Investigations on the soft-mode mechanism of the ferroelectric phase transition in

Dielectric and Raman spectroscopic measurements have been performed to investigate the ferroelectric phase transition in . Single crystals were grown by the zone melting method. The frequency dependence of the dielectric permittivity from 1 MHz to 1 GHz has been studied in a temperature range between 265 and 285 K. A Debye like dielectric dispersion was found, showing a critical slowing down around K. Polarized Raman spectra have been taken between 220 and 310 K. Two softening modes have been found, one of A- and another one of B / B g-symmetry. The phase transition mechanism in can be classified as partially order-disorder and partially displacive, confirming former structural results. It resembles strongly that of monoclinic . Received: 7 April 1998 / Revised: 5 June 1998 / Accepted: 16 June 1998     

Size dependence of dielectric properties and structural metastability in ferroelectrics

The size effect of the dielectric properties and the barrier height was investigated in the ferroelectric solid solution Ba_xSr_1-xTiO₃ system. The decrease of the grain size causes the suppression of the ferroelectricity, and the increase of the relaxation frequency. Barrier heights increase with increasing grain size. The result is analogous to magnetic phase transitions in nanocrystals and other solid-solid phase transitions in nanocrystals. It suggests a general rule that may be of use in the discovery of new metastable phases. An explanation of this phenomenon was given by an electric potential model that agrees well with the experimental results. For Ba_xSr_1-xTiO₃ system, the decrease of xcauses the decrease of the barrier height. Received 3 August 1998 and Received in final form 22 November 1998     

Fluctuation-dissipation ratio in lattice-gas models with kinetic constraints

We investigate by Monte-Carlo simulation the linear response function of three dimensional structural glass models defined by short-range kinetic constraints and a trivial equilibrium Boltzmann-Gibbs measure. The breakdown of the fluctuation-dissipation theorem in the glassy phase follows the prediction of mean field low temperature mode-coupling theory. Received: 24 April 1998 / Received in final form: 8 May 1998 / Accepted: 11 May 1998     

Apparent correlations between the static length of relaxation and the linear size of dynamic heterogeneity in fragile liquids

The most puzzling aspect of the glass transition observed in laboratory is the decoupling of the dynamics from the structure. As an attempt to reconcile the dynamic and the static lengthscales associated with the glass problem, we discuss the apparent correlations between the static relaxation length, defined as that lengthscale over which the potential energy fluctuation is correlated, with the linear size of the dynamic heterogeneity. The dynamic heterogeneous domains with long life-times, may therefore be linked to the droplets of low potential energy, or the tightly bound regions inside the liquid.     

Probing the material properties and phase transitions of ferroelectric liquid crystals by determination of the Landau potential

The full Landau potential of several, widely varying ferroelectric liquid-crystalline materials has been experimentally determined. Tilt angle and polarisation data is analysed across the SmA to SmC transition for varying applied electric-field amplitudes, allowing the determination of all the coefficients of the generalised Landau model of ferroelectric liquid crystals. The materials investigated encompass different materials, including low-polarisation mixtures to high-polarisation single-component materials. The materials also possess a variation in the order of the SmA to SmC phase transition from strongly first order to strongly second order. The effects of both the polarisation and order of phase transition of the system are discussed with respect to the various terms of the generalised Landau model. Further, the mechanisms behind the difference between a first- and second-order phase transition are discussed with respect to the Landau potential and the second Landau coefficient b .     

Incomplete ferroelectricity in SrTi 18O 3

Motivated by recent experiments demonstrating suppression of ferroelectricity with pressure in SrTi¹⁸O₃, the dynamics of the phase transition mechanism are reinvestigated within a nonlinear polarizability model. For temperatures far above the phase transition polar micro domains are formed which increase in size with decreasing temperature to freeze out at T_c without forming long range order. Experimentally, soft mode dynamics are simultaneously observed, evidencing that displacive and order/disorder features coexist. In the ferroelectric phase both components persist whereby an incomplete and inhomogeneous ferroelectric state is formed.     

