Inter and intra crystalline ion exchange equilibria in the system Fe Cr Al O

The tie lines delineating ion-exchange equilibria between FeCr2O4FeAl2O4 spinel solid solution and Cr2O3Al2O3 solid solution with corundum structure have been determined at 1373 K by electron microprobe and EDAX point count analysis of oxide phases equilibrated with metallic iron. Activities in the spinel solid solution are derived from the tie lines and the thermodynamic data on Cr2O3Al2O3 solid solution available in the literature. The oxygen potentials corresponding to the tie-line composition of oxide phases in equilibrium with metallic iron were measured using solid oxide galvanic cells with CaOZrO2 and Y2O3ThO2 electrolytes. These electrochemical measurements also yield activities in the spinel solid solution, in good agreement with those obtained from tie lines. The activity-composition relationship in the spinel solid solution is analysed in terms of the intra-crystalline ion exchange between the tetrahedral and octahedral sites of the spinel structures. The ion exchange is governed by site-preference energies of the cations and the entropy of cations mixing on each site.

Three phase equilibria for activity determinations: system Co Mn

A solid state e.m.f. cell with yttria-doped thoria as the electrolyte and a mixture of Cr + Cr sub 2 O sub 3 as the reference electrode, was employed for the measurement of the activity of manganese in the Co--Mn system at 1760 deg K, for 0.3 > X sub Mn > 0.05. The liquid alloy was contained in an alumina crucible and saturated with MnAl sub 2+2x O sub 4+3x . The cell can be represented by Pt, W, (Co--Mn) + MnAl sub 2+2x O sub 4+3x + Al sub 2 O sub 3 /ThO sub 2 --Y sub 2 O sub 3 /Cr + Cr sub 2 O sub 3 , Pt. The activity of manganese shows negative deviations from Raoult's law. The activities in the Co--Mn system are intermediate between those in the Fe--Mn and Ni--Mn systems. The Gibbs' energies of mixing in these systems follow the trends given by Miedema's model. 14 ref.--AA.

Computation of thermodynamic properties of quaternary and higher order systems from binary data using shortest distance composition paths

Equations for the computation of integral and partial thermodynamic properties of mixing in quarternary systems are derived using data on constituent binary systems and shortest distance composition paths to the binaries. The composition path from a quarternary composition to the i-j binary is characterized by a constant value of (Xi − Xj). The merits of this composition path over others with constant values for View the MathML source or Xi are discussed. Finally the equations are generalized for higher order systems. They are exact for regular solutions, but may be used in a semiempirical mode for non-regular solutions.

Current views on microscopic thermodynamics of liquid alloys

An attempt has been made to review current information on the microscopic thermodynamics of liquid alloys. For complex alloys, and for alloys of simple metals with strong "compound-forming" tendencies, the fluctuation approach developed by Bhatia and his co-workers provides a useful link between the fluctuation in concentration and number density of atoms in the mixture on the one hand, and macroscopic thermodynamic properties on the other. Some selected examples of the application of structural data of liquid alloys to estimating macroscopic thermodynamic properties such as the Gibbs free energy of mixing, coupled with the fluctuation approach are given. The relevant thermodynamic quantities such as vapor pressure and entropy are also discussed, to facilitate the understanding of the present status of the fundamental and powerful links between macroscopic and microscopic (atomic scale) structure of liquid alloys (Mg--Sn, Li--Pb, Hg--K). 63 ref.--AA

Knudsen effusion measurements on Cr Mn alloys

The equilibrium partial pressures of Mn over bcc Cr--Mn alloys have been measured using Knudsen cell technique in the temp. range 1200-1500K. The alloys in particulate form were contained in thoria crucibles inside Knudsen cells made of tungsten. The rates of mass loss of each cell under vacuum was monitered as a function of time at constant temp. using a microbalance. Activities exhibit mild negative deviations from Raoult's law, contrary to indications from an earlier study using a fused salt emf technique. The Cr--Mn system is characterized by negative enthalpy and excess entropy of mixing. There is close similarity between the composition dependence of enthalpy and excess entropy. These findings suggest strong vibrational and negligible magnetic contributions to excess entropy of mixing in bcc phase at high temp. 10 ref.--AA

Thermodynamic properties of Cr Mo solid alloys

The activity of Cr in solid Cr-Mo alloys has been measured at 1873 K using a metal-oxide-gas equilibrium technique. Thin foils of Mo were equilibrated with solid Cr203 under flowing gas mixtures of argon, hydrogen and watervapourof known composition. The equilibrium concentration of Cr in Mo was determined by chemical analysis. These measurements indicate positive deviations from Raoult's law. The activity data obtained in the study at 1873 K are combined with free energy of mixing at 1471 K, calorimetric enthalpy of mixing at 1673 K, and experimental evidence of phase separation at lower temperatures, reported in the literature, to obtain an optimised set of thermodynamic parameters for the Cr-Mosystem in the solid state.

