Representation of thermodynamic properties of ternary systems and its application to the system silver-gold-copper at 1350 K

The article presents a generalized analytical expression for description of the integral excess Gibbs free energy of mixing of a ternary system. Twelve constants of the equation are assessed by the least mean squares regressional analysis of the experimental integral excess data of the constituent binaries; three ternary parameters are evaluated by a regressional analysis based on the partial experimental data of a component of the ternary system. The assessed values of the ternary parameters describe the nature of the ternary interaction in the system. Activities and isoactivities of the components in the Ag-Au-Cu system at 1350 K are calculated and found to be in good agreement with the experimental data. This analytical treatment is particularly useful to ternary systems where the thermodynamic data are available from different sources.

The CaO-SrO-CuO-O-2 system: Phase equilibria and thermodynamic properties at 1123 K

Phase relationships in the CaO-SrO-CuO system in pure oxygen at 1.01 x 10(5) Pa pressure were determined by equilibrating different compositions at 1123 K for similar to 120 h and analyzing the phases present in the quenched samples using X-ray diffraction (XRD), optical and scanning electron microscopy, and energy dispersive analysis of X-rays (EDAX). Four solid solution series were observed in the system, The CawSr1-wO monoxide solid solution with rock-salt structure was found to exhibit an asymmetric miscibility gap, The mixing properties of the monoxide system were deduced using a subregular solution model, For the (CaxSr1-x)(2)CuO3 series, a complete solid solution range with orthorhombic space group Immm was obtained. Calcium substituted for strontium up to 68 at. % in SrCuO2+delta and 51.5 at. % in Sr14Cu24O41-delta. The tie lines between the solid solutions were determined accurately, The activity-composition relations in (CaxSr1-x)(2)CuO3, CaySr1-yCuO2+delta, and (Ca2Sr1-z)(14)Cu24O41-delta solid solutions were determined from experimental tie lines. Activities in the (CaxSr1-x)(2)CuO3 and CaySr1-yCuO2+delta series were close to the predictions of the Temkin model, The behavior of the (CazSr1-(z))(14)Cu24O41-delta solid solution was more complex, with the activity of SrCu(24/14)O-(41-delta/14) exhibiting both positive and negative deviations from ideality. Gibbs energy of formation of the CaCuO2+delta metastable phase at 1123 K was deduced from an analysis of the phase diagram.

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.

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.

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.

Representation of thermodynamic properties of quaternary systems using interaction parameters

Integral excess free energy of a quaternary system has been expressed in terms of the MacLaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction coefficients. The derivation of the partial functions involves extensive summation of various infinite series pertaining to the first order and quaternary parameters to remove any truncational error. The thermodynamic consistency of the derived partials has been established based on the Gibbs-Duhem relations. The equations are used to interpret the thermodynamic properties of the Fe-Cr-Ni-N system.

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 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.

A method for the calculation of the adsorbed phase volume and pseudo-saturation pressure from adsorption isotherm data on activated carbon

We propose a new method for evaluating the adsorbed phase volume during physisorption of several gases on activated carbon specimens. We treat the adsorbed phase as another equilibrium phase which satisfies the Gibbs equation and hence assume that the law of rectilinear diameters is applicable. Since invariably the bulk gas phase densities are known along measured isotherms, the constants of the adsorbed phase volume can be regressed from the experimental data. We take the Dubinin-Astakhov isotherm as the model for verifying our hypothesis since it is one of the few equations that accounts for adsorbed phase volume changes. In addition, the pseudo-saturation pressure in the supercritical region is calculated by letting the index of the temperature term in Dubinin's equation to be temperature dependent. Based on over 50 combinations of activated carbons and adsorbates (nitrogen, oxygen, argon, carbon dioxide, hydrocarbons and halocarbon refrigerants) it is observed that the proposed changes fit experimental data quite well.

High temperature phase chemistry of system Eu-Pd-O

An isothermal section of the phase diagram for the system Eu - Pd - O at 1223 K has been established by equilibration of samples representing 20 different compositions, and phase identification after quenching by optical and scanning electron microscopy, X-ray powder diffraction, and energy dispersive spectroscopy. Three ternary oxides, Eu4PdO7, Eu2PdO4, and Eu2Pd2O5, were identified. Liquid alloys and the intermetallic compounds EuPd2 and EuPd3 were found to be in equilibrium with EuO. The compound EuPd3 was also found to coexist separately with Eu3O4 and Eu2O3. The oxide phase in equilibrium with EuPd5 and Pd rich solid solution was Eu2O3. Based on the phase relations, four solid state cells were designed to measure the Gibbs energies of formation of the three ternary oxides in the temperature range from 925 to 1350 K. Although three cells are sufficient to obtain the properties of the three compounds, the fourth cell was deployed to crosscheck the data. An advanced version of the solid state cell incorporating a buffer electrode with yttria stabilised zirconia solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa as the reference electrode was used for high temperature thermodynamic measurements. Equations for the standard Gibbs energy of formation of the interoxide compounds from their component binary oxides Eu2O3 with C type structure and PdO have been established. Based on the thermodynamic information, isothermal chemical potential diagrams and isobaric phase diagrams for the system Eu - Pd - O have been developed.

