Showing papers on "Phase transition published in 2005"

Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition

Abstract: We investigate, for two water models displaying a liquid–liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid–liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid–liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid–liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.

Dynamics of a Quantum Phase Transition

Abstract: We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.

Prediction of TiO2 nanoparticle phase and shape transitions controlled by surface chemistry.

Abstract: The effects of surface chemistry on the morphology and phase stability of titanium dioxide nanoparticles have been investigated using a thermodynamic model based on surface free energies and surface tensions obtained from first principles calculations. It has been found that surfaces representing acidic and alkaline conditions have a significant influence on both the shape of the nanocrystals and the anatase-to-rutile transition size. The latter introduces the possibility of inducing phase transitions by changing the surface chemistry.

Dynamics of a quantum phase transition: exact solution of the quantum Ising model.

Abstract: The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.

Reaction coordinates and rates from transition paths

Abstract: The molecular mechanism of a reaction in solution is reflected in its transition-state ensemble and transition paths. We use a Bayesian formula relating the equilibrium and transition-path ensembles to identify transition states, rank reaction coordinates, and estimate rate coefficients. We also introduce a variational procedure to optimize reaction coordinates. The theory is illustrated with applications to protein folding and the dipole reorientation of an ordered water chain inside a carbon nanotube. To describe the folding of a simple model of a three-helix bundle protein, we variationally optimize the weights of a projection onto the matrix of native and nonnative amino acid contacts. The resulting one-dimensional reaction coordinate captures the folding transition state, with formation and packing of helix 2 and 3 constituting the bottleneck for folding.

Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices

Abstract: The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner's dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using Monte Carlo simulations and the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.

Relaxor ferroelectricity and colossal magnetocapacitive coupling in ferromagnetic CdCr2S4.

Abstract: Ferromagnets have been known since ancient times. Ferroelectrics were discovered 80 years ago, and both properties are important in many areas of technology and electronics. Materials displaying both ferroelectricity and ferromagnetism combine the potential applications of both parent phases, with a range of new applications in optics, electronic circuitry and multiple-state memory devices. Such materials are rare, but one described this week, the common sulpho-spinel CdCr2S4, shows promise. It combines reasonable ordering temperatures (the point at which magnetic properties disappear) with sizeable magnetization and polarization well suited for application. Materials in which magnetic and electric order coexist—termed ‘multiferroics’ or ‘magnetoelectrics’—have recently become the focus of much research1,2,3,4. In particular, the simultaneous occurrence of ferromagnetism and ferroelectricity, combined with an intimate coupling of magnetization and polarization via magnetocapacitive effects, holds promise for new generations of electronic devices. Here we present measurements on a simple cubic spinel compound with unusual, and potentially useful, magnetic and electric properties: it shows ferromagnetic order coexisting with relaxor ferroelectricity (a ferroelectric cluster state with a smeared-out phase transition), both having sizable ordering temperatures and moments. Close to the ferromagnetic ordering temperature, the magnetocapacitive coupling (characterized by a variation of the dielectric constant in an external magnetic field) reaches colossal values, approaching 500 per cent. We attribute the relaxor properties to geometric frustration, which is well known for magnetic moments but here is found to impede long-range order of the structural degrees of freedom that drive the formation of the ferroelectric state.

Local cooperativity mechanism in the DNA melting transition.

Abstract: We propose a statistical mechanics model for the melting transition of DNA. Base pairing and stacking are treated as separate degrees of freedom, and the interplay between pairing and stacking is described by a set of local rules which mimic the geometrical constraints in the real molecule. This microscopic mechanism intrinsically accounts for the cooperativity related to the free energy penalty of bubble nucleation. The model describes both the unpairing and unstacking parts of the spectroscopically determined experimental melting curves. Furthermore, the model explains the observed temperature dependence of the effective thermodynamic parameters used in models of the nearest neighbor type. We compute the partition function for the model through the transfer matrix formalism, which we also generalize to include nonlocal chain entropy terms.

