Description Of Phase Transitions Research Articles

Modeling Phase Transition in Battery Electrodes Using the Coupled Cahn-Hilliard – Phase Field Crystal Methods

Phase transitions in electrode materials are typically accompanied by lattice distortions and defect formations. These microscopic configurations affect an electrochemical cycle and influence the physical properties of electrode materials. Here, we explore the coupling between the lattice arrangements and Li-ion composition field in a representative FePO4 electrode particle. We develop and apply a 2D Cahn-Hilliard – phase-field crystal model that couples the Li-composition field with the underlying lattice symmetry of the FePO4 particle to describe phase transitions. We use this coupled model to explore lattice arrangements in uniformly lithiated/de-lithiated electrode particles, and to describe the lattice distortions across a diffuse phase boundary. Next, we model a Cahn-Hilliard type of diffusion for the Li-composition field and compute the accompanying structural evolution of atomic arrangements. In this theoretical study, we track the shape, size and orientation of grains during an electrochemical cycle. Furthermore, we report the electrode particles ability to reduce crystallographic imperfections through grain rotations and grain boundary migrations during an electrochemical cycle.

Weak and Strong Gels and the Emergence of the Amorphous Solid State.

Gels are amorphous solids whose macroscopic viscoelastic response derives from constraints in the material that serve to localize the constituent molecules or particles about their average positions in space. These constraints may either be local in nature, as in chemical cross-linking and direct physical associations, or non-local, as in case of topological “entanglement” interactions between highly extended fiber or sheet structures in the fluid. Either of these interactions, or both combined, can lead to “gelation” or “amorphous solidification”. While gels are often considered to be inherently non-equilibrium materials, and correspondingly termed “soft glassy matter”, this is not generally the case. For example, the formation of vulcanized rubbers by cross-linking macromolecules can be exactly described as a second order phase transition from an equilibrium fluid to an equilibrium solid state, and amorphous solidification also arises in diverse physical gels in which molecular and particle localization occurs predominantly through transient molecular associations, or even topological interactions. As equilibrium, or near equilibrium systems, such gels can be expected to exhibit universal linear and non-linear viscoelastic properties, especially near the “critical” conditions at which the gel state first emerges. In particular, a power-law viscoelastic response is frequently observed in gel materials near their “gelation” or “amorphous solidification” transition. Another basic property of physical gels of both theoretical and practical interest is their response to large stresses at constant shear rate or under a fixed macroscopic strain. In particular, these materials are often quite sensitive to applied stresses that can cause the self-assembled structure to progressively break down under flow or deformation. This disintegration of gel structure can lead to “yield” of the gel material, i.e., a fluidization transition, followed by shear thinning of the resulting heterogeneous “jelly-like” fluid. When the stress is removed, however, the material can relax back to its former equilibrium gel state, i.e., gel rejuvenation. In contrast, a non-equilibrium material will simply change its form and properties in a way that depends on processing history. Physical gels are thus unique self-healing materials in which the existence of equilibrium ensures their eventual recovery. The existence of equilibrium also has implications for the nature of both the linear and non-linear rheological response of gel materials, and the present paper explores this phenomenon based on simple scaling arguments of the kind frequently used in describing phase transitions and the properties of polymer solutions.

Lee-Yang zeros and large-deviation statistics of a molecular zipper.

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems. Today, Lee-Yang zeros are no longer just a theoretical concept; they have been determined in recent experiments. In one approach, the Lee-Yang zeros are extracted from the high cumulants of thermodynamic observables at finite size. Here we employ this method to investigate a phase transition in a molecular zipper. From the energy fluctuations in small zippers, we can predict the temperature at which a phase transition occurs in the thermodynamic limit. Even when the system does not undergo a sharp transition, the Lee-Yang zeros carry important information about the large-deviation statistics and its symmetry properties. Our work suggests an interesting duality between fluctuations in small systems and their phase behavior in the thermodynamic limit. These predictions may be tested in future experiments.

