Phase Relations in the System Cu-Gd-O and Gibbs Energy of Formation of CuGd204

The phase relations in the system Cu-Gd-O have been determined at 1273 K by X-ray diffrac- tion, optical microscopy, and electron microprobe analysis of samples equilibrated in quartz ampules and in pure oxygen. Only one ternary compound, CuGd2O4, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt, Cu2O + CuGd2O4 + Gd2O3 // (Y2O3) ZrO2 // CuO + Cu2O, Pt in the temperature range of 900 to 1350 K. For the formation of CuGd2O4 from its binary component oxides, CuO (s) + Gd2O3 (s) → CuGd2O4 (s) ΔG° = 8230 - 11.2T (±50) J mol-1 Since the formation is endothermic, CuGd2O4 becomes thermodynamically unstable with respect to CuO and Gd2O3 below 735 K. When the oxygen partial pressure over CuGd2O4 is lowered, it decomposes according to the reaction 4CuGd2O4 (s) → 4Gd2O3 (s) + 2Cu2O (s) + O2 (g) for which the equilibrium oxygen potential is given by Δμo 2 = −227,970 + 143.2T (±500) J mol−1 An oxygen potential diagram for the system Cu-Gd-O at 1273 K is presented.

Phase relations in the system Cu─Ho─O and stability of Cu2Ho2O5

The phase relations in the system Cu-Ho-O have been determined at 1300 K using X-ray diffraction, optical microscopy, and electron microprobe analysis of samples equilibrated in evacuated quartz ampules and in pure oxygen. Only one ternary compound, Cu2Ho2O5, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt,Cu2O + Cu2Ho2O5 + Ho2O3/(Y2O3)ZrO2/CuO + Cu2O,Pt in the temperature range of 973 to 1350 K. For the formation of Cu2Ho2O5 from its binary component oxides, 2CuO(s) + Ho2O3(S) --> Cu2Ho2O5(s) DELTAG-degrees = 11190 - 13.8T(+/- 120) J-mol-1 Since the formation is endothermic, CU2Ho2O5 becomes thermodynamically unstable with respect to CuO and Ho2O3 below 810 K. When the oxygen partial pressure over Cu2Ho2O5 is lowered, it decomposes according to the reaction 2Cu2Ho2O5(s) --> 2Ho2O3(s) + 2Cu2O(S) + O2(g) for which the equilibrium oxygen potential is given by DELTAmu(O2) = - 238510 + 160.2T(+/- 450) J.mol-1 The decomposition temperature at an oxygen partial pressure of 1.52 x 10(4) Pa was measured using a combined DTA-TGA apparatus. Based on these results, an oxygen potential diagram for the system Cu-Ho-O at 1300 K is presented.

Time scales for transitions between free-energy minima of a dense hard-sphere system

Time scales associated with activated transitions between glassy metastable states of a free-energy functional appropriate for a dense hard-sphere system are calculated by using a new Monte Carlo method for the local density variables. In particular, we calculate the time the system, initially placed in a shallow glassy minimum of the free-energy, spends in the neighborhood of this minimum before making a transition to the basin of attraction of another free-energy minimum. This time scale is found to increase as the average density is increased. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This time scale does not show any evidence of increasing with sample size

System Dy-Fe-O: thermodynamic properties of ternary oxides using Calvet calorimetry and solid-state electrochemical cell