Nitride synthesis using ammonia and hydrazine - a thermodynamic panorama

Because of the wide variety of projected applications of ultrapure nitrides in advanced technologies, there is interest in developing new cost-effective methods of synthesis. Explored in this study is the use of ammonia and hydrazine for the synthesis of nitrides from oxides, sulfides and chlorides. Even when the standard Gibbs energy change for the nitridation reactions involved are moderately positive, the reaction can be made to proceed by lowering the partial pressure of the product gas below its equilibrium value. Use of a metastable form of precursor in the nanometric size range is an alternative method to facilitate nitridation. Ellingham-Richardson-Jeffes diagrams are used for a panoramic presentation of the driving force for each set of reactions as a function of temperature. Oxides are the least promising precursors for nitride synthesis; sulfides offer a larger synthetic window for many useful nitrides such as BN, AlN, InN, VN, TiN, ThN and Si3N4. The standard Gibbs free energy changes for reactions involving chlorides with either ammonia or hydrazine are much more negative. Hydrazine is a more powerful nitriding agent than ammonia. The metastability of hydrazine requires that it be introduced into a reactor through a water-cooled lance. The use of volatile halides with ammonia or hydrazine offers the potential for synthesis of pure and doped nanocrystalline nitrides. Nitride thin films can also be prepared by suitable adaptations of the chloride route. (C) 2002 Kluwer Academic Publishers.

Phase diagram for the system Nd-Mn-O and thermodynamic properties of NdMnO3 and NdMn2O5

Studies on the phase relations in the system Nd-Mn-O at 1223 K showed two stable ternary compounds, NdMnO3 and NdMn2O5. An isothermal section of the ternary phase diagram for the system Nd-Mn-O was constructed based on phase analysis of samples quenched after equilibration using XRPD and EDS. An advanced version of the solid-state cell incorporating a buffer electrode was used to determine the Gibbs energies of decomposition of NdMnO3 and NdMn2O5 in the temperature range from 925 to 1400 K. Pure oxygen gas at 0.1 MPa was used as the reference electrode, and yttria-stabilized zirconia as the solid electrolyte. The buffer electrode was designed to prevent polarization of the three-phase electrode and ensure accurate data. The measured oxygen potential corresponding to the reaction,2 Nd2O3 + 4 MnO + O-2 --> 4 NdMnO3 can be represented by the equation,Amu(o2) / J.mol(-1) (+/-580) = -523 960 + 170.96 (T/K)Similarly, for the formation of NdMn2O5 according to the reaction,3 NdMnO3 + Mn3O4 + O-2 --> 3 NdMn2O5 Amu(o2) / J.mol(-1) (+/-660) = - 269 390 + 181.74 (T/K) (C) 2002 Elsevier Science Ltd. All rights reserved.

Systematic trends in structural and thermodynamic properties of ternary oxides in the systems Ln-Pd-O (Ln = lanthanide element)

Isothermal sections of the phase diagrams for the systems Ln-Pd-O (Ln = lanthanide element) at 1223 K indicate the presence of two inter-oxide compounds Ln(4)PdO(7) and Ln(2)Pd(2)O(5) for Ln = La, Pr, Nd, Sm, three compounds Ln(4)PdO(7), Ln(2)PdO(4) and Ln(2)Pd(2)O(5) for Ln = Eu, Gd and only one compound of Ln(2)Pd(2)O(5) for Ln = Tb to Ho. The lattice parameters of the compounds Ln(4)PdO(7), Ln(2)PdO(4) and Ln(2)Pd(2)O(5) show systematic nonlinear variation with atomic number. The unit cell volumes decrease with increasing atomic number. The standard Gibbs energies, enthalpies and entropies of formation of the ternary oxides from their component binary oxides (Ln(2)O(3) and PdO) have been measured recently using an advanced version of the solid-state electrochemical cell. The Gibbs energies and enthalpies of formation become less negative with increasing atomic number of Ln. For all the three compounds, the variation in Gibbs energy and enthalpy of formation with atomic number is markedly non-linear. The decrease in stability with atomic number is most pronounced for Ln(2)Pd(2)O(5), followed by Ln(4)PdO(7) and Ln(2)PdO(4). This is probably related to the repulsion between Pd2+ ions on the opposite phases Of O-8 cubes in Ln(2)Pd(2)O(5), and the presence of Ln-filled O-8 cubes that share three faces with each other in Ln4PdO7. The values for entropy of formation of all the ternary oxides from their component binary oxides are relatively small. Although the entropies of formation show some scatter, the average value for Ln = La, Pr, Nd is more negative than the average value for the other lanthanide elements. From this difference, an average value for the structure transformation entropy of Ln(2)O(3) from C-type to A-type is estimated as 0.87 J.mol(-1).K-1. The standard Gibbs energies of formation of these ternary oxides from elements at 1223 K are presented as a function of lanthanide atomic number. By invoking the Neumann-Kopp rule for heat capacity, thermodynamic properties of the inter-oxide compounds at 298.15 K are estimated. (C) 2002 Elsevier Science Ltd. All rights reserved.

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.

Thermodynamic analysis of enzyme catalysed reactions: new insights into the Michaelis-Menten equation

A simple thermodynamic analysis of the well-known Michaelis-Menten equation (MME) of enzyme catalysis is proposed that employs the chemical potential mu to follow the Gibbs free energy changes attending the formation of the enzyme-substrate complex and its turnover to the product. The main conclusion from the above analysis is that low values of the Michaelis constant KM and high values of the turnover number k(cat) are advantageous: this supports a simple algebraic analysis of the MME, although at variance with current thinking. Available data apparently support the above findings. It is argued that transition state stabilisation - rather than substrate distortion or proximity - is the key to enzyme catalysis.