Measurement and modeling of Alloy-Spinel-Corundum equilibrium in the Ni-Mn-Al-0 system at 1873 K

The oxygen content of liquid Ni-Mn alloy equilibrated with spinel solid solution, (Ni,Mn)O. (1 +x)A12O3, and α-Al2O3 has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential of the three-phase system has been determined with a solid state cell incorporating (Y2O3)ThO2 as the solid electrolyte and Cr + Cr2O3 as the reference electrode. The equilibrium composition of the spinel phase formed at the interface of the alloy and alumina crucible was obtained using EPMA. The experimental data are compared with a thermodynamic model based on the free energies of formation of end-member spinels, free energy of solution of oxygen in liquid nickel, interaction parameters, and the activities in liquid Ni-Mn alloy and spinel solid solution. Mixing properties of the spinel solid solution are derived from a cation distribution model. The computational results agree with the experimental data on oxygen concentration, potential, and composition of the spinel phase.

Phase equilibria in the Co Ni F system and activities in (CoxNi1 x)F2 solid solutions at 1373 K

The tie-lines delineating equilibria between CoF2-NiF2 and Co-Ni solid solutions in the ternary Co-Ni-F system at 1373 K have been determined by electron microprobe and EDAX point count analysis of the equilibrated phases. Activities in the fluoride solid solution have been derived from the knowledge of activitycomposition relation in the metallic solid solution and tie-line data,using a modified form of the Gibbs-Duhem integration. The fluorine potentials corresponding to the tie-line compositions have been calculated.The excess Gibbs' energy of mixing for the fluoride solid solution derived from the present data can be represented by the expression

Thermodynamics of Aluminium -Strontium Alloys

The activity of strontium in liquid Al-Sr alloys (X(Sr) less-than-or-equal-to 0.17) at 1323 K has been determined using the Knudsen effusion-mass loss technique. At higher concentrations (X(Sr) greater-than-or-equal-to 0.28), the activity of strontium has been determined by the pseudoisopiestic technique. Activity of aluminium has been derived by Gibbs-Duhem integration. The concentration - concentration structure factor of Bhatia and Thornton at zero wave vector has been computed from the thermodynamic data. The behaviour of the mean square thermal fluctuation in composition and the thermodynamic mixing functions suggest association tendencies in the liquid state. The associated solution model with Al2Sr as the predominant complex can account for the properties of the liquid alloy. Thermodynamic data for the intermetallic compunds in the Al-Sr system have been derived using the phase diagram and the Gibbs' energy and enthalpy of mixing of liquid alloys. The data indicate the need for redetermination of the phase diagram near the strontium-rich corner.

Tie lines and activities in the system CoO MgO SiO2 at 1373 K

The tie lines between (CoXMg1−X)O solid solution with rock salt structure and orthosilicate solid solution (CoYMg1−Y)-Si0.5O2, and between orthosilicate and metasilicate (CoZMg1-Z)SiO3 crystalline solutions, have been determined experimentally at 1373 K. The compositions of coexisting phases have been determined by electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples. The metasilicate solid solution exists only for 0 > Z > 0.213. The activity of CoO in the rock salt solid solution was determined as a function of composition and temperature in the range of 1023 to 1373 K using a solid-state galvanic cell: Pt, (CoXMg1−X)O+Co|(Y2O3)ZrO2|Co+CoO, Pt The free energy of mixing of (CoXMg1−X)O crystalline solution can be expressed by the equation ΔGE=X(1 −X)[(6048 − 2.146T)X+ (8745 − 3.09T)(1 −X)] J·mol−1 The thermodynamic data for the rock salt phase is combined with information on interphase partitioning of Co and Mg to generate the mixing properties for the ortho- and metasilicate solid solutions. For the orthosilicate solution (CoYMg1 −Y)Si0.5O2 at 1373 K, the excess Gibbs free energy of mixing is given by the relation ΔGE=Y(1 −Y)[2805Y+ 3261(1 −Y)] J·mol−1 For the metasilicate solution (CoZMg1 −Z)SiO3 at the same temperature, the excess free energy can be expressed by the relation ΔGE=Z(1 −Z)[2570Z+ 3627(1 −Z)] J·mol−1

A new matched thermochemical diagram for vacuum refining of nickel and cupronickel alloys

Sulfur and oxygen dissolved in nickel and cupronickel melts can be remwed as gaseous oxides of sulfur by a vacuum treatment. Presented in this paper is a new matched thermcxhemical disgran~ that permit.. direct evaluation of the equilibrium partial pressure of SO, as a function of temperature wer an alloy of specified compition. The matched thermochemical diagram consists of a central plot which shows the integral Gibbs' energy of mixing for the binary system SO, at different temperatures. The central plot is flanked on either side by terminal plots of the chemical potentials of oxygen and sulfur, as functions of temperature, for different alloy compositions. By projecting the chemical wtentials of oxygen and sulfur from the terminal lots on to the central diagram, ihe equilibrium partial pressure of S0,can be directly ;cad on the nomograms on the central plot at different temperatures. The matched therrnochemical diagrams are useful in assuring the efficiency of vacuum refining.

