Constraints,phase transitions and critical indices

The notion of first order phase transitions is examined for systems under external constraints. It is emphasized that only discontinuities with respect to “natural” variables (additive extensive variables and their conjugate internal forces) should be regarded as first order transitions. The Baker-Essam model is accordingly reviewed, and it is shown that the transition is always of the second order. Fisher's conjecture about renormalization is shown to be correct also for this model.     

Effect of point defects on phase transitions in ferroelectric nanocrystals

The dependences of the phase transition temperature of ferroelectric nanocrystals in a dielectric matrix on the point charged defect concentration have been obtained. The influence of point defects on the nonlinear characteristics of ferroelectric nanocrystals has been studied as a function of the strength and direction of an external electric field with the adequate inclusion of depolarizing electric fields and nonlocal effects.     

Inequalities and many phase transitions in ferromagnetic systems

A general construction of ferromagnetic systems with many phase transitions is given. It is based on two new results: an extension of one of the GKS inequalities to not necessarily ferromagnetic interactions, and a uniqueness of the Gibbs state theorem for perturbations of some simple systemsat all temperatures.     

Interrelation of critical indices in ferroelectric solid solutions

An analysis is presented within the limits of linear approximation of similarity parameters of ferroelectric solid solutions with respect to admixture concentration. A number of analytical expressions and relations for correction functions are obtained which allow to estimate the effect of admixture concentration on critical indices.     

Far infrared and phase transitions in ferroelectric materials

Abstract

A number of far infrared absorption bands are found in molecular and hydrogen-bonded crystals when there are several formula units in the primitive cell. They are very sensitive to the crystal structure and constitute a convenient probe for looking at small changes in the structure, especially at low temperatures where there is a lack of X-Ray data. As well known examples, the case of LTT (Lithium Thallium Tartrate) where the absorption band observed at 21 cm^?1 at room temperature softens down to 8 cm^?1 at the Curie temperature (T_c = 12 K), and LiNH₄SO₄ which has a phase transition at 26 K, will be considered.

It is less known that some ferroelectric crystals can be studied as very thick single crystal plates (thickness t up to 10 mm) at 4 K, and they show in some cases a far IR transmission that is much higher than expected from the study of thin plates (i.e. t = 20 μm). In fact the transmission does not decrease very much when thickness is higher than some specific value t ₀/2. The crystal is not homogeneous at 4 K. A model with a far IR absorbing surface layer (thickness t ₀/2) and a transparent bulk is a good first approximation.

At some temperature T ₀ located between liquid helium and liquid nitrogen temperatures, the center of the bulk undergoes a phase transition from the absorbing phase into the transparent one. When temperature is still lowered, the transparent phase is extended towards the surface with an incommensurate phase between the surface and the bulk.     

Isotropic to ferroelectric and antiferroelectric liquid crystals phase transitions

This review is an attempt towards a unified picture of the direct transitions from the isotropic liquid to ferroelectric and antiferroelectric liquid crystalline phases formed by rod-like and bent-core molecules. The Landau–Ginzburg theories of the phase transitions between the isotropic liquid to ferroelectric and antiferroelectric liquid crystalline phases in compounds composed of chiral rod-like molecules and achiral bent-core molecules are presented. This includes a discussion of the nature of the order parameters and the nature of the various types of phase transitions. The various predictions are compared with the available experimental results.     

Towards a microscopic theory of phase transitions: residual rays,correlation radii and critical indices

Bonds between atoms/molecules of condensed substances must be described within the framework of quantum electrodynamics (QED) as an exchange of virtual photons. Such representation is supported by the known conformity of latent heat with residual infrared (IR) rays and the possibility of latent heat removal by characteristic frequencies. These bonds are virtual if the duration of photons’ formation (their ‘dressing’) τ exceeds the duration of free path in substance ??=?1/σ _tot N, i.e. if τ?>??/c. It is assumed that reversing this inequality corresponds to bond breakage and phase transitions. With low σ _tot and τ frequencies, it leads to the universal radius of correlations, R _c?～?ω ^?ν, ν?=?2/3, and allows refinement of the Ginzburg–Landau model of phase transitions by expansion of thermodynamic potentials over R _c (instead of temperature distance), which results in the correct system of critical indices. Such a consideration offers an opportunity for the stimulation of definite phase transitions by resonant frequencies.     

