Smeared Phase Transition Research Articles

Mysteries of Water and Other Anomalous Liquids: “Slow” Sound and Relaxing Compressibility and Heat Capacity (Brief Review)

Reasons for the existence of “fast” sound at terahertz frequencies in various liquids have been analyzed. It has been shown that the fast sound speed is described well by the conventional formula from the theory of elasticity, where ρ is the density of a liquid andandare the bulk and shear moduli at the frequency ω, respectively. The excess of the speed of fast sound over the speed of normal sound in “normal” liquids is 10–20% and is almost completely determined by the contribution of the shear modulusat high frequencies, and vanishes on the Frenkel line. At the same time, the huge excess (50–120%) of the fast speed of sound over the speed of normal sound in some liquids (called “anomalous”), such as water and tellurium melt, is due mainly to the strong frequency dependence of the bulk modulus. Anomalously low relaxing bulk moduli were studied in our previous works for many oxide and chalcogenide glasses near smeared pressure-induced phase transitions. In anomalous liquids, smeared phase transitions also occur in a wide temperature and pressure region, which sharply reduces the bulk moduli and speeds of sound. Thus, the record large difference between speeds of fast and normal sound in anomalous liquids is due not to anomalously fast sound but to the fact that normal sound in such liquids is anomalously “slow” and bulk moduli are anomalously low. Ultrasonic studies of low- and high-density amorphous water ices show that their bulk moduli are indeed a factor of 4–5 higher than the bulk modulus of water. In addition, because of smeared phase transitions, the heat capacities of water and tellurium melt are a factor of 1.5–2 higher than those for normal liquids; i.e., anomalous liquids are characterized not only by an anomalous (nonmonotonic) behavior but also by anomalous magnitudes of physical quantities for most of the available measurement methods. A similar anomalous increase in the compressibility and heat capacity is observed for all fluids in the close vicinity of the liquid–gas critical point. In this case, anomalously fast sound is observed at terahertz frequencies, which is also due to a sharp increase in the bulk modulusat high frequencies. At the same time, high compressibility and heat capacity, as well as a large excess of the speed of fast sound over the speed of normal sound, for anomalous liquids and glasses near smeared phase transitions are not necessarily due to the proximity of critical points and occur in any scenario of the smeared phase transition.

Lattice Dynamics of the Strontium Ferrotungstate in the Temperature Range 300–700 K

The lattice dynamics of a strontium ferrotungstate SrFe2/3W1/3O3 ceramics is studied by the Raman spectroscopy method in the temperature range 300–700 K. The analysis of the Raman spectra confirms the tetragonal symmetry of strontium ferrotungstate, and this result agrees with the X-ray diffraction data. The features of the temperature behavior of phonon modes of the strontium ferrotungstate have been revealed and it is shown that a smeared phase transition from the tetragonal to the cubic phase takes place at temperatures 410–500 K.

Smeared phase transitions in percolation on real complex networks

Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability to describe the networks themselves. In many applications, correctly identifying the phase transition of percolation on real-world networks is of critical importance. Unfortunately, this phase transition is obfuscated by the finite size of real systems, making it hard to distinguish finite size effects from the inaccuracy of a given approach that fails to capture important structural features. Here, we borrow the perspective of smeared phase transitions and argue that many observed discrepancies are due to the complex structure of real networks rather than to finite size effects only. In fact, several real networks often used as benchmarks feature a smeared phase transition where inhomogeneities in the topological distribution of the order parameter do not vanish in the thermodynamic limit. We find that these smeared transitions are sometimes better described as sequential phase transitions within correlated subsystems. Our results shed light not only on the nature of the percolation transition in complex systems, but also provide two important insights on the numerical and analytical tools we use to study them. First, we propose a measure of local susceptibility to better detect both clean and smeared phase transitions by looking at the topological variability of the order parameter. Second, we highlight a shortcoming in state-of-the-art analytical approaches such as message passing, which can detect smeared transitions but not characterize their nature.

Preparation, Structure, and Dielectric and Magnetic Properties of SrFe2/3W1/3O3 Ceramics

Polycrystalline samples of SrFe2/3W1/3O3 (SFWO) ceramic were obtained by solid-phase reactions with subsequent sintering using conventional ceramic technology. X-ray diffraction analysis showed that at room temperature, the SFWO ceramic is single-phase and has a perovskite-type structure with tetragonal symmetry and parameters a = 3.941(9) A, c = 3.955(6) A, and c/a = 1.0035. In studying the magnetic properties and the Mossbauer effect in SFWO ceramics, it is found that the material is a ferrimagnet, and the iron ions are only in the valence state of Fe3+. It is suggested that in the temperature range of T = 150–210°C, a smeared phase transition from a cubic (paraelectric) phase to a tetragonal (ferroelectric) phase takes place in SFWO with decreasing temperature.