Numerical modeling of the waves evolution generated by the depressurization of the vessels containing a supercritical parameters coolant

The development of power plants focuses on increasing the parameters of water coolants up to a supercritical level. Depressurization of the unit circuits with such a coolant leads to emergency situations. Their scenarios can change significantly with the variation of initial pressure and temperature before the start of depressurization. When the pressure drops from the supercritical single-phase region of the initial thermodynamic parameters of the coolant, either the liquid boils up, or the vapor is condensed. Because of the rapid pressure decrease, the phase transition can be non-equilibrium that must be taken into account in the simulation. In the present study, an axisymmetric problem of the outflow of a water coolant from the pipe butt-end is considered. The equations of continuity, momentum and energy for a two-phase homogeneous mixture are solved numerically. The vapor and liquid properties are calculated using the TTSE software package (The Tabular Taylor Series Expansion Method). On the basis of the computer complex LCPFCT (The Flux-Corrected Transport Algorithm) the program code was developed for solving numerous problems on the depressurization of vessels or pipelines, containing superheated water or gas under high pressure. Different variants of outflow in the external model atmosphere and generation of waves are analyzed. The calculated data on the interaction of pressure waves with a barrier are calculated. To describe phase transitions, an asymptotic relaxation model of nonequilibrium evaporation and condensation has been created and tested.

Minimisers of the Allen–Cahn equation and the asymptotic Plateau problem on hyperbolic groups

We investigate the existence of non-constant uniformly-bounded minimal solutions of the Allen–Cahn equation on a Gromov-hyperbolic group. We show that whenever the Laplace term in the Allen–Cahn equation is small enough, there exist minimal solutions satisfying a large class of prescribed asymptotic behaviours. For a phase field model on a hyperbolic group, such solutions describe phase transitions that asymptotically converge towards prescribed phases, given by asymptotic directions. In the spirit of de Giorgi's conjecture, we then fix an asymptotic behaviour and let the Laplace term go to zero. In the limit we obtain a solution to a corresponding asymptotic Plateau problem by Γ-convergence.

Thermally assisted ordering in Mott insulators

Ginzburg-Landau theory describes phase transitions as the competition between energy and entropy: The ordered phase has lower energy, while the disordered phase has larger entropy. When heating the system, ordering is reduced entropically until it vanishes at the critical temperature. This established picture implicitly assumes that the energy difference between ordered and disordered phase does not change with temperature. We show that for the Mott insulator KCuF3 this assumption is strongly violated: thermal expansion energetically stabilizes the orbitally-ordered phase to such and extent that no phase transition is observed. This new mechanism explains not only the absence of a phase transition in KCuF3 but even suggests the possibility of an inverted transition in closed-shell systems, where the ordered phase emerges only at high temperatures.

The infinite limit as an eliminable approximation for phase transitions

It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.

Field-induced oblique helicoidal cholesteric phases in mixtures of chiral and achiral liquid crystalline molecules

ABSTRACTWe present a mean field theory to describe phase transitions in mixtures of chiral and achiral liquid crystalline molecules in the presence of an external field. When a longitudinal external field is applied parallel to the pitch axis of a chiral nematic phase (N*), the director of the N* phase can lead to an oblique heliconical cholesteric () state with a twist–bend distortion, in which a bend elastic constant is smaller than a twist elastic constant . We predict that the exists between N* and nematic (N) phases and can be controlled by temperature and concentration. We find various phase transitions: the first-order (isotropic) and the second-order , transitions, on the temperature–concentration plane. We also predict the pitch and the phase diagrams, depending on temperature and concentration under the external field.

Effect of stress nonhomogeneity on the shear melting of a thin boundary lubrication layer.

We consider the dynamical properties of boundary lubrication in contact between two atomically smooth solid surfaces separated by an ultrathin layer of lubricant. In contrast to previous works on this topic, we explicitly consider the heterogeneity of tangential stresses, which arises in a contact of elastic bodies that are moved tangentially relative to each other. To describe phase transitions between structural states of the lubricant we use an approach based on the field theory of phase transitions. It is assumed that the lubricant layer, when stressed, can undergo a shear-melting transition of first or second order. While solutions for the homogeneous system can be easily obtained analytically, the kinetics of the phase transitions in the spatially heterogeneous system can only be studied numerically. In our numerical experiments melting of the lubricant layer starts from the outer boundary of contact and propagates to its center. The melting wave is followed by a wave of solidification. This process repeats itself periodically, following the stick-slip pattern that is characteristic of such systems. Depending on the thermodynamic and kinetic parameters of the model, different modes of sliding with almost complete or only partial intermediate solidification are possible.

