Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.     

倒摆运动的混沌行为

设计一个受周期外力驱动的倒摆实验装置,并建立该系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法求解非线性方程并判断解的性质．通过改变系统参数,画出时域图、相图及分岔图,计算分析和实验发现,这个简单的力学系统存在十分丰富的动力学行为（分岔、混沌）．理论分析、数值模拟和实验结果一致．     

Boron nitride phase diagram. State of the art

Abstract

From recent experimental data on BN thermodynamic propeties, the equilibrium phase diagram for boron nitride has been plotted, which differs from the generally accepted Bundy-Wentorfs one. At atmospheric pressure cubic boron niride has been shown to be a thermodynamically stable modification up to temperatures of 1600 K, which drastically changes the established notions of BN polymorphism, based on assumed analogy of phase diagrams for carbon and boron nitride. These studies have shown that according to the proposed equilibrium phase diagram the threshold pressure of cBN crystallization can be reduced from 4 down to 2 GPa with the supercritical fluids present, which opens new fields for developing methods for cBN low-pressure synthesis.     

De-vitrification of nanoscale phase-separated amorphous thin films in the immiscible copper–niobium system

Copper and niobium are mutually immiscible in the solid state and exhibit a large positive enthalpy of mixing in the liquid state. Using vapour quenching via magnetron co-sputter deposition, far-from equilibrium amorphous Cu–Nb films have been deposited which exhibit a nanoscale phase separation. Annealing these amorphous films at low temperatures (~200?°C) initiates crystallization via the nucleation and growth of primary nanocrystals of a face-centred cubic Cu-rich phase separated by the amorphous matrix. Interestingly, subsequent annealing at a higher temperature (>300?°C) leads to the polymorphic nucleation and growth of large spherulitic grains of a body-centred cubic Nb-rich phase within the retained amorphous matrix of the partially crystallized film. This sequential two-stage crystallization process has been investigated in detail by combining transmission electron microscopy [TEM] (including high-resolution TEM) and atom probe tomography studies. These results provide new insights into the crystallization behaviour of such unusual far-from equilibrium phase-separated metallic glasses in immiscible systems.     

Cd1-xZnxTe晶体退火条件的选择及Zn压对退火晶体质量的影响

采用传统Bridgman方法和加入accelerated crucible rotation technique的Bridgman(缩写为ACRT-B)方法生长的Cd_1-xZn_xTe(x=0.04)晶体中存在有点缺陷、位错、杂质和Te沉淀等缺陷.为了减少甚至消除这些缺陷,必须将生长后的CdZnTe晶片在Cd气氛下退火.从Cd-Te和Cd_0.96Zn_0.04Te的PT相图出发,详细讨论了CdZnTe晶体的气固平衡条件,并 关键词： 1-xZn_xTe')" href="#">Cd_1-xZn_xTe 退火 气-固平衡     

Domain walls in modulated systems

The properties of discommensurations in modulated phases of the ANNNI-(Axial Next Nearest Neighbour Interaction) model are described. A method is presented for deriving wall profiles, free energies, and interaction energies from a fixed point expansion of the 4d mapping representing the MFA equilibrium equations. Implications for the characteristics of phase diagrams and transitions are discussed.     

Features of the doping effect on YAlO3 phase sequences during synthesis from an amorphous precursor state

Using X-ray diffraction methods, it has been shown that small lanthanum (La) dopants during solid-phase synthesis of YAlO₃ from an amorphous precursor state initiate the formation of the high-temperature hexagonal modification of yttrium aluminate in the first crystallization stages, whereas the equilibrium perovskite phase has an orthorhombic cell. At the same time, during YAlO₃ synthesis without dopants, yttrium-aluminum garnet Y₃Al₅O₁₂ is formed in the first crystallization stages, rather than the perovskite modification, as it follows from the precursor stoichiometry. The effect of lanthanum dopants on YAlO₃ phase sequences during synthesis from the amorphous precursor state is qualitatively explained.     

A probabilistic analysis of the Walker-Vause model for liquid binary mixtures

A simple method to calculate the probability distribution for a binary fluid mixture is presented. The method is applid to the Walker-Vause binary liquid model and different temperature vs composition phase diagrams are obtained. These diagrams are obtained using catastrophe theory methods. Comparison with some experimental data are also discussed and a simplified model leading to closed-loop phase diagrams is considered.     

