Conformal Ionic Mixtures

Blander, M.; Yosim, S. J.

doi:10.1063/1.1734071

Cited by 89 publications

(21 citation statements)

References 9 publications

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“…Hence, eq. [22] (or eq. [24] or [25] with the one ternary correction term in each case) can be used to calculate the Gibbs energy of the ternary solution.…”

Section: Discussionmentioning

confidence: 99%

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Phase diagram measurements and thermodynamic analysis of the PbCl₂–NaCl, PbCl₂–KCl, and PbCl₂–KCl–NaCl systems

Gabriel¹,

Pelton²

1985

Can. J. Chem.

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. Can. J. Chem. 63, 3276 (1985). The phase diagrams of the PbCI2-NaCI and PbC12-KC1 systems have been measured by the cooling curve technique. In addition, a number of measurements at compositions in the ternary system PbCIZ-KC1-NaCI have been made. The binary data have been analysed along with other available thermodynamic data for the binary systems in order to obtain mathematical expressions for the binary thermodynamic properties. Various estimation procedures were then used to calculate the Gibbs energy of the ternary liquid from the binary expressions, and the ternary phase diagram calculated therefrom was compared to the experimental ternary points. In the case of the Conformal lonic Solution equation, agreement was within 3°C at all measured points. In the case of two "geometric" estimation techniques, the Kohler and Toop equations, agreement was within 10°C but could be brought to within 3°C by the addition of only one small adjustable ternary correction term. The technique of coupled thermodynamic/phase diagram analysis permits a large reduction in the amount of experimental work necessary to measure the ternary diagram. In addition, the ternary thermodynamic expressions developed can be used to calculate all thermodynamic properties of the ternary liquid.ARMAND GABRIEL et ARTHUR D. PELTON. Can. J. Chem. 63, 3276 (1985). Faisant appel a la technique de la courbe de refroidissement, on a mesure les diagrammes de phase des systkmes PbC12-NaCI et PbC12-KCI. De plus, on a fait un certain nombre de mesures a des compositions comprises dans le systkme ternaire PbC12-KC1-NaCI. On a analyse les donnees binaires de concert avec d'autres donnies thermodynamiques disponibles pour les systkmes binaires dans le but d'obtenir des expressions mathtmatiques pour les propriCtCs thermodynamiques binaires. On a utilisC diverses methodes d'Cvaluation pour calculer 1'Cnergie de Gibbs du liquide ternaire a partir d'expressions binaires; on a compare les points ternaires expkrimentaux avec le diagramme de phase ternaire calculC en utilisant la mCthode dCcrite plus haut. Dans le cas de I'equation de Solution lonique Conformale, la correspondance se situe ? i moins de 3°C pour chacun des points mesurks. Dans les cas des deux techniques "gtomCtriques" d'evaluation, les equations de Kohler ou de Toop, la correspondance est meilleure que 10°C; toutefois, elle peut Ctre ramente a moins de 3°C par I'addition d'un seul petit terme ajustable ternaire de correction. La technique de I'analyse des diagrammes de phase couplCs a la thermodynamique permet de reduire considtrablement la quantite de travail expCrimental ntcessaire pour mesurer un diagramme ternaire. De plus, les expressions thermodynamiques ternaires dCvelopp6es peuvent Ctre utiliskes pour calculer toutes les propriCtCs therrnodynamiques du liquide ternaire.[Traduit par le journal]

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“…Hence, eq. [22] (or eq. [24] or [25] with the one ternary correction term in each case) can be used to calculate the Gibbs energy of the ternary solution.…”

Section: Discussionmentioning

confidence: 99%

“…Equations [22], [23] give G E in Jlequivalent. To convert to J/mol in the PbC1,-KC1-NaCl system, multiply by (2Xpbcl2 + XKCI + X N~C I ) .…”

Section: The Conformal Ionic Solution (Cis) Theorymentioning

confidence: 99%

Phase diagram measurements and thermodynamic analysis of the PbCl₂–NaCl, PbCl₂–KCl, and PbCl₂–KCl–NaCl systems

Gabriel¹,

Pelton²

1985

Can. J. Chem.