Theoretical study of disorder-order transition of sodium borohydride

The disorder-order phase transition of NaBH4 from the cubic to tetragonal structures has been studied based on density functional theory. The disordered high temperature phase is expressed as a statistical average of three substructures with a hypothesis that each BH4− tetrahedron has a fixed orientation. Our calculations show that the phase transition is mainly induced by synergic rotation of BH4− ion and the energy barrier is sensitive to volume change. We also investigated the role of van der Waals corrections in describing phase transition with DFT-D2 and vdW-DF methods.

Ab initio diffuse-interface model for lithiated electrode interface evolution.

The study of chemical segregation at interfaces, and in particular the ability to predict the thickness of segregated layers via analytical expressions or computational modeling, is a fundamentally challenging topic in the design of novel heterostructured materials. This issue is particularly relevant for the phase-field (PF) methodology, which has become a prominent tool for describing phase transitions. These models rely on phenomenological parameters that pertain to the interfacial energy and thickness, quantities that cannot be experimentally measured. Instead of back-calculating these parameters from experimental data, here we combine a set of analytical expressions based on the Cahn-Hilliard approach with ab initio calculations to compute the gradient energy parameter κ and the thickness λ of the segregated Li layer at the Li_{x}Si-Cu interface. With this bottom-up approach we calculate the thickness λ of the Li diffuse interface to be on the order of a few nm, in agreement with prior experimental secondary ion mass spectrometry observations. Our analysis indicates that Li segregation is primarily driven by solution thermodynamics, while the strain contribution in this system is relatively small. This combined scheme provides an essential first step in the systematic evaluation of the thermodynamic parameters of the PF methodology, and we believe that it can serve as a framework for the development of quantitative interface models in the field of Li-ion batteries.

Emergent spinless Weyl semimetals between the topological crystalline insulator and normal insulator phases with glide symmetry

We construct a theory describing phase transitions between the spinless topological crystalline insulator phase with glide symmetry and a normal insulator phase. We show that a spinless Weyl semimetal phase should intervene between these two phases. Here, because all the bands are free from degeneracy in general, a gap closing between a single conduction band and a single valence band at phase transition generally gives rise to a pair creation of Weyl nodes; hence the Weyl semimetal phase naturally appears. We show the relationship between the change of the ${\mathbb{Z}}_{2}$ topological number when the system goes through the Weyl semimetal phase, and the trajectory of the Weyl nodes.

Phase Diagram and Dielectric Studies in Hydrogen-Bonded Liquid Crystal System

ABSTRACTThe thermal and dielectric behaviors of mixtures were investigated for systems of p-n-hexyloxybenzoic acid (6OBA) and p-n-octyloxybenzoic acid (8OBA) by differential scanning calorimetry, polarized optical microscopy, and dielectric measurements. The T-X phase diagram was obtained for this system. Eutectic composition was calculated and received experimentally. Enthalpies of mixing were calculated to describe phase transitions physically. All mixtures show enantiotropic smectic and nematic phases. Dielectric permittivity has higher value for the mixture with fractional proportion of 30 to 70% mol for 8OBA than that for initial acid. It is assumed that co-crystallization of initial compound occurs when the ratio of components is close to equimolar ratio.

First passage times in homogeneous nucleation: Dependence on the total number of particles.

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.

Thermodynamic modeling of binary CH4–CO2 fluid inclusions

An equation of state (EOS) explicit in Helmholtz free energy has been improved to calculate the PVTx and vapor–liquid phase equilibrium properties of CH4–CO2 fluid mixture. This EOS, where four mixing parameters are used, is based on highly accurate EOSs recommended by NIST for pure components (CH4 and CO2) and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Comparison with experimental data available indicates that the EOS can calculate both vapor–liquid phase equilibrium and volumetric properties of this binary fluid system with accuracy close to that of experimental data up to high temperature and pressure within full range of composition. The EOS of CH4–CO2 fluid, together with the updated Gibbs free energy model of solid CO2 (dry ice), is applied to calculate the CH4 content (xCH4) and molar volume (Vm) of the CH4–CO2 fluid inclusion based on the assumption that the volume of an inclusion keeps constant during heating and cooling. Vm−xCH4 diagrams are presented, which describe phase transitions involving vapor, liquid and CO2 solid phases of CH4–CO2 fluid inclusions. Isochores of CH4–CO2 inclusions at given xCH4 and Vm can be easily calculated from the improved EOS.