Systematic studies on eight homologous series of supramolecular hydrogen bonded liquid crystals

Design, synthesis and characterization of hydrogen bonded liquid crystals (HBLC) formed by alkyloxy benzoic acids (referred as nOBA?:?ABOm) are discussed. Eight such homologous series of HBLC are synthesized with varying the carbon chain length from 5 to 12 referred as nOBA?:?ABOm. These complexes are characterized by polarizing optical microscope (POM), differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FTIR) studies. Phase diagrams of the individual series have been constructed from the data of POM and DSC respectively. The effect of the chain length on the phase formation is discussed. Thermodynamic evaluation of nOBA?:?ABOm homologues series has been carried out. It is observed that the entire eight homologous series possess thermodynamically equilibrium energy states. The results of phase variance influence of chain length, phase transitions and corresponding enthalpy values are discussed.     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

The thermodynamic characteristics of multicomponent reaction mixtures in the sub- and supercritical states

The paper presents mathematical models and calculation methods for solving particular research problems related to the thermodynamic characteristics of multicomponent and multiphase mixtures. The special features of chemical and phase equilibria in such mixtures are considered in the ideal gas approximation and taking nonideality into account. The conditions of equilibrium phase stability are studied for multiphase systems. The results of calculations of characteristic phase diagrams and binodal and spinodal are given for model systems with a fixed chemical composition, and a new interpretation of the mathematical model for localizing the critical point of a multicomponent mixture with a given composition is presented. A new interpretation of the well-known classic homotopy method is suggested for solving complex nonlinear systems of equations. Some anomalies of phase portraits and critical curves that are necessary to take into account in selecting (planning) experimental conditions and calculating chemical processes and reaction parameters are considered separately. The possibility of calculating thermodynamic and thermophysical properties (entropy, enthalpy, heat capacity, heat effects of reactions, and adiabatic heating) is demonstrated for the example of particular multicomponent nonideal mixtures. The conclusion is drawn that cubic equations of state can be used for predicting the deviations of these properties from the ideal gas state and their anomalies in the vicinity of the critical points of mixtures.     

Colloids as model systems for metals and alloys: a case study of crystallization

Metallic systems are widely used as materials in daily human life. Their properties depend very much on the production route. In order to improve the production process and even develop novel materials a detailed knowledge of all physical processes involved in crystallization is mandatory. Atomic systems like metals are characterized by very high relaxation rates, which make direct investigations of crystallization very difficult and in some cases impossible. In contrast, phase transitions in colloidal systems are very sluggish and colloidal suspensions are optically transparent. Therefore, colloidal systems are often discussed as model systems for metals. In the present work, we study the crystallization process of charged colloidal systems from the very beginning. Charged colloids offer the advantage that the interaction potential can be systematically tuned by a variation of the particle number density and the salt concentration. We apply light scattering and ultra-small angle x-ray scattering to investigate the formation of short-range order in the liquid state even far from equilibrium, crystal nucleation and crystal growth. The results are compared with equivalent studies on metallic systems.     

Crystal growth by dynamic gradient reversal techniques-I. Consequences of periodic gradient reversals of Gibbs' functions in crystal growth experiments

Energy term diagrams describe the possibilities of exchange between states of different free enthalpy (Gibbs' function) in crystallization processes. Such diagrams can serve as guide-lines for the experimental production of large and perfect single crystals by gradient reversal techniques in cases which were previously classed as impossible. Consequences of the gradient reversal techniques on recrystallization processes are discussed.     

Phase Diagrams of Semicrystalline Polymer–Crystalline Substances: Polyolefins–1,2,4,5-Tetrachlorobenzene

The full phase diagrams of low-density polyethylene (LDPE), high-density polyethylene (HDPE), and isotactic polypropylene (i-PP) mixtures with 1,2,4,5-tetrachlorobenzene (TeCB), including the solubility curve of TeCB in a solid polymer, were constructed by an optical method. The diagrams contain a eutectic point that corresponds to the situation when the crystallization of TeCB out of its solution in a polyolefin is accompanied by the crystallization of monomer units of the macromolecules. As a result, the polymer acquires a gel structure with crystallites as crosslinks and amorphous regions saturated with TeCB. It is demonstrated that the eutectic point position on the phase diagram can be used for ranking polymers with respect to their thermodynamic affinity to a solvent. For the studied systems, the affinity to TeCB was decreased in the order i-PP, HDPE, and LDPE. Direct experimental evidence was obtained that TeCB crystals can be dissolved in a solid polymer via a vapor phase mechanism, which leads to the polymer amorphization.     

