Thermodynamics and phase equilibria in the system Cu2O CuO ()Ga2O3

The standard Gibbs free energies of formation of CuAlO2 and CuAl2O4 were determined in the range 700° to 1100°C, using emf measurements on the galvanic cells (1) Pt,CuO +] Cu2O/CaO-ZrO2/O2,Pt; (2) Pt,Cu +] CuAlO2+] Al2O3/CaO-ZrO2/ Cu +] Cu2O,Pt; and (3) Pt,CuAl2O4+] CuAlO2+]Al2O3/CaO-ZrO2/O2,Pt. The results are compared with published information on the stability of these compounds. The entropy of transformation of CuO from tenorite to the rock-salt structure is evaluated from the present results and from earlier studies on the entropy of formation of spinels from oxides of the rock-salt and corundum structures. The temperatures corresponding to 3-phase equilibria in the system Cu2O-CuO-Al2O3 at specified O2 pressures calculated from the present results are discussed in reference to available phase diagrams.

Activities in the spinel solid solution, phase equilibria and thermodynamic properties of ternary phases in the system Cu Fe O

A review of the structural and thermodynamic information and phase equilibria in the Cu-Fe-O system suggested that a consistent, quantitative description of the system is hampered by lack of data on activities in the spinel solid solution CuFe2O4-Fe3O4. Therefore the activity of Fe3O4 in this solid solution is derived from measurements of the oxygen potentials established at 1000°C by mixtures containing Fe2O3 and spinel solid solutions of known composition. The oxygen pressures were measured manometrically for solid solutions rich in CuFe2O4, while for Fe3O4-rich compositions the oxygen potentials were obtained by an emf technique. The activities show significant negative deviations from Raoult’s law. The compositions of the spinel solid solutions in equilibrium with CuO + CuFeO2 and Cu + CuFeO2 were obtained from chemical analysis of the solid solution after magnetic separation. The oxygen potential of the three-phase mixture Cu + CuFeO2 + Fe3O4(spinel s.s.) was determined by a solid oxide galvanic cell. From these measurements a complete phase diagram and consistent thermodynamic data on the ternary condensed phases, CuFeO2 and CuFeO2O4, were obtained. An analysis of the free energy of mixing of the spinel solid solution furnished information on the distribution of cations and their valencies between the tetrahedral and octahedral sites of the spinel lattice, which is consistent with X-ray diffraction, magnetic and Seebeck coefficient measurements.

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.

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

Phase equilibria in the system NiO-CaO-SiO2 and Gibbs energy of formation of CaNiSi2O6

Phase relations in the pseudoternary system NiO-CaO-SiO2 at 1373 K are established. The coexisting phases are identified by X-ray diffraction and energy-dispersive X-ray analysis of equilibrated samples. There is only one quaternary oxide CaNiSi2O6 with clinopyroxene structure. The Gibbs energy of formation of CaNiSi2O6 is measured using a solid state galvanic cell incorporating stabilized zirconia as the solid electrolyte in the temperature range of 1000 to 1400 K:Pt, Ni + SiO2 + CaSiO3 + CaNiSi2O6 \ (Y2O3)ZrO2 \ Ni + NiO, Pt From the electromotive force (emf) of the cell, the Gibbs energy of formation of CaNiSi2O6 from NiO, SiO2, and CaSiO3 is obtained. To derive the Gibbs energy of formation of the quaternary oxide from component binary oxides, the free energy of formation of CaSiO, is determined separately using a solid state cell based on single crystal CaF2 as the electrolyte: Pt, O-2, CaO + CaF2 \ CaF2 \ CaSiO3 + SiO2 + CaF2, O-2, Pt The results can be expressed by the following equations: NiO (r.s) + CaO (r.s) + 2SiO(2) (qz) --> CaNiSi2O6 (pyr) Delta G degrees = -115,700 + 10.63T (+/-100) J mol(-1) CaO (r.s) + SiO2 (qz) --> CaSiO3 (wol) Delta G degrees = -90,030 -0.61T (+/-60) J mol(-1).

Phase equilibria and thermodynamics of the system Dy-Mg-Cl at 1073 K

The phase relations in the system Dy–Mg–Cl at 1073 K have been established by isothermal equilibration and chemical analysis of quenched samples. Liquid Mg-rich alloy was found to be in equilibrium with molten DyCl2. Therefore, DyCl2 can be synthesized by reduction of MgCl2 with excess of metallic Dy at 1073 K. The Gibbs energy of formation of DyCl2 at 1073 K was evaluated by two different methods. From voltammetric determination of decomposition voltage, the upper limit for the standard Gibbs energy of formation of DyCl2 was estimated to be −505(±20) kJ mol−1. A value of −543(±10) kJ mol−1 was deduced from phase relations using Gibbs–Duhem integration. The value for the standard Gibbs energy of DyCl2 indicates that the Dy2+ ion has a potential capability for reducing TiCl4 to metal titanium. At the same time, Mg is a reductant for Dy3+ produced during the reduction of TiCl4. Thus, it is thermodynamically confirmed that reduction of TiCl4 by magnesium using a reaction mediator in the salt phase is feasible.

