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Showing papers on "Phase transition published in 1998"


Journal ArticleDOI
TL;DR: A review of the metal-insulator transition can be found in this article, where a pedagogical introduction to the subject is given, as well as a comparison between experimental results and theoretical achievements.
Abstract: Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t\ensuremath{-}J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

5,781 citations


Journal ArticleDOI
26 Feb 1998-Nature
TL;DR: In this article, it was shown that a first-order ferromagnetic phase transition with a transition temperature nearly equal to the bulk value can be found in trifluoroethylene polymers with diameters as small as 10'A (two monolayers) even in these almost two-dimensional films.
Abstract: Ultrathin crystalline films offer the possibility of exploring phase transitions in the crossover region between two and three dimensions. Second-order ferromagnetic phase transitions have been observed in monolayer magnetic films1,2, where surface anisotropy energy stabilizes the two-dimensional ferromagnetic state at finite temperature3. Similarly, a number of magnetic materials have magnetic surface layers that show a second-order ferromagnetic–paramagnetic phase transition with an increased Curie temperature4. Ferroelectricity is in many ways analogous to ferromagnetism, and bulk-like ferroelectricity and finite-size modifications of it have been seen in nanocrystals as small as 250 A in diameter5, in perovskite films 100 A thick6 and in crystalline ferroelectric polymers as thin as 25 A (7-10). But these results can be interpreted as bulk ferroelectricity suppressed by surface depolarization energies, and imply that the bulk transition has a minimum critical size11,12,13. Here we report measurements of the ferroelectric transition in crystalline films of a random copolymer of vinylidene fluoride and trifluoroethylene just 10 A (two monolayers) thick. We see a first-order ferroelectric phase transition with a transition temperature nearly equal to the bulk value, even in these almost two-dimensional films. In addition, we see a second first-order transition at a lower temperature, which seems to be associated with the surface layers only. The near-absence of finite-size effects on the bulk transition implies that these films must be considered as two-dimensional ferroelectrics.

754 citations


Journal ArticleDOI
16 Jan 1998-Science
TL;DR: In situ scanning tunneling microscopy revealed that the smaller square-based pyramids transform abruptly during growth to significantly larger multifaceted domes, and that few structures with intermediate size and shape remain.
Abstract: Chemical vapor deposition of germanium onto the silicon (001) surface at atmospheric pressure and 600 degrees Celsius has previously been shown to produce distinct families of smaller (up to 6 nanometers high) and larger (all approximately 15 nanometers high) nanocrystals. Under ultrahigh-vacuum conditions, physical vapor deposition at approximately the same substrate temperature and growth rate produced a similar bimodal size distribution. In situ scanning tunneling microscopy revealed that the smaller square-based pyramids transform abruptly during growth to significantly larger multifaceted domes, and that few structures with intermediate size and shape remain. Both nanocrystal shapes have size-dependent energy minima that result from the interplay between strain relaxation at the facets and stress concentration at the edges. A thermodynamic model similar to a phase transition accounts for this abrupt morphology change.

736 citations


Journal ArticleDOI
TL;DR: In this paper, the phase diagram of QCD with two massless quark flavors in the space of temperature $T$ and chemical potential of the baryon charge \ensuremath{\mu} was analyzed.
Abstract: We analyze the phase diagram of QCD with two massless quark flavors in the space of temperature $T$ and chemical potential of the baryon charge \ensuremath{\mu} using available experimental knowledge of QCD, insights gained from various models, as well as general and model independent arguments including continuity, universality, and thermodynamic relations. A random matrix model is used to describe the chiral symmetry restoration phase transition at finite $T$ and \ensuremath{\mu}. In agreement with general arguments, this model predicts a tricritical point in the $T\ensuremath{\mu}$ plane. Certain critical properties at such a point are universal and can be relevant to heavy ion collision experiments.

