Phenomenological Theory Of Phase Transitions Research Articles

Magnetocaloric effect and magnetic phase diagram of Ni-Mn-Ga Heusler alloy in steady and pulsed magnetic fields

The work is devoted to the study of the phenomenon of irreversibility of the magnetocaloric effect (MCE) in the vicinity of the magnetostructural phase transition (PT) in Ni-Mn-Ga Heusler alloys. For this purpose, the MCE was studied by the direct method in stationary (up to 14 T) and pulsed magnetic fields (up to 50 T), and a magnetic phase diagram was constructed. Using a specially designed microscope, in-situ studies of the magnetostructural phase transition were carried out in magnetic fields of up to 14 T. Comparing the results of the MCE with those of the phase diagram, as well as in-situ studies, made it possible to determine the width of the irreversible MCE region. In-situ studies have shown, that the main reason of the occurrence of the irreversible MCE is the presence of the residual martensite formed as a result of the first magnetization of the sample. The results are discussed within the framework of Landau's phenomenological PT theory, which predicts the disappearance of thermal hysteresis under a field of 30 T. Within the framework of the same theory, a recommendation is made to reduce the value of the critical field and, as a result, the width of the hysteresis.

Differential model of friction based on bristle model and phase-transition theory

For high-precision position and angle control in robots, it is essential to compensate for the hysteretic behaviour caused by friction when the motion direction is reversed. An accurate friction model which is suitable for control system analysis and implementation is highly desirable. A differential model is proposed in the current paper for the modelling of hysteresis effects caused by friction phenomena. The model is constructed by employing a phenomenological phase-transition theory to mimic the friction mechanism. The bristle friction mechanism is adapted. The switching between static and dynamic friction is regarded as a reversible phase-transition phenomenon, which could be characterized by the local minima of a non-convex potential energy function. The Stribeck effect and the hysteretic relation between friction and velocity are modelled by a nonlinear ordinary differential equation. The comparison of the numerical simulation results and existing experimental friction data are presented. It is illustrated that the friction hysteresis loops are well captured, the capability of the proposed model is verified.

Особенности поведения прочностных свойств сплавов железа в области температур магнитных переходов на основе феноменологической теории фазовых переходов

Образование магнитного порядка в металлах и сплавах рассматривается как проявление в основной кристаллической решётке металлов и сплавов сопряжённой с ней магнитной структуры, обладающей достаточной жёсткостью и энергией. Изучение их взаимосвязи представляет большой интерес для использования промышленных металлов и сплавов. В результате проведённого исследования можно утверждать, что магнитное упорядочение искажает кристаллическую решётку: при температуре перехода она становится менее стабильной, что приводит к значительно более высокой пластичности вновь образующейся магнитоупорядоченной фазы. B температурных областях магнитных превращений пластичность антиферромагнитной или ферромагнитной фазы больше пластичности парамагнитной фазы и ведёт себя немонотонно. Ключевые слова и словосочетания: фазовые магнитные переходы, прочностные свойства при магнитных перестройках ферромагнетизм→парамагнетизм, антиферромагнетизм→парамагнетизм.

Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed.
 In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered.
 A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

Phenomenological theory of phase transitions in the MPB region of (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals

ABSTRACTA higher-order Landau–Ginzburg–Devonshire theory is proposed to describe phenomenologically the complex phase transitions in the MPB region of the relaxor ferroelectric (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3(PMN-PT) single crystals. Using the singularity theory, a structurally stable 10th-order potential with four varying expansion coefficients (a1, a11, a2 and a12) depending on temperature and composition is found out. By studying on two- and three-dimensional sections of a four-dimensional phase diagram a1-a11-a2-a12 in the space of phenomenological parameters, the range of coefficient parameters by which the structural stability of the potential model can be guaranteed is determined. The theoretical temperature-composition phase diagram is constructed and it is shown that this is in good agreement with both recent experimental data and first-principle calculation for the symmetry change. Moreover, temperature dependence of dielectric constants for various compositions is studied.

Structural Mechanisms and the Thermodynamic Description of the Isosymmetric Orbital Ordering in Rare-Earth Manganites

The observed specific features of the orbital phase transition in AMnO3 (A = La, Pr, …, Lu) are shown to be due to the appearance, at high temperatures, of rotational distortions of the cubic lattice, which cause anion displacements, which induce an “internal field” coinciding in symmetry with the order parameter, which describe the ordering of octahedra distorted due to the Jahn–Teller effect (orbital ordering). The effect of this “field” substantially determines the orbital ordering type, its temperature, and the phase transition order. The comparative analysis of the orbitally ordered states is performed for the entire AMnO3 series in both the framework of the phenomenological theory of phase transitions and on the base of the three-minimum multi-sublattice model proposed in this report. The peculiarities of magnetic transitions in manganites determined by the specific features of their structures are discussed.