A thermodynamic study of liquid Cu-Cr alloys and metastable liquid immiscibility

he thermodynamic acitivity of chromium in liquid Cu-Cr alloys is measured in the temperature range from 1473 to 1873 K using the solid state cell: Pt, W, Cr + Cr2O3 |(Y2O3) ThO2|Cu - Cr + Cr2O3, Pt The activity of copper and the Gibbs energy of mixing of the liquid alloy are derived. Activities exhibit large positive deviations from Raoult's law. The mixing properties can be represented by a pseudo-subregular solution model in which the excess entropy has the same type of functional dependence on composition as the enthalpy of mixing: ΔGE = XCr(1 - XCr)[60880 - 18750 XCr)-- T(16.25 - 7.55 XCr)]J mol-1 Pure liquid Cu and Cr are taken as the reference states. The results predict a liquid-liquid metastable miscibility gap, with TC = 1787 (±3) K and XCr = 0.436 (±0.02), lying below the liquidus. The results obtained in this study are in general agreement with experimental information reported in the literature, but provide further refinement of the thermodynamic parameters.

Thermodynamic activities in the Pb(Zr1−XTiX)O3 solid solution at 1373K

Although Pb(Zr1−XTiX)O3 solid solution is the cornerstone of the piezoelectric ceramics, there is no information in the literature on thermodynamic activities of the component phases in the solid solution. Using inter-crystalline ion exchange equilibria between Pb(Zr1−XTiX)O3 solid solution with cubic perovskite structure and (Zr1−YTiY)O2 solid solutions with monoclinic and tetragonal structures, activities of PbTiO3 and PbZrO3 in the perovskite solid solution have been derived at 1373 K using the modified Gibbs–Duhem integration technique of Jacob and Jeffes. Tie-lines from the cubic solid solution are skewed towards the ZrO2 corner. Activities in the zirconia-rich (Zr1−YTiY)O2 solid solutions are taken from a recent emf study. The results for the perovskite solid solution at 1373 K can be represented by a sub-regular solution model:View the MathML sourcewhere ΔGE,M is the excess Gibbs energy of mixing of the cubic solid solution and Xi represents the mole fraction of component i. There is a significant positive deviation from ideality for PbTiO3-rich compositions and mild negative deviation near the PbZrO3 corner. The cubic solid solution is intrinsically stable against composition fluctuations at temperatures down to 840 K. The results contrast sharply with the recent calorimetric data on enthalpy of mixing which signal instability of the cubic perovskite solid solution.

Thermodynamics of Al(1-x)Ga(x)N solid solution: Inclination for phase separation and ordering

Although Al(1-x)Ga(x)N semiconductors are used in lighting, displays and high-power amplifiers, there is no experimental thermodynamic information on nitride solid solutions. Thermodynamic data are useful for assessing the intrinsic stability of the solid solution with respect to phase separation and extrinsic stability in relation to other phases such as metallic contacts. The activity of GaN in Al(1-x)Ga(x)N solid solution is determined at 1100 K using a solid-state electrochemical cell: Ga + Al(1-x)Ga(x)N/Fe, Ca(3)N(2)//CaF(2)//Ca(3)N(2), N(2) (0.1 MPa), Fe. The solid-state cell is based on single crystal CaF(2) as the electrolyte and Ca(3)N(2) as the auxiliary electrode to convert the nitrogen chemical potential established by the equilibrium between Ga and Al(1-x)Ga(x)N solid solution into an equivalent fluorine potential. Excess Gibbs free energy of mixing of the solid solution is computed from the results. Results suggest an unusual mixing behavior: a mild tendency for ordering at three discrete compositions (x = 0.25, 0.5 and 0.75) superimposed on predominantly positive deviation from ideality. The lattice parameters exhibit slight deviation from Vegard's law, with the a-parameter showing positive and the c-parameter negative deviation. Although the solid solution is stable in the full range of compositions at growth temperatures, thermodynamic instability is indicated at temperatures below 410 K in the composition range 0.26 <= x <= 0.5. At 355 K, two biphasic regions appear, with terminal solid solutions stable only for 0 <= x <= 0.26 and 0.66 <= x <= 1. The range of terminal solid solubility reduces with decreasing temperature. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network. A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given. The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed. An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities. Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.