Vacancy Contents in MnZn Ferrites From TG Curves

Expressions for calculating the cation vacancy contents of MnZn ferrites from thermogravimetric curves are presented together with some experimental data. In a single-phase MnZn ferrite synthesized by conventional ceramic procedures, the O₂ evolution accompanying ferrite formation follows the formal equation. Mn²⁺ _σα Zn_σβ Fe³⁺ _2σ(1–γ) [V ]_{σ/4(1–2γ)} O₄ =σ'/σ Mn²⁺ _σ(α–2ϕ) Zn_σβ Fe²⁺ _2σθ Mn³⁺ _2σϕ Fe³⁺ _{2σ(1–γ–θ)} [V ]_{σ/4(1–2γ–3ϕ)} O₄ +σ'φ/2O₂ (g) where α and β denote the MnO and ZnO mole fractions in the primary mixture γ=α+β, θ and ϕ depend on the quantities of Fe²⁺ and Mn³⁺ formed, respectively, φ=θ–ϕ and σ'/σ is a function of the former parameters. Even though the relative amounts of Fe²⁺ /Fe³⁺ and Mn²⁺ /Mn³⁺ remain uncertain, the vacancy content [V ] of the ferrite can be determined because it depends on φ alone, which is related to the change in mass of the sample as the synthesis takes place through the equation φ=(1.5–γ) μ_β /μ_O2 (1–m _f /m _i ) Here, m _i and m _f are the masses of the sample before and after O₂ evolution, μ_B is the formula mass of the ferrite and μ_O2 is the O₂ molar mass. Practically vacancy-free single-phase MnZn ferrite samples were obtained by sintering in air at 1250°C and cooling in pure N₂ . This revised version was published online in July 2006 with corrections to the Cover Date.     

Geometrical interpretation of crystal-vapor phase equilibria and equilibria in helium systems

A geometrical interpretation of phase equilibria was suggested and used to determine several rules governing crystal-vapor equilibria, analytically describe the transition of helium systems into the superfluid state, and reveal the general properties of the low-temperature state of matter.     

Supercritical phase equilibria involving solids

The solubility of solids in supercritical solvents is reviewed in a phenomenological discussion of binary and ternary systems containing one highly volatile component. Solubility and selectivity are greatly determined by the course of the binary critical curves, the ternary critical end-point curves, and the locations of the triple points of the solids. The mean-field lattice-gas model is used to review some important molecular parameters.     

Free energies and phase equilibria of chain molecules

In this Article, a review is presented of recent developments in Monte Carlo simulations of chain molecules. The Rosenbluth chain insertion technique is used to calculate the free energy of the chain molecules. Furthermore, this insertion method is used to generate biased Monte Carlo moves. It is shown that this bias can be removed by adjusting the acceptance rules such that configurations are generated with their correct Boltzmann weight. This configurational-bias Monte Carlo method can be combined with the Gibbs-ensemble technique which results in an efficient method to simulate phase equilibria of chain molecules.     

Oxygen phase equilibria near 298 K

Raman spectra of fluid and solid oxygen have been measured at temperatures near 298 K to pressure greater than 180 kbar (18 GPa). At 298 K, fluid oxygen freezes at 59.1±0.5 kbar which is 2 kbar higher than the freezing pressure of n-H₂ at this temperature. Solid—solid phase transitions are observed near 96 and 99 kbar. The phase boundaries near room temperature and the intense visible absorption spectra of the very high pressure phase are described.     

Optoelectronic properties analysis of Ti-substituted GaP

A study using first principles of the electronic and optical properties of materials derived from a GaP host semiconductor where one Ti atom is substituted for one of the eight P atoms is presented. This material has a metallic intermediate band sandwiched between the valence and conduction bands of the host semiconductor for 0 < or = U < or = 8 eV where U is the Hubbard parameter. The potential of these materials is that when they are used as an absorber of photons in solar cells, the efficiency is increased significantly with respect to that of the host semiconductor. The results show that the main contribution to the intermediate band is the Ti atom and that this material can absorb photons of lower energy than that of the host semiconductor. The efficiency is increased with respect to that of the host semiconductor mainly because of the absorption from the intermediate to conduction band. As U increases, the contribution of the Ti-d orbitals to the intermediate band varies, increasing the d(z2) character at the bottom of the intermediate band.     

