Showing papers in "Phase Transitions in 1991"

Electric polarization in crystals and its response to thermal and elastic perturbations

Abstract: The basic properties of electric polarization response in crystalline dielectrics are theoretically analysed. Spontaneous polarization, pyroelectricity, piezoelectricity, flexoelectricity (polarization response to strain gradient) and thermopolarization effect (polarization response to temperature gradient) are discussed on the basis of a unified approach. Special attention is paid to the problem of the adequate theoretical definition of these phenomena. The effect of the sample termination on the polarization response is considered in detail.

How does dew form

Abstract: Dew is a phenomenon that is experienced daily. It is formed of water droplets that imperfectly wet the substrate on which they condense. The formation of dew is connected to rich and numerous physical phenomena: heterogeneous nucleation, phase transitions, heat transfer, wetting. Although the growth of an isolated droplet still remains imperfectly understood, growth of an assembly of drops is better comprehended: the fact that drops coalesce during their growth, and that the substrate (plane, line, fractal …) is of lower dimensionality than that of the drops is at the origin of surprising properties (self-similarity, constant and universal value of the surface coverage, correlation of position). Experiments and numerical simulations of condensation of water vapor on planar or unidimensional solid substrates are presented. Condensation on a liquid substrate (oil) modifies the interactions between drops because the substrate is locally curved; the drops can then self-organize in two-dimensional (he...

Influence of lattice imperfections on the transition temperatures of structural phase transitions: The plateau effect

Abstract: The influence of defects on the apparent phase transition temperature has been studied over a large range of defect concentrations. An interval was found for low concentrations (around 1 mol%) in which the transition temperature depends only weakly on the number of defects and where defect tails occur. This interval is called the plateau. For higher defect concentrations we find that chemical mixing leads to strong variations of the transition temperature which are well described in the approximation of a homogeneous crystal.

Optical study of the antiferromagnetic-paramagnetic phase transition in chromium oxide Cr2O3

Abstract: Optical effects of the first and second order with respect to the order parameter (1 is antiferromagnetic vector) have been studied in Cr2O3 around its phase transition at TN = 306 K from the antiferromagnetic to paramagnetic state. The magnetic linear birefringence is characterized by a rather large magnitude Δn sp ≃ 10−3 and by a large contribution of fluctuations of the order parameter to the birefringence. The study of the nonreciprocal optical rotation induced by an electric field has shown that the phase transition has a well defined first-order character. This result is also supported by the observation of a nonlinear (quadratic in the electric field) nonreciprocal rotation in a narrow temperature region ΔT = 0.15 K around TN . The temperature variation of the order parameter l(T) below TN is well described by a power low l where τβ = (TN - T)/TN and β = 0.355. We also observed a very reproducible effect of the rotation of the optical indicatrix in opposite directions for two types of anti...

Phase transitions in ferroelectric thin films

Abstract: We discuss theory and experiment for phase transitions in ferroelectric films, 70–400 nm thick. It is found that the Curie temperature Tc can be shifted up or down by temperatures as great as 70 K. In addition, transitions that are strongly first-order in bulk may become continuous in sufficiently thin films. Finally, the shape of the spontaneous polarization curve, plotted versus temperature, can become complicated, dropping to zero at an elevated Tc in two discrete jumps, with the higher temperature discontinuity arising from a residual ferroelectricity in a thick surface layer. These points are illustrated experimentally with data on PZT (PhZr1−x Ti x O3) and KNO3.

Phonons at martensitic phase transitions of bcc-Ti, bcc-Zr and bcc-Hf

Abstract: Inelastic neutron scattering on in situ grown bcc single crystals of the group 4 metals Ti, Zr and Hf show a band of low energy and strongly damped phonons. Geometrical considerations show how these damped lattice vibrations achieve the displacements necessary for the two martensitic phase transitions from bcc to ω (under pressure) and from bcc to hcp (upon lowering the temperature). The low energy and temperature dependent phonons are precursor fluctuations of the hcp or ω phase within the bcc phase.

