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

The isothermal section of the phase diagram for the system NiO-MgO-SiO2 at 1373 K is established, The tie lines between (NiXMg1-X)O solid solution with rock salt structure and orthosilicate solid solution (NiYMg1-Y)Si0.5O2 and between orthosilicate and metasilicate (NiZMg1-Z)SiO3 crystalline solutions are determined using electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples, Although the monoxides and orthosilicates of Ni and Mg form a continuous range of solid solutions, the metasilicate phase exists only for 0 < Z < 0.096, The activity of NiO in the rock salt solid solution is determined as a function of composition and temperature in the range of 1023 to 1377 K using a solid state galvanic cell, The Gibbs energy of mixing of the monoxide solid solution can be expressed by a pseudo-subregular solution model: Delta G(ex) = X(1 - X)[(-2430 + 0.925T)X + (-5390 + 1.758T)(1 - X)] J/mol, The thermodynamic data for the rock salt phase are combined with information on interphase partitioning of Ni and Mg to generate the mixing properties for the orthosilicate and the metasilicate solid solutions, The regular solution model describes the orthosilicate and the metasilicate solid solutions at 1373 K within experimental uncertainties, The regular solution parameter Delta G(ex)/Y(1 - Y) is -820 (+/-70) J/mol for the orthosilicate solid solution, The corresponding value for the metasilicate solid solution is -220 (+/-150) J/mol, The derived activities for the orthosilicate solid solution are discussed in relation to the intracrystalline ion exchange equilibrium between M1 and M2 sites. The tie line information, in conjunction with the activity data for orthosilicate and metasilicate solid solutions, is used to calculate the Gibbs energy changes for the intercrystalline ion exchange reactions, Combining this with the known data for NiSi0.5O2, Gibbs energies of formation of MgSi0.5O2, MgSiO3, and metastable NiSiO3 are calculated, The Gibbs energy of formation of NiSiO3, from its component oxides, is equal to 7.67 (+/-0.6) kJ/mol at 1373 K.

Activities in the spinel solid solution FeXMg1−XAl2O4

Abstract: Activities in the spinel solid solution FexMg1-xAl2O4 saturated with alpha-Al2O3 have been measured for the compositional range 0 < X < 1 between 1100 and 1350 K using a bielectrolyte solid-state galvanic cell, which may be represented as Pt, Fe + FexMg1-xAl2O4 + alpha-Al2O3//(Y2O3)ThO2/ (CaO)ZrO2//Fe + FeAl2O4 + alpha-Al2O3, Pt Activities of ferrous and magnesium aluminates exhibit small negative deviations from Raoult's law. The excess free energy of mixing of the solid solution is a symmetric function of composition and is independent of temperature: Delta G(E) = -1990 X(1 - X J/mol. Theoretical analysis of cation distribution in spinel solid solution also suggests mild negative deviations from ideality. The lattice parameter varies linearly with composition in samples quenched from 1300 K. Phase relations in the FeO-MgO-Al2O3 system at 1300 K are deduced from the results of this study and auxiliary thermodynamic data from the literature. The calculation demonstrates the influence of intracrystalline ion exchange equilibrium between nonequivalent crystallographic sites in the spinel structure on intercrystalline ion exchange equilibrium between the monoxide and spinel solid solutions (tie-lines). The composition dependence of oxygen partial pressure at 1300 K is evaluated for three-phase equilibria involving the solid solutions Fe + FexMg1-xAl2O4 + alpha-Al2O3 and Fe + FeyMg1-yO + FexMg1-xAl2O4. Dependence of X, denoting the composition of the spinel solid solution, on parameter Y, characterizing the composition of the monoxide solid solution with rock salt structure, in phase fields involving the two solid solutions is elucidated. The tie-lines are slightly skewed toward the MgAl2O4 corner.