487 citations


Journal ArticleDOI
12 Mar 1998-Nature
TL;DR: In this article, an experimental approach that is not restricted by the barrier imposed by TH, involving measurement of the decompression-induced melting curves of several high-pressure phases of ice in small emulsified droplets, is reported.
Abstract: Although liquid water has been the focus of intensive research for over 100 years, a coherent physical picture that unifies all of the known anomalies of this liquid1,2,3, is still lacking Some of these anomalies occur in the supercooled region, and have been rationalized on the grounds of a possible retracing of the liquid–gas spinodal (metastability limit) line into the supercooled liquid region4,5,6,7, or alternatively the presence of a line of first-order liquid–liquid phase transitions in this region which ends in a critical point8,9,10,11,12,13,14, But these ideas remain untested experimentally, in part because supercooled water can be probed only above the homogeneous nucleation temperature TH at which water spontaneously crystallizes Here we report an experimental approach that is not restricted by the barrier imposed by TH, involving measurement of the decompression-induced melting curves of several high-pressure phases of ice in small emulsified droplets We find that the melting curve for ice IV seems to undergo a discontinuity at precisely the location proposed for the line of liquid–liquid phase transitions8 This is consistent with, but does not prove, the coexistence of two different phases of (supercooled) liquid water From the experimental data we calculate a possible Gibbs potential surface and a corresponding equation of state for water, from the forms of which we estimate the coordinates of the liquid–liquid critical point to be at pressure Pc ≈ 01 GPa and temperature Tc ≈ 220 K

480 citations


Journal ArticleDOI
TL;DR: In this paper, a surface force balance with extremely high resolution in measuring shear forces has been used to study the properties of films of the simple organic solvents cyclohexane, octamethylcyclotetrasiloxane, and toluene, confined in a gap between smooth solid surfaces.
Abstract: A surface force balance with extremely high resolution in measuring shear forces has been used to study the properties of films of the simple organic solvents cyclohexane, octamethylcyclotetrasiloxane, and toluene, confined in a gap between smooth solid surfaces. We were able to probe in detail the transition between liquidlike and solidlike behavior of the films as the gap thickness decreased. Our results reveal that in such confined layers the liquids are fluid down to a film thickness of few molecular layers (typically seven, depending on the particular liquid examined). On further decreasing the gap thickness by a single molecular layer, the films undergo an abrupt transition to become solidlike in the sense that they are able to sustain a finite shear stress for macroscopic times. At the transition, the effective rigidity of the films, quantified in terms of an effective creep viscosity, increases by at least seven orders of magnitude. This sharp transition is reversible and occurs as a function of the confinement alone: it does not require external applied pressure. Following the transition the confined films behave under shear in a manner resembling ductile solids.

431 citations


Journal ArticleDOI
TL;DR: In this paper, the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a one-dimensional lattice was considered.
Abstract: We consider the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a one- dimensional lattice. The long-term system dynamics, stationary states, and the nature of phase transitions between steady states can be understood in terms of the interplay of two characteristic velocities, the collective velocity and the shock (domain wall) velocity. This interplay results in two distinct types of domain walls whose dynamics is computed. We conclude that the phase diagram of the ASEP is generic for one-component driven lattice gases with a single maximum in the current-density relation.

357 citations



Journal ArticleDOI
TL;DR: In this article, the phase diagram of strongly interacting matter as a function of temperature and baryon number density is explored, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons.
Abstract: We explore the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. Our treatment allows us to investigate the possible simultaneous formation of condensates in the conventional quark--anti-quark channel (breaking chiral symmetry) and in a quark--quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs via a first order transition between a phase with low (or zero) baryon density and a high density color superconducting phase. We find color superconductivity in the high density phase for temperatures less than of order tens to 100 MeV, and find coexisting $ $ and $ $ condensates in this phase in the presence of a current quark mass. At high temperatures, the chiral phase transition is second order in the chiral limit and is a smooth crossover for nonzero current quark mass. A tricritical point separates the first order transition at high densities from the second order transition at high temperatures. In the presence of a current quark mass this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.