Growth exponent in the Domany-Kinzel cellular automaton

Dynamic heterogeneities, i.e. the presence of molecules with different mobilities, have been established as one of the key features of the physics of supercooled liquids. Here we study in detail how the mobility of an individual molecule fluctuates with time. Our analysis is based on a time series of molecular dynamics simulations for a low molecular weight glass-former, propylene carbonate. We find that the variation of mobility with time of initially slow molecules significantly differs from that of initially fast molecules. We explicitly show the relation to the rate memory parameter which recently has been introduced to quantify the mobility fluctuations as observed via multidimensional NMR experiments. In this way qualitative agreement between simulation and experiment can be established although the time scales of simulation and NMR experiment differ by many orders of magnitude. Received 10 April 2000 and Received in final form 21 September 2000     

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems. Received 4 December 1998 and Received in final form 10 March 1999     

Diffusion and rheology in a model of glassy materials

We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses (J.-P. Bouchaud, J. Phys. I France 2, 1705 (1992)), as extended to describe rheological properties (P. Sollich, F. Lequeux, P. Hébraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)).) We investigate the breakdown, near the glass transition, of the (generalized) Stokes-Einstein relation between self-diffusion of a tracer particle and the (frequency-dependent) viscosity of the system as a whole. This stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology. We also investigate the effect of flow (oscillatory shear) on self-diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition (where this was previously zero). At higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response. The relevance of these findings to soft glassy materials (foams, emulsions etc.) as well as to conventional glass-forming liquids is discussed. Received 31 August 1998 and Received in final form 25 January 1999     

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation. Received: 9 January 1998 / Revised: 24 April 1998 / Accepted: 2 July 1998     

Surface state on first-order ferroelectrics

In the presence of a surface the Landau-Devonshire equations of ferroelectricity must be extended to include a boundary condition. For a ferroelectric with a second-order transition in the case when the polarization p(z) increases at the surface, it is well known that a surface state occurs in a range of temperature above the bulk critical temperature t_CB . Here we explore the corresponding effect for a first-order ferroelectric. We show that a surface state can occur, but only if the surface effect is sufficiently strong. Analytic expressions are derived and illustrated for p(z), the surface value p_S =p(0) and the free energy. The transition from the paraelectric state (p=0) to the surface state is first order, and for completeness we establish the dependence of the three critical temperatures (supercooling, thermodynamic and superheating) on a boundary-condition parameter y. In a final section, we derive and illustrate expressions for p(z)in the temperature range t<t_CB .     

Phase transitions of a spin-one alternating magnetic superlattice

We examine the critical behavior of a magnetic superlattice which made up of two magnetic materials, A and B. Using the effective field theory with a probability distribution technique that accounts for the single-site spin correlation, we derive the analytical equation for the Curie temperature of the superlattice which alternates as ABAB...AB. The dependence of the Curie temperature on the interface coupling strength J_ab and the layer number of the finite superlattice was calculated. The effects of the surface modification are also studied. Received 2 March 2001     

Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)

The mean field spin glass model is analyzed by a combination of exact methods and a simple Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution. Received 14 February 2000     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

P-adic numbers and replica symmetry breaking

The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic Fourier transform seems to be a promising tool. Received 9 June 1999     

