Application of emf-method to determination of thermodynamic properties of slag systems

Abstract

Applications of EMF-method to thermodynamic investigation of slag systems are briefly surveyed. The various types of cell-schemes used and comments on these are presented.

Résumé

Les applications de la méthode de la force électromotrice à la recherche thermodynamique des systémes de scories sont rapidement présentées. Différents types de cellules sont présentés et commentés.     

Representation of thermodynamic properties of multi-component systems using interaction parameters

Integral excess free energy of a multi-component – ternary 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 parameters. The partial thermodynamic property of component 1 derived by the use of logarithmic functions together with a geometric progression is presented. The equation is found to be capable of interpreting thermodynamic data over a wide compositional range of the ternary system and is independent of compositional paths. An alternative approach for the determination of generalised relations between interaction parameters to that of Lupis and Elliott has been developed.     

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.     

Representation of excess thermodynamic properties of ternary systems using interaction parameters

A ternary function has been developed based on the Maclaurin infinite series, which is expressed in the neighborhood of each of the pure components of the system. Each of the series is subjected to various boundary conditions. The ternary function is based on the summation of these series. In the process of converting the terms of these infinite series to the corresponding infinite dilution constants and interaction parameters, the ternary function also distinguishes between the binary and ternary interaction parameters of the system. The truncation of the infinite series pertaining to the binary and ternary interaction terms is adjusted by a suitable technique which is described in the text. The function is thermodynamically consistent and capable of interpreting properties of the ternary system.     

An investigation of high temperature thermodynamic properties in the Pt-Zr and Pt-Hf systems

High-temperature thermodynamic properties of Pt−Zr alloys containing 2 to 25 at. pct Zr and Pt−Hf alloys containing 20 to 25 at. pct Hf have been measured over the temperature range 1100 to 1400 K by a galvanic cell technique using a thoria-based electrolyte. Activities of Zr and Hf show large negative deviations from Raoult's Law; at 1300 K and 23 at. pct Zr of Hf, for instance,a _Zr=6.5×10⁻¹⁶ anda _Hf=7.9×10⁻¹⁷. Correlation of emf results with X-ray phase data enables calculation of standard free energies of formation of the intermetallic compounds ZrPt₅, ZrPt₃, and HfPt₃. At 1300 K ΔG _f ⁰ (ZrPt₅) =−92,680 cal/mole; ΔG _f ⁰ (ZrPt₃)=−91,740 cal/mole; and ΔG _f ⁰ (HfPt₃)=−97,350 cal/mole. The high stabilities of phases in the Pt−Ti, Pt−Zr, and Pt−Hf systems verify the predictions of the Engel-Brewer correlation. The large negative entropies of formation of TiPt₃, ZrPt₃ are discussed. Applications including side reactions in fuel cells and thermocouple systems are mentioned. P. J. MESCHTER, formerly a Graduate Student at the University of Pennsylvania This paper is based upon a dissertation submitted by P. J. Meschter in partial fulfillment of the requirements of the degree of Doctor of Philosophy at the University of Pennsylvania.