Course Of Phase Transitions Research Articles

Microprocesses at Second-Order Phase Transitions in Crystals with Strong Interband Electron-Phonon Interaction

A system of strongly interacting electrons and phonons in a crystal has been considered. If the temperature changes, the systemundergoes changes equivalent to those occurring at the phase transition of the second kind, when the equilibrium positions of atoms become shifted. It has been demonstrated that the expansion of the thermodynamic potential in a series in the order parameter, which is a standard routine in the Landau phenomenological theory, can lead to equilibrium states that do not correspond to any real state of the crystal. It has also been shown that, in the course of phase transitions that occur with varying temperature, the deformation energy is released in the form of Barkhausen-like pulses.

Production of Nanocellulose by Enzymatic Treatment for Application in Polymer Composites.

In the last few years, the scientific community around the world has devoted a lot of attention to the search for the best methods of obtaining nanocellulose. In this work, nanocellulose was obtained in enzymatic reactions with strictly defined dispersion and structural parameters in order to use it as a filler for polymers. The controlled enzymatic hydrolysis of the polysaccharide was carried out in the presence of cellulolytic enzymes from microscopic fungi—Trichoderma reesei and Aspergillus sp. It has been shown that the efficiency of bioconversion of cellulose material depends on the type of enzymes used. The use of a complex of cellulases obtained from a fungus of the genus Trichoderma turned out to be an effective method of obtaining cellulose of nanometric dimensions with a very low polydispersity. The effect of cellulose enzymatic reactions was assessed using the technique of high-performance liquid chromatography coupled with a refractometric detector, X-ray diffraction, dynamic light scattering and Fourier transform infrared spectroscopy. In the second stage, polypropylene composites with nanometric cellulose were obtained by extrusion and injection. It was found by means of X-ray diffraction, hot stage optical microscopy and differential scanning calorimetry that nanocellulose had a significant effect on the supermolecular structure, nucleation activity and the course of phase transitions of the obtained polymer nanocomposites. Moreover, the obtained nanocomposites are characterized by very good strength properties. This paper describes for the first time that the obtained cellulose nanofillers with defined parameters can be used for the production of polymer composites with a strictly defined polymorphic structure, which in turn may influence future decision making about obtaining materials with controllable properties, e.g., high flexibility, enabling the thermoforming process of packaging.

Finite element analysis of a new phase field model with [formula omitted]-Laplacian operator

In this paper, we propose a new phase field model involving the p-Laplacian operator with 1<p≤2. This newly developed model can be used to simulate the sub-diffuse interface phenomena in the course of phase transitions during microstructure evolution. We also propose an energy-stable finite element approximation for the proposed nonlinear parabolic problem and rigorously prove that the finite element approximation is unconditionally energy stable. Moreover, we give the optimal error estimate and convergence rate with respect to the mesh sizes. Numerical examples are carried out to demonstrate the stability and accuracy of the proposed scheme, which is in accordance with the theoretical ones. Numerical results also indicate that the evolution of free energy is in consistency with the discrete dissipation theory. Moreover, the energy initially decreases sharply when the parameter p becomes larger. Meanwhile, we can observe that the parameter p affects the spatial patterns during phase transition. More precisely, the phase field value will be changed more slowly as well when the parameter p becomes smaller.

Complex structure and Mössbauer effect observed in the course of phase transitions in PbZr0.72Sn0.28O3 single crystal.

The Mössbauer effect was used to study the structural transitions in a PbZr0.72Sn0.28O3 single crystal. Two kinds of quadrupole splittings were registered and connected with two different environments of the Sn ion occupying the center of SnO6 octahedra. What is responsible for the existence of these two environments is the disorder in tilts of oxygen octahedra and antiparallel shifts of pairs of lead ions. Both disorders decide on structural transitions which the PbZr0.72Sn0.28O3 single crystal undergoes. The two kinds of quadruple splittings that have been observed do not disappear at temperatures far above phase transitions. This indicates that the structure of the paraelectric phase is locally non-centrosymmetric and confirms pre-transitional effects previously reported for Sn doped PbZrO3 single crystals.

Thermal expansion anisotropy of β-TlInS2 crystals in the course of phase transitions

ABSTRACTBasing on the thermal expansion studies performed for β-TlInS2 crystals in the course of their phase transitions, we have found that the crystals aged for one year are composed from at least two polytypes, which undergo phase transitions at different temperatures. The detailed analysis of anisotropy of the thermal expansion demonstrates that all of the diagonal components of the thermal expansion tensor associated with the eigensystem have almost the same modules but differ by their signs. This leads to appearance of an elliptical conical surface of zero thermal expansion. The orientation of this surface does not depend on the temperature in the temperature interval under study. We have also found that the thermal expansion coefficients along the crystallographic a and b axes are close to zero.