Formation of Regular Domain Structures in Quenched Ferroelectrics Under the Influence of an External High-frequency Electric Field

Introduction: Within the framework of the phenomenological theory of phase transitions of the second kind of Ginzburg-Landau, the kinetics of ordering of a rapidly quenched highly nonequilibrium domain structure is considered using the lithium tantalate and lithium niobate crystals as an example. Experimental: Using the statistical approach, evolution equations describing the formation of the domain structure under the influence of a high-frequency alternating electric field in the form of a standing wave were obtained. Numerical analysis has shown the possibility of forming thermodynamically stable mono- and polydomain structures. It turned out that the process of relaxation of the system to the state of thermodynamic equilibrium can proceed directly or with the formation of intermediate quasi-stationary polydomain asymmetric phases. Results: It is shown that the formation of Regular Domain Structures (RDS) is of a threshold character and occurs under the influence of an alternating electric field with an amplitude less than the critical value, whose value depends on the field frequency. The conditions for the formation of RDSs with a micrometer spatial scale were determined. Conclusion: As shown by numerical studies, the RDSs obtained retain their stability, i.e. do not disappear even after turning off the external electric field. Qualitative analysis using lithium niobate crystals as an example has shown the possibility of RDSs formation in high-frequency fields with small amplitude under resonance conditions

Nonuniform polarized states of ferroelectric nanoparticles in a dielectric matrix

In the framework of the phenomenological theory of phase transitions (PT) Landau are showed that in nanoscale ferroelectrics (FE), a phase transition to a non-uniform polar state is possible. As a result of solving the eigenvalue problem for the equilibrium equation of polar-ization and electrostatic equations, a wave vector is defined, that characterizes a non-uniform phase in a thin ferroelectric film (FEF), temperature ranges of the «domain-like» phase are found, depending on the characteristic size of the FE inclusion and its surface properties. The possibility of controlling the domain structure in ferroelectric particles (FEP) using an external electric field is shown.

Структурные механизмы и термодинамическое описание изосимметрийного орбитального упорядочения в редкоземельных манганитах

It is shown that the observed features of the orbital phase transition in AMnO3 perovskites (A = La, Pr, ..., Lu) are due to the occurrence of rotational distortions of a cubic lattice at high temperatures, causing anion displacements that create an “internal field” which, by symmetry, coincides with the order parameter describing the ordering of octahedra distorted due to the Jahn-Teller effect (orbital ordering). The influence of this “field” essentially determines the type of orbital ordering, its temperature and the nature of the phase transition. A comparative analysis of orbitally ordered states was carried out for the entire series of AMnO3, both in the framework of the phenomenological theory of phase transitions and on the basis of the three-minimum multi-lattice model proposed in the article. The specific features of the magnetic transitions in manganites, due to the specific features of the structure, are discussed.

Effect of Polydispersity on the Phase Diagram of Colloid Systems

A theoretical model is proposed that describes the experimentally observed phase diagram of colloidal dispersions of disk-shaped polydisperse particles. In the framework of the phenomenological theory of phase transitions, it is shown that if disk-shaped particles have polydispersity comparable in thickness and disk diameter, then the following sequence of phase transitions should be expected with increasing volume fraction of ϕ particles: an isotropic liquid (I); a nematic liquid crystal (N), in which the director n sets the preferred orientation of the disk normal; and the discotic (columnar) phase (C), in which the disklike molecules aggregate into liquid columns, and the latter form a two-dimensional hexagonal crystal consisting of liquid columns. However, when the particles forming the colloidal dispersion do not have any polydispersity in thickness (but the polydispersity in the particle diameter is preserved), another sequence of phase transitions takes place, in which the columnar phase is replaced by a smectic liquid crystal (S); that is, particles form a system of equidistant liquid layers. This work proposes and discusses the mechanisms of this behavior and new predictions that follow from this consideration.

Piezoelectric coefficients of the barium-strontium titanate film on a (111)-oriented substrate

Within the framework of the phenomenological theory of phase transitions, we consider properties of the Ba0.8Sr0.2TiO3 (BST80) film grown on a (111)-oriented cubic substrate. The film was revealed to exhibit three ferroelectric phases with different orientations of spontaneous polarization. It is shown that some piezoelectric moduli should demonstrate anomalous behavior near the phase boundaries.

Phenomenological model of dielectric properties for PMN-PT

ABSTRACTThe temperature behavior of the dielectric properties of PMN-PT has been considered in the framework of phenomenological theory of phase transitions in the systems with defects. The results are presented for the region of the diffuse phase transition, where dynamics of the charge localization on defects affects the dielectric properties. The consideration has been performed on the basis of simple thermodynamic ideas.