Получение, структура, диэлектрические и магнитные свойства керамики SrFe-=SUB=-2/3-=/SUB=-W-=SUB=-1/3-=/SUB=-O-=SUB=-3-=/SUB=-

AbstractPolycrystalline samples of SrFe_2/3W_1/3O_3 (SFWO) ceramic were obtained by solid-phase reactions with subsequent sintering using conventional ceramic technology. X-ray diffraction analysis showed that at room temperature, the SFWO ceramic is single-phase and has a perovskite-type structure with tetragonal symmetry and parameters a = 3.941(9) Å, c = 3.955(6) Å, and c/a = 1.0035. In studying the magnetic properties and the Mössbauer effect in SFWO ceramics, it is found that the material is a ferrimagnet, and the iron ions are only in the valence state of Fe^3+. It is suggested that in the temperature range of T = 150–210°C, a smeared phase transition from a cubic (paraelectric) phase to a tetragonal (ferroelectric) phase takes place in SFWO with decreasing temperature.

Modeling the magnetic field control of phase transition in ferromagnetic shape memory alloys

In the framework of finite deformations a model has been constructed to describe the process of controlling the austenite-to-martensite phase transformation in ferromagnetic polycrystalline materials with shape memory effects (Heusler alloys) under the action of temperature, force and magnetic fields. The control of the phase transition is realized with the help of the magnetic field, which shifts the specific transformation temperatures. The kinematic and constitutive equations, satisfying the principles of thermodynamics and objectivity, have been developed both, for the martensitic and austenitic phases and also for the mixed austenitic-martensitic state, which takes place in the process of smeared phase transition of the first order. To solve the connected magnetomechanical problem two variational equations have been used. The available experimental data have been used to verify the proposed model.

Vollhardt invariant and phase transition in the helical itinerant magnet MnSi

In this paper we argue that rounded "hills" or "valleys" demonstrated by the heat capacity, thermal expansion coefficient, and elastic module are indications of a smeared second order phase transition, which is flattened and spread out by the application of a magnetic field. As a result, some of the curves which display a temperature dependence of the corresponding quantities cross almost at a single point. Thus, the Vollhardt crossing point should not be identified with any specific energy scale. The smeared phase transition in MnSi preceding the helical first order transition most probably corresponds to the planar ferromagnetic ordering, with a small or negligible correlation between planes. At lower temperatures, the system of ferromagnetic planes becomes correlated, acquiring a helical twist.

Modeling the magnetic field control of phase transition in ferromagnetic shape memory alloys

In the framework of finite deformations a model has been constructed to describe the process of controlling the austenite-to-martensite phase transformation in ferromagnetic polycrystalline materials with shape memory properties (Heusler alloys) under the action of temperature, force and magnetic fields. The control of the phase transition is realized with the help of the magnetic field, which changes (shifts) the specific transformation temperatures. The kinematic and constitutive equations, satisfying the principles of thermodynamics and objectivity, have been developed both, for the martensitic and austenitic phases and also for the mixed austenitic–martensitic state, which takes place in the process of smeared phase transition of the first order. The last is considered as a sequence of the point first-order phase transformations. Relations, describing the shift of characteristic temperature of the phase transition according to the generalized Clausius–Clapeyron law, have been derived. This shift is defined by the stresses generated in the body in the process of its deformation and is controlled by the internal magnetic field induced in the material by the external magnetic field. Moreover, the internal magnetic field produces in the body the mass (ponderomotive) and surface forces in addition to ordinary external forces of another physical nature. Deformation of the body under the influence of all forces, including the above mentioned ones, and the internal magnetic field, induced in the material, disturb the external magnetic field. To solve this connected magnetomechanical problem two connected variational equations have been used. One of these equations is the well-known Lagrange variational equation and the other corresponds to a weak formulation of the problem considering the behavior of a magnetizable body of finite geometry located in the space, which is under the action of the magnetic field, and takes into account the surface magnetic effect. The procedure for numerical implementation of these equations has been described. The model and variational equations have been used to solve the problem, in which the austenite-to-martensite phase transformation in the specimen made of polycrystalline Ni–Mn–Fe–Ga alloy (ferromagnetic shape memory material) is realized at fixed external temperature due to shift of specific phase transition temperature induced by the magnetic field. The available experimental data for this problem have been used to verify the proposed model.

