Phase Diagram Boundaries Research Articles

Thermodynamics of particle coarsening

The coarsening of precipitate particles during the heat treatment of alloys depends both on the diffusivity of the surrounding phase and on the concentration differences given by the Gibbs-Thomson equation, both of which depend on the solution thermodynamics of the surrounding phase. However, it is now known that thermodynamic terms cancel in the theory; therefore coarsening is independent of solution behavior. The equations that confirm this prediction for multicomponent systems are derived and discussed. In addition, it is shown for ternary and higher order systems that a generalized form of the Gibbs-Thomson equation gives a vector that is normal to the matrix-precipitate phase diagram boundary.

Modelling of Phase Diagram Boundaries at Equilibrium of Two Binary Regular Phases

The conditions of occurrence of extremes on the solidus and liquidus curves in a binary isobaric phase diagram are specified. The solid and liquid phases are regarded as regular solutions in equilibrium. Two simplifying assumptions are made: (i) the Gibbs function of melting of the pure components is a linear function of temperature; (ii) the two phases in equilibrium are regular solutions with a temperature-dependent regular solution parameter. The conditions of occurrence of inflexion points on the solidus and/or liquidus curves are obtained by modelling.

Resistive transition of Bi(2223) silver clamped thick film

Detailed measurements of voltage-current (V-I) curves and magnetoresistance (R-H) for Bi(2223) thick film were carried out for various temperatures and magnetic fields. The results indicate that a flux lattice melting transition takes place as the temperature and the field are raised. This transition boundary in the (H,T) phase diagram was found to follow the irreversibility line described by the function of H=H0(1−T/Tc)3/2. Above this line, the V-I curves display a flux-flow-like character. Temperature and magnetic field dependencies of flow resistance Rf-T and Rf-H show a varied viscosity in different temperature and field ranges. Below this line, V-I curves in the low voltage region present a thermally activated flux creep property. The R-H measurements indicate that the fields at the onset and the midpoint of the magnetoresistive transition also follow a (1−T/Tc)3/2 dependence.

Concentration-dependent diffusivity and phase diagram boundaries of the FeV system

Electron microprobe analysis is used to determine the composition variation on a FeV diffusion couple at 1373 K. The variation of diffusion coefficients with vanadium concentration is experimentally determined by using Matano-Boltzmann technique. The discontinuities in the diffusion coefficient variation with composition are interpreted in terms of providing a more accurate distinction between various phases present in the FeV system at the studied temperature. At 1373 K, the upper concentration of the γ-α domain boundary was found at 2 at% V, whereas the lower concentration boundary of the α-σ domain was at 26 at% V. La microsonde electronique est utilisee afin de determiner les variations de composition dans un couple de diffusion du systeme FeV a une temperature de 1373 K. Les coefficients d'interdiffusion sont calcules a l'aide de la methode Matano-Boltzmann. Les discontinuites des coefficients d'interdiffusion sont utilisees afin d'identifier les differentes phases presentes dans le systeme FeV a la temperature de 1373 K. Il est trouve que la concentration superieure critique du domaine γ-α se situe a 2 at% V et que la concentration inferieure critique de domaine α-σ se situe a 26 at% V.

Guidelines for binary phase diagram assessment

The recent publication of Binary Alloy Phase Diagrams,2nd ed, [90Mas] and our extensive screening of phase diagram graphics for this edition has revealed many phase diagram features, which while not explicitly violating phase diagram rules, are to a lesser or greater extent unlikely to represent thermodynamically acceptable conditions. In two previous papers, several thermodynamically improbable features or boundaries in binary phase diagrams were pointed out [91Oka2], and some unlikely thermodynamic models were shown to be unrealistic, or in error [91Okal]. In the present paper, we discuss some of the unlikely features in more detail in order to develop a set of guidelines that may be useful for checking future proposed phase diagram boundaries, or some specific phase diagram features resulting from both experimental and theoretical work, including also phase diagram assessments.

Effect of glycosphingolipid fatty acid chain length on behavior in unsaturated phosphatidylcholine bilayers: A deuterium NMR study

Deuterium-labeled glycosphingolipids, N-lignoceroyl[d47]galactosylceramide (24:0 fatty acid form) and N-stearoyl[d35]galactosylceramide (18:0 fatty acid form) were prepared by partial synthesis. These probe-labeled species, differing only in the lengths of their fatty acids, were compared via 2H NMR with regard to arrangement and behavior in bilayers of the monounsaturated phospholipid 1-stearoyl-2-oleoylphosphatidylcholine (SOPC). Results were used to consider the physical significance of the great range of common acyl chain lengths that is a frequent feature of cell membrane glycosphingolipids. N-lignoceroyl[d47]- and N-stearoyl[d35]galactosylceramide were incorporated at concentrations ranging from 5 to 50 mol % into unsonicated phospholipid liposomes, and their spectra were analyzed in the range +73 to -14 degrees C. For the 18:0 fatty acid derivative, first spectral moments, M1, were calculated and plotted as a function of temperature for each sample composition. Spectral inspection for regions of phase coexistence, in conjunction with consideration of M1 curves, permitted derivation of phase diagram boundaries which were then refined using spectral subtraction techniques. The phase diagram for galactosylceramide with short fatty acid in SOPC was compared to the corresponding phase diagram for its long-chain analogue, derived previously in the same fashion [Morrow, M. R., Singh, D., Lu, D., & Grant, C. W. M. (1992) Biochim. Biophys. Acta 1106, 85-93]. The binary phase diagrams referred to above, which reflect the behavior of short- and long-chain glycolipids in a common phospholipid host matrix, displayed important similarities and differences. In fluid membranes, the behavior appeared to be remarkably alike, as reflected in superimposable fluidus curves over the concentration range studied.(ABSTRACT TRUNCATED AT 250 WORDS)