Modelling of water droplets heat and mass transfer in the course of phase transitions. II: Peculiarities of the droplet radial coordinate and the time grid calibration

This paper continues optimization of numerical solution algorithm of iterative scheme grid for the droplet task, which was presented in the first article of this series. Assumptions were made by optimal assessable number of members which was already defined in numerical experiment in case of compound heat spread by conduction and radiation and an unsteady temperature field was described by infinite integral equation sum. For the convenience of numerical analysis, droplet thermal parameters PT were described by universal Fourier criteria Fo and by dimensionless radial coordinate η function PT(Fo,η). This function is given in form of infinite integral equation sum with each thermal parameter having a distinct initial member and individually defined subsidiary function. This function is given in form of infinite integral equation sum with each thermal parameter having a distinct initial member and individually defined subsidiary function. The droplet time and radial coordinate grading change influence for calculated function graphs PT(Fo,η) was evaluated by water droplets heat transfer and phase transformation numerical experiment. Summarizing by conduction and radiation heated water droplets thermal parameter variation patterns a methodology of forming an optimal grid for droplet task' task iterative solving, is provided.

Comparative study of structural phase transitions in bulk and powdered Fe–27Ga alloy by real-time neutron thermodiffractometry

Phase transformations in an iron–gallium alloy have been analyzed by in situ real-time neutron diffraction in the temperature range from 293 to 1223 K. Two compositionally identical samples were studied: the first was in the as-cast bulk state, and the second was ground into a powdered state. In both samples, the same sequence of structural transitions was recorded on heating with a constant heating rate (D03 → A2 → L12 → D019 → A2), and the same structural state (D03 + L12) was recorded after slow cooling to room temperature. Owing to strong texture in the bulk sample, only diffraction patterns of the powdered sample were treated with the Rietveld method to determine the volume fractions of the coexisting phases, the coefficients of thermal expansion, and the thermal and static atomic disorder parameters. The occupancy of Ga positions and the ordered iron magnetic moment were refined at selected temperatures. The level of microstrain in the crystallites in the initial as-quenched state is small, but it sharply increases in the course of phase transitions when the alloy is heated. The microstrains are high and strongly anisotropic after slow cooling. Generally, phase transformations occur similarly in the powdered and bulk samples, but with a noticeable difference in details. The fulfilled analysis of the bulk and powdered samples allowed the real possibilities of the quantitative neutron diffraction analyses of phase transitions in ferromagnetic ordered alloys to be assessed.

Structure and Properties of NiTi Shape Memory Alloy after Cold Rolling in Martensitic State

Due to unique features, like shape memory effects and superelasticity, NiTi alloys with nearly equiatomic composition are used in various branches of industry. Application of severe plastic deformation can drastically change properties of the materials. In the present paper the Ni50.4Ti49.6 alloy after cold rolling in the martensitic state and further annealed is studied. Phase transformations were studied using X-ray diffraction and differential scanning calorimetry measurements. Microstructure was examined using transmission electron microscopy and electron backscattering diffraction methods. Mechanical properties of obtained alloys has been studied using Vickers microhardness tests. Based on the performed measurements it can be seen that in studied alloys two steps B2 ↔ R ↔ B19′ phase transitions occurred. Performed plastic deformation influences course of phase transitions and phases composition. Due to the reduction of grain size microhardness of the studied material is increasing with increase of deformation degree.

The Structure and Properties Formation of the NiTi Shape Memory Rods after Hot Rotary Forging

Shape memory effects, the course and characteristic temperatures of phase transitions and mechanical properties and surface properties of NiTi alloys strongly depend on the chemical composition, the production process used and the plastic working and thermomechanical treatment as well as surface treatment. The test alloy was obtained by vacuum metallurgy by melting the components in a graphite crucible and casting into a graphite ingot mould. In order to obtain the rods in the process of hot plastic working, hot forging was applied using a smith hammer and rotary hot forging on a swaging machine. The resulting rods were subjected to an appropriate heat treatment and thermo mechanical treatment to obtain, at room temperature, a parent phase structure B2.The paper presents the results of the research of NiTi rods after hot rotary forging. The phase composition of the samples of the tested alloy after different heat treatments were determined by X-ray powder diffraction technique. It was found that at room temperature, depending upon the processing the samples had a structure parent phase with a small amount of martensite. The courses of phase transitions and the changes of the temperature characteristic were determined on the basis of the recorded DSC curves. It was found that the test rate after aging in the temperature range of 400-500 °C transitions take place involving the rhombohedral R phase. The temperature ranges of shape recovery of samples after various heat treatments were determined by recording the recovery of the shape during heating, in tests performed according to the standard ASTM 2082-06.

