Evolution of the structure of amorphous ice - from low-density amorphous (LDA) through high-density amorphous (HDA) to very high-density amorphous (VHDA) ice

We report results of molecular dynamics simulations of amorphous ice for pressures up to 22.5 kbar. The high-density amorphous ice (HDA) as prepared by pressure-induced amorphization of Ih ice at T=80 K is annealed to T=170 K at various pressures to allow for relaxation. Upon increase of pressure, relaxed amorphous ice undergoes a pronounced change of structure, ranging from the low-density amorphous ice (LDA) at p=0, through a continuum of HDA states to the limiting very high-density amorphous ice (VHDA) regime above 10 kbar. The main part of the overall structural change takes place within the HDA megabasin, which includes a variety of structures with quite different local and medium-range order as well as network topology and spans a broad range of densities. The VHDA represents the limit to densification by adapting the hydrogen-bonded network topology, without creating interpenetrating networks. The connection between structure and metastability of various forms upon decompression and heating is studied and discussed. We also discuss the analogy with amorphous and crystalline silica. Finally, some conclusions concerning the relation between amorphous ice and supercooled water are drawn.Comment: 11 pages, 12 postscript figures. To be published in The Journal of Chemical Physic

Orthorhombic Phase of Crystalline Polyethylene: A Constant Pressure Path Integral Monte Carlo Study

In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles. This work represents a quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918 (1997)). It is aimed both at exploring the applicability of the PIMC method on such polymer crystal systems, as well as on a detailed assessment of the importance of quantum effects on different quantities. We used the $NpT$ ensemble and simulated the system at zero pressure in the temperature range 25 - 300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size effects, we used chains of two different lengths, C_12 and C_24, corresponding to the total number of atoms in the super-cell being 432 and 864, respectively. We show here the results for structural parameters, like the orthorhombic lattice constants a,b,c, and also fluctuations of internal parameters of the chains, such as bond lengths and bond and torsional angles. We have also determined the internal energy and diagonal elastic constants c_11, c_22 and c_33. We discuss the temperature dependence of the measured quantities and compare to that obtained from the classical simulation. For some quantities, we discuss the way they are related to the torsional angle fluctuation. In case of the lattice parameters we compare our results to those obtained from other theoretical approaches as well as to some available experimental data. In order to study isotope effects, we simulated also a deuterated polyethylene crystal at a low temperature. We also suggest possible ways of extending this study and present some general considerations concerning modeling of polymer crystals.Comment: 18 pages, RevTex, 18 figures, 3 tables, submitted to Phys. Rev.

Orthorhombic Phase of Crystalline Polyethylene: A Monte Carlo Study

In this paper we present a classical Monte Carlo simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles and periodic boundary conditions. We used a recently developed algorithm which apart from standard Metropolis local moves employs also global moves consisting of displacements of the center of mass of the whole chains in all three spatial directions as well as rotations of the chains around an axis parallel to the crystallographic c-direction. Our simulations are performed in the NpT ensemble, at zero pressure, and extend over the whole range of temperatures in which the orthorhombic phase is experimentally known to be stable (10 - 450 K). In order to investigate the finite-size effects in this extremely anisotropic crystal, we used different system sizes and different chain lengths, ranging from C_12 to C_96 chains, the total number of atoms in the super-cell being between 432 and 3456. We show here the results for structural parameters, such as the orthorhombic cell parameters a,b,c, and the setting angle of the chains, as well as internal parameters of the chains, such as the bond lengths and angles. Among thermodynamic quantities, we present results for thermal expansion coefficients, elastic constants and specific heat. We discuss the temperature dependence of the measured quantities as well as the related finite-size effects. In case of lattice parameters and thermal expansion coefficients, we compare our results to those obtained from other theoretical approaches as well as to some available experimental data. We also suggest some possible ways of extending this study.Comment: 27 pages, RevTex, 24 figures, submitted to Journal of Chemical Physic

Polyamorphism of ice at low temperatures from constant-pressure simulations

We report results of MD simulations of amorphous ice in the pressure range 0 - 22.5 kbar. The high-density amorphous ice (HDA) prepared by compression of Ih ice at T = 80 K is annealed to T = 170 K at intermediate pressures in order to generate relaxed states. We confirm the existence of recently observed phenomena, the very high-density amorphous ice and a continuum of HDA forms. We suggest that both phenomena have their origin in the evolution of the network topology of the annealed HDA phase with decreasing volume, resulting at low temperatures in the metastability of a range of densities.Comment: 11 pages, 5 postscript figures. To be published in Physical Review Letter