313 citations


Journal ArticleDOI
TL;DR: In this paper, the authors measured and analyzed the Extended X-ray Absorption Fine Structure (EXAFS) of BaTiO3 at the barium k edge and the X-rays absorption near edge Structure (XANES) at the titanium K edge.
Abstract: We have measured and analyzed the Extended X-ray Absorption Fine Structure (EXAFS) of BaTiO3 at the barium k edge and the X-ray Absorption Near Edge Structure (XANES) at the titanium K edge. Our structural data show that the sequence of phase transitions in this material as the temperature increases is explained by a disordering of domains wherein the local structural environment remains approximately rhombohedrally distorted at all temperatures around both metal sites. As the temperature is raised, the long range correlations between these local distortions change, resulting in the observed sequence of phase transitions. Our measurements confirm the model of eight-site disorder used to explain the phase diagram of BaTiO3. We show that EXAFS and XANES are sensitive probes of both the magnitude and direction of the local structural distortions which accompany ferroelectricity and therefore are sensitive probes of the microscopic mechanism of ferroelectricity.

283 citations


Journal ArticleDOI
01 Sep 1998-Polymer
TL;DR: A review of the role of metastability in phase and phase transition behaviors can be found in this paper, where the authors describe the general principles of metastable in polymer phases and phase transitions and provide illustrations from current experimental works.

Journal ArticleDOI
19 Jun 1998-Science
TL;DR: In this paper, the light-induced insulator-metal transition in the "colossal magnetoresistance" compound Pr0.7Ca0.3MnO3 is shown to generate a well-localized conducting path while the bulk of the sample remains insulating.
Abstract: The light-induced insulator-metal transition in the “colossal magnetoresistance” compound Pr0.7Ca0.3MnO3 is shown to generate a well-localized conducting path while the bulk of the sample remains insulating. The path can be visualized through a change of reflectivity that accompanies the phase transition. Its visibility provides a tool for gaining insight into electronic transport in materials with strong magnetic correlations. For example, a conducting path can be generated or removed at an arbitrary position just because of the presence of another path. Such manipulation may be useful in the construction of optical switches.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the magnetic-field-induced phase transitions of the charge carriers and found that the destruction of the real-space ordering is accompanied with a structural phase transition as well as with the magnetic phase transition and the colossal magnetoresistance effect.
Abstract: We have investigated the magnetic-field-induced phase transitions of ${R}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ ($R=\mathrm{Pr}$ and Nd, $x=0.50,$ 0.45 and 0.50, 0.45, 0.40) by measurements of magnetization, magnetoresistance, and magnetostriction utilizing a nondestructive long-pulse magnet (generating up to 40 T). We observed processes where magnetic fields destroy the real-space ordering of the charge carriers and cause insulator-to-metal phase transitions over the whole temperature region below about 250 K. We found that the destruction of the charge ordering is accompanied with a structural phase transition as well as with the magnetic phase transition and the colossal magnetoresistance effect. The different profiles of the temperature vs transition field curve depending on the carrier concentration $x$ may be ascribed to the difference in the entropy between the commensurate and the discommensurate charge-ordered state. It turned out that the stability of the charge-ordered state is strongly correlated with the colinear antiferromagnetic ordering of the localized Mn moments.


Journal ArticleDOI
TL;DR: In this article, the 3D nonlinear Ginzburg-landau (GL) equations were solved numerically and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth were investigated.
Abstract: Solving numerically the 3D nonlinear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multivortex superconducting state to a giant vortex state by increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as a function of the magnetic field, a reentrant behavior between the multivortex and the giant vortex state.

Journal ArticleDOI
TL;DR: In this paper, a phenomenological stochastic field kinetic model of coherent precipitation of L12 ordered intermetallics from a disordered f.c. solid solution has been developed explicitly taking into account both the lattice misfit strain and the four types of antiphase domains formed as a result of the L12 ordering.

