. A factor limiting the accuracy of DAC experiments is the lack of an accurate pressure scale for the calibration materials that extends to the ever-increasing pressure and temperature limits of the technique. In this communication, we address this problem by applying a newly developed technique that allows the calculation of accurate thermodynamic properties from first-principles calculations [Phys. Rev. B 84 (2011) 024109, 84 (2011) 184103]. Three elements are key in this method: i) the quasiharmonic approximation (QHA) and the static energies and phonon frequencies obtained from an electronic structure calculation ii) the appropriate representation of the equation of state by using averages of strain polynomials and iii) the correction of the systematic errors caused by the exchange-correlation functional approximation. As a result, we propose accurate equations of scale for typical pressure calibrants that can be used in the whole experimental range of pressures and temperatures. The internal consistency and the agreement with the ruby scale based on experimental data is examined.   

Low-temperature phases of dense hydrogen and deuterium by first-principles path-integral molecular dynamics

The low-temperature phases of dense hydrogen and deuterium have been investigated using first-principles path-integral molecular dynamics, a technique that we have recently implemented in the ABINIT code and that allows to account for the quantum fluctuations of atomic nuclei. A massively parallelized scheme is applied to produce trajectories of several tens of thousands steps using a 64-atom supercell and a Trotter number of 64. The so-called phases I, II and III are studied and compared to the structures proposed in the literature. The quantum fluctuations produce configurational disorder and are shown to systematically enhance the symmetry of the system: a continuous gain of symmetry in the angular density of probability of the molecules is found from classical particles to quantum D2 and finally to quantum H2. Particular emphasis is made on the ``broken-symmetry'' phase (phase II).   

Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Requirements for Predictive Density Functional Theory Methods for Heavy Materials Equation of State

The difficulties in experimentally determining the Equation of State of actinide and lanthanide materials has driven the development of many computational approaches with varying degree of empiricism and predictive power. While Density Functional Theory (DFT) based on the Schr\"{o}dinger Equation (possibly with relativistic corrections including the scalar relativistic approach) combined with local and semi-local functionals has proven to be a successful and predictive approach for many materials, it is not giving enough accuracy, or even is a complete failure, for the actinides. To remedy this failure both an improved fundamental description based on the Dirac Equation (DE) and improved functionals are needed. Based on results obtained using the appropriate fundamental approach of DFT based on the DE we discuss the performance of available semi-local functionals, the requirements for improved functionals for actinide/lanthanide materials, and the similarities in how functionals behave in transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

High pressure/temperature equation of state of gold silver alloys

Gold-silver alloys crystallize in face centered cubic structures, like their constituent pure elements [McKeehan -- Phys.Rev. 20, 424 (1922)]. The cell parameter of the alloys does not scale linearly with the ratio of Ag/Au. In this work we investigate the high-pressure/temperature behavior of gold-silver alloys with different Au/Ag ratios. Powder x-ray diffraction experiments performed at HPCAT/Advanced Photon Source confirm the stability of the alloy's fcc structure to pressures/temperatures exceeding 100 GPa/1000 K. We will present isothermal EOS of the alloys from ambient temperature up to 1000 K, discuss the thermal expansion and its variation with pressure.   

Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-ray Scattering

Metallic liquid silicon at 1787K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17{\%} via a maximally-localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state.   

Effects of the Structure of the Confinement Matrix on Liquid-Liquid Phase Transition and Density Anomaly

We investigate using molecular dynamics the effect of geometrical order in nanoconfinement of liquids with water-like anomalies that display liquid-liquid coexistence at low pressure and low temperature. Our studies using both a ramp and a shoulder interaction potentials show that regularly structured confinement matrices preserve the anomalies, while the phase diagram is shifted to lower temperatures, higher pressures and higher densities with respect to bulk. On the contrary, if the confinement matrices have no geometrical order, we find a drastically different phase diagram: the liquid-liquid coexistence region shrinks significantly and the anomalies are washed out. To understand this effect we calculate the changes in the system at the microscopic level. In the vicinity of the confining nanoparticles we observe that the liquid has a dramatic increase of density that we interpret as an entropic effect. We explain the macroscopic effect of confinement as a consequence of the amount of disorder that is introduced through the configuration of the confining nanoparticles.   

First-principles calculations for pressure-induced transition of Sr2CuO3

One-dimensional cuprate, Sr$_{2}$CuO$_{3}$ has attracted much attention from the theoretical and material research. Recently, it is found that Sr$_{2}$CuO$_{3}$ exhibits the pressure-induced structural transition with the space group change. In this work, we perform the first-principles calculations in order to investigate the mechanism for the pressure-induced structural transition of Sr$_{2}$CuO$_{3}$. The calculation results are in good accordance with the experimental ones. The structural transition of Sr$_{2}$CuO$_{3}$ are related with the ionic interaction between strontium and oxygen atoms. We also discuss the electronic and magnetic structure of Sr$_{2}$CuO$_{3}$.   

Magnetic Phase Transition in Rare Earth Metal Holmium at Low Temperatures and High Pressures

The heavy rare earth metal Holmium has been studied under high pressures and low temperatures using a designer diamond anvil cell and neutron diffraction using a Paris-Edinburgh Cell at the Spallation Neutrons and Pressure (SNAP) Diffractometer. The electrical resistance measurement using designer diamond shows a change in slope at the Neel temperature as the temperature is lowered at high pressures. At atmospheric pressure TN=120 K and decreases with a slope of -4.7 K/GPa as pressure is increased, until reaching 9 GPa, at which pressure the magnetic ordering is lost. This correlates to the pressure at which there is a structural change from an hcp phase to an $\alpha $-Sm structure. Neutron diffraction measurements made above and below the Neel temperature at increasing pressures show the reversibility of the change between the paramagnetic and antiferromagnetic states. The parameters of the low temperature incommensurate magnetic phase will be reported at various pressures.