Potentiometric determination of the gibbs energies of formation of SrZrO3 and BaZrO3

The Gibbs free energies of formation of strontium and barium zirconates have been determined in the temperature range 960 to 1210 K using electrochemical cells incorporating the respective alkaline-earth fluoride single crystals as solid electrolytes. Pure strontium and barium monoxides were used in the reference electrodes. During measurements on barium zirconate, the oxygen partial pressure in the gas phase over the electrodes was maintained at a low value of 18.7 Pa to minimize the solubility of barium peroxide in the monoxide phase. Strontium zirconate was found to undergo a phase transition from orthorhombic perovskite to) with space group Cmcm; D-2h(17) to tetragonal perovskite (t) having the space group 14/mcm; D-4h(18) at 1123 (+/- 10) K. Barium zirconate does not appear to undergo a phase transition in the temperature range of measurement. It has the cubic perovskite (c) structure. The standard free energies of formation of the zirconates from their component binary oxides AO (A = Sr, Ba) with rock salt (rs) and ZrO2 with monoclinic (m) structures can be expressed by the following relations:SrO (rs) + ZrO2 (m) --> SrZrO3 (o) Delta G degrees = -74,880 - 14.2T (+/-200) J mol(-1) SrO (rs) + ZrO2 (m) --> SrZrO3 (t) Delta G degrees = -73,645 - 15.3T (+/-200) J mol(-1) BaO (rs) + ZrO2 (m) --> BaZrO4 (c) Delta G degrees = -127,760 - 1.79T (+/-250) J mol(-1) The results of this study are in reasonable agreement with calorimetric measurements reported in the literature. Systematic trends in the stability of alkaline-earth zirconates having the stoichiometry AZrO(3) are discussed.

Thermodynamic properties of LaFeO3-delta and LaFe12O19

The standard Gibbs energies of formation of lanthanum orthoferrite (LaFeO3-delta) and hexaferrite (LaFe12O19)were determined using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte and pure oxygen gas at ambient pressure as the reference electrode. From emf of the solid-state cell, the Gibbs energy of formation of nonstoichiometric orthoferrite (LaFeO3-delta) is obtained. To derive values for the stoichiometric phase, variation of the oxygen nonstoichiometric parameter with oxygen partial pressure was measured using thermogravimetry under controlled gas mixtures. The results obtained for LaFeO3 and LaFe12O19 can be summarized by the following equations, which represent the formation of ternary oxides from their component binary oxides: 1/2 La2O3 + 1/2 Fe2O3 -> LaFeO3: Delta G degrees (LaFeO3) (+/- 450) (J mol(-1)) = -62920 - 2.12T (K), and 1/2 La2O3 + 9/2Fe(2)O(3) + Fe3O4 -> LaFe12O19; Delta G degrees (LaFe12O19) (+/- 200) (J mol(-1)) = -103900 + 21.25T (K). These data are discussed critically in comparison with thermodynamic values reported in the literature from a variety of measurements. The values obtained in this study are consistent with calorimetric entropy and enthalpy of formation of the perovskite phase and with some of the Gibbs energy measurements reported in the literature. For the lanthanum hexaferrite (LaFe12O19) there are no prior thermodynamic measurements for comparison. (c) 2011 Elsevier B.V. All rights reserved.

Measurement of Gibbs energy of formation of Ca2PbO4 using a solid-state cell with three electrodes

Phase relations in the system Ca-Pb-O at 1100 K have been determined by equilibrating 18 compositions in the ternary and identifying the phases present in quenched samples by X-ray diffraction and energy dispersive X-ray analysis (EDX). Only one ternary compound Ca2PbO4 was found to be present. The compound coexists with CaO and PbO. The intermetallic compounds Ca2Pb, Ca5Pb3 and CaPb and liquid alloys are in equilibrium with CaO. The standard Gibbs energies of formation of Ca2PbO4 (880 - 1100 K) and Pb3O4 (770 - 910 K) were determined using solid-state cells based on yttria-stabilized zirconia as the solid electrolyte. Pure oxygen gas at 0.1 MPa was used as the reference electrode. For measurements on Ca2PbO4, a novel cell design with three electrodes in series, separated by solid electrolyte membranes, was used to avoid polarization of the electrode containing three solid phases. Two three-phase electrodes were used. The first absorbs the electrochemical flux of oxygen from the reference electrode to the measuring electrode. The other three-phase electrode, which is unaffected by the oxygen flux through the solid electrolyte, is used for electromotive force (EMF) measurement. The results from EMF studies were cross-checked using thermogravimetry (TG) under controlled oxygen partial pressures. The stability of Pb3O4 was investigated using a conventional solid-state cell with RuO2 electrodes. The results can be summarized by the following equations: 2CaO + PbO +1/2O(2) --> Ca2PbO4 Delta(r)G degrees/J mol(-1) = (- 128340 + 93.21 T/K) +/- 200 3PbO + 1/2O(2) --> Pb3O4 Delta(r)G degrees/J mol(-1) = (- 70060 + 77.5 T/K) +/- 150