Journal ArticleDOI
TL;DR: In this article, the second-order elastic constant Cik softens as a linear function of temperature with a slope in the low-symmetry phase that depends on the thermodynamic character of the transition.
Abstract: Landau theory provides a formal basis for predicting the variations of elastic constants associated with phase transitions in minerals. These elastic constants can show substantial anomalies as a transition point is approached from both the high-symmetry side and the low-symmetry side. In the limiting case of proper ferroelastic behaviour, individual elastic constants, or some symmetry­ adapted combination of them, can become very small if not actually go to zero. When the driving order parameter for the transition is a spontaneous strain, the total excess energy for the transition is purely elastic and is given by: which has the same form as a Landau expansion. In this case, the second-order elastic constant Cik softens as a linear function of temperature with a slope in the low-symmetry phase that depends on the thermodynamic character of the transition. If the driving order parameter, Q, is some structural feature other than strain, the excess energy is given by: G = ia(T Tc )Q2 + ±bQ4 + . . . + .LAi,m,neFQn + i � Ci%eiek l,m,n l,k In this case, the effect of coupling, described by the term in AemQn, is to cause a great diversity of elastic variations depending on the values of m and n (typically 1, 2 or 3), the thermodynamic character of the transition and the magnitudes of any non-symmetry-breaking strains. The elastic constants are obtained by taking the appropriate second derivatives of G with respect to strain in a manner that includes the structural relaxation associated with Q. The symmetry properties of second-order elastic constant matrices can be related to the symmetry rules for individual phase transitions in order to predict elastic stability limits, and to derive the correct form of Landau expansion for any symmetry change. Selected examples of \"ideal\" behaviour for different types of driving order parameter, coupling behaviour and thermodynamic character have been set out in full in this review. Anomalies in the elastic properties on a macroscopic scale can also be understood in terms of the properties of acoustic phonons. These microseopie processes must be considered if elastic anomalies due to dynamical effects are to be accounted for 0935122 1/98/00 10-0693 $ 30.00 001:1 0.1127/ejm/1 0/4/0693 © 1998 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart

Book
27 Feb 1998
TL;DR: In this paper, the authors present a model for the second-order phase transition in a single-Ion model of a Diatomic crystal and apply the Landau theory to phase transitions in Uniaxial Ferroelectrics and demonstrate the applicability of Landau Theory to Phase Transitions of Displacive and Order-Disorder types.
Abstract: 1. General Characteristics of Structural Phase Transitions in Crystals.- 1.1 First- and Second-Order Structural Phase Transitions.- 1.2 Structural Phase Transitions of Displacive and Order-Disorder Types.- 1.3 The Domain Structure.- 1.4 Ferroelectric Phase Transitions.- 1.5 Basic Types of Ferroelectric Crystals.- 2. Phenomenological Theory of Second-Order Structural Transitions in Crystals.- 2.1 The Incomplete Thermodynamic Potential.- 2.2 Structural Phase Transitions Described by a One-Component Order Parameter.- 2.3 Structural Phase Transitions Described by Two- and Three-Component Order Parameters.- 3. Proper Ferroelectrics: Anomalies of Physical Properties in Phase Transitions.- 3.1 Anomalies of Thermal and Electrical Properties (One-Component Order Parameter).- 3.2 Anomalies of Electrical Properties (Multicomponent Order Parameter).- 3.3 First-Order Phase Transitions Close to Second-Order Transitions.- 3.4 The Tricritical Point.- 4. Dielectric Anomalies in Structural Nonferroelectric and Improper Ferroelectric Phase Transitions.- 4.1 Nonferroelectric Phase Transitions: Dielectric Anomalies.- 4.2 Improper Ferroelectric Phase Transitions: Dielectric Anomalies.- 5. Anomalies of Elastic and Electromechanical Characteristics of Crystals in Second-Order Phase Transitions.- 5.1 One-Component Order Parameter: Elastic Properties of an Isotropic Liquid.- 5.2 One-Component Order Parameter: Elastic Properties of an Anisotropic Crystal.- 5.3 Ferroelectric-Ferroelastics: One-Component Order Parameter with Transformation Properties of the Component of a Second-Rank Tensor and the Polar Vector.- 5.4 Temperature Dependences of "Morphic" Moduli of Elasticity.- 5.5 Two-Component Order Parameter: Elastic Properties of Crystals.- 5.6 Piezoelectric Effect and Electrostriction in the Case of One-Component Order Parameter and Centrosymmetric Paraelectric Phase.- 5.7 Piezoelectric Effect in the Case of One-Component Order Parameter and Noncentrosymmetric Paraelectric Phase.- 6. Fluctuations of the Order Parameter in Phenomenological Theory.- 6.1 Spatially Inhomogeneous Fluctuations of the Order Parameter in the Incomplete Thermodynamic Potential.- 6.2 Applicability of Landau Theory to Nonferroelectric Structural Phase Transitions.- 6.3 Applicability of Landau Theory to Phase Transitions in Uniaxial Ferroelectrics.- 6.4 Fluctuational Phenomena in Ferroelectric-Ferroelastics and in Phase Transitions in Multiaxial Ferroelectrics.- 7. Structural Phase Transitions in the Single-Ion Model.- 7.1 Problems of the Microscopic Theory.- 7.2 The Single-Ion Model of a Diatomic Crystal.- 7.3 Phase Transitions of Displacive and Order-Disorder Types in the Single-Ion Model.- 7.4 Applicability of the Landau Theory to Phase Transitions of Displacive and Order-Disorder Types.- 8. Statistical Theory of Ferroelectric Phase Transitions of the Order-Disorder Type.- 8.1 The Hamiltonian of a Uniaxial Ferroelectric with an Order-Disorder Phase Transition.- 8.2 The Free Energy of an Order-Disorder Crystal in the Self-Consistent Molecular Field Approximation.- 8.3 Tunneling Effects in Hydrogen-Containing Ferroelectrics.- 8.4 The Cluster Approximation: Crystals of the KH2P04 Group.- 9. Dynamics of Displacive and Order-Disorder Phase Transitions.- 9.1 The Equation of Motion of the Order Parameter.- 9.2 Dynamic Dielectric Constant: Order-Disorder Phase Transitions.- 9.3 Dynamic Dielectric Constant: Displacive Phase Transitions.- 9.4 Microscopic Theory of Dynamic Processes in Displacive Phase Transitions.- 9.5 Microscopic Theory of Dynamic Processes in Order-Disorder Phase Transitions.- 9.6 Dielectric Constant and Soft Mode: The Lyddane-Sachs-Teller Relation.- 10. Domain Structure and Defects.- 10.1 Nucleation of Domains in a Structural Phase Transition.- 10.2 Domain Wall Structure: One-Component Order Parameter.- 10.3 Domain Wall Structure: Two-Component Order Parameter.- 10.4 Motion of the Domain Wall in an Ideal and a Real Crystal.- 10.5 Motion of the Domain Wall: Account of the Discreteness of the Crystal.- 10.6 Domain Walls and Defects.- 10.7 Defects in the Symmetrical Phase.- 10.8 Domains in Proper Ferroelectrics.- 10.9 Domains in Ferroelastics.- 10.10 Domains in Polyaxial Ferroelectrics.- 11. Ferroelectrics with an Incommensurate Phase.- 11.1 Phase Transitions into an Incommensurate Phase.- 11.2 Phenomenological Theory of Phase Transitions into an Incommensurate Phase.- 11.3 Specific Features of Crystal Lattice Vibrations in an Incommensurate Phase.- 11.4 The Incommensurate Phase in a Real Crystal.- 11.5 The Commensurate-Incommensurate Phase Transition: A Special Type of Phase Transition.- 11.6 Evolution of the Structure of the Incommensurate Phase (General Picture).- 11.7 Evolution of the Structure of the Incommensurate Phase (the Continuum Approximation).- 12. Ferroelectric Liquid Crystals.- 12.1 Basic Types of Orientational Ordering in Liquid Crystals.- 12.2 Conditions for Existence of Dipolar Ordering in Liquid Crystals.- 12.3 Phenomenological Theory of Phase Transition SmA* -? SmC*.- 12.4 The Behavior of a Ferroelectric Smectic Liquid Crystal in an External Electric Field.- 13. Crystallochemical Aspects of the Theory of Ferroelectric Phenomena.- 13.1 Calculation of the Constants of the Hamiltonians of Some Crystals.- 13.2 An Approach Based on the Classical Theory of Ionic Crystals.- 14. Recommended Literature.- References.