The phase transition in inhomogeneous random graphs

Abstract: We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p) used to study the phase transition; also, it seems to be a property of many large real-world graphs. Our model includes as special cases many models previously studied. We show that under one very weak assumption (that the expected number of edges is `what it should be'), many properties of the model can be determined, in particular the critical point of the phase transition, and the size of the giant component above the transition. We do this by relating our random graphs to branching processes, which are much easier to analyze. We also consider other properties of the model, showing, for example, that when there is a giant component, it is `stable': for a typical random graph, no matter how we add or delete o(n) edges, the size of the giant component does not change by more than o(n).

Finite-size and pressure effects on the Raman spectrum of nanocrystalline anatase Ti O 2

Abstract: The Raman scattering behavior of anatase nanocrystals with average diameters of 4, 8, 20, and 34 nm has been compared with bulk crystal data in order to establish size-dependent changes to the phonon spectrum at ambient conditions. Further, the high-pressure behavior of the anatase nanocrystals was examined at room-temperature using in situ Raman scattering data obtained in diamond-anvil cells to a maximum pressure of 41 GPa. The size-dependent changes to the Raman spectrum are best explained in terms of three-dimensional confinement of phonons in finite-sized nanocrystalline anatase. The difference in slopes obtained for the pressure shifts of Raman modes between nanocrystalline and single crystal anatase is in conformity with the observed size-dependent bulk modulus values. The metastability of anatase as a function of pressure is demonstrated to be size dependent, with smaller crystallites preserving the structure to higher pressures. Three size regimes have been recognized for the pressure-induced phase transition of anatase at room temperature: an anatase-amorphous transition regime at the smallest crystallite sizes, an anatase-baddeleyite transition regime at intermediate crystallite sizes, and an anatase--$\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{O}}_{2}$ transition regime comprising large nanocrystals to macroscopic single crystals. This size-dependent phase selectivity of anatase at high pressures explains the recent contradictory experimental data. A semiquantitative phase diagram for anatase metastability as a function of size and pressure at room temperature is proposed.

A Phenomenological Thermodynamic Potential for BaTiO3 Single Crystals

Abstract: A phenomenological thermodynamic potential was constructed based on the properties of bulk BaTiO3 single crystals. An eighth-order polynomial of Landau-Devonshire expansion was employed. It reproduces bulk properties including the three possible ferroelectric transition temperatures and their dependence on electric fields, as well as the dielectric and piezoelectric constants. Different from the existing thermodynamic potential, it is applicable to predicting the ferroelectric phase transitions and properties of BaTiO3 thin films under large compressive biaxial strains.

Universal adiabatic dynamics in the vicinity of a quantum critical point

Abstract: We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second-order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated near the critical point, the number of created excitations still goes to zero in the limit of infinitesimally slow variation of the tuning parameter. It scales with the adiabaticity parameter as a power related to the critical exponents $z$ and $\ensuremath{ u}$ characterizing the phase transition. We support general arguments by direct calculations for the Boson Hubbard and the transverse field Ising models.

Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review

Abstract: Second-harmonic generation (SHG) in magnetically ordered crystals is reviewed. The symmetry of such crystals is determined by the arrangement of both the charges and the spins, so their contributions to the crystallographic and the magnetic structures, respectively, must be distinguished. Magnetic SHG is introduced as a probe for magnetic structures and sublattice interactions. The specific degrees of optical experiments - including spectral, spatial, and temporal resolution - lead to the observation of novel physical effects that cannot be revealed by other techniques of probing magnetism. These include local or hidden phase transitions, interacting magnetized and polarized sublattices and domain walls, and magnetic interfaces. SHG in various centrosymmetric and noncentrosymmetric crystal classes of antiferromagnetic oxides such as Cr2O3, hexagonal RMnO3(R=Sc,Y,In,Ho-Lu), magnetic garnet films, CuB2O4, CoO, and NiO, is discussed.

Destruction of spin cycloid in (111)c-oriented BiFeO3 thin films by epitiaxial constraint: Enhanced polarization and release of latent magnetization

Abstract: In BiFeO3 films, it has been found that epitaxial constraint results in the destruction of a space modulated spin structure. For (111)c films, relative to corresponding bulk crystals, it is shown (i) that the induced magnetization is enhanced at low applied fields; (ii) that the polarization is dramatically enhanced; whereas, (iii) the lattice structure for (111)c films and crystals is nearly identical. Our results evidence that eptiaxial constraint induces a transition between cycloidal and homogeneous antiferromagnetic spin states, releasing a latent antiferromagnetic component locked within the cycloid.

Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments

Abstract: Foreword Preface to the English edition Nematic and Cholesteric Liquid Crystals PART A: OVERVIEW Some History Georges Friedel and Liquid Crystals The Discovery of Birefringence in Fluid Biological Substances by Buffon, Virchow, and Mettenheimer: Lyotropic Liquid Crystals Observation of the Surprising Behavior of Cholesteryl Esters by Planer and Reinitzer: Thermotropic Liquid Crystals Fliessende Kristalle or "The Flowing Crystals" of Otto Lehmann Modern Classification of Liquid Crystals The Terminology Introduced by Georges Friedel Modern Definition of Mesophases Broken Symmetries Short- and Long-Distance Order Classification of Smectic Phases Classification of Columnar Phases Chiral Smectic Phases Mesogenic anatomy Thermotropic Liquid Crystals Lyotropic Liquid Crystals Liquid Crystal Diblock Copolymers Colloidal Liquid Crystals PART B: MESOPHASES WITH AN ORIENTATIONAL ORDER Structure and Dielectric Properties of the Nematic Phase Quadrupolar Order Parameter The Uniaxial Nematic-Isotropic Liquid Phase Transition The Uniaxial Nematic-Biaxial Nematic Phase Transition Low-Frequency Dielectric Properties Optical Properties Nematoelasticity: Frederiks Transition and Light Scattering Grupp Experiment Frank-Oseen Free Energy Free Energy Minimization: Molecular Field and Elastic Torques Interpretation of the Grupp Experiment Magnetic Field Action Action of an Electric Field: Displays Elastic Light Scattering and the Determination of the Frank Constants Nonlinear Optics Appendix 1: Calculating the Scattering Cross-Section Appendix 2: Free Energy Expression in the Fourier Space Nematodynamics and Flow Instabilities Preliminary Observations Illustrating Some Fundamental Differences Between a Nematic and an Ordinary Liquid Equations of the Linear Nematodynamics Laminary Couette and Poiseuille Flows Laminary Flows and Their Stability Convective Instabilities of Electrohydrodynamic Origin Thermal Instabilities Appendix 1: "Derivation Under the Integral" Theorem Appendix 2: Rotational Identity Appendix 3: Calculation of the Irreversible Entropy Production Appendix 4: Energy Dissipation and Constitutive Laws in the Formalism of Leslie-Ericksen-Parodi Appendix 5: The Rayleigh-Benard Instability in Isotropic Fluids Defects and Textures in Nematics Polarizing Microscope Observations The Volterra-de Gennes-Friedel process Energy of a Wedge Planar Line in Isotropic Elasticity Continuous Core Model: Landau-Ginzburg-de Gennes Free Energy Interaction Energy Between Two Parallel Wedge Lines Dynamics of a Planar Wedge Line: Calculating the Friction Force Wedge line Stability: Escape in the Third Dimension Bloch and Ising Walls Induced by the Frederiks Instability Anchoring and Anchoring Transitions of Nematics on Solid Surfaces Precursors On the Notion of Interface Interface Symmetry and Classification of the Different Types of Anchoring Wetting and Anchoring Selection Anchoring Transitions Measuring the Anchoring Energy in the Homeotropic Case The nematic-isotropic liquid interface:static properties and directional growth instabilities. Anchoring Angle, Surface Tension, and Width of the Nematic-Isotropic Interface Landau-Ginzburg-de Gennes Theory Instabilities in Confined Geometry Elastic Correction to the Gibbs-Thomson Relation Directional Growth of the Nematic-Isotropic Liquid Front Cholesterics: the First Example of a Frustrated Mesophase Cholesteric Frustration Cholesteric Order Parameter and the Cholesteric-Isotropic Liquid Phase Transition Optical Properties of the Cholesteric Phase Defects and Textures of the Cholesteric Phase Unwinding Transition Cholesteric Hydrodynamics Blue Phases: a Second Example of a Frustrated Mesophase Experimental Evidence for the Cubic Symmetry of Blue Phases I and II Uniaxial Models for the Blue Phases: Disclination Lattices Biaxial Model of the Blue Phases by Grebel, Hornreich, and Shtrikman Landau Theory of the Blue Phases by Grebel, Hornreich, and Shtrikman Experiments BPIII or Blue Fog Overview of Growth Phenomena and _the Mullins-Sekerka Instability Gibbs-Thomson Relation and the Phase Diagram of a Diluted Binary Mixture The Minimal Model Stationary Plane Front Plane Front in the Diffusive Regime (GBPG

