Gibbs Energy of Formation of MnO: Measurement and Assessment

Based on the measurements of Alcock and Zador, Grundy et al. estimated an uncertainty of the order of +/- 5 kJ mol(-1) for the standard Gibbs energy of formation of MnO in a recent assessment. Since the evaluation of thermodynamic data for the higher oxides Mn3O4, Mn2O3, and MnO2 depends on values for MnO, a redetermination of its Gibbs energy of formation was undertaken in the temperature range from 875 to 1300 K using a solid-state electrochemical cell incorporating yttria-doped thoria (YDT) as the solid electrolyte and Fe + Fe1-delta O as the reference electrode. The cell can be presented as Pt, Mn + MnO/YDT/Fe + Fe1+delta O, Pt Since the metals Fe and Mn undergo phase transitions in the temperature range of measurement, the reversible emf of the cell is represented by the three linear segments. Combining the emf with the oxygen potential for the reference electrode, the standard Gibbs energy of formation of MnO from alpha-Mn and gaseous diatomic oxygen in the temperature range from 875 to 980 K is obtained as: Delta G(f)(o)/Jmol(-1)(+/- 250) = -385624 + 73.071T From 980 to 1300 K the Gibbs energy of formation of MnO from beta-Mn and oxygen gas is given by: Delta G(f)(o)/Jmol(-1)(+/- 250) = -387850 + 75.36T The new data are in excellent agreement with the earlier measurements of Alcock and Zador. Grundy et al. incorrectly analyzed the data of Alcock and Zador showing relatively large difference (+/- 5 kJ mol(-1)) in Gibbs energies of MnO from their two cells with Fe + Fe1-delta O and Ni + NiO as reference electrodes. Thermodynamic data for MnO is reassessed in the light of the new measurements. A table of refined thermodynamic data for MnO from 298.15 to 2000 K is presented.

Trends in the stability of ternary oxides: Systems M-Pb-O (M = Ca, Sr, Ba)

Recent experimental investigations of phase equilibria and thermodynamic properties of the systems M-Pb-O, where M = Ca, Sr or Ba, indicate a regular increase in thermodynamic stability of ternary oxides, MPbO3 and M2PbO4, with increasing basicity of the oxide of the alkaline-earth metal. Number of stable interoxide compounds at 1100 K in the systems M-Pb-O (M = Mg, Ca, Sr, Ba) increases in unit increments from Mg to Ba. In this paper, experimentally determined standard Gibbs energies of formation of M2PbO4 (M = Ca, Sr, Ba) and MPbO3 (M = Sr, Ba) from their component binary monoxides and oxygen gas are combined with an estimated value for CaPbO3 to delineate systematic trends in thermodynamic stability of the ternary oxides. The trends are interpreted using concepts of tolerance factor and acid-base interactions. All the ternary oxides in these systems contain lead in the tetravalent state. The small Pb4+ ions polarize the surrounding oxygen ions and cause the formation of oxyanions which are acidic in character. Hence, the higher oxidation state of lead is stabilized in the presence of basic oxides of alkaline-earth group. A schematic subsolidus temperature-composition phase diagram is presented for the system BaO-PbO-O-2 to illustrate the change in oxidation states in binary and ternary oxides with temperature.

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.

Modeling the solubilities of fatty acids in supercritical carbon dioxide

A thermodynamic model was developed for modeling the solubilities of fatty acids in supercritical carbon dioxide. The model combines the Peng-Robinson equation of state (EOS) with the two parameter van der Waal's mixing rules. The model is applied to predict the solubilities of various fatty acids. The two adjustable interaction parameters in the model are found to vary linearly with the chain length of the fatty acids. Thus this model can be used to predict the solubilities of various fatty acids in supercritical carbon dioxide. (C) 2003 Elsevier Science B.V. All rights reserved.