Journal ArticleDOI
TL;DR: The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena as mentioned in this paper.
Abstract: The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena. It arose following the discovery in 1932 of a suprising new phase transition in liquid helium, the “lambda transition,” when W. H. Keesom and coworkers in Leiden, Holland observed a λhaped “jump” discontinuity in the curve giving the temperature dependence of the specific heat of helium at a critical value. This apparent jump led Ehrenfest to introduce a classification of phase transitions on the basis of jumps in derivatives of the free energy function. This classification was immediately applied by A.J. Rutgers to the study of the transition from the normal to superconducting state in metals. Eduard Justi and Max von Laue soon questioned the possibility of its class of “second-order phase transitions” -- of which the “lambda transition was believed to be the arche type -- but C.J. Gorter and H.B.G. Casimir used an “order parameter to demonstrate their existence in superconductors. As a crossroads of study, the Ehrenfest classification was forced to undergo a slow, adaptive evolution during subsequent decades. During the 1940s the classification was increasingly used in discussions of liquid-gas, order-disorder, paramagnetic-ferromagnetic and normal-super-conducting phase transitions. Already in 1944 however, Lars Onsagers solution of the Ising model for two-dimensional magnets was seen to possess a derivative with a logarithmic divergence rather than a jump as the critical point was approached. In the 1950s, experiments further revealed the lambda transition in helium to exhibit similar behavior. Rather than being a prime example of an Ehrenfest phase transition, the lambda transition was seen to lie outside the Ehrenfest classification. The Ehrenfest scheme was then extended to include such singularities, most notably by A. Brain Pippard in 1957, with widespread acceptance. During the 1960s these logarithmic infinities were the focus of the investigation of “scaling” by Leo Kadanoff, B. Widom and others. By the 1970s, a radically simplified binary classification of phase transitions into “first-order” and “continuous” transitions was increasingly adopted.

Journal ArticleDOI
TL;DR: In this paper, a thermodynamic analysis of shape transition based on the free energy of the swollen network is provided, which includes the elasticity of network chains as well as magnetic interactions of finely dispersed solid particles with the external magnetic field.
Abstract: Magnetic field sensitive gels, called ferrogels, are chemically cross-linked polymer networks swollen by a ferrofluid. The monodomain magnetic particles, with a typical size of about 10 nm, couple the shape of the polymer gel to the nonuniform external magnetic field. Shape distortion occurs instantaneously and disappears abruptly when an external magnetic field is applied or removed, respectively. This work provides a thermodynamic analysis of shape transition based on the free energy of the swollen network that includes the elasticity of network chains as well as magnetic interactions of finely dispersed solid particles with the external field. It is shown that noncontinuous shape transition is due to a shift of equilibrium state from one local minimum to another one, similar to a first-order phase transition. The discussions presented here may be useful for the design of magnetically active soft polymeric actuators.