Graphite to ultrafine nanocrystalline diamond phase transition model and growth restriction mechanism induced by nanosecond laser processing

To have a clear insight into nanocrystal growth from graphite to diamond upon high energy pulsed laser irradiation of graphite suspension, synthesis of ultrafine nanocrystalline diamonds with laser energy set up from 0.3 J to 12 J, repetition rate of 10 Hz has been studied. The method allows synthesizing ultrafine nanocrystalline particles continuously at the ambient temperature and normal pressure. The particle size is shown independent of laser energy, which is ultrafine and ranges in 2–6 nm. The theoretical grown size of nano-diamonds is found in well agreement with the experiment results. Four kinds of production were found: nano-diamond, spherical carbon nano-particles, flocculent amorphous carbon, and graphene nano-ribbon rolls. A solid-vapor-plasma-liquid coexistence model describing phase transition from graphite to diamond induced by nanosecond laser processing was proposed. Graphene nano-ribbon rolls might be the intermediate phase in the conversion from graphite to diamond.

Thermal fluctuations in 1D superconducting samples

For a system that obeys diffusive evolution, an additional term due to thermal fluctuations should be added. We present an intuitive derivation of the distribution of this term. The formalism developed to deal with fluctuations can be incorporated into two models that are widely used in the dynamics of superconductors: the time-dependent Ginzburg–Landau model and the Kramer–Watts-Tobin model. We review three problems that can be studied with these models: supercurrent flow around a ring close to Tc; fluctuations of the supercurrent in a filament that bridges between two bulk superconductors with order parameters at a given phase difference; and the Kibble–Zurek mechanism, intended to describe phase transitions that are governed by kinetics rather than by thermodynamics, in the case of a superconducting loop.

Evidence of liquid-liquid transition in glass-forming La50Al35Ni15 melt above liquidus temperature.

Liquid–liquid transition, a phase transition of one liquid phase to another with the same composition, provides a key opportunity for investigating the relationship between liquid structures and dynamics. Here we report experimental evidences of a liquid–liquid transition in glass-forming La50Al35Ni15 melt above its liquidus temperature by 27Al nuclear magnetic resonance including the temperature dependence of cage volume fluctuations and atomic diffusion. The observed dependence of the incubation time on the degree of undercooling is consistent with a first-order phase transition. Simulation results indicate that such transition is accompanied by the change of bond-orientational order without noticeable change in density. The temperature dependence of atomic diffusion revealed by simulations is also in agreement with experiments. These observations indicate the need of two-order parameters in describing phase transitions of liquids.

Experimental Establishment of Mother–Daughter Orientation Relationships and Twinning Effects in Phase Transitions: A Great Legacy from Jack Gougoutas and Peggy Etter

A simple procedure, with an available program, may readily be used to establish the three-dimensional relationships between a mother and daughter phase, where mother and daughter are either two different phases of a material or a reactant and product in a solid-state transformation. The only requirements are that (i) the process involves a crystal-to-crystal transformation, and (ii) the experiment must be carried out without changing the alignment of the mother crystal. Application of the method supports the inferred alignment of mother and daughter phases in the published structures of two polymorphs of 4-cyanopyridinium perchlorate monohydrate 1. A new low-temperature, monoclinic polymorph of ferrocenium tetrafluoroborate 2 is produced when the known orthorhombic polymorph is cooled from 173 to 120 K. The major features of the transformation include “conservative twinning” and a modulation of the structure along the crystallographic b direction upon cooling. Redetermination of the structure of the low-temperature polymorph of ferrocenium hexafluorophosphate 3 reveals that the phase change is accompanied by reproducible four-component twinning, providing a proper explanation for the previously reported, very high R-factor of 12.4%. Included tutorial information on the process will assist the reader in obtaining topotactic relationships, as well as in preparing figures and animations describing phase transitions or reactions.

Sharp limit of the viscous Cahn–Hilliard equation and thermodynamic consistency

Diffuse and sharp interface models represent two alternatives to describe phase transitions with an interface between two coexisting phases. The two model classes can be independently formulated. Thus there arises the problem whether the sharp limit of the diffuse model fits into the setting of a corresponding sharp interface model. We call a diffuse model admissible if its sharp limit produces interfacial jump conditions that are consistent with the balance equations and the second law of thermodynamics for sharp interfaces. We use special cases of the viscous Cahn–Hilliard equation to show that there are admissible as well as non-admissible diffuse interface models.