Effect of the sixth period elements on the melting and transformation temperatures of praseodymium: Part II. Thermodynam
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GSCHNEIDNER, J R . AND R. B. G R I F F I N
A thermodynamic analysis of the praseodymium-rich alloys containing Os, Ir, Pt, Au, Hg, Tl, Pb, and Bi indicated that most of the solutes dissolved in praseodymium follow ideal solution theory over a limited range of temperatures up to 40° to 135°C below the melting point of praseodymium (or concentrations out to 3 to 8 at. pct solute). The activity coefficients, activities, and excess partial free energies were calculated for liquid praseodymium at its melting point and for ~-Pr at its ~ to ~ transformation temperature. The so-called Q parameter has also been determined for these praseodymium systems, and it was found to exhibit the usual periodic dependence on the solute metal. As a result of these analyses a method has been developedwhich makes it possible to calculate phase boundaries for undetermined systems. This technique is shownto be especially valuable in calculating unknown phase boundaries for lantlmnide-rich alloys, but for other metal solvents this method will probably be of a lesser utility.
IN the previous paperI we have
presented the experimental results of our investigation of the praseodymium-rich phase diagrams with the sixth period elements (Cs, Ba, Hf, andRe throughBi). For the first time rare earth-metal phase diagrams have been established well enough to test whether or not they obey ideal and regular solution theories. Because the solutes Cs, Ba, Hf, and Re had little effect on the melting or transformation temperature of praseodymium, and because accurate phase boundaries were not determined, the praseodymium phase diagrams with these solutes will not be considered in this paper. The precisely determined praseodymiumrich end of the phase diagrams Pr-Os, -Ir, -Pt, -Au, -Hg, -Tl, -Pb, and -Bi were analyzed by several standard thermodynamic techniques to obtain a better understanding of the alloying behavior of the rare earth metals, especially praseodymium. THEORY
F r o m b a s i c t h e r m o d y n a m i c p r i n c i p l e s it is p o s s i b l e to d e r i v e a n e q u a t i o n w h i c h d e s c r i b e s the t e m p e r a t u r e d e p e n d e n c e of the liquidus, X ~ , a n d s o l i d u s , X ~ , o r the t w o s o l v u s l i n e s n e a r the m e l t i n g o r t r a n s f o r m a t i o n point of the solvent2 AHI(T_T1)+RT TI
In
- ~x 2
=RT
- X2 _
~,I i n --~ y1
=
Aff-XS,2 = j
AF--~S,1 [1]
In E q . [1] the s u b s c r i p t s 1 a n d 2 r e f e r t o s o l v e n t (praseodymium) and solute, respectively; the s u p e r s c r i p t s r e f e r to t h e two p h a s e s i n v o l v e d , i . e . , 1 b e i n g t h e high t e m p e r a t u r e p h a s e a n d 2 b e i n g t h e low t e m p e r a t u r e p h a s e of t h e s o l v e n t ; a n d A H I i s t h e e n t h a l p y K. A. GSCHNEIDNER, Jr., is Professor, Department of Metallurgy and Senior Metallurgist, Institute for Atomic Research, Iowa State University, Ames, Iowa. R. B. GRIFFIN, formerly Graduate Assistant, Institute for Atomic Research, Iowa State University, is now Researc
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