The standard free energy of formation of nonstoichiometric niobium sulfides
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HODOUIN
The c h e m i c a l p o t e n t i a l of Nb was m e a s u r e d in the t h r e e - p h a s e e q u i l i b r i a : Nb3S4-2sNbz~xS2NbO 2 and 2sNbl.xS2-3sNb,~xS2-Nb2Os, using a s o l i d oxide galvanic cell. The t h e r m o c h e m i c a l p r o p e r t i e s of 2 s N b , § 2 a r e d e s c r i b e d by the " s u r r o u n d e d a t o m " t h e o r y applied to two types of i n t e r a c t i v e c r y s t a l l i n e d e f e c t s . S i m u l t a n e o u s use of EMF v a l u e s , sulfur p a r t i a l p r e s s u r e data, and m o d e l i n g l e a d s to the s t a n d a r d f r e e e n e r g i e s of f o r m a t i o n of Nb3S4, 2sNbz§ 3sNbz§ 2 at 1000~ f o r all v a l u e s < x < .
I ~ E C E N T w o r k has f a i r l y w e l l e l u c i d a t e d the c r y s t a l l o g r a p h i c s t r u c t u r e s of the v a r i o u s n i o b i u m sulfide p h a s e s , z which in m o s t c a s e s p r e s e n t a r a t h e r l a r g e c o m p o s i t i o n r a n g e . H o w e v e r , only a l i m i t e d knowledge of the b i n a r y d i a g r a m e x i s t s , and s o m e d i s c r e p a n c i e s for the phase l i m i t s can be found b e t w e e n v a r i o u s a u t h o r s . In a p r e v i o u s p a p e r , " an i s o t h e r m a l s e c t i o n of p a r t of the t e r n a r y N b - O - S p h a s e d i a g r a m , l i m i t e d to the r a n g e NbO-NbzO s on the N b - O side and NbS-NbS2 on the Nb-S side and v a l i d at 1000~ was p r o p o s e d . This d i a g r a m is r e p r o d u c e d in Fig. 1. In the s a m e p a p e r , a r e a l i s t i c r a n g e f o r the s t a n d a r d f r e e e n e r g y of f o r m a t i o n of the v a r i o u s s u l f i d e s was e s t i m a t e d u s ing the phase d i a g r a m , the known f r e e e n e r g y data f o r the oxides, and the data of L a r s o n and E l l i o t t . s In the p r e s e n t work, an e l e c t r o m o t i v e f o r c e c e l l with a m e t a l - m e t a l oxide as oxygen p o t e n t i a l r e f e r e n c e , and a s o l i d - s t a t e e l e c t r o l y t e w e r e used to study the t h r e e phase e q u i l i b r i a b e t w e e n two m e t a l s u l f i d e s and an o x Ide. The c e l l was of the following type: Pt
Three-phase equilibrium NbxS , NbyS, N b O 2 m
Solid s t a t e electrolyte O 2-
Metal-metal oxide reference
Pt.
[A] The r e v e r s i b l e c h e m i c a l r e a c t i o n which takes p l a c e in t h i s c e l l is a t r a n s f e r of oxygen v i a the e l e c t r o l y t e , i . e . an oxidation or a r e d u c t i o n of the l e f t e l e c t r o d e d e pending on the n a t u r e of the r e f e r e n c e . Using the N e r n s t equation, the c h e m i c a l p o t e n t i a l of 02 in this e l e c t r o d e can be computed as: 4 tt
p.02
=
s
~0 z
--
4FE
[1]*
*Thesymbolg stands for the chemicalpotentialreferred to the usual standard states.
is t
/.tNb = AG ~ -- m/.tO2 + 4 x n F E
[3]
w h e r e AG~ is the s t a n d a r d f r e e e n e r g y of f o r m a t i o n of NbOzm. T h e s e e q u a t i o n s a r e f a i r l y g e n e r
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