Melting behavior of large disordered sodium clusters

The melting-like transition in disordered sodium clusters Na₉₂ and Na₁₄₂ is studied by performing density functional constant-energy molecular dynamics simulations. The orbital-free version of the density functional formalism is used. In Na₁₄₂ the atoms are distributed in two distinct shells (surface and inner shells) and this cluster melts in two steps: the first one, at ≈130 K, is characterized by the development of a high intrashell atomic mobility, and the second, homogeneous melting at ≈270 K, involves diffusive motion of all the atoms across the whole cluster volume. On the contrary, the melting of Na₉₂ proceeds smoothly over a very broad temperature interval, without any abrupt change in the thermal or structural indicators. The occurrence of two steps in the melting transition is suggested to be related to the existence of a grouping of the atoms in radial shells, even if those shells present a large degree of internal disorder. It then appears that a cluster can be considered fully amorphous (totally disordered) only when there are no radial regions of low atomic density separating shells. The isomer of Na₉₂ studied here fulfills this criterion and its thermal behavior can be considered as representative of that expected for fully amorphous clusters. Disordered Na₁₄₂, on the other hand, that has a discernible structure of an inner and a surface shell, should be considered as not fully disordered. The thermal behavior of these two clusters is also compared to that of icosahedral (totally ordered) sodium clusters of the same sizes. Received 5 February 2001 and Received in final form 21 May 2001     

Phase transitions in Sr 0.61 Ba 0.39 Nb 2 O 6 :Ce 3+ : II. Linear birefringence studies of spontaneous and precursor polarization

The linear birefringence (LB) of Sr _0.61-x Ba _0.39 Nb ₂ O ₆ :Ce ³⁺ x (SBN61:Ce) has been measured as a function of temperature within the range of . Large tails have been observed above the ferroelectric phase transition temperatures T _c = 350, 328, 320 and 291 K for the concentrations x = 0, 0.0066, 0.0113 and 0.0207, respectively. Within an Ornstein-Zernike analysis the critical exponents , and are determined. It suggests that pure SBN61 belongs to the 3D Ising universality class. Doping with Ce ³⁺ ions, which seem to act as random fields, enhances the relaxor properties. The critical exponents and of SBN61:Ce shift against those of the three-dimensional random-field Ising model. Received 1 October 1999     

Scaling of broadband dielectric data of glass-forming liquids and plastic crystals

The Nagel scaling and the modified scaling procedure proposed recently by Dendzik et al. have been applied to broadband dielectric data on two glass-forming liquids (glycerol and propylene carbonate) and three plastic crystals (ortho-carborane, meta-carborane, and 1-cyano-adamantane). Our data extend the upper limit of the abscissa range to considerably higher values than in previously published analyses. At the highest frequencies investigated, deviations from a single master curve show up which are most pronounced in the Dendzik scaling plot. The loss curves of the plastic crystals do not scale in the Nagel plot, but they fall onto a separate master curve in the Dendzik plot. In addition, we address the question of a possible divergence of the static susceptibility near the Vogel-Fulcher temperature. For this purpose, the low-temperature evolution of the high-frequency wing of the dielectric loss peaks is investigated in detail. No convincing proof for such a divergence can be deduced from the present broadband data. Received 14 June 1999 and Received in final form 4 October 1999     

Dielectric relaxation of poly(ethylenglycol)- b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers above the glass transition temperature

The complex dielectric permittivity has been measured for three poly(ethylenglycol)-b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers with different content of poly(ethylenglycol) (15%, 33% and 80%), and increasing degree of crystallinity (0%, 10% and 20%, respectively). Only the non-crystalline sample shows the normal mode relaxation together with the segmental (α-relaxation) and the Johari-Goldstein (β-relaxation) modes. The crystalline samples show also polarization contributions due to the existence of interfaces between the crystallites and the amorphous phase. The relaxation times of the (α and normal modes can be described by a VFT equation with the same value of T₀. There is a slowing-down of the segmental mode due to the presence of crystallites. The temperature dependence of the α and β relaxations in the copolymers is very similar to that found in pure PPG, while there are significant differences in the case of the normal mode of the non-crystalline sample. The size of the cooperatively rearranging regions CRR, and the width of the glass transition region increase slightly with the degree of crystallinity. The temperature dependence of the size of CRRs is compatible with the prediction of fluctuation theory. No systematic effect of the degree of crystallinity on the β-relaxation has been found. Near T _g the β-relaxation time is close to the primitive time of the coupling model. Received: 31 May 2000