The enthalpy increments and the standard molar Gibbs energies of formation-of DyFeO3(s) and Dy3Fe5O12(s) have been measured using a Calvet micro-calorimeter and a solid oxide galvanic cell, respectively. A co-operative phase transition, related to anti-ferromagnetic to paramagnetic transformation, is apparent. from the heat capacity data for DyFeO3 at similar to 648 K. A similar type of phase transition has been observed for Dy3Fe5O12 at similar to 560 K which is related to ferrimagnetic to paramagnetic transformation. Enthalpy increment data for DyFeO3(s) and Dy3Fe5O12(s), except in the vicinity of the second-order transition, can be represented by the following polynomial expressions:{H(0)m(T) - H(0)m(298.15 K)) (Jmol(-1)) (+/-1.1%) = -52754 + 142.9 x (T (K)) + 2.48 x 10(-3) x (T (K))(2) + 2.951 x 10(6) x (T (K))(-1); (298.15 less than or equal to T (K) less than or equal to 1000) for DyFeO3(s), and {H(0)m(T) - H(0)m(298.15 K)} (Jmol(-1)) (+/-1.2%) = -191048 + 545.0 x (T - (K)) + 2.0 x 10(-5) x (T (K))(2) + 8.513 x 10(6) x (T (K))(-1); (208.15 less than or equal to T (K) less than or equal to 1000)for Dy3Fe5O12(s). The reversible emfs of the solid-state electrochemical cells: (-)Pt/{DyFeO3(s) + Dy2O3(s) + Fe(s)}/YDT/CSZ//{Fe(s) + Fe0.95O(s)}/Pt(+) and (-)Pt/{Fe(s) + Fe0.95O(s)}//CSZ//{DyFeO3(s) + Dy3Fe5O12(s) + Fe3O4(s)}/Pt(+), were measured in the temperature range from 1021 to 1250 K and 1035 to 1250 K, respectively. The standard Gibbs energies of formation of solid DyFeO3 and Dy3Fe5O12 calculated by the least squares regression analysis of the data obtained in the present study, and data for Fe0.95O and Dy2O3 from the literature, are given by Delta(f)G(0)m(DyFeO3,s)(kJmol(-1))(+/-3.2)= -1339.9 + 0.2473 x (T(K)); (1021 less than or equal to T (K) less than or equal to 1548)and D(f)G(0)m(Dy3Fe5O12,s) (kJmol(-1)) (+/-3.5) = -4850.4 + 0.9846 x (T (K)); (1035 less than or equal to T (K) less than or equal to 1250) The uncertainty estimates for Delta(f)G(0)m include the standard deviation in the emf and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagram and chemical potential diagrams for the system Dy-Fe-O were developed at 1250 K. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

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.

Thermodynamics of oxide sulfate melts: The system PbO PbSO4

Activities in the PbO-PbSO4 melts at 1253 K have been measured by emf and gas-equilibration techniques. The activity of PbO was directly obtained from the emf of the solid oxide cell, Pt, Ni-NiO/CaO-ZrO2/Auo.92PbO.08, PbOx-PbSO4(1-x), Ir, Pt for 1.0 >XPbO > 0.6. The melt and the alloy were contained in closed zirconia crucibles. Since the partial pressure of SO2 gas in equilibrium with the melt and alloy was appreciable (>0.08 atm) atXPbO < 0.6, activities at lower PbO concentrations were derived from measurements of the weight gain of pure PbO under controlled gas streans of Ar + SO2 + O2. The partial and integral free energies of mixing at 1253 K were calculated and found to fit a subregular model: ΔGEPbO =X2PbSO4 {-42,450 + 20,000X2PbSO4} J mol-1 ΔGEPbO =X2pbSO {-12,450 - 20,000XPbS} J mol-1 ΔGEpbSOXPbSO4 {-32,450XPbS - 22,450XPbSO4 } J mol-1. The standard free energy of formation of liquid PbSO4 from pure liquid PbO and gaseous SO3 at 1 atm at 1253 K was evaluated as -88.02 (±0.72) kJ mol-1.

Mass spectrometric and electrochemical studies of thermodynamic properties of liquid and solid phases in the CaO Al2O3 system

The activities of CaO and Al2O3 in lime-alumina melts were studied by Knudsen cell-mass spectrometry at 2060 K. Emf of solid state cells, with CaF2 as the electrolyte, was measured from 923 to 1223 K to obtain the free energies of formation of the interoxide compounds. The results are critically evaluated in the light of data reported in the literature on phase equilibria, activities in melts, and stabilities of compounds. A coherent set of data is presented, including the previously unknown free energy of formation of CaO.6Al2O3 and the temperature dependence of activities in the liquid phase.