Evolutionary Metadynamics: a Novel Method to Predict Crystal Structures

A novel method for crystal structure prediction, based on metadynamics and evolutionary algorithms, is presented here. This technique can be used to produce efficiently both the ground state and metastable states easily reachable from a reasonable initial structure. We use the cell shape as collective variable and evolutionary variation operators developed in the context of the USPEX method [Oganov, Glass, \textit{J. Chem. Phys.}, 2006, \textbf{124}, 244704; Lyakhov \textit{et al., Comp. Phys. Comm.}, 2010, \textbf{181}, 1623; Oganov \textit{et al., Acc. Chem. Res.}, 2011, \textbf{44}, 227] to equilibrate the system as a function of the collective variables. We illustrate how this approach helps one to find stable and metastable states for Al$_2$SiO$_5$, SiO$_2$, MgSiO$_3$, and carbon. Apart from predicting crystal structures, the new method can also provide insight into mechanisms of phase transitions.Comment: 7 pages, 7 figures; CrystEngComm 2012, The Royal Society of Chemistr

Predicting crystal structures: the Parrinello-Rahman method revisited

By suitably adapting a recent approach [A. Laio and M. Parrinello, PNAS, 99, 12562 (2002)] we develop a powerful molecular dynamics method for the study of pressure-induced structural transformations. We use the edges of the simulation cell as collective variables. In the space of these variables we define a metadynamics that drives the system away from the local minimum towards a new crystal structure. In contrast to the Parrinello-Rahman method our approach shows no hysteresis and crystal structure transformations can occur at the equilibrium pressure. We illustrate the power of the method by studying the pressure-induced diamond to simple hexagonal phase transition in a model of silicon.Comment: 5 pages, 2 Postscript figures, submitte

Influence of Temperature and Anisotropic Pressure on the Phase Transitions in α-Cristobalite

The role of temperature and anisotropy of the applied load in the pressure–induced transformations of α -cristobalite is investigated by means of first principles molecular dynamics combined with the metadynamics algorithm for the study of solid-solid phase transitions. We reproduce the transition to α-PbO2 as found in experiments and we observe that the transition paths are qualitatively different and yield different products when a nonhydrostatic load is applied, giving rise to a new class of metastable structures with mixed tetrahedral and octahedral coordination

Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.Comment: 6 pages, minor correction

Ultraviolet and soft X--ray photon--photon elastic scattering in an electron gas

We have considered the processes which lead to elastic scattering between two far ultraviolet or X--ray photons while they propagate inside a solid, modeled as a simple electron gas. The new ingredient, with respect to the standard theory of photon--photon scattering in vacuum, is the presence of low--energy, nonrelativistic electron--hole excitations. Owing to the existence of two--photon vertices, the scattering processes in the metal are predominantly of second order, as opposed to fourth order for the vacuum case. The main processes in second order are dominated by exchange of virtual plasmons between the two photons. For two photons of similar energy $\hbar \Omega$, this gives rise to a cross section rising like $\Omega^2$ up to maximum of around $10^{-32}$~cm$^2$, and then decreasing like $\Omega^{-6}$. The maximal cross section is found for the photon wavevector $k \sim k_{F}$, the Fermi surface size, which typically means a photon energy $\hbar \Omega$ in the keV range. Possible experiments aimed at checking the existence of these rare but seemingly measurable elastic photon--photon scattering processes are discussed, using in particular intense synchrotron sources.Comment: 33 pages, TeX, Version 3.1, S.I.S.S.A. preprint 35/93/C

Residual Energies after Slow Quantum Annealing

Features of the residual energy after the quantum annealing are investigated. The quantum annealing method exploits quantum fluctuations to search the ground state of classical disordered Hamiltonian. If the quantum fluctuation is reduced sufficiently slowly and linearly by the time, the residual energy after the quantum annealing falls as the inverse square of the annealing time. We show this feature of the residual energy by numerical calculations for small-sized systems and derive it on the basis of the quantum adiabatic theorem.Comment: 4 pages, 2 figure