Modelling of water droplets heat and mass transfer in the course of phase transitions. I. Phase transitions cycle peculiarities and iterative scheme of numerical research control and optimization

The peculiarities of the widely applied in practice sprayed water droplets phase transition cycle are discussed in this article. Theoretical fundamentals of droplets heat and mass transfer modelling by combined analytical-numerical method and numerical simulation peculiarities are outlined. Water droplet phase transitions were modelled on the energy flow balance condition basis. The control mechanism of iterative scheme used to determine the droplet surface temperature was highlighted. The optimal finite number of members in the infinite integral equation set for droplet temperature field and its gradient parameter calculation was defined by the numerical experiment.

Special points on the phase diagrams of langbeinites. The case of (x, T)-phase diagram of mixed K2xRb2(1−x)Cd2(SO4)3 crystals

We have studied special points that appear on the (x, T)-phase diagram of mixed K2xRb2(1−x)Cd2(SO4)3 crystals. This phase diagram has been constructed issuing from the changes in domain structure occurring in the course of phase transitions. We have found that two triple points on the (x, T)-phase diagram of the above solid solutions are very close to each other in the phase space and can change their places or transform into a quadruple point. These special points are associated with disappearance of ferroelectric phases with the symmetries P1 and P21 taking place when Rb2+ are substituted with K2+ ions.

Excitation of the uranyl ion in U(IV) oxidation with xenon difluoride in frozen aqueous sulfuric acid solutions: II. Effect of solvent and H2SO4 concentration

The effect of solvent (aqueous solutions of HClO4 and H2SO4) on the low-temperature (T 220 K. In the similar experiments performed with 0.05–0.5 M H2SO4 as solvent, the emission appears at a considerably lower temperature, 165–175 K. The chemiluminescence (CL) intensity increases in the course of exothermic phase transitions occurring when the temperature of H2SO4 solutions (at [H2SO4] > 0.05 M) is changed. The increase in the CL intensity in the course of a phase transition is associated with the appearance in a multicomponent frozen system of a juvenile surface of H2SO4 crystal hydrates. The lack of CL at T < 220 K in HClO4 solutions is associated with the fact that heating of the samples after their quick cooling to 77 K is not accompanied by formation of crystalline phases exhibiting catalytic properties toward the oxidation of U(IV) with XeF2.

Phase diagram and domain structure of the Rb2 x Tl2(1− x )Cd2(SO4)3 solid solutions

From measurements of temperature dependences of the birefringence and from observations of the domain structure the x, T–phase diagram for the Rb2 x Tl2(1− x )Cd2(SO4)3 solid solutions have been obtained. Ferroelastic domain structure and movement of phase boundaries have been studied in the course of phase transitions in Rb2 x Tl2(1− x )Cd2(SO4)3 crystals. Possible reasons for the appearance of mechanically non-compatible (‘forbidden’) ferroelastic domain walls are given.

Influence of Temperature on the Lifetime of Electronically Excited Uranyl Ion: III. Effect of Solvent Deuteration

The shape of the temperature dependences of the lifetime (τ) of electronically excited uranyl ion (UO22+)*, measured on warming from 77 K of UO2SO4 solutions in H2SO4 + H2O, differs from that measured in D2SO4 + D2O. The lifetime in glassy D2SO4 is shorter than in the polycrystalline sample, whereas in frozen H2SO4 solutions the pattern is opposite. The isotope effect is due both to different course of phase transitions in H2SO4 and D2SO4 solutions and to the fact that the probability of nonradiating deactivation of (UO22+)* adsorbed on the surface of D2SO4·4H2O crystal hydrate is appreciably lower than that of (UO22+)* adsorbed on the surface of H2SO4·4H2O and H2SO4·6.5H2O crystal hydrates. We suggest that the increase in τ due to adsorption appreciably exceeds the concentration quenching of excited uranyl ions in the course of crystallization of deuterated sulfuric acid.

Structural peculiarities of phase transitions in heterospin systems

New heterospin complexes of metal hexafluoroacetylacetonates with pyrazole-substituted nitronyl nitroxides were synthesized and structurally characterized. For all compounds, detail X-ray investigations (Smart Apex diffractometer, Bruker AXS) in the temperature range 100-300 K were performed. It has been shown that the temperature range of magnetic phase transition coincided with the the temperature range of density changing. Movements of atoms in the course of phase transitions have been analized.