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.

Alloy oxide equilibria in the system Ca Al O at 1373 K

The tie lines delineating equilibria between different oxides of the Ca-Al-O system and liquid Ca-Al alloy has been determined at 1373 K. Equilibration of the alloy with two adjacent oxide phases in the CaO-Al2O3 pseudo-binary system was established in a closed cell made of iron. Equilibrium oxide phases were confirmed by x-ray analysis and alloy compositions were determined by chemical analysis. The compound 12CaO.7Al2O3 Ca12Al14O33 was found to be a stable phase in equilibrium with calcium alloys. The experimental diagram is consistent with that calculated from the free energies of formation of the oxide phases and activities in liquid Ca-Al alloys at 1373 K reported in the literature.

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

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).

System Nd-Pd-O: Phase diagram and thermodynamic properties of oxides using a solid-state cell with advanced features

An isothermal section of the phase diagram for the system Nd-Pd-O at 1350 K has been established by equilibration of samples representing 13 different compositions and phase identification after quenching by optical and scanning electron microscopy, x-ray diffraction, and energy dispersive analysis of x-rays. The binary oxides PdO and NdO were not stable at 1350 K. Two ternary oxides Nd4PdO7 and Nd2Pd2O5 were identified. Solid and liquid alloys, as well as the intermetallics NdPd3 and NdPd5, were found to be in equilibrium with Nd2O3. Based on the phase relations, three solidstate cells were designed to measure the Gibbs energies of formation of PdO and the two ternary oxides. An advanced version of the solid-state cell incorporating a buffer electrode was used for high-temperature thermodynamic measurements. The function of the buffer electrode, placed between reference and working electrodes, was to absorb the electrochemical flux of the mobile species through the solid electrolyte caused by trace electronic conductivity. The buffer electrode prevented polarization of the measuring electrode and ensured accurate data. Yttria-stabilized zirconia was used as the solid electrolyte and pure oxygen gas at a pressure of 0.1 MP a as the reference electrode. Electromotive force measurements, conducted from 950 to 1425 K, indicated the presence of a third ternary oxide Nd2PdO4, stable below 1135 (±10) K. Additional cells were designed to study this compound. The standard Gibbs energy of formation of PdO (†f G 0) was measured from 775 to 1125 Kusing two separate cell designs against the primary reference standard for oxygen chemical potential. Based on the thermodynamic information, chemical potential diagrams for the system Nd-Pd-O were also developed.

An advanced design of the solid-state cell for accurate thermodynamic measurements on ternary oxides: system Sm–Pd–O

An advanced design of the solid-state cell incorporating a buffer electrode has been developed for high temperature thermodynamic measurements. The function of the buffer electrode, placed between reference and working electrodes, was to absorb the electrochemical flux of the mobile species through the solid electrolyte caused by trace electronic conductivity. The buffer electrode prevented polarization of the measuring electrode and ensured accurate data. The application of the novel design and its advantages have been demonstrated by measuring the standard Gibbs energies of formation of ternary oxides of the system Sm–Pd–O. Yttria-stabilized zirconia was used as the solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa as the reference electrode. For the design of appropriate working electrodes, phase relations in the ternary system Sm–Pd–O were investigated at 1273 K. The two ternary oxides, Sm4PdO7 and Sm2Pd2O5, compositions of which fall on the Sm2O3–PdO join, were found to coexist with pure metal Pd. The thermodynamic properties of the ternary oxides were measured using three-phase electrodes in the temperature range 950–1425 K. During electrochemical measurements a third ternary oxide, Sm2PdO4, was found to be stable at low temperature. The standard Gibbs energies of formation (Δf(ox)Go) of the compounds from their component binary oxides Sm2O3 and PdO, can be represented by the equations: Sm4PdO7: Δf(ox)Go (J mol−1)=−34,220+0.84T(K) (±280); Sm2PdO4: Δf(ox)Go (J mol−1)=−33,350+2.49T(K) (±230); Sm2Pd2O5: Δf(ox)Go (J mol−1)=−59,955+1.80T(K) (±320). Based on the thermodynamic information, three-dimensional P–T–C and chemical potential diagrams for the system Sm–Pd–O were developed.

