Phenomenological Theory Of Phase Transitions Research Articles

Half-Quantum Vortices in Polar Phase of Superfluid $$^{3}$$ 3 He

The magnetic dipole-dipole interaction does not prevent existence of half-quantum vortices in the polar phase of superfluid He-3 which can be stable in uniaxial anisotropic aerogel. Here we discus this exotic possibility. After developing a phenomenological theory of phase transition from the normal to polar superfluid state and then to axipolar superfluid state we calculate the NMR properties of such type superfluids at the rest or under rotation filled by an array either single quantum or half quantum vortices.

Simulation of phase diagrams of oxychromites with a spinel structure

Phase diagrams of oxychromites with a spinel structure are described in the context of the Landau phenomenological theory of phase transitions. As an approximation of the thermodynamic potential of the sixth degree with respect to components of the order parameter, the implementation conditions of each type of phase diagrams are found. Equations for calculation of coordinates of tricritical and triple points are obtained. A qualitative agreement of the theoretically calculated results of the phase diagrams and experimental phase diagrams of some oxychromites with a spinel structure is observed.

Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry

The majority of magnetoelectric crystals show complex temperature–magnetic field or temperature–pressure phase diagrams with alternating antiferromagnetic incommensurate, magnetoelectric, and commensurate phases. Such phase diagrams occur as a result of successive magnetic instabilities with respect to different order parameters, which usually transform according to different irreducible representations (IRs) of the space group of the crystal. Therefore, in order to build a phenomenological theory of phase transitions in such magnetoelectrics one has to employ several order parameters and assume the proximity of various instabilities on the thermodynamic path. In this work we analyze the magnetoelectrics MnWO4, CuO, NaFeSi2O6, NaFeGe2O6, Cu3Nb2O8, α-CaCr2O4 and FeTe2O5Br using the praphase concept and the symmetry of the exchange Hamiltonian. We find that in all the considered cases the appearing magnetic structures are described by IRs entering into a single exchange multiplet, whereas in the cases of MnWO4 and CuO by a single IR of the space group of the praphase structure. Therefore, one can interpret the complex phase diagrams of magnetoelectrics as induced by a single IR either of the praphase or of the symmetry group of the exchange Hamiltonian. Detailed temperature–magnetic field phase diagrams of MnWO4 and CuO for certain field directions are obtained and the magnetic structures of the field-induced phases are determined.

On the possibility of two phase transitions in liquid helium

An explanation is proposed for the maxima in the dielectric constant and density observed in liquid helium slightly above the superfluid transition temperature. It is shown that they may be caused by a phase transition that results in spontaneous polarization of the helium. This kind of transition is possible in the liquid because when an atom is polarized its energy levels are lowered, so that the polarization is energetically favorable, especially for light atoms. In addition, the development of a dipole moment in an atom leads to the appearance of an additional electric field and, therefore, to an increase in the energy. The possible spontaneous polarization of the system of atoms is determined by the competition among these factors. In accordance with this concept, as the temperature of liquid helium is lowered there is an initial phase transition into a polarized normal phase, followed by one from this nonzero polarization state into the superfluid state. The transition of the normal fluid into the polarized phase is described in terms of a phenomenological theory of phase transitions. The transition can be of first or second order.

Incommensurate phases in the statistical theory of the crystalline state

The paper is devoted to the elaboration of a mathematical apparatus for studying second-order phase transitions, both commensurate and incommensurate, and the properties of emerging phases on the basis of the approach in equilibrium statistical mechanics proposed earlier by the author. It is shown that the preliminary symmetry analysis for a concrete crystal can be performed analogously with the one in the Landau phenomenological theory of phase transitions. The analysis enables one to deduce a set of transcendental equations that describe the emerging phases and corresponding phase transitions. The treatment of an incommensurate phase is substantially complicated because the symmetry of the phase cannot be described in terms of customary space groups. For this reason, a strategy of representing the incommensurate phase as the limit of a sequence of long-period commensurate phases whose period tends to infinity is worked out.

Phase behavior of two-component lipid membranes: Theory and experiments

The structure of the ripple phase of phospholipid membranes remains poorly understood in spite of a large number of theoretical studies, with many experimentally established structural features of this phase unaccounted for. In this article we present a phenomenological theory of phase transitions in single- and two-component achiral lipid membranes in terms of two coupled order parameters: a scalar order parameter describing lipid chain melting, and a vector order parameter describing the tilt of the hydrocarbon chains below the chain-melting transition. This model reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure. In addition, it predicts a variant of this phase that does not seem to have been experimentally observed. Using this model we have calculated generic phase diagrams of two-component membranes. We have also determined the phase diagram of a two-component lipid membrane from x-ray diffraction studies on aligned multilayers. This phase diagram is found to be in good agreement with that calculated from the model.