Atomic-scale visualization of inertial dynamics

Abstract: The motion of atoms on interatomic potential energy surfaces is fundamental to the dynamics of liquids and solids. An accelerator-based source of femtosecond x-ray pulses allowed us to follow directly atomic displacements on an optically modified energy landscape, leading eventually to the transition from crystalline solid to disordered liquid. We show that, to first order in time, the dynamics are inertial, and we place constraints on the shape and curvature of the transition-state potential energy surface. Our measurements point toward analogies between this nonequilibrium phase transition and the short-time dynamics intrinsic to equilibrium liquids.

Multicomponent alloy solidification: phase-field modeling and simulations.

Abstract: A general formulation of phase-field models for nonisothermal solidification in multicomponent and multiphase alloy systems is derived from an entropy functional in a thermodynamically consistent way. General expressions for the free energy densities, for multicomponent diffusion coefficients, and for both weak and faceted types of surface energy and kinetic anisotropy are possible. A three-dimensional simulator is developed to show the capability of the model to describe phase transitions, complex microstructure formation, and grain growth in polycrystalline textures.

Pressure-induced anomalous phase transitions and colossal enhancement of piezoelectricity in PbTiO3.

Abstract: We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase transition sequence induced by pressure, and a morphotropic phase boundary in a pure compound using first-principles calculations. Huge dielectric and piezoelectric coupling constants occur in the transition regions, comparable to those observed in the new complex single-crystal solid-solution piezoelectrics such as Pb(Mg(1/3)Nb(2/3))O3-PbTiO3, which are expected to revolutionize electromechanical applications. Our results show that morphotropic phase boundaries and giant piezoelectric effects do not require intrinsic disorder, and open the possibility of studying this effect in simple systems.

Gigantic Photoresponse in ¼-Filled-Band Organic Salt (EDO-TTF)2PF6

Abstract: We report that the organic salt (EDO-TTF)2PF6 with ¾-filled-band (¼-filled in terms of holes), which forms an organic metal with strong electron and lattice correlation, shows a highly sensitive response to photoexcitation. An ultrafast, photoinduced phase transition from the insulator phase to the metal phase can be induced with very weak excitation intensity at near room temperature. This response makes the material attractive for applications in switching devices with room-temperature operation. The observed photo-induced spectroscopic change shows that this photoinduced phase transition process is caused by the cooperative melting of charge ordering assisted by coherent phonon generation.

Unconventional critical behaviour in a quasi-two-dimensional organic conductor

Abstract: Changing the interactions between particles in an ensemble--by varying the temperature or pressure, for example--can lead to phase transitions whose critical behaviour depends on the collective nature of the many-body system. Despite the diversity of ingredients, which include atoms, molecules, electrons and their spins, the collective behaviour can be grouped into several families (called 'universality classes') represented by canonical spin models. One kind of transition, the Mott transition, occurs when the repulsive Coulomb interaction between electrons is increased, causing wave-like electrons to behave as particles. In two dimensions, the attractive behaviour responsible for the superconductivity in high-transition temperature copper oxide and organic compounds appears near the Mott transition, but the universality class to which two-dimensional, repulsive electronic systems belongs remains unknown. Here we present an observation of the critical phenomena at the pressure-induced Mott transition in a quasi-two-dimensional organic conductor using conductance measurements as a probe. We find that the Mott transition in two dimensions is not consistent with known universality classes, as the observed collective behaviour has previously not been seen. This peculiarity must be involved in any emergent behaviour near the Mott transition in two dimensions.