Direct spectroscopic speciation of schoepite-aqueous phase equilibria

UV-Vis spectra of solutions in solid-aqueous phase equilibrium with UO₃·2H₂O(s) and 0.03 kPa CO₂ partial pressure are quantitatively analyzed by single component spectra of hydrolysis species UO ₂ ²⁺ (aq), (UO₂)₂(OH) ₂ ²⁺ and (UO₂)₃(OH) ₅ ⁺ . From the deconvoluted spectra, single species concentrations are obtained and interpreted by various statistical methods. Relationship of UV-Vis data to fluorescence spectroscopic analysis of the same system is discussed. Calculation of thermodynamic quantities gave consistent results, both within experimental data and with results from solubility studies and spectroscopic analysis from literature. A reinterpretation of some literature data is proposed.     

Biocompatible lecithin organogels: structure and phase equilibria

The microstructure of organogels formed upon the addition of tiny amounts of water to a solution of lecithin in fatty acid esters (viz. isopropylpalmitate and ethyloleate) was investigated by means of molecular self-diffusion measurements. In both systems lecithin and water form disconnected cylindrical reverse micelles. The ternary phase map for the lecithin/water/isopropylpalmitate has been investigated in detail. The organogel exists in a narrow region close to the lecithin-oil binary axis; for higher water content equilibrium between lamellae and reverse micelles is found. Lamellar phase occupies the lecithin-rich region, close to the lecithin corner (with the exception of a small island of hexagonal phase) and coexists with neat water close to the water-lecithin axis. The remaining part of the phase map shows the three-phase coexistence of water, oil, and lamellar phase.     

Calculation of phase equilibria and construction of phase diagrams by convex hull method

Recent findings for a new method developed to calculate phase equilibria are reviewed and analyzed. This method is based on the construction of the convex hulls for characteristic functions in heterogeneous systems. The theoretical basis of this method, as well as the possibilities and features of its practical application in scientific research and teaching chemical thermodynamics, is considered. Software packages developed at the Department of Chemistry of Moscow State University are briefly described.     

Chemical equilibria involved in the oxygen-releasing step of manganese ferrite water-splitting thermochemical cycle

Sodium ferrimanganite carbonatation reaction was investigated at different temperatures/carbon dioxide partial pressures to evaluate the feasibility of the thermochemical water-splitting cycle based on the MnFe₂O₄/Na₂CO₃/Na(Mn_1/3Fe_2/3)O₂ system.After thermal treatments in selected experimental conditions, the obtained powder samples were investigated by using the X-ray diffraction (XRD) technique and Rietveld analysis.Two different lamellar Na_1−xMn_1/3Fe_2/3O_2−δ phases were observed together with the expected MnFe₂O₄/Na₂CO₃ mixture. Different equilibrium regions among sodium-depleted lamellar phases, manganese ferrite and sodium carbonate were found as a function of the different reaction conditions. A hypothesis concerning the regeneration mechanism of the initial compounds is proposed. Chemical equilibrium between stoichiometric and sub-stoichiometric forms of sodium ferrimanganite and sodium carbonate formation/dissociation appears to be essential factors governing the oxygen-releasing step of the manganese ferrite thermochemical cycle.     

Calculation of chemical and phase equilibria via simulated annealing

We present a new class of techniques for the solution of the chemical and phase equilibria problem for reacting species in a closed system. The minimisation of the Gibbs free energy for all the species in the system is conducted using the technique of simulated annealing (SA). The SA objective function incorporates non‐ideal equations of state. This new approach is demonstrably able to solve multi‐species and multi‐phase LTCE problems in ideal‐gas solutions, ideal solutions and mixtures of ideal and non‐ideal solutions. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the geometry of chemical reaction and phase equilibria

Kuhn-Tucker optimization theory is employed to obtain new results for the problem of the determination of equilibria in multi-phase multi-reaction systems. The results provide a complete classification of the possible types of behaviour that can occur for such systems. In this classification, there is an essential difference between the cases of systems for which no reactions have a set of stoichiometric coefficients that sum algebraically to zero, and systems for which this is not the case. The results yield a geometric interpretation that can be viewed as an extension of the corresponding interpretation of the geometry of systems undergoing phase equilibria alone. Illustrations are given of all possible cases of binary and ternary reacting systems.     

Calculation of chemical and phase equilibria via simulated annealing

We present a new class of techniques for the solution of the chemical and phase equilibria problem for reacting species in a closed system. The minimisation of the Gibbs free energy for all the species in the system is conducted using the technique of simulated annealing (SA). The SA objective function incorporates non‐ideal equations of state. This new approach is demonstrably able to solve multi‐species and multi‐phase LTCE problems in ideal‐gas solutions, ideal solutions and mixtures of ideal and non‐ideal solutions.     

