Session U42: Focus Session: Simulations of Matter at Extreme Conditions II

Condensed Matter and its Orderings: The Pressure Variable.

Advances in experimental high pressure condensed matter physics have led to near order-of-magnitude static isothermal compressions (high densities are also realizable in dynamic compressions). In sufficiently light systems the new realms of density have associated zero-point effects, which are substantial. Also generally anticipated are significant changes in electronic structure (band widths not always increasing with density, however) and effective state dependent interparticle potentials. Propitious use of the pressure variable can elucidate the many-body problem in incisive ways through new orderings including structural, magnetic and especially superconducting. Significant challenges to theory include the appearance at higher densities of exceedingly complex structures in systems hitherto regarded as 'simple'. Invasion of the valence electron domain by core space appears to impel an interesting clash of length scales. Not unrelated to the rise of quantum effects is the possibility (and even observation) of depression of melting points in low mass systems. Hydrogen, a tenacious insulator (but now a decreasingly reluctant alkali) remains a candidate for significant superconductivity in a metallic state, one which may also be manifested as a quantum liquid. In combination with other light elements further orderings are also predicted, but at pressures less than anticipated for pure hydrogen itself. For the future, this area of experimental investigation appears to be ideally matched to advanced electronic structure and simulation techniques.   

The Nature of the Hydrogen Plasma Phase Transition

We present details of a study of pure hydrogen fluid at high pressure. Using the Coupled Electron-Ion Monte Carlo (CEIMC) method [1,2], a quantum Monte Carlo scheme capable of accurately simulating systems at low temperature, we study the nature of the plasma phase transition (PPT): the mechanism by which a molecular to non-molecular transformation occurs under increasing pressure. We find no evidence for a first-order PPT. The CEIMC method centers on exploring the nuclear configuration space (classically or with quantum path integrals) using a modified Metropolis algorithm. Configurational energy differences are computed within the Born-Oppenheimer (BO) approximation using accurate ground-state quantum Monte Carlo techniques. \\ \\ 1. D. Ceperley, M. Dewing and C. Pierleoni, in Bridging Time Scales: Molecular Simulations for the Next Decade, eds. P. Nielaba {\it et al}, Springer-Verlag, pgs. 473-500 (2002). \\ 2. C. Pierleoni, D. M. Ceperley and M. Holzmann, Phys. Rev. Lett. {\bf 93}, 146402 (2004)   

Developments in the path integral Monte Carlo method for simulating fluids under extreme conditions

We summarize a number of improvements we have developed for the quantum simulation of fluids under extreme conditions with path integral Monte Carlo (PIMC). PIMC provides way to combine fully-correlated quantum effects with thermal fluctuations in a natural formalism by sampling the many-body thermal density matrix. These developments include the construction of accurate pseudohamiltonians and their incorporation into PIMC, computation of high-accuracy pair density matrices, improved optimization of the long/short-range breakup, a fast embedded band-structure calculation for the fermion nodal restriction, Brillouin-zone integration through twist-averaged boundary conditions, and coupled PIMC/Langevin dynamics. We present preliminary results for the simulation of sodium near its liquid/vapor critical point.   

Vibron Dynamics of Hydrogen at High Pressures and Temperatures

There is currently great interest in the behavior of molecular hydrogen at high pressures and temperatures. The van Kranendonk theory of vibrons in solid hydrogen has been used previously to provide a description of the Raman response as a function of pressure and para-ortho concentrations at low temperature. Here we apply the same model to very different environments, namely to the solid at high P-T conditions, and, with less justification, to the dense fluid. The effect of temperature is presumed to be to renormalize the hopping parameter. Within our model of the vibrons and approximate harmonic lattice dynamics, a $1/R^6$ dependence of the hopping parameter on intermolecular distance, $R$, gets averaged over fluctuations in the interatomic distance, and the average increases with temperature. Preliminary results using configurations obtained from hybrid path integral molecular dynamics calculations with empirical potentials suggest that there is very little change in the Raman peak upon melting at high pressure, in agreement with previous high P-T measurements.   

A systematic search method for finding new high-pressure phases of polymeric nitrogen

A recent discovery of single-bonded polymeric form of nitrogen in diamond anvil cell high pressure experiments [Nature Mat. \textbf{3}, 558 (2004)] opens a new promising direction in the development of high energy density materials. Besides the cubic gauche phase of polynitrogen stabilized in experiment, other yet unidentified metastable phases could emerge under certain experimental conditions. We present a systematic search method for finding metastable phases of single bonded nitrogen based on a set of Peierls distortions of a given reference structure. Using the most basic reference structure, a simple cubic unit cell, our approach not only reproduces all the single-bonded nitrogen phases reported so far, but also reveals many new metastable structures with promising properties. The equations of state of the structures calculated at the first-principles level are studied over a broad range of pressures up to 300 GPa. The stability of the structures is analyzed using directly calculated phonon spectra. This approach can be extended using more complex reference structures and relaxing the constraint of a pure single bonded phase.   