The role of ferroelasticity in toughening of brittle materials

Abstract: Ferroelastic materials, which are characterized by the existence of a hysteresis between strain and stress, can exhibit enhanced toughness relative to the paraelastic, prototypic phase. Domain switching in the near crack tip stress field provides the requisite energy absorption mechanism and thus a toughening mechanism. Experimental evidence (X-ray diffraction) is presented on three different types of ferroelastics; namely, tetragonal (t') zirconia, gadolinium molybdate (GMO) and its terbium (TMO) and dysprosium (DMO) analogs, and lead zirconate titanate (PZT). It is shown that ferroelastic domain switching occurs in these materials in the vicinity of a crack tip. The fracture toughness of the ferroic phase is shown to be two to three times that of the nonferroic phase in all three materials. The results of the present study demonstrate that ferroelastic domain switching is viable toughening mechanism.

The reversible crystal-quasicrystal transitions in icosahedral Al—Cu—Fe alloys

Abstract: A perfect icosahedral phase, which shows narrow diffraction peaks, exists in Al—Cu—Fe alloys only within a restricted temperature range, between 1020 K and 1120 K. It undergoes two types of reversible transitions. Above the upper temperature limit, the icosahedral phase transforms to a mixture of crystalline phases and residual liquid by a peritectic reaction. Below the lower-temperature limit, it turns into a closely related rhombohedral modification through a solid state transition. The two types of reactions were studied in detail by powder neutron diffraction techniques the results of which are reported on. These results are complemented by electron microscopy data.

Birefringence and phase transitions in liquid crystals

Abstract: The birefringence of liquid-crystalline phases is the result of the parallel order of molecules exhibiting a polarizability anisotropy. The magnitude and sign of the birefringence are determined by the structure and order of the liquid-crystalline phase types as well as by the polarizability properties of the constituent molecules. The characteristic change of the birefringence at phase transitions between liquid-crystalline phases indicates more or less pronounced structural changes. The temperature dependence of the birefringence is due to the temperature change of the molecular order. It is shown that the structural variety of the liquid crystalline state is reflected by a big variety of their optical anisotropy properties.

Coupled order parameters in the Landau theory of phase transitions in solids

Abstract: We discuss the role of both primary and secondary order parameters in a transition between two solid phases. We show how microscopic distortions which appear at the transition can be calculated using group-theoretical methods. We also show how the form of the coupling term in the Landau free energy influences the behavior of secondary order parameters.

Dielectric relaxation in ferroelectric (CH3)2NH2Al(SO4)2.6H2O crystal

Abstract: This paper presents the results of the investigation of dielectric dispersion and ultrasonic velocity in the ferroelectric (CH3)2NH2Al(SO4)2 · 6H2O crystal. The crystal shows a critical slowing down process of polarization with an extremely long relaxation time of the dipole system (τ = 1.6 · 10−7s at the phase transition point). The dielectric response over the frequency range up to 56 GHz in the paraelectric phase can be well described in terms of a monodispersive Debye-type formula. The activation energy of dipoles in the paraelectric phase is 0.11 eV = 8.5 kTc . The results show that the proper ferroelectric phase transition is nearly critical and of the order-disorder type.

Optical studies of the ferroelastic phase transitions in Rb3H(SeO4)2, (NH4)3H(SO4)2 and (NH4)3H(SeO4)2

Abstract: Optical observations of growth twins and ferroelastic domains and measurements of the rotation of the optical indicatrix were carried out for Rb3H(SeO4)2 and (NH4)3H(SO4)2 using an optical microscope Taking into account the symmetry reduction from the rhombohedral (Rm) to the monoclinic phase (B2/a) the occurrence of domains and growth twins can be well described The orientations of oblique ferroelastic walls are well determined by the spontaneous strains s e 11 and s e 23 at room temperature