Liquid-liquid phase equilibria for some polystyrene-methylcyclohexane mixtures

Liquid-liquid cloud point diagrams of solutions of nearly monodisperse samples of polystyrene (PS), and binary mixtures of nearly monodisperse PS’s, both in methylcyclohexane (MCH), were determined for several polymer molecular weights (M_w) at 0.1 MPa. The bimodal mixtures (PS[M_w(1),ρ(1)] + PS[M_w(2),ρ(2)], M_w(1)=90×10³ g/mol, M_w(2)=13×10³ g/mol, 5.78 × 10³ g/mol, and 2.2 × 10³ g/mol, ρ=1.06) were prepared constraining 〈M_w〉=38.6×10³ g/mol, ρ=M_w/M_n is the polydispersity index. In each case the cloud point curves (CPC’s) for the bimodal mixtures are strongly skewed, lying well above CPC for 〈M_w〉 when φ<φ_CRITICAL, and below CPC for 〈M_w〉 when φ>φ_CRITICAL; φ is volume fraction polymer in the polymer/solvent mixture. The experimental results are discussed in the context of empirical and mean-field representations.     

Simulation of phase equilibria in lamellar surfactant systems

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.     

Monte carlo simulation of carboxylic acid phase equilibria

Configurational-bias Monte Carlo simulations were carried out in the Gibbs ensemble to generate phase equilibrium data for several carboxylic acids. Pure component coexistence densities and saturated vapor pressures were determined for acetic acid, propanoic acid, 2-methylpropanoic acid, and pentanoic acid, and binary vapor-liquid equilibrium (VLE) data for the propanoic acid + pentanoic acid and 2-methylpropanoic acid + pentanoic acid systems. The TraPPE-UA force field was used, as it has recently been extended to include parameters for carboxylic acids. To simulate the branched compound 2-methylpropanoic acid, certain minor assumptions were necessary regarding angle and torsion terms involving the -CH- pseudo-atom, since parameters for these terms do not exist in the TraPPE-UA force field. The pure component data showed good agreement with the available experimental data, particularly with regard to the saturated liquid densities (mean absolute errors were less than 1.1%). On average, the predicted critical temperature and density were within 1% of the experimental values. All of the binary simulations showed good agreement with the experimental x-y data. However, the TraPPE-UA force field predicts saturated vapor pressures of pure components that are larger than the experimental values, and consequently the P-x-y and T-x-y data of the binary systems also deviate from the measured data.     

Liquid-liquid phase equilibria in polymer solutions and polymer mixtures

The pressure dependence of liquid-liquid equilibria in weakly interacting binary macromolecular systems (homopolymer solutions and blends) will be discussed. The common origin of the separate high-temperature/low-temperature and high-pressure/low-pressure branches of demixing curves will be demonstrated by extending the study into the region of metastable liquid states including the undercooled, overheated and stretched states (i.e. states at negative pressures). The seemingly different response of the UCST-branch of solutions and blends when pressurized (pressure induced mixing for most polymer solutions, pressure induced demixing for most blends) will be explained in terms of the location of a hypercritical point found either at positive (most solutions) or negative pressure (most blends). Further, it is shown that the pressure dependence of demixing of homopolymer solutions and blends may be described using a ‘master-curve’ which, however, is sometimes partly masked by degradation or by vapour-liquid and/or solid-liquid phase transitions. Experimental results demonstrating the extension of liquid-liquid phase boundary curves into the metastable regions will be presented, and the existence of solubility islands in the vicinity of the hypercritical points discussed.     

Calculation of phase equilibria in random copolymer systems

Synthesis and application of copolymers are not seldom connected with different phase equilibria. Their precise knowledge is of importance for industrial processing as well as it is a profound basis for a better understanding of the nature and thermodynamics of such systems. As a common situation today, enough experimental information is seldom available in the necessary or desired amount, and a lot of model calculation is, therefore, more or less unavoidable to cover the desired ranges of application. Different equations-of-state as well as lattice models are discussed with respect to their applicability for calculating liquid-liquid and gas-liquid phase equilibria in copolymer solutions and blends. Examples for high-pressure phase equilibria in monomer/copolymer mixtures, liquid-liquid demixing in copolymer blends and for the isotropicnematic phase equilibrium in systems with rigid rod-like copolymers characterized by distributions of rigid and flexible chain parts are given. The effects of copolymer polydispersity are included by means of continuous thermodynamics. Literature references for original sources, earlier reviews and further applications round up this paper.