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“…24) Sundman et al 25) proposed that the effect of the SRO due to pair probabilities can be approximated by introducing reciprocal parameters into the CALPHAD method and reported a thermodynamic assessment of the Au-Cu system. This approximation is based on the quasichemical formalism for the ionic liquid phase, 26,27) and the effect of the SRO for the two-sublattice CEF is described as ........... (11) where z represents the coordination number and R is the gas constant (0) (ϭs 0 /T), was involved in the Gibbs energy as listed in Table 3, which represents that its ordering contribution is described in the following formula. Figure 8 shows the calculated and experimentally determined thermodynamic properties related to the chemical potential of Fe in f.c.c alloys at 1 200°C. 28) The result of the calculation is in good agreement with the experimental data.…”

Section: Approximation Of the Gibbs Energy Of Sromentioning

confidence: 99%

Phase Equilibria and Thermodynamic Evaluation Approximating Short-range Ordering Energy in the Fe–Rh Binary System

et al. 2009

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Phase equilibria between the a (A2), aЈ (B2) and g (A1) phases in the Fe-Rh binary system were investigated using electron probe micro-analysis (EPMA) and differential scanning calorimetry (DSC) techniques. The A2/B2 order-disorder transformation temperature was also examined by a transmission electron microscope (TEM) observations and high-temperature X-ray diffraction (HTXRD). It was confirmed that while the transition temperature from the a (A2) phase to the g (A1) phase decreases with increasing Rh content up to about 20 at% Rh, the b.c.c. region is stabilized by further Rh addition in the composition range between about 20 and 50 at% Rh, and then again the stability of b.c.c. phase decreases in the composition region over 50 at% Rh. It was also shown by TEM observation and HTXRD examination that the compositions of the phase boundary of the A2/B2 ordering at 500°C and 600°C were determined to be 16.5 and 19.1 at% Rh, respectively. On the basis of those experimental results, a thermodynamic analysis was carried out. The results of the thermodynamic calculation suggest that the anomalous behavior of the stability of the b.c.c. phase is caused by the A2/B2 ordering.KEY WORDS: CALPHAD; order-disorder transition; short-range ordering; magnetic ordering; phase stability. terials were Fe (99.9 mass%) and Rh (99.97 mass%), and the composition range of the prepared alloys was Fe-(10-55)at%Rh as listed in Table 1. Each as-cast specimen was sealed in an evacuated quartz capsule, back-filled with argon, and annealed at temperatures between 650°C and 1 350°C for duration of between 24 h and 4 380 h. After the heat-treatment for equilibration, the specimens were quenched into ice water. Results of chemical analysis of ascast specimens are listed in Table 1. After microstructure examination by an optical microscope, equilibrium compositions were determined by electron probe microanalysis (EPMA: JEOL JXA-8100) using a standard calibration method. The transition temperature of some alloys at about 20 at% Rh was also determined by differential scanning calorimetry (DSC: SEIKO DSC-320) at heating rate of 3°C/min.In order to determine the A2/B2 ordering temperature, DSC measurement, transmission electron microscopic (TEM: JEOL JEM-2000EX II) examination and high temperature X-ray diffraction (HTXRD: Phillips X'part) were performed. The specimens for the TEM observation were solution-treated at 1 300°C for 1 h, cooled down to 500°C or 600°C, and aged at those temperatures for 72 h. The centers of disks cut from the as-aged specimens were processed into thin foils by dimple-grinding and ionmilling. TEM examination at room temperature was carried out on the thin foils. Powdered specimens were annealed at 1 300°C and analyzed by HTXRD at 500°C and 600°C. Experimental Results 3.1.Phase Equilibria between the a a (A2), a a (B2), g g (A1) Phases A typical example of the microstructure of the aЈ (B2)ϩg (A1) two-phase alloy annealed at 1 200°C for 96 h is shown in Fig. 2. It can be seen that the size of the precipitated aЈ (B2) phase i...

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“…(where q,, q,, q,, qy are the absolute charges on the ions), and the edges of the square represent compositions in the binary subsystems. The extended CIS theory (19,20) for reciprocal ternary systems has been applied with success (6,9, 2 1-23) to calculate the thermodynamic properties of a large number of ternary reciprocal systems from the properties of the binary subsystems. The excess Gibbs energy per equivalent of solution at a point P (see Fig.…”

Section: Reciprocal Ternariesmentioning

confidence: 99%

“…[13] is composition-independent. It has been shown (19,20) that, for liquid salts, to a first approximation A is given by:…”

Section: Reciprocal Ternariesmentioning

confidence: 99%

Calculation of phase diagrams and thermodynamic properties of 14 additive and reciprocal ternary systems containing Li₂CO₃, Na₂CO₃, K₂CO₃, Li₂SO₄, Na₂SO₄, K₂SO₄, LiOH, NaOH, and KOH

Pelton¹,

Bale²,

Lin³

1984

Can. J. Chem.