Some aspects of the thermodynamic behaviour of ferroelastic and co-elastic phase transitions

Abstract: Ferroelastic phase transitions and phase transitions involving coupling between the driving order parameter and elastic degrees of freedom (i.e. co-elastic phase transitions) follow empirically a Landau-type mean field behaviour over large temperature intervals. At temperatures close to the transition point the upper critical dimension is reduced to three if fluctuations are sufficiently constrained in reciprocal space. At low temperatures, the observed temperature independence of the order parameter in the saturation regime (S-regime) is correlated with the quantum limit of the dissipation-fluctuation theorem. The good agreement between experimental observations and the predictions of a Landau-type treatment of the excess Gibbs free energy even for large values of the order parameter leads to the conclusion that the convergency of the polynomial form of the Gibbs free energy is due to small energy coefficients rather than due to the order parameter being small.

Structure of the incommensurate phase of BCCD at 130 K

Abstract: The incommensurate structure of BCCD at 130 K with q = 0.296c∗ has been determined in the superspace-group P(Pnma):(1, s, −1) by means of single crystal X-ray diffraction data including main and first-order satellite reflections. Only zero and first-order harmonics have been considered in the modulation functions. The final agreement factors are R = 0.048, Ro = 0.042 and R1 =0.067, for all, main and first-order satellite reflections respectively. Only the atomic modulations of the betaine molecule could be interpreted in terms of rigid-body modulated motions. The symmetry of the structure is in accordance with a single A3 soft-mode model for the phase transition sequence.

The changes in electronic structure and optical properties of magnetic semiconductors at magnetic phase transitions

Abstract: The influence of magnetic phase transitions on electronic structure and optical properties of magnetic semiconductors is discussed. Europium chalcogenides and chromium chalcogenide spinels are the main subjects of the investigation. It is shown, that many-body effects are responsible for the changes of optical properties and non-rigid band behavior of electronic structure. Magnetic phase transition leads to energy shift of wide bands and change in density of states of “magnetic” d(f)-electrons without any significant shift of their energies. The influence of fluctuations at T ∼ T c and antiferromagnetic semiconductors are also considered.

Birefringence studies of A2BX4 compounds with incommensurate phases

Abstract: A large number of A2BX4 compounds possess a structurally incommensurate phase. Studies of linear optical properties belong to the most frequently used methods for their investigations. In this contribution we give a review of these results. The paper concentrates on the following topics: fluctuation phenomena near the normal-incommensurate (IC) phase transition; changes in absorption spectra; specific features of light propagation in the IC phase; behaviour of birefringence and its connection with the order parameters in the IC phase as well as in the lock-in phase C; use of birefringence for elucidating the transformation process IC-C and for determining the phase diagrams; memory effects. Areas where additional data or theoretical analyses would be worthwhile are indicated.

Electron microscopy study of domain wall wetting in ordered copper-palladium

Abstract: The nature of domain walls (also called antiphase boundaries) in a Cu-Pd alloy ordered on the FCC lattice has been studied as a function of temperature, using conventional and high-resolution microscopy. At low temperature, the domain walls are perfectly thin and faceted. Complete interfacial wetting by the disordered phase, characterized by a divergence of the width of the walls, is shown to occur when approaching the order-disorder transition.

EPR evidence of possibility of incommensurate and ferroelastic phase in KSc(MoO4)2

Abstract: EPR investigations of KSc(MoO4)2 below the first phase transition are presented. It has been established that in the low temperature phase KSc(MoO4)2 exists in a simultaneously incommensurate and ferroelastic phase. It has also been shown that on lowering the temperature the incommensurate phase transition is followed by another first order transition.

Relations between curie temperature and chemical bond in octahedral monodimensional ferroelectrics

Abstract: Octahedral monodimensional ferroelectrics are an important group of compounds due to their great number, the theoretical studies made on them, their property modulation by various ionic substitutions and their applications. They belong to different structural families: perovskites, tetragonal tungsten bronzes, LiNbO3… The Curie temperature is related to the chemical bond of these materials. Various aspects are described. They concern the influence of the size, the charge, the coordination, the electronic configuration of the cations, either in or out of the octahedron, the bond covalency and the degree of cationic order.