Anatomization of hysteresis loops in pure bending of ideal pseudoelastic SMA beams

The results of qualitative analysis of the variation of stress and the phase content distribution in arbitrary symmetric cross-section of the beam are discussed for single bending cycle. The explicit analytical equations for the moment–curvature hysteresis loop are derived. The interrelation between formation of characteristic points on this diagram and movement of the beam planes separating the regions occupied by single phase (austenite or martensite) and their mixture (austenite and martensite) in the course of phase transitions is discussed. It is shown that at such mobile surfaces the gradient of macroscopic stress suffers jump discontinuity. The dimensionless bending diagrams (nomograms) for rectangular beams are constructed. They enable rough quantitative estimation of some basic design parameters without recourse to the computer-aided numerical calculations. One-dimensional Müller–Xu thermodynamic theory of ideal pseudoelasticity is used as the theoretical foundation for the analysis. The theory is briefly discussed and its generalization that accounts for the tension–compression asymmetry effect is presented.

Evolution of the density of states during phase transitions in films of cadmium sulfotellurides synthesized under profoundly nonequilibrium conditions

The results of structural, electrical, and photoelectric investigations of phase transitions in layers of cadmium-sulfide and cadmium-telluride solid solutions synthesized under profoundly nonequilibrium conditions are reported. As a model process, the thermally activated decomposition of a CdSxTe1−x single-phase solution containing the α1 (x1=0.4–0.6) phase was chosen. Increasing the temperature was shown to result in the formation a heterophase system with two phases α2 (x2=0.1–0.2) and α3 (x3=0.78–0.99). The electron diffraction patterns, the photoelectric-current spectrum, and the temperature dependences of the dark electrical conductivity in the course of and after phase transitions are reported. The results of electrical and photoelectric investigations are compared with the results of structural investigations. Changes in the dark conductivity in the course of phase transitions are shown to simultaneously account for the evolution of the density of states near the Fermi level.

Relation of magnetic and structural factors in the course of phase transitions in MnAs-based alloys

A phenomenological analysis of the magnetic and structural phase states observed in the manganese arsenide-based alloys over a wide range of temperatures and pressures has been performed. The unique first-order phase transitions from the paramagnetic and metamagnetic states to the ferromagnetic state are studied experimentally. It is found that these transitions exhibit characteristic features associated with the magnetostriction suppression of nucleation when the lability boundary of the paramagnetic phase is absent and the transition from the metamagnetic state is not thermodynamically “forbidden.” The phase behavior of manganese arsenide-based alloys is interpreted within the proposed model. This model accounts for the interrelation of the magnetic, structural, and elastic properties of alloys and also the specific features of phase transformations in real crystals.

DEVELOPMENT OF IDEAS PUT FORWARD BY S. S. KUTATELADZE CONCERNING THE PHYSICAL RELATIONSHIPS GOVERNING THE INITIAL BOILING AND CONDENSATION STAGES

The theoretical and experimental studies of heat transfer in boiling and condensation performed by Prof. S. S. Kutateladze are of seminal significance in the development of many aspects of the theory of heat transfer in the course of phase transitions and for their practical application in designing heat transfer equipment [4, 5]. The most important aspects in the development of heat transfer theory are those related to the role of the initial stage of the boiling and condensation mechanism, developing of a model of the inception of vapor bubble nuclei [ 6-9] and also those associated with heat transfer in boiling of liquid metals and prospects for the use of new coolants [ 10-12]. The question of enhancement of heat transfer in boiling and condensation, which was developed on the basis of seminal theoretical work of Kutateladze is of great importance in designing of modern, high-rate heat exchangers with phase transitions for nuclear energetics, chemical machinery and vehicular engines. The most recent studies point to the feasibility of highly increasing the boiling heat transfer by employing heating surfaces with special manufactured macro- and micro-structures [ 13-15]. The determination of permissible limits of implementation of boiling heat transfer and optimization of the structure of heating surfaces, which have been solved in a manner fully applicable at the design stage are of great importance for new technologies which employ small heat exchangers operating at high heat flux densities [ 16, 17].

Dynamics of bubbles in general relativity.

This is a systematic study of the evolution of thin shell bubbles in general relativity. We develop the general thin-wall formalism first elaborated by Israel and apply it to the investigation of the motion of various bubbles arising in the course of phase transitions in the very early Universe including new phase bubbles, old phase remnants, and domains. We consider metric junction conditions and derive constraints both on the decay of metastable states and on the evolution of non- equilibrium scalar field configurations (fluctuations) following from the global geometry of spacetime.