Solid solubilities of molybdenum and tungsten in F.C.C. transition metal alloys

Abstract A method for evaluating solid solubilities of alloys proposed by Morinaga, Yukawa, Ezaki and Adachi has been applied to the transition-metal based f.c.c. alloys containing molybdenum and tungsten. It has been shown that the method is useful in fitting the phase boundaries in ternary phase diagrams. This method has been shown to be applicable to the quantitative estimation of the phase boundaries relevant not only to the intermetallic compounds (for example, the μ phase and the Laves phase) but also to the terminal solid-solutions such as the α-tungsten phase.

Calculated greenschist facies mineral equilibria in the system CaO?FeO?MgO?Al2O3?SiO2?CO2?H2O

The kinetic problems associated with the experimental determination of reactions among complex solidsolution phases at low temperatures have hindered our understanding of the phase relations in greenschist facies rocks. In the absence of reliable experimental data, we have used the new, expanded internally-consistent thermodynamic dataset of Holland and Powell (1990), to present calculated phase equilibria for the system CaO−FeO−MgO−Al2O3−SiO2−H2O−CO2 (CaFMASCH) with quartz in eccess, in the range 400°–500°C at low to intermediate pressures, involving the minerals amphibole, chlorite, anorthite, clinozoisite, dolomite, chloritoid, garnet, margarite, andalusite, and calcite. By solving independent sets of non-linear equations formed from equilibrium relationships, we calculate not only the loci of reactions in pressuretemperature-x(CO2) space, but also the compositions of coexisting minerals in terms of the substitutions, FeMg-1 and (Fe,Mg)SiAl-1Al-1. Invariant, univariant and divariant equilibria are calculated and discussed in relation to naturally-occurring greenschist facies metabasic and siliceous dolomitic mineral assemblages. We thus avoid the use of activity-corrected curves so commonly presented in the literature as a substitute for genuine univariant phase diagram boundaries.

The theorem of corresponding relation between neighboring phase regions and their boundaries in phase diagrams (I)

Several fundamental concepts in phase diagrams have been discussed. The theorem of corresponding relation between the number of different phases in the neighboring phase regions Φ and the dimension R 1 of their phase boundary in the phase diagrams is derived from the phase rule. The five corollaries of this theorem for isobaric phase diagrams are derived also. By applying this theorem and its corollaries, the following results can be obtained. Both the boundary rule and contact rule of phase regions in phase diagrams may be deduced. The ten empirical rules for constructing the complex ternary isobaric phase diagrams from phase diagram units may be put on a theoretical basis. The relation between neighboring phase regions and their boundary in phase diagrams of one-, two-, three- and four-components of all types and in the different horizontal and vertical sections of ternary phase diagrams may be explained without introducing any supplementary concept.

Temperature dependence of the sound velocity and ultrasonic attenuation in liquid BiGa and BiSn alloys

The temperature dependence of the sound velocity and ultrasonic attenuation in several liquid BiGa and BiSn alloys was determined by means of an ultrasonic pulse technique. The sound velocity is shown to be linear with temperature and parabolic with concentration in BiSn alloys, and in BiGa alloys in the miscibility region. This behavior indicates a correlation between the behavior of the electrical resistivity and of the sound velocity. A rapid gravitational separation was observed at 262°C for the critical composition in the Bi-43.77wt.% Ga alloy. Ultrasonic attenuation measurements permitted the accurate determination of the position of the interface (meniscus) between the separated liquid phases. The rate of motion of the meniscus as a function of temperature and composition was measured. The ultrasonic technique is shown to be useful for the accurate determination of phase diagram boundaries in systems with a liquid miscibility gap.

Application des mesures de pouvoir thermoélectrique à la caractérisation métallurgique des alliages de titane

We show that thermoelectric power measurements are a useful tool for studying titanium alloys. In effect with this technique it is possible — to demonstrate the cold working anisotropy in sheets, — to determine impurity concentration and phase diagram boundaries and — to study phase transformations and especially precipitation phenomena. Several alloys (α, β, α + β) are chosen as examples.

Numerical techniques for the calculation of multicomponent phase diagrams

A stepwise method has been developed for the calculation of two-phase boundaries in multicomponent phase diagrams. It is based on a direct minimization of the Gibbs free energy and places no restriction on the number of components. An alternate search technique has also been developed and is used to guard against any possible divergence of the stepwise technique. At infinite dilution of a componentm or in the case of an island miscibility gap, the method is not directly applicable. The difficulty is circumvented, however, through a study of the slopes of the phase boundaries at infinite dilution of componentm and a calculation of the critical points of the miscibility gap. Finally, a computer program is described and its applications are illustrated by examples of calculation of ternary diagrams.