[Show abstract][Hide abstract] ABSTRACT: We report in this paper detailed measurements of the linear and nonlinear optical properties of thin films of P(VDF-TrFE) copolymers (with composition 70/30 mol%). The polymer films are cast from solutions using the spin coating technique and poled at saturation using very low-frequency a.c. fields. The refractive index (n = 1.42) is determined from measurements of the Brewster incidence, and the thickness from measurements of the optical path close to the normal incidence. Recording of the Maker fringes and calibration of the set-up with a quartz plate allow us to determine the second-harmonic coefficients: d33 = 4.3, d31 = 0.22 10−12 m/V and the optical dispersion n(2ω) − n(ω) = 0.0077 (ω is the frequency of the incident laser beam at 1060 nm). The spin-coated copolymer films are optically unaxial due to a preferential orientation of the chain axes parallel to the plane of the film, and measurement of their birefringence gives ne − no = −0.0083. Therefore, this feature allows us to find a direction of phase matching along which the first- and second-harmonic waves have an infinite coherence length. It is observed using an index-matching liquid.
[Show abstract][Hide abstract] ABSTRACT: A phenomenological theory of the incommensurate phase transition which occurs close to the alpha - beta transition in quartz is presented. This theory assumes that the coupling between the soft optic mode of the alpha - beta transition and the acoustic modes play an important role in the formation of the modulated structure. According to the values of the phenomenological parameters, different kinds of incommensurate structures can form, in particular single-k or triple-k structures. The available experimental data concerning the quartz transition are discussed.
Journal of Physics C Solid State Physics 11/2000; 16(35):6705.
[Show abstract][Hide abstract] ABSTRACT: Structural relaxations near surfaces and interfaces are analysed in a simple, generic model with first-, second- and third-layer interactions. The relaxations have exponential envelopes with three types of structural distortion: (i) ferrodistortive, (ii) antiferrodistortive, and (iii) modulated (incommensurable). Their stability conditions in the field of control parameters and their relationship with structural phase transitions is derived. A tricritical point is found for three-layer interactions and a transition to an incommensurate phase. All phase transitions to the ferrodistortive phase are first-order in the model. The theory is applied to the analysis of lattice relations near internal interfaces in ionic polytypic materials (e.g. PbI2). Diffuse X-ray scattering and the shift of diffraction angles are the typical fingerprints for such relaxations. The relevant structure factors are calculated. There is tentative agreement between the calculated and observed diffraction profiles.
[Show abstract][Hide abstract] ABSTRACT: Biquadratic coupling between two order parameters Q1 Q2 can lead to transitions between a phase with only one of the two order parameters active (phase I or II) and a mixed phase III in which both order parameters are symmetry breaking. Domain walls for positive coupling energies are chiral under thermodynamic conditions close to the transition points I-III and II-III. Annihilation of chirality in the wall leads to wall widening and wall bifurcations. The widths of the walls are different for the two order parameters leading to greater lattice distortions on either side of the wall than in the centre of the wall.
[Show abstract][Hide abstract] ABSTRACT: From surface tension measurements we extract the melting entropy Deltas2D of fatty-alcohol monolayers on water. Deltas2D is found to be 4kB/mol lower than in the bulk. Because of the role of the conformational entropy, the melting transition is discontinuous for long chains, but tends to be continuous for molecules shorter than 1-nonanol. For 1-decanol Deltas2D is sufficiently small to allow observation of critical fluctuations; the diffraction peak, measured with a high resolution synchrotron experiment, is described by a power-law singularity which broadens as the temperature approaches the melting point.
[Show abstract][Hide abstract] ABSTRACT: Owing to macroscopic electric fields arising from thermal fluctuations of a ferroelectric domain wall, the attraction energy of two parallel walls decays at large distances between the walls (h) as h-2 with a prefactor that is proportional to T and to a ratio of dielectric constants that is equal to unity for the isotropic medium. For proper ferroelectrics, and improper ones with a quadratic dependence of the spontaneous polarization on the order parameter, this law is valid for all h greater than the domain wall thickness (which is the minimum length of the problem). For improper ferroelectrics with cubic (or higher-order) dependence of the polarization on the order parameter, there exists a region with a logarithmic dependence of the interaction energy on h. This attraction, which proves to prevail over the Van der Waals one, leads to a discontinuity of the ferroelectric-incommensurate transition. Estimation of the period of the incommensurate phase at the transition provides a reasonable order of magnitude and shows that this period does not depend much on the crystal parameters other than the width of the domain wall. The interaction of the ferromagnetic and ferroelastic domain walls is qualitatively analogous to that of the ferroelectric ones. The role of quantum fluctuations becomes important at not very low temperatures. For nonferroelectric, nonferroelastic, nonferromagnetic domain walls the power-law fluctuation-induced attraction is shown to arise as well.
[Show abstract][Hide abstract] ABSTRACT: We argue that any commensurate-incommensurate phase transition in a crystalline media is discontinuous due to power-law attraction of the domain walls. The main origin of this attraction are the thermal fluctuations of the walls which are always accompanied, in a crystal, by at least one of the long-range fields: electric, magnetic, elastic.