Thermodynamics and phase equilibria involving the spinel solid solution FexMg1-xCr2O4

Activities of FeCr2O4 in the spinel solid solutions Fe X Mg1−X Cr2O4 (0phase relations in the FeO-MgO-Cr2O3 system have been deduced from the results obtained in this study together with other relevant thermodynamic data from the literature. The tie-lines between the solid solutions with rock salt and spinel structures represent the influence of intercrystalline ion exchange. The tie-lines are skewed toward the FeCr2O4 corner, primarily because of the higher stability of FeCr2O4 compared to MgCr2O4, with respect to their component binary oxides. The oxygen partial pressure corresponding to the two three-phase regions, Fe + Fe X Mg1−X Cr2O4 + Cr2O3 and Fe + Fe Y Mg1−Y O + Fe X Mg1−X Cr2O4, have been evaluated as a function of composition at 1200 K.

Phase Equilibria in the System Al2O3-CaO-CoO and Gibbs Energy of Formation of Ca3CoAl4O10

An isothermal section of the system Al2O3-CaO-CoO at 1500 K has been established by equilibrating 22 samples of different compositions at high temperature and phase identification by optical and scanning electron microscopy, X-ray diffraction, and energy dispersive spectroscopy after quenching to room temperature. Only one quaternary oxide, Ca3CoAl4O10, was identified inside the ternary triangle. Based on the phase relations, a solid-state electrochemical cell was designed to measure the Gibbs energy of formation of Ca3CoAl4O10 in the temperature range from 1150 to 1500 K. Calcia-stabilized zirconia was used as the solid electrolyte and a mixture of Co + CoO as the reference electrode. The cell can be represented as: ( - )\textPt,\textCaAl 2 \textO 4 + \textCa 1 2 \textAl 1 4 \textO 3 3 + \textCa 3 \textCoAl 4 \textO 10 + \textCo//(CaO)ZrO 2 \text// \textCoO + \textCo,\text Pt ( + ). (−)PtCaAl2O4+Ca12Al14O33+Ca3CoAl4O10+Co//(CaO)ZrO2//CoO+Co Pt (+) From the emf of the cell, the standard Gibbs energy change for the Ca3CoAl4O10 formation reaction, CoO + 3/5CaAl2O4 + 1/5Ca12Al14O33 → Ca3CoAl4O10, is obtained as a function of temperature: \Updelta Gr\texto Unknown control sequence '\Updelta'/J mol−1 (±50) = −2673 + 0.289 (T/K). The standard Gibbs energy of formation of Ca3CoAl4O10 from its component binary oxides, Al2O3, CaO, and CoO is derived as a function of temperature. The standard entropy and enthalpy of formation of Ca3CoAl4O10 at 298.15 K are evaluated. Chemical potential diagrams for the system Al2O3-CaO-CoO at 1500 K are presented based on the results of this study and auxiliary information from the literature.

System Ho-Rh-O: Phase Equilibria, Chemical Potentials and Gibbs Energy of Formation of HoRhO3

The thermodynamic properties of the HoRhO3 were determined in the temperature range from 900 to 1300 K by using a solid-state electrochemical cell incorporating calcia-stabilized zirconia as the electrolyte. The standard Gibbs free energy of formation of orthorhombic perovskite HoRhO3, from Ho2O3 with C-rare earth structure and Rh2O3 with orthorhombic structure, can be expressed by the equation; Delta G(f)degrees((ox)) (+/- 78)/(J/mol) = -50535 + 3.85(T/K) Using the thermodynamic data of HoRhO3 and auxiliary data for binary oxides from the literature, the phase relations in the Ho-Rh-O system were computed at 1273 K. Thermodynamic data for intermetallic phases in the binary Ho-Rh were estimated from experimental enthalpy of formation for three compositions from the literature and Miedema's model, consistent with the phase diagram. The oxygen potential-composition diagram and three-dimensional chemical potential diagram at 1273 K, and temperature-composition diagrams at constant oxygen partial pressures were computed for the system Ho-Rh-O. The decomposition temperature of HoRhO3 is 1717(+/- 2) K in pure O-2 and 1610(+/- 2) K in air at a total pressure p(o) = 0.1 MPa.