A bibliographical review of the high pressure studies of ferroelectric phase transitions

Abstract: A brief review of the various high pressure studies on the phase transitions in ferroelectric crystals carried out over the past two decades is presented. The theoretical framework in which high pressure studies have to be viewed is given. The pressure data of ferroelectric crystals are organized in the form of tables. High pressure spectroscopic and structural studies are included. The review contains a bibliography of over two hundred references.

Electronic properties of Pb(ZrTi)O3 solid solutions

Abstract: The theoretical backgrounds and some experimental data on the electronic properties of polycrystalline Pb(Zr, Ti)O3 solid solutions are summarized. These substances occur in the perovskite structure, and so their electronic band structure is presumed to be analogous to other perovskite compounds. Their forbidden gap energy has been determined to be about 3.30–3.56 eV on the basis of optical, photoacoustical, and photoelectrical measurements. Many local levels and traps exist in the forbidden gap because of the polycrystalline character and heterovalent doping. Their actual configurations and states strongly influence the optical, photoelectrical, piezoelectrical, and other physical properties of Pb(Zr, Ti)O3 solid solutions.

Disordered magnetic phases and magnetic transitions in non anisotropic frustrated systems

Abstract: Numerous studies have been devoted to disordered magnetic phases which show the existence of several types of disorder in non-anisotropic systems Semi-disordered systems which retain at least partially long-range order (reentrant properties and randomly canted structures) and fully disordered systems (spin cluster and soft transition systems, true spin glass state) are shortly reviewed Several characteristic experiments and results are presented and commented on, such as alternative, nonlinear and static susceptibilities, thermoremanence, ageing effects, neutron diffraction and Mossbauer spectroscopy The possible types of disordered magnetic phases are discussed as a function of a sharp (or soft) transition and of a more or less fast dynamics In true spin glasses, some problems are still open while in the other disordered phases the unresolved questions are numerous

Phase transitions in LiKSO4: Low-temperature neutron diffraction results

Abstract: Results of a detailed crystallographic study of the structural phase transitions in LiKSO4, carried out using single crystal neutron diffraction at ambient and below-ambient temperatures (300–100 K), are presented. The study indicates two clear phase transitions at 205 K (from space group P63 to space group P31c), at 189 K (to space group Cc) and a third transition at about 130 K in the cooling cycle. The corresponding temperatures are 250 K, 200 K and 138 K in the heating cycle. The existence of twins, mixed phases, and extremely sluggish kinetics for the various phase transitions, as well as the structural details of the various phases in this mixed salt, can explain the apparent inconsistencies in the results of several experimental investigations reported in the literature.

Magnetic phase transition in cobalt iodine boracite

Abstract: Neutron diffraction investigation of crystal structures and magnetic ordering of cobalt iodine boracite (Co3 11B-O13I) is reported. The canted antiferromagnetic structure has been determined at 31 K and 9 K, and revealed a magnetic ordering in two steps, without any change in the symmetry of the antiferromagnetic arrangement.

Applications of optical activity to studies of phase transitions

Abstract: This article reviews at an introductory level the physics of optical activity and its recent applications to studies of phase transitions of ferroelectrics. Optical activity is a kind of internal perturbation of the refractive index, and accordingly induces a resonating effect on the eigenstates of the susceptibility. This is the reason why optical activity provides us with unreplaceable information concerning the chirality of the structure and specific bonding nature of constituent atoms. The principles of our high accuracy universal polarimeter (defined as HAUP) method are described, which realized for the first time simultaneous measurements of birefringence, optical activity, and rotation angles of the indicatrices of any crystals, even those belonging to monoclinic and triclinic systems. The utility of the HAUP method is exemplified by our recent experiments. The origin of the occurrence of incommensurate states in some A2BX4 crystals was theoretically explained from the fact that they showe...