[Show abstract][Hide abstract] ABSTRACT: Some analogies exist between parametrically driven dynamical system and anisotropic XY model. We discuss one aspect of this analogy : the existence of domain walls, their different structures and the existence of “wetting” like transitions. The work is done in a Landau-Ginzburg framework.
[Show abstract][Hide abstract] ABSTRACT: The morphology of gamma' precipitates of AM1 single crystal superalloys has been studied by small neutron scattering (SANS), and electron microscopy. Due to the single crystal nature of the samples, the SANS patterns are anisotropic and exhibit a fourfold symmetry corresponding both to the shape and to the spatial arrangement of the precipitates in a (001) plane. Measurements for other sample orientations have allowed us to improve the analysis of the shape of the precipitates. After creep deformation along the <001> axis, a twofold symmetry corresponding to the “rafting” of the gamma' precipitates is observed in the (010) plane. The main effect of heat treatments at 1 050 °C, commonly used for industrial applications, is the coarsening of the precipitates. From the displacement of the correlation peaks towards smaller angles, we deduce an average centre-to-centre spacing between the precipitates which increases with the annealing time from 0.3 to 0.6 micrometer according to the Lifshitz, Slyosov, Wagner behaviour. The results are compared to electron microscopy measurements, performed on the same samples.
[Show abstract][Hide abstract] ABSTRACT: The results of a consistent perturbation theory of the non mean-field contributions to the ultrasonic attenuation anomalies are presented. The cases of one-and two-components order parameter (including incommensurate systems)are discussed. The main conclusions are : i) the fluctuation conmbunon in the non-symmetrical phase includes terms which were overlooked before. ii) the phason contribution to the longitudinal sound attenuation near incommensurate phase transition, is small in the low frequency limit.
[Show abstract][Hide abstract] ABSTRACT: The problem of winding of a long polymer chain around an attractive rigid rod is studied in relation with the localization transition exhibited by this system. The role of chiral and polar interactions is considered. The results are compared with previous models of adsorption of a polymer and of helix-coil transition. On étudie le problème de l'enroulement d'une longue chaîne de polymère autour d'une barre rigide, en relation avec la transition de localisation présentée par ce système. Le rôle des interactions chirales et polaires est considéré. Ces résultats sont comparés à des modèles précédemment proposés pour décrire l'adsorption d'un polymère et la transition hélice-pelote.
[Show abstract][Hide abstract] ABSTRACT: We consider second order phase transitions with formation of superstructure and show that anomaly of diffuse X-ray and neutron scattering in the symmetrical phase takes place not only at the reciprocal lattice vectors corresponding to the Bragg reflections to appear in the non symmetrical phase but also at other ‘‘rigid'’ points. The number of these points is infinite for the incommensurate transition. Diffuse scattering both in perfect crystals and in crystals containing random field defects is considered. It is argued that to observe the predicted anomalies one has to investigate scattering corresponding to fairly large reciprocal lattice vectors.
[Show abstract][Hide abstract] ABSTRACT: In the high temperature racemic solid solution of tetramethyl 2,2,5,5 hydroxy 3 pyrrolidine (TMHP), there is on each molecular site either a right molecule, or a left molecule (chirality disorder) each molecule having two possible orientations (orientational disorder). There are then four possible states on each site. Such a situation is described using three order parameters. The “Landau free energy” of the system contains a third order term that couples these three parameters. We have numerically evaluated (Kitaïgorodski methode) the intermolecular interaction energies as a function of the order parameters. This allows us to predict from the experimental results that the orientational order parameter condensates the first, and, because of the third order term, leads to ordering of the chiralities at lower temperatures. The symmetry changes found and the calculated transition temperatures are in agreement with the observations. Dans la phase solution solide haute température du tétraméthyl 2,2,5,5 hydroxy 3 pyrrolidine (TMHP), on a sur chaque site moléculaire soit une molécule droite soit une molécule gauche (désordre de chiralité) chaque molécule pouvant prendre deux orientations différentes (désordre orientationnel). Il y a donc quatre états possibles sur chaque site. Une telle situation se décrit à l'aide de trois paramètres d'ordre. L'“énergie libre” (type Landau) du système présente un terme du troisième ordre qui couple ces trois paramètres. Nous avons évalué numériquement (méthode de Kitaïgorodski) les énergies d'interaction intermoléculaire en fonction des paramètres d'ordre. Ceci nous a permis de prévoir, conformément aux résultats expérimentaux, que le paramètre d'ordre d'orientation condense le premier entraînant à plus basse température, grâce aux termes du troisième ordre la mise en ordre des chiralités. Les changements de symétrie trouvés et les températures de transition calculées sont en accord avec les observations.
[Show abstract][Hide abstract] ABSTRACT: In P(VDF-TrFE) random copolymers with compositions from 60/40 to 80/20 mol%, the ferroelectric phase transition exhibits a strong first order character and is accompanied by a large expansion of the crystal lattice. In the ferroelectric structure, the polymer chains have an all-trans conformation and are close-packed parallel to one another in a pseudo-hexagonal lattice. According to the m2m symmetry, the spontaneous polarization Py is perpendicular to the chain axis 2. In the paraelectric phase, the structure is disordered : the chains undergo continuous conformational changes, they have a statistical Cm symmetry and the expanded lattice is hexagonal (6/m point group)