Journal ArticleDOI
TL;DR: This work investigates the behavior of the response functions, equation of state, and entropy of a schematic waterlike model that exhibits singularity-free behavior, and illustrates the simplest thermodynamically consistent interpretation that is in accord with existing experimental evidence on water’s low-temperature anomalies.
Abstract: According to the singularity-free interpretation of the thermodynamics of supercooled water, the isothermal compressibility, isobaric heat capacity, and the magnitude of the thermal expansion coefficient increase sharply upon supercooling, but remain finite. No phase transition or critical point occurs at low temperatures. Instead, there is a pronounced but continuous increase in volume and a corresponding decrease in entropy at low temperatures, the sharpness of which becomes more pronounced the lower the temperature and the higher the pressure. We investigate the behavior of the response functions, equation of state, and entropy of a schematic waterlike model that exhibits singularity-free behavior, and thereby illustrate the simplest thermodynamically consistent interpretation that is in accord with existing experimental evidence on water’s low-temperature anomalies. In spite of its simplicity, the model captures many nontrivial aspects of water’s thermodynamics semiquantitatively.

Journal ArticleDOI
TL;DR: In this article, a variational method was proposed to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice, and the variational space can be systematically expanded to achieve high accuracy with modest computational resources.
Abstract: We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the 1d polaron energy at intermediate coupling). We compute ground and low-lying excited state properties of the model at continuous values of the wavevector $k$ in essentially all parameter regimes. Our results for the polaron energy band, effective mass and correlation functions compare favorably with those of other numerical techniques including DMRG, Global Local and exact diagonalization. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong coupling perturbation theory.

Journal ArticleDOI
TL;DR: In this paper, an expanded form of the 2-4-6 Landau potential was developed to account for these strains and to permit calculation of the elastic constant variations, which are compatible with previous determinations of the order parameter variation in a quartz only if there is a nonlinear relationship between the individual strains and the square of the ordering parameter.
Abstract: Spontaneous strains for the a ↔ b transition in quartz were determined from lattice parameter data collected by X-ray powder diffraction and neutron powder diffraction over the temperature range ;5‐1340 K. These appear to be compatible with previous determinations of the order parameter variation in a quartz only if there is a non-linear relationship between the individual strains and the square of the order parameter. An expanded form of the 2-4-6 Landau potential usually used to describe the phase transition was developed to account for these strains and to permit calculation of the elastic constant variations. Calibration of the renormalized coefficients of the basic 2-4-6 potential, using published heat capacity data, provides a quantitative description of the excess free energy, enthalpy, entropy, and heat capacity. Values of the unrenormalized coefficients in the Landau expansion that include all the strain-order parameter coupling coefficients were used to calculate variations of the elastic constants. Values of the bare elastic constants were extracted from published elasticity data for b quartz. Calculated variations of C11 and C12 match their observed variations closely, implying that the extended Landau expansion provides a good representation of macroscopic changes within the (001) plane of quartz. Agreement was not as close for C33, suggesting that other factors may influence the strain parallel to [001]. The geometrical mechanism for the transition involves both rotations and shearing of SiO4 tetrahedra, with each coupled differently to the driving order parameter. Only the shearing part of the macroscopic distortions appears to show the same temperature dependence as other properties that scale with Q 2 . Coupling between the strain and the order parameter provides the predominant stabilization energy for a quartz and is also responsible for the first-order character of the transition.

Journal ArticleDOI
TL;DR: In this article, the thermodynamic theory of the pseudoelastic behaviour of SMA is generalized to include new observed effects in isotropic solids, and conditions for the initiation of martensitic phase transitions (p.t.) are derived.
Abstract: The thermodynamic theory of the pseudoelastic behaviour of SMA is generalized to include new observed effects in isotropic solids. It has been shown that macroscopic eigenstrain due to martensitic phase transitions (p.t.) is a homogeneous function of the stress of order zero, provided that partial thermodynamic equilibrium occurs. The specific form of the Gibbs potential is presented and new conditions for the initiation of p.t. are derived. They are expressed in terms of the temperature, second and third invariants of the stress deviator. The thermostatic properties and phenomenological constants are found for a NiTi alloy using experimental data reported in the literature. The theoretical and experimental results are compared for simple tension compression and pure shear.

