Calculation of a Binary Solidus from the Liquidus and Minimal Additional Thermodynamic Information

Abstract

In a binary system, if the liquidus has been measured, if the thermodynamic properties of the liquid phase are known, and if the entropy of the solid phase is known or may be assumed to be ideal, then an exact thermodynamic calculation of the solidus as well as of the enthalpy of the solid can be made. The equations are derived and sample calculations are made for several systems. General relationships between binary phase diagrams and the thermodynamic properties of the phases are then developed. It is shown that a knowledge of any four of the following six quantities is sufficient to permit the other two to be calculated exactly: the solidus, the liquidus, enthalpy of the liquid, entropy of the liquid, enthalpy of the solid, entropy of the solid.In einem binaren System ist eine exakte thermodynamische Berechnung der Soliduskurve und der Enthalpie des Festkorpers moglich, wenn die Liquiduskurve gemessen wurde, wenn die thermodynamischen Eigenschaften der fliissigen Phase bekannt sind, und wenn die Entropie der festen Phase bekannt ist oder als ideal angenommen werden kann. Es werden die Gleichungen hergeleitet und fur einige Beispiele Berechnungeu durchgefiihrt. Danach werden generelle Beziehungen zwischen binaren Phasendiagrammen und den thermodynamischen Eigenschaften der Phasen entwickelt. Es wird gezeigt, daB die Kenntnis von jeweils vier der folgenden sechs GroBen ausreicht, um die beiden restlichen genau auszurechnen: Die Soliduskurve, die Liquiduskurve, die Enthalpie der Fliissigkeit, die Entropie der Flussigkeit, die Enthalpie des Festkorpers, die Entropie des Festkorpers.

Critical Evaluation and Thermodynamic Optimization of the Binary Systems in the Mg-Ce-Mn-Y System

“…Since it has been reported that Mn does not dissolve in Y(HCP), [16] these two measured points are almost certainly in error because they violate the limiting liquidus slope rule. [21] Figure 4 shows the enthalpy of formation of intermetallic compounds. Calorimetrically determined data by Pisch et al [19] are compared with calculations from the present optimization and from those of Flandorfer et al [16] and Gröbner et al [17] As seen in the figure, the measured enthalpy of formation of Mn 2 Y is higher than the average of Section I: Basic and Applied Research Basic and Applied Research: Section I the enthalpies of Mn 23 Y 6 and Y(HCP).…”

Critical Systematic Evaluation and Thermodynamic Optimization of the Mn-RE System (RE = Tb, Dy, Ho, Er, Tm and Lu) with Key Experiments for the Mn-Dy System

“…The liquidus at Mn-rich side in the phase diagram suggested by Kirchmayr and Lugscheider [22] are also unlikely to happen from the viewpoint of the limiting slope rule. [47] The enthalpy data of Ivanov et al [45] were not available at that time. Consequently, the calculated integral and partial enthalpies of mixing at 1723 K from Wang et al [26] are notably different from the data of Ivanov et al [45] as shown in Fig.…”

“…It should be also noted that the experimental data [21] in the liquidus of Mn-rich side is less acceptable from the viewpoint of the limiting slope rule. [47] The calculated invariant reactions are tabulated in Table 4 in comparison to the experimental data.…”