Dielectric and Pyroelectric Properties of PMN-29PT Single Crystals near MPB

This paper presents a systematic investigation of the dielectric and pyroelectric properties of PMN-29PT single crystals, oriented and poled along three different crystallographic directions, <001>, <011> and <111>as a function of temperature and frequency. Dielectric measurements were performed over a temperature range of 300 K–500 K and at frequencies of 20 Hz–1 MHz. During the heating cycle, two phase transitions are detected: one at ~380 K from rhombohedral to tetragonal phase, another at ~410 K from tetragonal to cubic phase. However, during the cooling cycle only one smeared phase transition is observed, i.e. phase transition from cubic to rhombohedral phase. Pyroelectric measurements were performed from 220 K to 420 K during the heating cycle. The variations of pyroelectric coefficients with temperature shows two maxima, one at 370 K and another at 400 K for the <111>- and <011>-oriented crystals, respectively, while only one maximum is observed at 360 K for the crystal oriented along the <001> direction.

Formation of the molecular crystal structure during the vacuum sublimation of paracetamol

The results from structural and thermal studies on the formation of molecular crystals during the vacuum sublimation of paracetamol from its vapor phase are given. It is established that the vapor-crystal phase transition proceeds in a complicated way as the superposition of two phase transitions: a first-order phase transition with a change in density, and a second-order phase transition with a change in ordering. It is shown that the latter is a smeared phase transition that proceeds with the formation of a pretransitional phase that is irreversibly dissipated during phase transformation, leading to the formation of crystals of the rhombic syngony. Data from differential scanning calorimetry and X-ray diffraction analysis are presented along with microphotographs.

Effect of electric field on the smeared phase transition in crystals PbIn1/2Nb1/2O3-28PbTiO3 and PbIn1/2Nb1/2O3-37PbTiO3

The effect of a direct-current electric field (0 < E < 3 kV/cm) on the smearing of the phase transition and the Curie-Weiss exponent (γ) for two PbIn1/2Nb1/2O3-28PbTiO3 and PbIn1/2Nb1/2O3-37PbTiO3 crystals lying at different distances from the morphotropic phase boundary has been investigated. The universal Curie-Weiss law has been used to approximate the temperature dependences of the dielectric permittivity. It has been shown that the more remote is the crystal from the morphotropic phase boundary, the larger is the exponent γ and, consequently, the more smeared is the phase transition (in the zero field, γ = 1.67 and 1.49 for PbIn1/2Nb1/2O3-28PbTiO3 and PbIn1/2Nb1/2O3-37PbTiO3, respectively). It has been found that a weak electric field (no greater than 2–3 kV/cm) in the case of the more smeared phase transition almost does not affect the Curie-Weiss exponent, whereas for the PbIn1/2Nb1/2O3-37PbTiO3 crystal, this exponent decreases with increasing electric field strength and approaches γ = 1, which is characteristic of the conventional ferroelectric.

Slow dynamics of the contact process on complex networks

The Contact Process has been studied on complex networks exhibiting different kinds of quenched disorder. Numerical evidence is found for Griffiths phases and other rare region effects, in Erd\H os R\'enyi networks, leading rather generically to anomalously slow (algebraic, logarithmic,...) relaxation. More surprisingly, it turns out that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of sole topological heterogeneity in networks with finite topological dimension. In case of scale-free networks, exhibiting infinite topological dimension, slow dynamics can be observed on tree-like structures and a superimposed weight pattern. In the infinite size limit the correlated subspaces of vertices seem to cause a smeared phase transition. These results have a broad spectrum of implications for propagation phenomena and other dynamical process on networks and are relevant for the analysis of both models and empirical data.

Slow dynamics and rare-region effects in the contact process on weighted tree networks

We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (nontopological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.

Electroluminescence of (Pb0.91La0.09)(Zr0.65Ti0.35)O3 ceramics with nanopolar structure

Lanthanum-doped lead zirconate titanate (PLZT) relaxor ceramics with (Pb0.91La0.09)(Zr0.65Ti0.35)O3 composition exhibits a repolarization-induced electroluminescence (EL) with a pronounced discrete character of emission. It is established that this behavior is related to the reorientation of nanodimensional polar regions in a strong pulsed electric field in the vicinity of a smeared phase transition. The temporal and temperature dependences of the EL intensity have been studied.

Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys ${\mathrm{A}}_{1\ensuremath{-}x}$B${}_{x}$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x&lt;1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.

Effect of Ba incorporation on pressure-induced structural changes in the relaxor ferroelectricPbSc0.5Ta0.5O3

Pressure-induced structural changes in the canonical relaxor ${\text{Pb}}_{0.78}{\text{Ba}}_{0.22}{\text{Sc}}_{0.5}{\text{Ta}}_{0.5}{\text{O}}_{3}$ were studied with both in-house and synchrotron single-crystal x-ray diffraction as well as Raman spectroscopy at pressures up to 9.8 GPa. The results reveal that the substitution of Ba for Pb in $AB{\text{O}}_{3}$ perovskite-type structures, i.e., the substitution of a two-valent element with an isotropic electron shell for an isovalent element with a stereochemically active lone pair, leads to a ``diffuse pressure-induced phase transition,'' a structural transformation over a broad pressure range, without a well-defined critical pressure point. The smeared phase transition of the average structure results from the existence of local structural deformations in the vicinity of A-positioned Ba cations.

High hydrostatic pressure effect on magnetic state of anion-deficient La 0.70Sr 0.30MnO x perovskite manganites

The magnetic state of La 0.70Sr 0.30MnO x ( x=2.85, 2.80) anion-deficient manganites is studied experimentally under hydrostatic pressure up to 5.2 GPa. These materials possessing the properties of a spin-glass state. The La 0.70Sr 0.30MnO 2.85 exhibits a coexistence of the rhombohedral (R3¯c) and tetragonal (I4/mcm) crystal structures and below T f ∼50 K the spin-glass state is formed. The La 0.70Sr 0.30MnO 2.80 exhibits the tetragonal (I4/mcm) crystal structure. For this compound a phase-separated magnetic state below T f is formed, involving coexistence of C-type antiferromagnetic (AFM) clusters within spin-glass matrix. In both compounds the crystal structure and magnetic states remain stable upon compression. Under the hydrostatic pressure up to 1 GPa, the La 0.70Sr 0.30MnO 2.85 is a spin glass with a smeared phase transition to the paramagnetic state. The freezing temperature T f of the magnetic moments of the ferromagnetic clusters increases at a rate of 4.30 K/GPa and the magnetic ordering temperature T MO increases at a rate of 12.90 K/GPa. The enhancement of the ferromagnetic properties of La 0.70Sr 0.30MnO 2.85 anion-deficient manganite under hydrostatic pressure is explained by the redistribution of oxygen vacancies and a decrease in the unit cell parameters.

Slow dynamics at the smeared phase transition of randomly layered magnets

We investigate a model for randomly layered magnets, viz. a three-dimensional Ising model with planar defects. The magnetic phase transition in this system is smeared because static long-range order can develop on isolated rare spatial regions. Here, we report large-scale kinetic Monte Carlo simulations of the dynamical behavior close to the smeared phase transition which we characterize by the spin (time) autocorrelation function. In the paramagnetic phase, its behavior is dominated by Griffiths effects similar to those in magnets with point defects. In the tail region of the smeared transition the dynamics is even slower: the autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small asymptotic value following a power law at late times. Our Monte-Carlo results are in good agreement with recent theoretical predictions based on optimal fluctuation theory.

Effect of gamma irradiation on the dielectric response of a Sr0.75Ba0.25Nb2O6 relaxor single crystal

The effect of gamma irradiation from a 60Co source at a dose D = 4.75 × 104 R on the dielectric properties of a Sr0.75Ba0.25Nb2O6 (SBN-75) single crystal with a smeared phase transition is investigated in the low-and infralow-frequency ranges. The behavior of the dielectric response is compared with the behavior of the depolarization currents induced in unirradiated and irradiated samples of the Sr0.75Ba0.25Nb2O6 compound. The observed changes in the electrical properties of the Sr0.75Ba0.25Nb2O6 single crystal in the temperature range of the smeared phase transition are associated with the stabilization of the ferroelectric phase of the material in an internal bias field generated by radiation-induced defects.

Influence of the prehistory of NaNbO3-Gd1/3NbO3 ceramics and single crystals on their dielectric properties

The dielectric properties of a ceramic and a single crystal of the same composition 0.9NaNbO3-0.1Gd1/3NbO3 (NNG10) with different prehistories of the material are investigated in the low-and infralow-frequency ranges. It is revealed that the dielectric aging of the material based on the NaNbO3 antiferroelectric with a smeared phase transition differs in character from similar phenomena observed in relaxor ferroelectrics.