Thermodynamics of TmRhO3, Phase Equilibria, and Chemical Potentials in the System Tm-Rh-O

Phase equilibria in the system Tm-Rh-O at 1200 K is established by isothermal equilibration of selected compositions and phase identification after quenching to room temperature. Six intermetallic phases (Tm3Rh, Tm7Rh3, Tm5Rh3, Tm3Rh2, TmRh, TmRh2 +/-delta) and a ternary oxide TmRhO3 are identified. Based on experimentally determined phase relations, a solid-state electrochemical cell is devised to measure the standard free energy of formation of orthorhombic perovskite TmRhO3 from cubic Tm2O3 and beta-Rh2O3 in the temperature range from (900 to 1300) K. The results can be summarized as: Delta G(f,ox)(o) +/- 104/J.mol(-1) = -46474 + 3.925(T/K). Invoking the Neumann-Kopp rule, the standard enthalpy of formation of TmRhO3 from its constituent elements at 298.15 K is estimated as -1193.89 (+/- 2.86) kJ.mol(-1). The standard entropy of TmRhO3 at 298.15 K is evaluated as 103.8 (+/- 1.6) J.mol(-1).K-1. The oxygen potential-composition diagram and three-dimensional chemical potential diagram at 1200 K and temperature-composition diagrams at constant partial pressures of oxygen are computed from thermodynamic data. The compound TmRhO3 decomposes at 1688 (+/- 2) K in pure oxygen and at 1583 (+/- 2) K in air at standard pressure.

Experimental study of phase equilibria in the system Cu-Al-Sn

Phase equilibria in the Cu-rich corner of the ternary system Cu-Al-Sn have been re-investigated. Final equilibrium microstructures of 20 ternary alloy compositions near Cu3Al were used to refine the ternary phase diagram. The microstructures were characterized using optical microscopy (OM), x-ray diffraction (XRD), electron probe microanalysis and transmission electron microscopy. Isothermal sections at 853, 845, 833, 818, 808, 803 and 773 K have been composed. Vertical sections have been drawn at 2 and 3 at% Sn, showing beta(1) as a stable phase. Three-phase fields (alpha + beta + beta(1)) and (beta + beta(1) + gamma(1)) result from beta -> alpha + beta(1) eutectoid and beta + gamma(1) -> beta(1) peritectoid reactions forming metastable beta(1) in the binary Cu-Al. With the lowering of temperature from 853 to 818 K, these three-phase fields are shifted to lower Sn concentrations, with simultaneous shrinkage and shifting of (beta + beta(1)) two-phase field. The three-phase field (alpha + beta + gamma(1)) resulting from the binary reaction beta -> alpha + gamma(1) shifts to higher Sn contents, with associated shrinkage of the beta field, with decreasing temperature. With further reduction of temperature, a new ternary invariant reaction beta + beta(1) -> alpha + gamma(1) is observed at similar to 813 K. The beta disappears completely at 803 K, giving rise to the three-phase field (alpha + beta(1) + gamma(1)). Some general guidelines on the role of ternary additions (M) on the stability of the ordered beta(1) phase are obtained by comparing the results of this study with data in the literature on other systems in the systems group Cu-Al-M.

Phase equilibria in the system Sm-Rh-O and thermodynamic and thermal studies on SmRhO3

Using isothermal equilibration, phase relations are established in the system Sm-Rh-O at 1273 K. SmRhO3 with GdFeO3-type perovskite structure is found to be the only ternary phase. Solid-state electrochemical cells, containing calcia-stabilized zirconia as an electrolyte, are used to measure the thermodynamic properties of SmRhO3 formed from their binary component oxides Rh2O3 (ortho) and Sm2O3 (C-type and B-type) in two different temperature ranges. Results suggest that C-type Sm2O3 with cubic structure transforms to B-type Sm2O3 with monoclinic structure at 1110 K. The standard Gibbs energy of transformation is . Standard Gibbs energy of formation of SmRhO3 from binary component oxides Rh2O3 and Sm2O3 with B-type rare earth oxide structure can be expressed as . The decomposition temperature of SmRhO3 estimated from the extrapolation of electrochemical data is 1665 (+/- 2) K in air and 1773 (+/- 3) K in pure oxygen. Temperature-composition diagrams at constant oxygen pressures are constructed for the system Sm-Rh-O. Employing the thermodynamic data for SmRhO3 from emf measurement and auxiliary data for other phases from the literature, oxygen potential-composition phase diagram and 3-D chemical potential diagram for the system Sm-Rh-O at 1273 K are developed.

Oxygen potentials and phase equilibria in the system Ca-Co-O and thermodynamic properties of Ca3Co2O6 and Ca3Co4O9.163

Oxygen potentials established by the equilibrium between three condensed phases, CaOss+CoOss+ Ca3Co2O6 and CoOss+Ca3Co2O6+Ca3CO3.93+O-alpha(9.36-delta), are measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte and pure oxygen as the reference electrode. Cation non-stoichiometry and oxygen non-stoichiometry in Ca3Co3.93+alpha O9.36-delta are determined using different techniques under defined conditions. Decomposition temperatures and thermodynamic properties of Ca3Co2O6 and Ca3Co4O9.163 are calculated from the results. The standard entropy and enthalpy of formation of Ca3Co2O6 at 298.15 K are evaluated. Using thermodynamic data from this study and auxiliary information from the literature, phase diagram for the ternary system Ca-Co-O is computed. Isothermal sections at representative temperatures are displayed to demonstrate the evolution of phase relations with temperature. (C) 2014 Elsevier Inc. All rights reserved.

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.