Relation between integral and partial properties of ternary solutions along different composition trajectories

The relations between partial and integral properties of ternary solutions along composition trajectories suggested by Kohler, Colinet and Jacob, and along an arbitrary path are derived. The chemical potentials of the components are related to the slope of integral free energy by expressions involving the binary compositions generated by the intersections of the composition trajectory with the sides of the ternary triangle. Only along the Kohler composition trajectory it is possible to derive the integral free energy from the variation of the chemical potential of a single component with composition or vice versa. Along all other paths the differential of the integral free energy is related to two chemical potentials. The Gibbs-Duhem integration proposed by Darken for the ternary system uses the Kohler isogram. The relative merits of different limits for integration are discussed.

Stabilities of ternary carbides UWC1.75 and UWC2

The methane-hydrogen gas equilibration technique has been used to measure the chemical potential of carbon associated with two three-phase fields of the system U-W-C in the temperature range 973 to 1173 K. By combining the values of the chemical potential of carbon in the three-phase fields UC + W + UWC1.75 and UC + UWC1.75 + UWC2 Obtained in this study with the data on the Gibbs energy of formation of UC available in the literature, expressions for the Gibbs energies of formation of the two ternary carbides were derived: Delta(f)G degrees [UWC1.75] = -131, 600 - 300 T (+/-8000) J mol(-1) Delta(f)G degrees [UWC2] = -144, 800 - 32.0 T (+/- 10,000) J mol(-1) Although estimates of Gibbs energies of formation of the two ternary carbides TSWC1.75 and UWC2 have been reported, there have been no previous experimental determinations of thermodynamic properties of these compounds.

Thermodynamic constraints along isograms in ternary systems: application to three-phase equilibria

Thermodynamic constraints on component chemical potentials in three-phase fields introduced by the various isograms suggested in the literature are derived for a ternary system containing compounds. When compositions of two compounds lie on an isogram, it is associated with specific characteristics which can be used to obtain further understanding of the interplay of thermodynamic factors that determine phase equilibria. When two compounds are shared by adjacent three-phase fields, the constraints are dictated by binary compositions generated by the intersection of a line passing through the shared compounds with the sides of the ternary triangle. Generalized expressions for an arbitrary line through the triangle are presented. These are consistent with special relations obtained along Kohler, Colinet and Jacob isograms. Five axioms are introduced and proved. They provide valuable tools for checking consistency of thermodynamic measurements and for deriving thermodynamic properties from phase diagrams. (C) 1997 Elsevier Science S.A.

Local environmental structures of Mo in the superionic conducting glass (AgI)(0.6)(Ag2MoO4)(0.4) by anomalous X-ray scattering

The anomalous X-ray scattering (AXS) method using Mo K absorption edges has been employed for obtaining the local structural information of superionic conducting glass having the composition (AgI)(0.6)(Ag2MoO4)(0.4). The possible atomic arrangements in the near-neighbor region of this glass were estimated by coupling the results with the least-squares variational analysis so as to reproduce the differential intensity profile for Mo as well as the ordinary scattering profile. The coordination number of oxygen around Mo is found to be about 4 at the distance of 0.180 mn. This implies that the most probable structural entity in the glass is the MoO4 tetrahedral unit which has been proposed based on infrared spectroscopy. The value of the coordination number of I- around Ag+ is estimated as 4.4 at 0.287 nm, suggesting an arrangement similar to that of crystalline or molten AgI.

Thermodynamic properties of the calcium ferrites CaFe2O4 and Ca2Fe2O5

The chemical potentials of CaO in the two-phase fields Fe2O3 + CaFe2O4 and CaFe2O4 + Ca2Fe2O5 of the pseudobinary system CaO - Fe2O3 have been measured in the temperature range from 975 to 1275 K, relative to pure CaO as the reference state, using solid state galvanic cells incorporating single-crystal CaF2 as the solid electrolyte. The cell was operated under pure oxygen at ambient pressure. The standard Gibbs energies of formation of calcium ferrites, CaFe2O4 and Ca2Fe2O5, were derived from the reversible emfs. The results can be summarized by the following equations:CaO + Fe2O3 --> CaFe2O4;Delta G degrees = - 37,480 + 1.16 T (+/- 250) J/mol 2 CaO + Fe2O3 --> Ca2Fe2O5;Delta G degrees = - 45, 280 - 13.51 T (+/- 275) J/mol These values are compared with thermodynamic data reported in the literature. The results of this study are in excellent agreement with heat capacity data, and in reasonable agreement with earlier measurements of enthalpy and Gibbs energy of formation, but suggest significant revision of enthalpies of formation of calcium ferrites given in current thermodynamic compilations.