A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales

By integrating four lines of thoughts: symmetry breaking originally advanced by Anderson, bifurcation from nonlinear dynamical systems, Landau’s phenomenological theory of phase transition, and the mechanism of emergent rare events first studied by Kramers, we introduce a possible framework for understanding mesoscopic dynamics that links (i) fast microscopic (lower level) motions, (ii) movements within each basin-of-attraction at the mid-level, and (iii) higher-level rare transitions between neighboring basins, which have slow rates that decrease exponentially with the size of the system. In this mesoscopic framework, the fast dynamics is represented by a rapidly varying stochastic process and the mid-level by a nonlinear dynamics. Multiple attractors arise as emergent properties of the nonlinear systems. The interplay between the stochastic element and nonlinearity, the essence of Kramers’ theory, leads to successive jump-like transitions among different basins. We argue each transition is a dynamic symmetry breaking, with the potential of exhibiting Thom-Zeeman catastrophe as well as phase transition with the breakdown of ergodicity (e.g., cell differentiation). The slow-time dynamics of the nonlinear mesoscopic system is not deterministic, rather it is a discrete stochastic jump process. The existence of these discrete states and the Markov transitions among them are both emergent phenomena. This emergent stochastic jump dynamics then serves as the stochastic element for the nonlinear dynamics of a higher level aggregates on an even larger spatial and slower time scales (e.g., evolution). This description captures the hierarchical structure outlined by Anderson and illustrates two distinct types of limit of a mesoscopic dynamics: A long-time ensemble thermodynamics in terms of time t→∞ followed by the size of the system N→∞, and a short-time trajectory steady state with N→∞ followed by t→∞. With these limits, symmetry breaking and cusp catastrophe are two perspectives of the same mesoscopic system on different time scales.

Theory of phase transitions in systems with defects and development of phenomenological theory of relaxors

ABSTRACTTheory of phase transitions in systems with defects is considered and phenomenological theory of the diffuse phase transition has been proposed. The temperature behavior and dispersion of the dielectric properties in the region of the diffuse phase transition has been associated with the dynamics of the charge delocalization on defects. The consideration has been performed on the basis of simple thermodynamic ideas in the framework of the Sigov-Levanyuk approach to the phenomenological theory of phase transitions in the system with defects.

The problem of determining elastic constants of thin ferroelectric films

A method of determining the constants of the linear equations of the piezoelectric effect dependent on the external conditions is proposed for thin ferroelectric films on the basis of the Landau potential of the phenomenological theory of phase transitions. By the example of single-crystalline barium—titanate thin films, the behavior of material constants is investigated in dependence on the value of the misfit strain. The investigation of material equations is implemented on the basis of the Landau potential of the eighth degree at room temperature. The substantial difference in the elastic, electric, and piezoelectric properties of a thin film from those of a bulk material is shown; the anomalous behavior of constants on the phase boundaries and the extremal behavior inside the r-phase is revealed.

Magnetocaloric effect in ferromagnet/paramagnet multilayer structures

The magnetocaloric effect in ferromagnet/paramagnet multilayer structures is studied in the framework of the Landau phenomenological theory of phase transitions. The performed estimations demonstrate the possibility of achieving record cooling efficiency with such structures.

An investigation on the field strength and loading rate dependences of the hysteretic dynamics of magnetorheological dampers

This paper is an extended study on the model of the hysteretic dynamics of magnetorheological dampers based on a phenomenological phase transition theory (Wang and Kamath in Smart Mater. Struct. 15(6):1725–1733, 2006). It is demonstrated that, by appropriately choosing model parameters, the frequency dependence of the hysteretic dynamics can be captured very well by the model based on phase transition theory. Whilst by introducing an appropriate rescaling coefficient to account for the strength of the magnetized particle chains with various magnetic field strengths, the field strength dependence of the hysteretic dynamics can also be captured very well by the same differential equation with the same set of model parameters. There are in total eight model parameters introduced for capturing the hysteretic dynamics, including its dependence on the loading rate and field strength.

Phenomenological theory of phase transitions in solutions of nanotubes in liquid crystal

A phenomenological model of thermodynamic potential is constructed that describes phase transitions in homogeneous monodisperse solutions of achiral carbon tubes in liquid crystal. Possible phase diagrams of such a systems are constructed and investigated.

Giant dielectric permittivity and magneto-capacitance effects in low doped manganites

The effect of giant dielectric permittivity due to phase separation accompanied by charged inhomogeneities in low-doped manganites is discussed. The effect appears in the vicinity of the second-order magnetic phase transition and is caused by long-range Coulomb forces. The long-range Coulomb interaction is responsible for the formation of inhomogeneous charged states and determines their characteristic length scales. We derive the phase diagram of the inhomogeneous charged states in the framework of the phenomenological theory of phase transitions. The large value of the static dielectric function reduces the characteristic value of the Coulomb energy of the inhomogeneous state and makes the appearance of the magnetoelectric effect possible. We discuss the formation of a state with giant dielectric permittivity and magneto-capacitance effects in that case.

Modeling the Rate Dependent Hysteretic Dynamics of Magnetostrictive Transducers

In the current paper, the rate dependent hysteretic dynamics of a magnetostrictive transducer is investigated by using a coupled nonlinear macroscopic differential model. The transducer is modeled as a one-dimensional magnetostrictive structure based on the Landau phenomenological theory of phase transition. The hysteresis loops and butterfly-shaped behaviors in the magnetic and mechanical fields are both successfully modeled with estimated model parameter values. The capability of the proposed model for capturing the driving rate dependency is illustrated by numerical experiments.