On the structural phase transitions in the incommensurate Cs2CdBr4

Abstract: In the series of incommensurate A2BX4 halides with the β-K2SO4 type structure, Cs2CdBr4 exhibits an unusual behaviour since the “lock-in” phase transition occurs at the centre of the Brillouin zone The observed phase sequence is the following: Pnma (Z = 4)⇔INC(k0 ≈ 1/6a∗)⇔P21/n(Z = 4)⇔P1 (Z = 4) These phase transitions have been studied by means of Raman scattering and ultrasonic measurements It is shown that the Pnma⇔INC⇔P21/n sequence is governed by order-disorder processes due to CdB2-4 tetrahedra reorientations coupled with translations of the Cs+ cations, and that the low-temperature P21/n⇔P1 transition is of a displacive nature, governed by a soft optical mode The “pseudo-proper” ferroelastic character of these transformations is clearly established A model potential developed in the framework of Landau theory is proposed; this model is able to reproduce the general trends observed in the temperature dependence of the soft-modes and of the elastic constants in the different phases

The Para-ferroelectric phase transition in (NH3CH3)5 Bi2Cl11 (P.M.A.C.B.)

Abstract: A new ferroelectric crystal, (CH3NH3)5 Bi2Cl11 has been grown. It reveals a second-order phase transition at 307 K with a high peak in the dielectric permittivity along c: ∊c ⋍ 8.5 × 103. The structures of the ferro and paraelectric phases are orthorhombic. In the paraelectric phase, three of the five methylammoniums are disordered, while in the ferroelectric phase two of them are still disordered. The packing is ensured by N—H…Cl hydrogen bonds between anions and cations. The ordering of the methylammonium cation in the ferroelectric phase leads to a new hydrogen bond formation responsible for the high dipolar properties of this compound.

Phase transitions and dynamics driven incommensurability in thiophene

Abstract: Thermodynamic, dynamic and structural properties of crystalline thiophene are reviewed. Calorimetric, NMR and dielectric spectroscopies reveal in both phase sequences that there exists an in-plane non-perfect five-fold reorientational motion which persists in all phases, with only slight modifications at phase transitions. This motion ultimately freezes on cooling, thus leading to a glassy crystalline state below ∼40 K in both sequences. Incommensurate phases have been found in the metastable phase sequence: they are related to the same molecular motion. The existence of incommensurability in the stable sequence and the nature of the expected commensurate-incommensurate phase transitions are discussed. It is concluded that the glass transitions are due to a symmetry departure and that the pseudo-pentagonal molecular symmetry is the origin of the dynamics-driven incommensurability.

Structures and magnetic properties of RM x compounds (R = rare earth, M = Ge or Si, 1.5 ≤ x ≤ 2) as observed by neutron diffraction

Abstract: Rare earth germanides and silicides of the type RMx (M = Ge or Si) with x values close to 2 occur in four different structure types: the hexagonal AlB2 type, the tetragonal α-ThSi2 type, the orthorhombic α-GdSi2 type and the orthorhombic TbGe2 type. A review is given of the occurrence of these structure types in the various R–M systems as observed by neutron diffraction. The occurrence of Si or Ge vacancies in these structures is emphasized and discussed in relation to the magnetic structures observed for these materials.

Local order in the cubic phase of ABO3 perovskites

Abstract: The existence of polarization clusters in the cubic phase of the ABO3 compounds has been revealed for a long time by various experimental techniques, including now the direct measurement of the dielectric dispersion. These clusters are described in terms of correlated displacements of the B ions in the 〈111〉 directions, out of the centre of the oxygen cage. In this paper, we show how the improvement of both the crystalline quality and the performance of the experimental devices led to the actual concept of “relaxator ferroelectrics”. Some experimental results are reviewed within the scope of this relaxation concept and its microscopic origin is questioned.