A possible generalization of the phenomenological theory of phase transitions in type II ferroelectrics with incommensurate phase

We develop a generalized phenomenological theory of the paraelectric – incommensurate – commensurate phase transitions in type II ferroelectrics. The linear temperature dependence of the sixth-power term coefficient in the thermodynamic potential expansion is proposed. Contrary to the pre-existing theoretical approaches, the developed model eliminates a number of long-standing problems in the theory of type II ferroelectrics and can provide a correct description of the experimental data on the temperature dependence of the properties of type II ferroelectrics in the incommensurate phase.

Spectroscopic study of the behavior of the order parameter in model ferroelastic crystals of Hg2Cl2

Information is obtained about the temperature behavior of the order parameter of a phase transition by theoretical and experimental investigation of odd (acoustic and IR-active) phonons that appear in the Raman scattering spectra from the X points of the Brillouin zone (BZ) boundary in the paraphase of Hg2Cl2 crystals and are induced by the phase transition, unit-cell doubling, and the X → Γ folding in the BZ. The relevant critical exponents are determined, whose values are in agreement with the results of X-ray diffraction measurements and, within the Landau phenomenological theory of phase transitions, indicate that the phase transition in these crystals is close to the tricritical point.

Modeling the Loading-Rate Dependency of the Hysteretic Dynamics of Magnetorheological Dampers

The loading rate dependency of the hysteretic dynamics of Magnetorheological (MR) dampers is investigated in the current paper. The model is constructed on the basis of a phenomenological phase-transition theory. The hysteretic dynamics is treated as the responses of a nonlinear system upon external loadings. With appropriately chosen coefficients, the proposed model is able to capture the loading-rate dependency feature of the hysteretic dynamics. Comparisons between the numerical and experimental results are presented, and perfect agreements are obtained.

Dielectric spectra of Bi0.98Nd0.02FeO3.00 multiferroic thin films in the terahertz frequency range

Transmission and reflection spectra of Bi0.98Nd0.02FeO3.00 multiferroic thin films on MgO single-crystal substrates have been measured using submillimeter spectroscopy (on a backward-wave tube spectrometer) and Fourier-transform infrared spectroscopy in the frequency range from 8 to 1000 cm−1 at room temperature. The complex permittivity spectra of the films have been calculated in terms of the layered medium model. It has been revealed that a decrease in the film thickness leads to a considerable increase in the losses in a range of 30 cm−1 and the corresponding fivefold increase in the static permittivity (to 500 for a film 32 nm thick). This phenomenon has been discussed in the framework of the phenomenological theory of phase transitions.

Phenomenological theory of phase transitions in multiferroicMnWO4: magnetoelectricity and modulated magnetic order

The phenomenological theory of phase transitions in multiferroicMnWO4 issuggested. The theoretical model uses the assumption that the magnetic order is driven by the instabilityin the (1/4;1/2;1/2) point of the Brillouin zone, which is justified by the symmetry of the low-temperaturemagnetic phase. It is shown that the experimentally observed incommensurate magneticorder is due to the Lifshitz invariants allowed for the corresponding order parameters.Invariants responsible for the magnetoelectric interaction are found and a schematic phasediagram is calculated. The influence of the magnetic field on the phase transition sequenceis also analyzed. It is suggested that the description of the phase transitions inMnWO4 starting from the orthorhombic praphase significantly simplifies the approach and allows usto draw important conclusions.

Dynamic Models for Magnetorheological Dampers and its Feedback Linearization

In the current paper, the hysteretic dynamics of magnetorheological dampers is modeled by a differential model. The differential model is constructed on the basis of a phenomenological phase transition theory. The model is expressed as a second order nonlinear ordinary differential equation with bifurcations embedded in. Due to the differential nature of the model, the hysteretic dynamics of the MR dampers can be linearized and controlled by introducing a feedback linearization strategy.

Adventures of a Theoretical Physicist, Part II: America

This second part of my interview with Andor Frenkel focuses on my life and work in America. After arriving in New York in March 1941 and visiting relatives and friends in Cambridge and Boston, Massachusetts, my friend Edward Teller, who had a professorship at George Washington University, invited me to his home in Arlington,Virginia, where I stayed until June while he attempted to locate a position for me. Eventually, John Clarke Slater, Head of the Physics Department of the Massachusetts Institute of Technology (MIT), offered me a one-year instructorship beginning in the fall of 1941, which evolved into an assistant professorship in 1945, an associate professorship in 1948, and a full professorship in 1960. During these years, I established close friendships at MIT with Herman Feshbach, Philip Morrison,Victor Weisskopf, and other colleagues, and pursued productive researches with my graduate students. I developed a new course on thermodynamics in 1941 based on my notes of Max Born’s lectures at the University of Gottingen in 1929, Lev Landau and Evgenii Lifshitz’s book, Statistical Physics of 1938, and Slater’s book, Introduction to Chemical Physics of 1939, which I revised and refined over the following years. In 1966 I published my book, Generalized Thermodynamics. I also reflected on the role that my two-fluid theory of 1938 played in clarifying superfluidity, as well as on my relations with Lev Landau and Fritz London, and on their controversial relations with each other. In 1947 I widened Landau’s phenomenological theory of phase transitions to include mathematical singularities. Subsequently, I concentrated more and more on the paradoxes of quantum mechanics, a first result being an unpublished manuscript of 1950, which I reproduce in the Appendix. In later decades, both before and after my retirement from MIT in 1973, my concern with the foundation of quantum mechanics continued unabated. The first part of this interview, covering my life and work in Europe, appeared in the previous issue.