Thermodynamic properties of SmFeO3(S) and SM3R5O12(S)

The enthalpy increments and the standard molar Gibbs energy (G) of formation of SmFeO3(S) and SM3Fe5O12(s) have been measured using a Calvet micro-calorimeter and a solid oxide galvanic cell, respectively. A X-type transition, related to magnetic order-disorder transformation (antiferromagnetic to paramagnetic), is apparent from the heat capacity data at similar to673 K for SmFeO3(s) and at similar to560 K for Sm3Fe5O12(S). Enthalpy increment data for SmFeO3(s) and SM3Fe5O12(s), except in the vicinity of X-transition, can be represented by the following polynomial expressions: {H-m(0)(T) - H-m(0)(298.15 K){/J mol-(1)(+/-1.2%) = -54 532.8 + 147.4 . (T/K) + 1.2 . 10(-4) . (T/K)(2) +3.154 . 10(6) . (T/K)(-1); (298.15 less than or equal to T/K less than or equal to 1000) for SmFeO3(s), and {H-m(0)(T) - H-m(0)(298.15 K)}/J mol(-1) (+/-1.4%) = -192 763 + 554.7 . (T/K) + 2.0 . 10(-6) . (T/K)(2) + 8.161 . 10(6) - (T/K)(-1); (298.15 less than or equal to T/K less than or equal to 1000) for Sm3Fe5O12(s). The reversible emf of the solid-state electrochemical cells, (-)Pt/{SmFeO3(s) + Sm2O3(S) + Fe(s)) // YDT / CSZ // {Fe(s) + Fe0.95O(s)} / Pt(+) and (-)Pt/{Fe(s) + Fe0.95O(S)} // CSZ // {SmFeO3(s) + Sm3Fe5O12(s) + Fe3O4(s) / Pt(+), were measured in the temperature ranges of 1005-1259 K and 1030-1252 K, respectively. The standard molar G of formation of solid SmFeO3 and Sm3Fe5O12 calculated by the least squares regression analysis of the data obtained in the current study, and data for Fe0.95O and Sm2O3 from the literature, are given by: Delta(f)G(m)(0)(SmFeO3, s)/kj . mol(-1)(+/-2.0) = -1355.2 + 0.2643 . ; (1005 less than or equal to T/K less than or equal to 1570) and Delta(f)G(m)(0)(Sm3Fe5O12, s)/kj . mol(-1) (+/- 3.1) = -4891.0 + 1.0312 . (T/K); (1030 less than or equal to T/K less than or equal to 1252) The uncertainty estimates for Delta(f)G(m)(0) include the standard deviation in the emf and uncertainty in the data taken from the literature. Based on these thermodynamic data, the oxygen potential diagram for the system Sm-Fe-O was constructed at 1250 K.

Reactive Diffusion Between Vanadium and Silicon

Interdiffusion study is conducted in the V-Si system to determine integrated diffusion coefficients of the phases. Activation energy values are calculated from the experiments conducted at different temperatures. The average values are found to be 208, 240 and 141 kJ/mol, respectively, for the V(3)Si, V(5)Si(3) and VSi(2) phases. The low activation energy for the VSi(2) phase indicates very high concentration of defects or the significant contribution from the grain boundary diffusion. The error in calculation of diffusion parameters from a very thin phase layer in a multiphase diffusion couple is discussed. Further the data available in the literature in this system is compared and the problems in the indirect methodology followed previously to calculate the diffusion parameters are discussed.

Flux Partitioning of Species Approach in Binary Interdiffusion Process

Validation of the flux partitioning of species model has been illustrated. Various combinations of inequality expression for the fluxes of species A and B in two successively grown hypothetical intermetallic phases in the interdiffusion zone have been considered within the constraints of this concept. Furthermore, ratio of intrinsic diffusivities of the species A and B in those two phases has been correlated in four different cases. Moreover, complete and or partial validation or invalidation of this model with respect to both the species, has been proven theoretically and also discussed with the Co-Si system as an example.