Journal ArticleDOI
TL;DR: In this paper, a non-local anisotropic model for phase separation in two-phase fluids at equilibrium is considered, and it is shown that when the thickness of the interface tends to zero in a suitable way, the classical surface tension model is recovered.
Abstract: In this paper we consider a non-local anisotropic model for phase separation in two-phase fluids at equilibrium, and show that when the thickness of the interface tends to zero in a suitable way, the classical surface tension model is recovered. Relevant examples are given by continuum limits of ferromagnetic Ising systems in equilibrium statistical mechanics.

Journal ArticleDOI
TL;DR: In this article, the authors studied hysteresis for a two-dimensional spin-$1/2$ nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations.
Abstract: We study hysteresis for a two-dimensional spin- $1/2$ nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{ u}$.

Journal ArticleDOI
01 Sep 1998-Polymer
TL;DR: In this article, the volume phase transition of PNIPAM microgels was studied by a combination of static and dynamic laser light scattering and the thermodynamically stable collapsed single-chain globule was observed for the first time.

Journal ArticleDOI
TL;DR: In this paper, the structural switching fluctuations of the local structure in liquid water are studied with the molecular-dynamics simulation and the order parameter to describe this structural switching fluctuation is derived by carefully filtering out the fast oscillating components from the simulation data.
Abstract: Spatiotemporal fluctuations of the local structure in liquid water are studied with the molecular-dynamics simulation. At temperatures around and above the melting point, each molecule alternately goes through the structured period and the destructured period. Lifetime of each period spreads from several hundred fs to 10 ps at 0 °C at 1 atm. The order parameter to describe this structural switching fluctuations is derived by carefully filtering out the fast oscillating components from the simulation data. By analyzing the neutron-weighted pair correlation function, we find that the clusters of the structured molecules and the clusters of the destructured molecules are similar to the clusters of low-density amorphous (LDA) ice and the clusters of high-density amorphous (HDA) ice, respectively. Simulated liquid water is, therefore, a composite of the LDA-like clusters and the HDA-like clusters even at temperatures well above the melting point. The large amplitude structural fluctuation of water at around an...

Journal ArticleDOI
TL;DR: In this article, a scalar function u represents the macroscopic density profile of a system which has two equilibrium pure phases described by the profiles u ≡ +1 and u ≡ −1.
Abstract: where u is a scalar density function on a domain of R and takes values in [−1, 1], W is a positive double-well potential which vanishes at ±1, and J is a positive, possibly anisotropic, interaction potential which vanishes at infinity (see paragraph 1.2 for precise definitions). The scalar function u represents the macroscopic density profile of a system which has two equilibrium pure phases described by the profiles u ≡ +1 and u ≡ −1. The integral ∫ W (u) at the right side of (1.1) forces a minimizer of F to take values close to +1 and −1 (phase separation), while the double integral represents an interaction energy which penalizes the spatial inhomogeneity of the system (surface tension). In equilibrium Statistical Mechanics functionals of the form (1.1) arise as free energies of continuum limits of Ising spin systems on lattices; in this setting u plays the role of a macroscopic magnetization density and J is a ferromagnetic Kac potential (see for instance [2] and references therein). We underline the analogy with the more familiar gradient theory for phase transition proposed in [9], where the free energy of the system is of the form

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TL;DR: In this paper, the MSSM finite temperature electroweak phase transition with lattice Monte Carlo simulations was studied for a large Higgs mass (mH ≈ 95 GeV) and light stop masses (mtR ∼ 150-160 GeV).