Solute-solute and solute-solvent interactions in transition metal alloys: Pt-Ti system

An isothermal section of the phase diagram for (silver + rhodium + oxygen) at T = 1173 K has been established by equilibration of samples representing twelve different compositions, and phase identification after quenching by optical and scanning electron microscopy (s.e.m.), X-ray diffraction (x.r.d.), and energy dispersive analysis of X-rays (e.d.x.), Only one ternary oxide, AgRhO2, was found to be stable and a three phase region involving Ag, AgRhO2 and Rh2O3 was identified. The thermodynamic properties of AgRhO2 were measured using a galvanic cell in the temperature range 980 K to 1320 K. Yttria-stabilized zirconia was used as the solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa was used as the reference electrode. The Gibbs free energy of formation of the ternary oxide from the elements, ΔfGo (AgRhO2), can be represented by two linear equations that join at the melting temperature of silver. In the temperature range 980 K to 1235 K, ΔfGo(AgRhO2)/(J . mol-1) = -249080 + 179.08 T/K (±120). Above the melting temperature of silver, in the temperature range 1235 K to 1320 K, ΔfGo(AgRhO2)/(J . mol-1) = -260400 + 188.24 T/K (±95). The thermodynamic properties of AgRhO2 at T = 298.15 K were evaluated from the high temperature data. The chemical potential diagram for (silver + rhodium + oxygen) at T = 1200 K was also computed on the basis of the results of this study.

Phase relations and Gibbs energies of spinel phases and solid solutions in the system Mg-Rh-O

Pure stoichiometric MgRh(2)O(4) could not be prepared by solid state reaction from an equimolar mixture of MgO and Rh(2)O(3) in air. The spinel phase formed always contained excess of Mg and traces of Rh or Rh(2)O(3). The spinel phase can be considered as a solid solution of Mg(2)RhO(4) in MgRh(2)O(4). The compositions of the spinel solid solution in equilibrium with different phases in the ternary system Mg-Rh-O were determined by electron probe microanalysis. The oxygen potential established by the equilibrium between Rh + MgO + Mg(1+x)Rh(2-x)O(4) was measured as a function of temperature using a solid-state cell incorporating yttria-stabilized zirconia as an electrolyte and pure oxygen at 0.1 MPa as the reference electrode. To avoid polarization of the working electrode during the measurements, an improved design of the cell with a buffer electrode was used. The standard Gibbs energies of formation of MgRh(2)O(4) and Mg(2)RhO(4) were deduced from the measured electromotive force (e.m.f.) by invoking a model for the spinel solid solution. The parameters of the model were optimized using the measured composition of the spinel solid solution in different phase fields and imposed oxygen partial pressures. The results can be summarized by the equations: MgO + beta -Rh(2)O(3) -> MgRh(2)O(4); Delta G degrees (+ 1010)/J mol(-1) = -32239 + 7.534T; 2MgO + RhO(2) -> Mg(2)RhO(4); Delta G degrees(+/- 1270)/J mol(-1) = 36427 -4.163T; Delta G(M)/J mol(-1) = 2RT(xInx + (1-x)In(1-x)) + 4650x(1-x), where Delta G degrees is the standard Gibbs free energy change for the reaction and G(M) is the free energy of mixing of the spinel solid solution Mg(1+x)Rh(2-x)O(4). (C) 2011 Elsevier B. V. All rights reserved.