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, 457 (1984). Phase diagrams and thermodynamic properties of five additive molten salt ternary systems and nine reciprocal molten salt ternary systems containing the ions Li', Na', K'/CO;-, SO:-, OH-are calculated from the thermodynamic properties of their binary subsystems which were obtained previously by a critical assessment of the thermodynamic data and the phase diagrams in these binary systems. Thermodynamic properties of ternary liquid phases are estimated from the binary properties by means of the Conformal Ionic Solution Theory. The ternary phase diagrams are then calculated from these thermodynamic properties by means of computer programs designed for the purpose. It is found that a ternary phase diagram can generally be calculated in this way with a maximum error about twice that of the maximum error in the binary phase diagrams upon which the calculations are based. If, in addition, some reliable ternary phase diagram measurements are available, these can b e used to obtain small ternary correction terms. In this way, ternary phase diagram measurements can be smoothed and the isotherms drawn in a thermodynamically correct way. The thermodynamic approach permits experimental data to be critically assessed in the light of thermodynamic principles and accepted solution models. A critical assessment of error limits on all the calculated ternary diagrams is made, and suggestions as to which composition regions merit further experimental study are given.A. D. PELTON, C. W. BALE et P. L. LIN. Can. J. Chem. 62, 457 (1984) On a calculC les diagrammes de phase et les propriCtCs thermodynamiques de 5 systkmes ternaires additifs de sels fondus et de 9 systkmes ternaires rkciproques de sels fondus contenant des ions Li', Na', K'/co:-, SO:-, OH-; ces calculs ont Ct C effectuks a partir des propriCtCs thermodynamiques de leurs sous-systkmes binaires que l'on a obtenues antkrieurement par un Cvaluation critlque des donnCes thermodynamiques et des diagrammes de phase de ces systkmes binaires. On a CvaluC les propriCtCs thermodynamiques des phases liquides ternaires en faisant appel a la thCorie des solutions ioniques conformales. On calcule alors les dlagrammes de phases ternaires i partir de ces propriCtCs thermodynamiques au moyen de programmes d'ordinateurs rCalisCs dans ce but. On a trouvC qu'un diagramme de phase ternaire peut gCnCralement &re calculC de cette f a~o n avec une erreur maximale qui n'est que le double de l'erreur maximale obtenue avec les diagrammes de phases binaires sur lesquels reposent ces calculs. De plus, si on dispose de mesures fiables pour les diagrammes de phases ternaires, on peut alors utiliser ces mesures pour dCduire des petits termes de correction ternaires. De cette f a~o n , on peut raffiner les mesures de diagrammes de phases ternaires et tracer les isothermes d'une manikre qui est thermodynamlquement correcte. L'approche thermodynamique permet dlCvaluer les donnCes expCrimentales d'une f a~o n critique a la lumikre de principes thermodynamiques et de modkles acceptables pour ...

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Conformal Ionic Mixtures

Cited by 89 publications

References 9 publications

Phase diagram measurements and thermodynamic analysis of the PbCl₂–NaCl, PbCl₂–KCl, and PbCl₂–KCl–NaCl systems

Phase diagram measurements and thermodynamic analysis of the PbCl₂–NaCl, PbCl₂–KCl, and PbCl₂–KCl–NaCl systems

Phase Equilibria and Thermodynamic Evaluation Approximating Short-range Ordering Energy in the Fe–Rh Binary System

Calculation of phase diagrams and thermodynamic properties of 14 additive and reciprocal ternary systems containing Li₂CO₃, Na₂CO₃, K₂CO₃, Li₂SO₄, Na₂SO₄, K₂SO₄, LiOH, NaOH, and KOH

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Conformal Ionic Mixtures

Cited by 89 publications

References 9 publications

Phase diagram measurements and thermodynamic analysis of the PbCl2–NaCl, PbCl2–KCl, and PbCl2–KCl–NaCl systems

Phase diagram measurements and thermodynamic analysis of the PbCl2–NaCl, PbCl2–KCl, and PbCl2–KCl–NaCl systems

Phase Equilibria and Thermodynamic Evaluation Approximating Short-range Ordering Energy in the Fe&ndash;Rh Binary System

Calculation of phase diagrams and thermodynamic properties of 14 additive and reciprocal ternary systems containing Li2CO3, Na2CO3, K2CO3, Li2SO4, Na2SO4, K2SO4, LiOH, NaOH, and KOH

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Phase diagram measurements and thermodynamic analysis of the PbCl₂–NaCl, PbCl₂–KCl, and PbCl₂–KCl–NaCl systems

Phase diagram measurements and thermodynamic analysis of the PbCl₂–NaCl, PbCl₂–KCl, and PbCl₂–KCl–NaCl systems

Phase Equilibria and Thermodynamic Evaluation Approximating Short-range Ordering Energy in the Fe–Rh Binary System

Calculation of phase diagrams and thermodynamic properties of 14 additive and reciprocal ternary systems containing Li₂CO₃, Na₂CO₃, K₂CO₃, Li₂SO₄, Na₂SO₄, K₂SO₄, LiOH, NaOH, and KOH