Distribution of current in nonequilibrium diffusive systems and phase transitions.

Abstract: We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains constant and another regime where the density becomes time dependent. Numerical data confirm this phase transition. This time dependent profile persists in the large drift limit and allows one to understand on physical grounds the results obtained earlier for the totally asymmetric exclusion process on a ring.

Review of crystal and domain structures in the PbZrxTi1−xO3 solid solution

Abstract: Several intermediate phases have recently been identified in the PbZrxTi1−xO3 (PZT) phase diagram, located close to the antiferroelectric-ferroelectric and morphotropic phase boundaries. Superlattice reflections from some of these phases are clearly visible in the appropriate electron diffraction patterns and have therefore been used to provide further information concerning their symmetry. Here, the structural distortions giving rise to the new phases are discussed and their domain structures compared with those of tetragonal and rhombohedral PZT. Coherent structural arguments are presented to explain the observed phase transition sequences.

Temperature and field hysteresis of the antiferromagnetic-to-ferromagnetic phase transition in epitaxial FeRh films

Abstract: The temperature and field hysteresis of the magnetization in the first order antiferromagnetic to ferromagnetic phase transition in FeRh films grown onto $c$-axis sapphire and MgO (001) are investigated. The transition to the ferromagnetic state upon heating and antiferromagnetic state upon cooling is generally broad indicating a heterogeneous transition due to defects so that antiferromagnetic and ferromagnetic domains coexist during the transition. However, the nucleation of antiferromagnetic domains upon cooling is abrupt for FeRh on $c$-axis sapphire which is indicative of homogeneous nucleation and growth of antiferromagnetic domains. The transition is further broadened when measuring with fields applied out of plane of the sample due to internal demagnetization fields. Temperature dependent remanent magnetization measurements reveal that field induced magnetization changes are irreversible during heating, but reversible during cooling. The field dependence of the shift in transition temperature is qualitatively modeled with an Ising spin type model utilizing a mean field approach. From this calculation a shift of $\ensuremath{-}10\phantom{\rule{0.3em}{0ex}}\mathrm{K}∕\mathrm{T}$ in transition temperature is determined in good agreement with the experimentally observed shift of $\ensuremath{-}8$ and $\ensuremath{-}9\phantom{\rule{0.3em}{0ex}}\mathrm{K}∕\mathrm{T}$ for FeRh films grown onto MgO (001) and c-axis sapphire, respectively.

Physical Acoustics in the Solid State

Abstract: Experimental Techniques.- Elasticity.- Thermodynamics and Phase Transitions.- Acoustic Waves in the Presence of Magnetic Ions.- Ultrasonics at Magnetic Phase Transitions.- Ultrasonics at Structural Transitions.- Metals and Semiconductors.- Unstable Moment Compounds.- Ultrasonics in Superconductors.- Coupling to Collective Excitations.- Ultrasonics in Low Dimensional Spin and Electronic Peierls-Systems.- Symmetry Effects with Sound Waves.- Ultrasonic Propagation in Tunneling Systems.- Conclusion and Outlook.

Spin chirality on a two-dimensional frustrated lattice.

Abstract: The collective behaviour of interacting magnetic moments can be strongly influenced by the topology of the underlying lattice. In geometrically frustrated spin systems, interesting chiral correlations may develop that are related to the spin arrangement on triangular plaquettes. We report a study of the spin chirality on a two-dimensional geometrically frustrated lattice. Our new chemical synthesis methods allow us to produce large single-crystal samples of KFe3(OH)6(SO4)2, an ideal Kagome lattice antiferromagnet. Combined thermodynamic and neutron scattering measurements reveal that the phase transition to the ordered ground-state is unusual. At low temperatures, application of a magnetic field induces a transition between states with different non-trivial spin-textures.

Space–time thermodynamics of the glass transition

Abstract: We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called “glass transition” is a manifestation of low action tails in these distributions where the entropy of trajectory space is subextensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order–disorder phenomenon in space–time occurring at a temperature Tg, which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models and note how these ideas apply more generally.