Maps of intervals with indifferent fixed points: Thermodynamic formalism and phase transitions

We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields onedimensional systems with many-body infinite-range interactions for which the thermodynamics is well defined but Gibbs states are not. (Piecewise linear systems of this kind yield the soluble, in a sense, Fisher models.) We prove that such systems exhibit phase transitions, the order of which depends on the behavior at the indifferent fixed points. We obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures. Our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable (expanding) induced version. The technique allows one also to obtain a version of the Bowen-Ruelle formula for the Hausdorff dimension of repellers for maps with indifferent fixed points, and to generalize Fisher results to some nonsoluble models.Meyerhoff Visiting Professor, on leave from the Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.     

Pressure-induced ferroelectric-antiferroelectric phase transitions in lead zirconate-tatanate-based solid solutions

The ferroelectric-antiferroelectric phase transitions induced by hydrostatic pressure in solid solutions based on lead zirconate-titanate (PZT) with introducing 20 at % tin into B sites and composites based on these ceramics have been studied. In the composites with the same composition of solid solution, the transition pressure can be varied within wide ranges depending on the type of binders. The latter is due to the vitrification of the binder and, consequently, the formation of a rigid framework preventing the transmission of pressure to the ceramic matrix.     

A phase formalism for excitonic transitions

We develop a matrix formalism for the phase involved in quantum transitions experienced by excitons on the basis of the quantum mechanics of the hydrogen atom. Both photon emission and absorption within the context of the above transitions are modelled.     

Evolution of phase transitions in SrTiO3-BiFeO3 solid solutions

The dielectric and acoustic properties of (1 ? x)SrTiO₃?xBiFeO₃ solid solutions (0 ≤ x ≤ 1) have been studied in the temperature range from 4.2 to 850 K. Evolution of the antiferrodistortive transition and its suppression in the concentration range 0.1 < x < 0.2 have been revealed. X-ray diffraction data obtained at room temperature, as well as the observed acoustic anomalies combined with dielectric measurements, have been used to estimate the concentration range of the existence of the relaxor state, as well as of the formation and coexistence of the antiferromagnetic and ferroelectric phases at high BiFeO₃ concentrations.     

Structure and phase transitions of lead zirconate hafnate solid solutions

Solid solutions of two antiferroelectrics, namely, lead zirconate and lead hafnate, i.e., PbZr_{1 − x} Hf _x O₃ (x = 0, 0.3, 0.5, 0.7, 1.0), have been prepared by solid-phase synthesis from simple oxides. The elemental composition of the samples and their structure have been studied using X-ray fluorescence and X-ray diffraction analyses. The phase transformations of the solid solutions have been determined in the temperature range 20°C < T < 300°C.     

Thermodynamic data for solid AgI and its phase transitions from ENF measurements

From EMF measurements in the cell Ag(s)/AgI(s)/I₂(g), graphite as a function of temperature, the enthalpy and entropy values for the formation of γ-, β- and α-AgI were obtained. From these data, the following thermodynamic quantities corresponding to the phase transitions were also calculated: Δ_tH_γ→β= -34.3 ±2 kJmol^-1, Δ_tS_γ→β= -107 ± 4 Jmol^-1K^-1, Δ_tH_β→α = 5.4 ± 2 kJmol^-1, Δ_tS_β→α = 23 ± 4 Jmol^-1K^-1.     

Study of ferroelectric phase transitions in solid solutions based on bismuth vanadate

The structural, thermal, nonlinear optical, and conducting properties of Bi₄(V_{1 ? x} Me _x )₂O_{11 ? y} solid solutions (Me = Zr, Ga, Fe) have been investigated. The effect of domain wall pinning, accompanying the α ? β ferroelectric phase transition, is revealed. It is found that the conductivity in all studied series of solid solutions increases with an increase in x.     

Thermodynamic studies of successive phase transitions in BaZnGeO4 and a new solid phase below 186.1 K

The successive phase transitions of BaZnGeO₄ have been studied on meltsolidified samples. A new solid phase (named phase VI) has been found below 186.1 K in samples of large particle size (diameter:D0.1 mm). The higher temperature crystalline phase V can be supercooled easily down to liquid helium temperature. On heating, however, it transforms into phase VI above 95 K in a slow exothermic process. Heat capacities have been measured by adiabatic calorimetry between 14 and 300 K. The enthalpy and entropy of the V–VI phase transition are 187.1 Jmol^–1 and 0.971 J K^–1 mol^–1, respectively. The corresponding data for the IV–V phase transition at 199.8 K are 229.3 J mol^–1 and 1.168 JK^–1 mol^–1. The phase VI does not appear in samples of smaller particle size (D0.1 mm).     

Counterion phase transitions in dilute polyelectrolyte solutions

In dilute solutions of rodlike polyelectrolytes some counterions are distributed far from polyions while others are located in their vicinity in the regions of cylindrical symmetry of the electrostatic potential. For these cylindrical regions around rodlike polyelectrolytes we find an exact solution of the nonlinear Poisson-Boltzmann equation for the case of nonzero net charge in these regions. This exact solution implies three qualitatively different phases of counterion distribution around the polyions with second order phase transitions between these phases.     