Potentiometric determination of the Gibbs free energy of formation of cadmium and magnesium chromites

The standard Gibbs free energy of formation of magnesium and cadmiumchromites have been determined by potentiometric measurements on reversiblesolid-state electrochemical cells [dformula (Au-5%Cd, , Au-5%Cd; Pt, + , CaO-ZrO[sub 2], + ,Pt; CdO, , CdCr[sub 2]O[sub 4] + Cr[sub 2]O[sub 3])] in the temperature range 500°–730°C, and [dformula Pt, Cr + Cr[sub 2]O[sub 3]/Y[sub 2]O[sub 3]-ThO[sub 2]/Cr + MgCr[sub 2]O[sub 4] + MgO, Pt] in the temperature range 800°–1200°C. The temperature dependence of the freeenergies of formation of the ternary compounds can be represented by theequations [dformula CdO(r.s.) + Cr[sub 2]O[sub 3](cor) --> CdCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 42,260 + 7.53T ([plus-minus]400) J] and [dformula MgO(r.s.) + Cr[sub 2]O[sub 3](cor) --> MgCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 45,200 + 5.36T ([plus-minus]400) J] The entropies of formation of these spinels are discussed in terms of cationdisorder and extent of reduction of Cr3+ ions to Cr2+ ions. Thermodynamicdata on the chromates of cadmium and magnesium are derived by combiningthe results obtained in this study with information available in the literatureon high temperature, high pressure phase equilibria in the systems CdO-Cr2O3-O2 and MgO-Cr2O3-O2.

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.

A new semi-empirical model for correlating the solubilities of solids in supercritical carbon dioxide with cosolvents

The equilibrium solubilities of the solids in supercritical carbon dioxide (SCCO(2)) are considerably enhanced in the presence of cosolvents. The solubilities of m-dinitrobenzene at 308 and 318 K over a pressure range of 9.5-14.5 MPa in the presence of 1.13-2.17 mol% methanol as cosolvent were determined. The average increase in the solubilities in the presence of methanol compared to that obtained in the absence of methanol was around 35%. A new semi-empirical equation in terms of temperature, pressure, density of SCCO(2) and cosolvent composition comprising of 7 adjustable parameters was developed. The proposed model was used to correlate the solubility of the solids in SCCO(2) for the 44 systems available in the literature along with current data. The average absolute relative deviation of the experimental data from the model equation was 3.58%, which is better than the existing models. (C) 2011 Elsevier B.V. All rights reserved.

Thermodynamics of SmMnO3 and SmMn2O5 phases determined by the E.M.F. method

Streszczenie angielskie: Using solid oxide galvanic cells of the type: MnO + Sm2O3 + SmMnO3 / O-2/ Ni + NiO and Mn3O4 + SmMnO3 + SmMn2O5 / O-2 / air the equilibrium oxygen pressure for three-phase equilibria described by the following reactions of formation of ternary phases: MnO + 1/2Sm2O3 + 1/4O2 = SmMnO3 1/3Mn3O4 + SmMnO3 + 1/3O2 = SmMn2O5 was determined in the temperature range from 1173 to 1450 K. From the obtained experimental data the corresponding Gibbs free energy change for above reactions of phases formation was derived: ΔG0f,SmMnO3(+/ - 250J) = -131321(+/ - 2000) + 48.02(+/ - 0:35)T / K ΔG0f,SmMn2O5(+/ - 2000 J) = -107085(+/ - 2200) + 69.74(+/ - 1:70)T / K Using obtained results and available literature data, thermodynamic data tables for the two ternary phases have been compiled from 298.15 to 1400 K. Streszczenie polskie: W pracy przedstawiono wyniki badań dotyczące własności termodynamicznych manganinów samaru, wyznaczone metodą pomiaru SEM ogniw ze stałym elektrolitem: MnO + Sm2O3 + SmMnO3 / O-2/ Ni + NiO ogniwo I Mn3O4 + SmMnO3 + SmMn2O5 / O-2 / powietrze ogniwo II oraz określono równowagowe ciśnienie parcjalne tlenu dla reakcji tworzenia SmMnO3 i SmMn2O5 w zakresie temperatur 1173�1450 K: MnO + 1/2Sm2O3 + 1/4O2 = SmMnO3 1/3Mn3O4 + SmMnO3 + 1/3O2 = SmMn2O5 Z tych danych doświadczalnych wyznaczono zależności temperaturowe energii swobodnych tworzenia powyższych manganinów samaru: ΔG0f,SmMnO3(+/ - 250J) = -131321(+/ - 2000) + 48.02(+/ - 0:35)T / K ΔG0f,SmMn2O5(+/ - 2000 J) = -107085(+/ - 2200) + 69.74(+/ - 1:70)T / K W tablicach I i II zamieszczono dane termodynamiczne dla dwóch potrójnych faz otrzymane poprzez kompilacje własnych danych doświadczalnych z danymi literaturowymi.