Diffuse ferroelectric phase transitions in cubically sabilized perovskites

Typical examples of ferroelectrics with diffuse phase transitions (relaxor ferroelectrics), like Pb(Mg_1/3Nb_2/3)O₃ are actually non transforming. The paraelectric phase is fully stablized against a ferroelectric phase transition in this case. A phase transition can be induced, however, by an electric field with appropriate orientation below the temperature of the dielectric constant maximum. The analogy with stress-induced martensitic phase transitions in metallic alloys is pointed out. Pecularities of the properties and of the polarization reversal of such systems are demonstrated. Actual diffuse ferroelectric phase transitions in disordered solid solutions and mixed compounds with a partially stabilized parent phase are compared with athermal martensitic transformations. With particular regard to technical ceramics based on PZT, the influence of interfaces between transformed regions and remnants of the parent phase which have to distinguished from domain walls, and of the reduced stability of the ferroelectric phase on the properties of these systems is discussed. Some effects usually explained solely by domain processes may be understood also from this point of view.

Stabilization of a parent phase against an order-disorder-type phase transition is supposed to be caused by glass-like freezing caused by inelastic cooperative interactions between disordered molecular groups.     

Renormalization group treatment of phase transitions in ferromagnetic superconductors

We investigate the nature of the phase transition from the superconducting to the uniformly ordered magnetic phase in ferromagnetic superconductors by renormalization group methods. For this purpose Halperin, Lubensky, Ma's application of the-expansion to pure superconductors is extended to include the influence of magnetic order as well. Our treatment shows that in the vicinity of the ferromagnetic to superconducting phase-boundary critical fluctuations of the magnetization are absorbed into fluctuations of the magnetic field. As a consequence the transition always is first order. An additional indication to the dominance of electromagnetic effects is the irrelevance of the coupling corresponding to spin flip scattering.     

Phase transitions and critical indices of a phospholipid bilayer model

A model is described which has been used in theoretical studies of a variety of phenomena (which are briefly summarized) relating to biological membranes. It is shown that the Hamiltonian describing this model can be mapped onto an Ising Hamiltonian with a temperature dependent field. It is also shown that this field varies linearly with temperature in the critical region. Exact solutions of this model are presented and its first and second order transitions are discussed with an emphasis on obtaining its critical indices. General considerations lead to the following relations: =1/, =, =, where , , , are the critical indices for the specific heat, magnetization, susceptibility and critical isotherm respectively (the primes denoting low temperature indices). These relations are demonstrated explicitly for the Bethe lattice with coordination numbersq=2 and 6.     

Phase transitions and critical indices of a phospholipid bilayer model

A model is described which has been used in theoretical studies of a variety of phenomena (which are briefly summarized) relating to biological membranes. It is shown that the Hamiltonian describing this model can be mapped onto an Ising Hamiltonian with a temperature dependent field. It is also shown that this field varies linearly with temperature in the critical region. Exact solutions of this model are presented and its first and second order transitions are discussed with an emphasis on obtaining its critical indices. General considerations lead to the following relations: β=1/δ, α=γ, α′=γ′, where α, β, γ, δ are the critical indices for the specific heat, magnetization, susceptibility and critical isotherm respectively (the primes denoting low temperature indices). These relations are demonstrated explicitly for the Bethe lattice with coordination numbersq=2 and 6.     

First-order superconducting transition near a ferromagnetic quantum critical point

We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and T(c) is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger T(c). A second order superconducting transition emerges only at some distance from the FQCP.     

High-temperature phase transitions in the improper ferroelectric KIO3

The ac conductivity (σ_ac) and dielectric permittivity (?) are determined in the temperature range 300?K?T3 compound. The results indicated that the compound behaves as an improper ferroelectric and undergoes a ferroelectric phase transition from a high temperature rhombohedral phase I to a low temperature monoclinic phase II at T _c?=?(486?±?1)?K. A second structural phase transition was observed around 345?K. The conductivity varies with temperature range and for T?>?428?K intrinsic conduction prevails. Different activation energies in the different temperature regions were calculated. The frequency dependence of σ(ω) was found to follow the universal dynamic response [σ(ω)∝(ω) ^s(T)]. The thermal behaviour of the frequency exponent s(T) suggests the hopping over the barrier model rather than the quantum mechanical tunneling model for the conduction mechanism.     