Complexity and Pressure Induced Fermi Surface Deformation in Lithium

Recently reported structural complexity and high temperature superconducting transition in lithium under pressure has increased the interest in light alkalis, otherwise considered as simple and well known systems under normal conditions. In this work we present an analysis of the pressure induced Fermi surface deformation in lithium and its relation to the observed complexity. According to our calculations, the Fermi surface becomes increasingly anisotropic with pressure and at around 8 GPa it contacts the Brillouin zone boundary, which preludes the bcc to fcc phase transition. Furthermore, at around 30 GPa, besides the increasing necks in the Fermi surface along the fcc $\Gamma $L direction, it develops an extended and well defined nesting in the $\Gamma $W direction, which enhances the electronic response for the nesting momentum and induces an strong phonon softening along the $\Gamma $K. The increasing electron-phonon coupling associated to this softening, besides preluding the transition to complex structures, also provides a better understanding of the observed superconducting transition in lithium at around the same pressure range.   

Prediction of a superionic phase of hydrogen fluoride (HF) at high temperature and pressure

We report first principles simulations of hydrogen fluoride. Ab initio molecular dynamics simulations of HF were conducted at densities of 1.8 -- 4.0 g/cc along the 900 K isotherm. At experimentally observable conditions, we find a transition to a superionic phase, in which the fluorine ions exhibit a stable lattice and the hydrogen ions exhibit rapid diffusion. This phase is similar to the recently reported superionic phase in water, in that there is a symmetrization of the hydrogen bond, and we observe a transient partially covalent network at pressures greater than 66 GPa. In addition, we describe a mechanism for hydrogen diffusion through the fluorine sub- lattice. Our results provide evidence that superionic solids are prevalent in solids that manifest low temperature symmetric hydrogen bonding. The pressures needed to induce superionic diffusion in HF are significantly lower than what is required for other known superionic hydrides, and thus will permit much more extensive experimental studies of this exotic phase.   

High-pressure and high-temperature phases of nitrous oxide

The phase diagram of nitrous oxide (N$_{2}$O) is investigated up to 50 GPa and 1000 K using first principles theory. The calculated stability and properties of numerous crystalline structures are compared with experimental results. We identify the structure of phase II of N$_{2}$O. On the basis of its stability with respect to orthorhombic deformations, an explanation for measured Raman spectra is provided. Similarly to CO$_{2 }$[1], crystalline structures with bent molecules are found to be extremely unfavorable energetically. \newline \newline [1] Bonev et al., Phys. Rev. Lett. 91, 065501 (2003).   

Mechanical strength and coordination defects in compressed silica glass

Contrary to ordinary solids, which are normally known to harden by compression, the mechanical strength of compressed SiO$_{2}$ glass shows a minimum around 10 GPa. Around this pressure, the compression of silica glass undergoes a change from purely elastic to plastic, leading to the recovery of a densified amorphous polymorph. The compressibility of silica glass is also anomalous, with a maximum at about 2-4 GPa. Despite the large pressure difference between the onset of the two anomalies, microscopic theories have traditionally attempted to explain both anomalies with the pressure induced appearance of coordination defects. Such models are seriously questioned however by the lack of evidence for coordination defects below 10 GPa, in Raman and NMR experiments. Here we show, using an improved interatomic potential for SiO$_{2}$, that a correct description of the pressure-induced appearance of five-fold coordination defects in silica glass is crucial to address the above phenomenology and to obtain a theoretical model consistent with experiments.   

USPEX - Predicting crystal structures of new phases

We have developed an very efficient and reliable method for crystal structure prediction [1], merging an evolutionary algorithm, based on local optimization and spatial heredity, with \textit{ab initio} total-energy calculations. This method allows one to predict the most stable crystal structure and a large number of robust metastable structures for a given compound at any $P-T$ condition, without requiring experimental input. The success rate is extremely high -- USPEX succeeded in all of the 25 tests performed so far, including ionic, covalent, metallic, and molecular structures with up to 20 atoms per unit cell. Using this methodology we have succeeded in predicting hitherto unknown structures [2]. Implementation of the algorithm, several applications and physical reasons for its success will be discussed. [1] Glass C.W, Oganov A.R., Hansen N. (2005). USPEX: a universal structure prediction algorithm. \textit{In prep.} [2] Oganov A.R., Glass C.W., Ono S. (2005). High-pressure phases of CaCO$_{3}$: crystal structure prediction and experiment. \textit{Earth Planet. Sci. Lett, in.press.}