Phase transitions in SrTiO3-based solid solutions

Phase transitions in solid solutions of strontium titanate with titanates of the divalent metals Pb, Ba, and Ca are considered. It is shown that the critical concentration x _c in the well-known expression relating the transition temperature to the polar state in SrTiO₃ with the concentration x of divalent metals, T _c=A(x−x _c)^1/2, is practically the same for all impurities. For large values of x, the ferroelectric transition temperature T _c depends linearly on x. The volume and impurity contributions to the T _c(x) relation are determined for this concentration range. Fiz. Tverd. Tela (St. Petersburg) 39, 1645–1651 (September 1997)     

Universality of phase transitions at solid surfaces

Recent progress in theoretical and experimental studies on various order-disorder phase transitions at solid surfaces is reviewed. An emphasis is put on the problem of the universality class of surface phase transitions.     

Thermodynamic parameters of diffuse phase transitions in Ag2Te

A differential thermal analysis in vacuum and studies of the coefficients of electrical conductivity and thermal conductivity, and of the thermal emf are made in Ag₂Te in the neighborhood of the structural phase transition. It is shown that these data can be used to calculate the switching factor L(T), determine the region in which the phases coexist within the transition, and calculate the thermodynamic parameters. Prior to and after the main phase transition, additional displacement transitions are observed. It is found that the phase transition takes place roughly according to the scheme α _{385 K}→α′_{405 K}→β′_{420 K}→β _{440 K}. The specific heat C _p, changes in entropy ΔS and transition enthalpy ΔH, as well as the minimum phase fluctuation volume V, and the heat Q of the phase transition are determined. It is shown that excesses of Te and Ag have almost no effect on the transition temperatures T ₀, but have a substantial effect on the thermodynamic parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1693–1697 (September 1998)     

Description of ferroelectric phase transitions in solid solutions of relaxors in the framework of the random-field theory

A model based on the random-field theory is proposed for calculating the properties of solid solutions of ferroelectric relaxors. The electric dipoles randomly distributed in the system are treated as sources of random fields. The random field distribution function is calculated taking into account the contribution of nonlinear and correlation effects and the differences in the dipole orientations for different solid solution components. The dependence of the phase transition temperature T _c on the concentration of solid solution components is analyzed. Numerical calculations are performed for the lead scandoniobate and lead scandotantalate solid solutions (PbSc_1/2Nb_1/2O₃)_1?x (PbSc_1/2Ta_1/2O₃)_x with different degrees of ordering and the lead magnoniobate and lead titanate solid solution (PbMg_1/3Nb_2/3O₃)_1?x (PbTiO₃)_x. It is shown that the higher transition temperature for more disordered solid solutions of the composition (PbSc_1/2Nb_1/2O₃)_1?x (PbSc_1/2Ta_1/2O₃)_x in the range 0≤x<0.5 is associated with the larger nonlinearity coefficient for PbSc_1/2Nb_1/2O₃ as compared to that for PbSc_1/2Ta_1/2O₃. The theory provides a means for calculating the region of the coexistence of the phases with different symmetry groups in the temperature-composition phase diagram of the (PbMg_1/3Nb_2/3O₃)_1?x (PbTiO₃) solid solution. Numerical calculations with the use of the fitting parameters obtained from the known transition temperatures T _c for the solid solution components adequately describe the experimental phase diagrams for the aforementioned solid solutions of ferroelectric relaxors.     

Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

We investigate the superposition of multifractals in the generalized thermodynamic formalism. It is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior. We demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities. Therefore, the obtained results are of importance for the interpretation of experimental systems.     

Thermodynamic properties of successive phase transitions in Rb2ZnBr4

Heat capacity measurements have given the following transition temperatures and entropies: 0.027 J K^?1mol^?1 at 76.5 K, 0.47 J K^?1mol^?1 at 111.7 K, and 0.048 J K^?1mol^?1 at 193.6 K. These are interpreted as “lock-in”, soft-mode, and “lock-in” transitions, respectively, from comparison with analogous results for Rb₂ZnCl₄ and K₂SeO₄. The N-IC transition was located at 347 K by DTA.     

Thermal behavior of Jonscher’s formalism in relaxor ferroelectrics showing diffuse phase transitions

A theoretical study of the thermal behavior of the exponent s of Jonscher’s power law in ferroelectric materials showing diffuse phase transitions (DPTs) is presented. The proposed model is applied to the experimental results of lanthanum-doped lead zirconate titanate ferroelectric ceramics. Both the proposed model and the experimental results show a critical point (a maximum) around the maximum of the dielectric loss factor, which moves to higher temperatures when the frequency increases, the typical behavior of a relaxor material with DPTs. PACS 77.22.Gm; 77.80.Bh; 77.84.Dy