Oscillatory flow and temperature fields in an open tube with temperature difference across the ends

The oscillating flow and temperature field in an open tube subjected to cryogenic temperature at the cold end and ambient temperature at the hot end is studied numerically. The flow is driven by a time-wise sinusoidally varying pressure at the cold end. The conjugate problem takes into account the interaction of oscillatory flow with the heat conduction in the tube wall. The full set of compressible flow equations with axisymmetry assumption are solved with a pressure correction algorithm. Parametric studies are conducted with frequencies of 5-15 Hz, with one end maintained at 100 K and other end at 300 K. The flow and temperature distributions and the cooldown characteristics are obtained. The frequency and pressure amplitude have negligible effect on the time averaged Nusselt number. Pressure amplitude is an important factor determining the enthalpy flow through the solid wall. The frequency of operation has considerable effect on penetration of temperature into the tube. The density variation has strong influence on property profiles during cooldown. The present study is expected to be of interest in applications such as pulse tube refrigerators and other cryocoolers, where oscillatory flows occur in open tubes. (C) 2011 Elsevier Ltd. All rights reserved.

Crystal structure and thermal and electrical properties of the perovskite solid solution Nd1-xSrxFeO3-delta (0 <= x <= 0.4)

The crystal structure, thermal expansion and electrical conductivity of strontium-doped neodymium ferrite (Nd1-xSrxFeO3-delta where 0less than or equal toxless than or equal to0.4) were investigated. All compositions had the GdFeO3-type orthorhombic perovskite structure. The lattice parameters were determined at room temperature by X-ray powder diffraction. The orthorhombic distortion decreases with increasing Sr substitution. The pseudocubic lattice parameter shows a minimum at x=0.3. The thermal expansion curves for x=0.2-0.4 displayed rapid increase in slope at higher temperatures. The electrical conductivity increased with Sr content and temperature. The calculated activation energies for electrical conduction decreased with increasing x. The electrical conductivity can be described by the small polaron hopping mechanism. The charge compensation for divalent ion on the A-site is provided by the formation of Fe4+ ions on the B site and vacancies on the oxygen sublattice. The results indicate two defect domains: for low values of x, the predominant defect is Fe4+ ions, whereas for higher values of x, oxygen vacancies dominate. (C) 2002 Elsevier Science B.V. All rights reserved.

Crystal structure, thermal expansion and electrical conductivity of Nd0.7Sr0.3Fe1-xCoxO3 (0 <= x <= 0.8)

The crystal structure, thermal expansion and electrical conductivity of the solid solution Nd0.7Sr0.3Fe1-xCoxO3 for 0 less than or equal to x less than or equal to 0.8 were investigated. All compositions had the GdFeO3-type orthorhombic perovskite structure. The lattice parameters were determined at room temperature by X-ray powder diffraction (XRPD). The pseudo-cubic lattice constant decreased continuously with x. The average linear thermal expansion coefficient (TEC) in the temperature range from 573 to 973 K was found to increase with x. The thermal expansion curves for all values of x displayed rapid increase in slope at high temperatures. The electrical conductivity increased with x for the entire temperature range of measurement. The calculated activation energy values indicate that electrical conduction takes place primarily by the small polaron hopping mechanism. The charge compensation for the divalent ion on the A-site is provided by the formation of Fe4+ ions on the B-site (in preference to Co4+ ions) and vacancies on the oxygen sublattice for low values of x. The large increase in the conductivity with x in the range from 0.6 to 0.8 is attributed to the substitution of Fe4+ ions by Co4+ ions. The Fe site has a lower small polaron site energy than Co and hence behaves like a carrier trap, thereby drastically reducing the conductivity. The non-linear behaviour in the dependence of log sigmaT with reciprocal temperature can be attributed to the generation of additional charge carriers with increasing temperature by the charge disproportionation of Co3+ ions. (C) 2002 Elsevier Science B.V. All rights reserved.