Localized charge inhomogeneities and phase separation near a second-order phase transition

Localized charge inhomogeneities and phase separation are described in the framework of the phenomenological theory of phase transitions. It is shown that Coulomb interaction determines the charge distribution and the characteristic size of the emerging inhomogeneities. Phase separation associated with charge segregation becomes possible because of a high dielectric constant and a low excess charge density in the localization region. The phase diagram of the system is calculated, and estimates are obtained for the gain in energy associated with the emerging state. The role of Coulomb interaction is exposed, and corresponding estimates are given.

Phase transitions and structural mechanisms of the formation of LiCoO2 polymorphic modifications

The structural mechanisms of formation of the low-symmetry phases of the LiCoO2 compound from the praphase with a sodium chloride structure are investigated in the framework of the Landau phenomenological theory of phase transitions. The possibility of forming new modifications of the LiCoO2 compound is predicted. The calculated structures of some possible low-symmetry phases of lithium cobaltite are described, and the possible phase diagrams are calculated. It is demonstrated that the most stable modifications of the LiCoO2 compound (the spinel-like and rhombohedral modifications) can transform into each other through a first-order phase transition.

Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics

A new approach is proposed for constructing the phenomenological theory of phase transitions. The approach is based on the classical Landau theory with allowance made for the order parameter that corresponds to changes in the charge distribution probability density of a crystal and does not affect the symmetry of the high-symmetry phase. It is demonstrated that this approach makes it possible to describe phase transitions in terms of a nonequilibrium polynomial Landau potential of degree four in the components of the order parameters. The capabilities of the proposed approach are illustrated with three systems that undergo ferroelastic phase transitions.

The rhombohedral phase with incommensurate modulation in Na1/2Bi1/2TiO3

The phase transition from tetragonal to rhombohedral phase in sodium bismuth titanate (NBT) is studied by means of neutron scattering. It is found that the rhombohedral phase has incommensurate modulation along the four-fold axis of the precursor tetragonal phase. The appearance of the incommensurate modulation is discussed on the symmetry grounds in the framework of the phenomenological theory of phase transitions.

Crystals of cubic symmetry in statistical theory

General results obtained earlier by the author for the crystalline state with the help of statistical methods based upon utilization of distribution functions are applied to investigate the properties of cubic-symmetry crystals. An approximation relevant to the potential of interaction between particles is used, which enables one to reduce an infinite set of equations for Fourier coefficients of the crystal density to one equation. The form of such an equation depends upon the crystal symmetry and for the purpose of establishing this form the symmetry of Fourier series for all 36 cubic space groups is analysed. The resulting equation and properties of a crystal that follow from it are investigated using four space groups O h 9,O 8,O h 5,O h 7 as an example. In the case of space group O h 9 the temperature–pressure phase diagram is constructed, its peculiarities are found out, the temperature dependence of diverse characteristics of the crystal is calculated. It is shown also how statistical theory can treat second-order phase transitions. Results given by statistical theory are in agreement with the Landau phenomenological theory of phase transitions.

Ferroelectric and ferroelastic phase states of crystals caused by atomic ordering

The effect of atomic ordering on displacive-type structural phase transitions is considered for crystals with several atomic sublattices. On the basis of group-theoretical analysis and general crystallographic and thermodynamic principles, it is shown that ordering gives rise to qualitative restructuring of phase diagrams and changes in atomic states up to the formation of new ferroelectric and ferroelastic phases proper. Specific physical properties of crystals provided by atomic ordering are considered in the vicinity of structural transitions within the framework of the phenomenological theory of phase transitions.

Orbital phase transition in Pr1−x CaxMnO3

The phenomenological theory of phase transition in Pr0.6 Ca0.4 MnO3 manganite is developed. It is shown that this is the orbital phase transition and that the two electronic states of the manganese ion, which are discussed in the literature, result from two different types of condensation of the same orbital order parameter. Thus, the manganese ions in Pr1−xCax MnO3 manganites with 0.3≤x≤0.5 may be in either of the two electronic states, depending on the thermodynamic parameters.