Peraluminous sapphirine-cordierite pods in Mg-rich orthopyroxene granulite from southern India: Implications for lower crustal processes

Sapphirine-cordierite intergrowths occur as pods within garnet-absent, high-Mg orthopyroxene-granulite xenoliths in the Kambam valley, Madurai Block, southern India. Whereas the cores of the pods are composed of sapphirine (X-Mg = 0.871-0.897) - cordierite (X-Mg = 0.892-0.931) intergrowth along with rutile, zircon and monazite, the rims are characterized by cordierite, apatite, plagioclase, K-feldspar, quartz and minor calcite. The surrounding matrix comprises orthopyroxene (maximum Al2O3 4.1 wt.%, X-Mg 0.848-0.850), plagioclase, biotite and quartz, similar to the assemblage in the surrounding charnockites. Sapphirine in the Kambam rocks is characterized by high Al contents with an end-member composition in the range of 7:9:3 and 3:5:1. The occurrence of peraluminous sapphirine in association with cordierite and in the absence of phases such as sillimanite and garnet is distinct from ultrahigh-temperature assemblages in other localities within the Madurai Block. The peraluminous composition of the pods suggests that these domains could represent cryptic pathways through which aluminous melts migrated. The reaction of such peraluminous melts with Mg-rich orthopyroxene in the host granulite at temperatures of 1025 degrees C and pressures around 8 kbar as computed from phase equilibria modeling followed by an isobaric cooling is inferred to have generated the sapphirine-cordierite pods. The unusual high-Mg orthopyroxene granulite suggests interaction of supracrustal rocks with mafic magmas, which probably acted as the heat source for the partial melting of lower crust and UHT metamorphism.

Thermodynamics of Congruent Oxidation

Congruent oxidation occurs when an alloy oxidizes at constant oxygen chemical potential and temperature to an oxide in which the ratio of metallic components is the same as in the alloy. In alloys that undergo congruent oxidation concentration gradients near the surface are minimized. In this work thermodynamic conditions for congruent oxidation of binary and ternary alloys are formulated using the regular solution model to describe thermodynamic mixing properties. The conditions under which congruent oxidation can occur are identified. Congruent oxidation of a binary alloy X-Y will occur only if difference in oxygen potential for the oxidation of the two pure metals is less than twice the difference in regular solution parameters for the oxide and alloy phases (Omega(O)-Omega(A)). In the case of ternary alloys, congruency requirements for both two-phase and three-phase equilibria are discussed. Since the conditions for congruent oxidation of ternary alloy X-Y-Z depends on many parameters, the effect of systematic variation of the binary sets of regular solution parameters on the congruent composition is explored by numerical solution of the governing equations.

Growth of Phases and Diffusion of Components in the W-Pt System

Growth kinetics, phase boundary compositions, interdiffusion coefficients and the relative mobilities of the components are determined in the W-Pt system. The measured phase boundary compositions for the gamma phase are found to be different from the reported phase diagram. The interdiffusion coefficient and the activation energy decrease in the Pt(W) solid solution with increasing W content. An estimation of the parabolic growth constants and average interdiffusion coefficients in the gamma phase indicates that the diffusion process should be explained based on the estimation of diffusion parameters, which otherwise could lead to a wrong conclusion. The estimation of the relative mobilities of the components in the gamma phase indicates that Pt has a much higher diffusion rate than W. This is explained with the help of the crystal structure and the possible point defects present on different sublattices.