Strain-induced ferroelectric phase transitions in incipient ferroelectric rutile TiO2

Uniaxial strain induced ferroelectric phase transitions in rutile TiO₂ are investigated by first-principles calculations. The calculated results show that the in-plane tensile strain induces rutile TiO₂, paraelectric phase with P_4-2/mnm (D_4h) space group, to a ferroelectric phase with P_m (C_s) space group,driven by the softening behaviour of the E_u1 mode. In addition, the out-of-plane tensile strain, vertical to the ab plane, leads to a ferroelectric phase with P_42nm (C_4v) space group, driven by the softening behaviour of the A_2u mode. The critical tensile strains are 3.7% in-plane and 4.0% out-of-plane, respectively. In addition, the in-plane compression strain, which has the same structure variation as out-of-plane tensile strain due to Poisson effect, leads the paraelectric rutile TiO₂ to a paraelectric phase with P_nnm (D_2h) space group driven by the softening behaviour of the B_1g mode. These results indicate that the sequence ferroelectric (or paraelectric) phase depends on the strain applied. The origin of ferroelectric stabilization in rutile TiO₂ is also discussed briefly in terms of strain induced Born effective charge transfer.     

Identification of first- and second-order magnetic phase transitions in ferromagnetic perovskites

A criterion used for the determination of first- and second-order magnetic phase transitions from purely magnetic methods is applied to manganese perovskites of formula La_2/3(Ca_1−xSr_x)_1/3MnO₃. A crossover from first- to second-order character at a tolerance factor t=0.92 is found, which also brings about several variations in other physical properties. At t=0.92 a change from orthorhombic to rhombohedral symmetry also takes place. The impossibility of establishing static cooperative Jahn–Teller distortions in the rhombohedral symmetry is suggested as being responsible for the observed behaviour.     

Size dependence of phase transition temperatures of ferromagnetic, ferroelectric and superconductive nanocrystals

With the miniaturization of devices, size and interface effects become increasingly important for the properties and performances of nanomaterials. Here, we present a thermodynamic approach to the mechanism behind size-induced unusual behavior in the phase stabilities of ferromagnetic (FM), antiferromagnetic (AFM), ferroelectric (FE), and superconductive (SC) nanocrystals, which are different dramatically from their bulk counterparts. This method is based on the Lindemann criterion for melting, Mott’s expression for the vibrational melting entropy, and the Shi model for the size-dependent melting temperature. Simple and unified functions, without any adjustable parameter, are established for the size and interface dependences of thermal and phase stabilities of FM, AFM, FE and SC nanocrystals. According to these analytic functions, as the size of nanocrystals is reduced, the thermal and phase stabilities may strengthen or weaken, depending on the confluence of the surface/volume ratio of nanocrystals and the FM(AFM, FE or SC)/substrate interface situations. The validity of this model is confirmed by a large number of experimental results. This theory will be significant for the choice of materials and the design of devices for practical application.     

Micromagnetic phase transitions and spin wave excitations in a ferromagnetic stripe

Magnetic excitations of micrometer-wide ferromagnetic stripes subjected to a transverse applied field have been measured between 1 and 20 GHz. The complexity of the observed response is attributed to the spatially nonuniform equilibrium spin distribution. This one is modeled analytically and numerically, which allows one to distinguish two micromagnetic phases governing the ground state. The nucleation-related phase transitions are evidenced by soft modes, while the different observed resonances are attributed to spin wave modes localized in the two phases and at their interface.     

Size dependence of phase transition temperatures of ferromagnetic ,ferroelectric and superconductive nanocrystals

With the miniaturization of devices, size and interface effects become increasingly important for the properties and performances of nanomaterials. Here, we present a thermodynamic approach to the mechanism behind size-induced unusual behavior in the phase stabilities of ferromagnetic (FM), antiferromagnetic (AFM), ferroelectric (FE), and superconductive (SC) nanocrystals, which are different dramatically from their bulk counterparts. This method is based on the Lindemann criterion for melting, Mott’s expression for the vibrational melting entropy, and the Shi model for the size-dependent melting temperature. Simple and unified functions, without any adjustable parameter, are established for the size and interface dependences of thermal and phase stabilities of FM, AFM, FE and SC nanocrystals. According to these analytic functions, as the size of nanocrystals is reduced, the thermal and phase stabilities may strengthen or weaken, depending on the confluence of the surface/volume ratio of nanocrystals and the FM(AFM, FE or SC)/substrate interface situations. The validity of this model is confirmed by a large number of experimental results. This theory will be significant for the choice of materials and the design of devices for practical application.