Theory of the generalized collision integral. IV

In the maximum time interval of kinetic evolution of the single-particle distribution function of a spatially homogeneous system summation of the step diagrams (without intersections of the lines of propagation and interaction) is carried out for an arbitrary nonequilibrium state in the Markov limit, as well as for a local equilibrium state with regard for memory effects. Procedures are indicated for the step renormalization of diagrams of arbitrary order with respect to the density in the Markov limit, with subsequent ladder renormalization. Ring diagrams with preliminary step and ladder renormalizations are summed. A more correct derivation is given for the generalized Boltzmann (Boltzmann-Landau) collision integrals for dense systems with a strong short-range (as well as strong long-range) potential. It is shown that the step, ring, and ladder renormalizations yield a nondivergent two-particle distribution function in a classical equilibrium plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–91, August, 1978.     

Coupling of the phase-field and CALPHAD methods for predicting multicomponent,solid-state phase transformations

The development of an effective microstructure design method for multicomponent alloys is of considerable importance for improving both the design of alloys and the design of processes for producing alloys with unique properties. The coupling of the phase-field method and the calculation of phase diagrams (CALPHAD) method can be used for predicting the evolution of microstructures in multicomponent alloys. Such predictions make use of CALPHAD thermodynamic information with the chemical free energy function in the phase-field method. This article reviews several of these coupling methods, focusing on solid-state phase transformations in multicomponent systems, such as phase separation and disordered or ordered phase precipitation from a matrix. When calculating disordered phase transformations, the Gibbs energy function derived from the CALPHAD database can be used directly in the phase-field method. On the other hand, when dealing with an order/disorder transition, the degrees of freedom of the element site fraction for an ordered phase in the CALPHAD method can be reduced using the Gibbs energy single formalism for constituent phases, by using a database that stores the Gibbs energy and chemical equilibrium conditions, or by obtaining the driving force calculated using the Thermo-Calc software. The current status and future directions for further development of these coupled methods are discussed.     

GeS2-In2S3硫系玻璃的物化性质与晶化行为研究

认识玻璃组成-性能-结构之间关系是玻璃科学中经久不衰的研究课题之一. 在制得(100-x) GeS₂-xIn₂S₃ (x=10, 15, 20, 25或30 mol%) 系列玻璃和玻璃陶瓷样品的基础上, 利用可见-近红外透过光谱, DSC, XRD和Raman光谱等测试技术表征了随组份变化的光学带隙, 玻璃转变温度以及晶化行为等, 并结合GeS₂-Ga₂S₃玻璃研究结果探讨了Ga, In 元素及其形成的网络结构对玻璃性质的影响.研究发现, 在硫系玻璃中In比Ga对光学带隙和玻璃转变温度等性质的影响要大. 它们所形成玻璃的晶化行为也截然不同, 但与其各自的材料相图有着密切的联系. 利用偏振拉曼光谱获得玻璃网络中的基本结构单元信息.最后, 结合材料相图, 玻璃随组成变化的物化性质和晶化行为以及基本网络结构单元的认识, 探讨了玻璃的化学拓扑与网络拓扑之间的联系, 为今后研究提供一种新的研究思路.     

Phase diagrams of the CoMnO system in air

A retrospective critical analysis of phase diagrams of the CoMnO system in air has been made. A high-temperature phase equilibrium of the CoMnO system in air and phase diagrams of this system under different cooling conditions (quenching in water, quenching in air, cooling at rate of 25°K h^?1) have been constructed. A comparative analysis of these diagrams shows that whatever the cooling rate, cooling does not preserve the high-temperature state of the system and is accompanied (depending on cooling conditions, temperature and Co/Mn ratio) by one or more of the following phenomena: (1) oxidation of the Co_NMn_1?NO solution to spinel-type solid solutions (2) merging of a cubic and tetragonal spinel phase and formation of a homogeneous tetragonally distorted spinel (3) tetragonal distortion of the spinel lattice (4) decomposition of the cubic spinel into a cubic and tetragonal spinel. (5) decomposition of the cubic spinel into a cubic, tetragonal and slightly distorted tetragonal spinel. Therefore, the form of the phase diagram of the CoMnO system in air is entirely determined by the method of cooling.     

Magnetic phase diagrams of axial third-nearest-neighbour Ising model

The magnetic phase diagrams of axial third-nearest-neighbour Ising (A3NNI) model under an external field have been studied by means of the molecular field approximation. The phase boundaries among paramagnetic, (anti)ferromagnetic and various modulated phases are determined by analysing the frequency-dependent susceptibility, or by solving the coupled equations for magnetisations for spins up to 17, iteratively. The resultant phase diagram is found to be very consistent with the exact results for the ground state spin ordering and to be far improved than existing finite temperature phase diagrams for the same model.