Communications Discussion of "Concerning the Sulfidation of Pure Iron in H /H 2 S Gas Mixtures "* W. L. WORRELL

AND

E. T. TURKDOGAN

N a r e c e n t t e c h n i c a l note Zelouf and Simkovich p o s t u l a t e d that there is sufficient solubility of hydrogen a s an ionized i n t e r s t i t i a l in p y r r h o t i t e (FeS) r e s u l t i n g in an i n c r e a s e of the cation v a c a n c y and e l e c t r o n hole c o n c e n t r a t i o n . F r o m a d e r i v e d rate equation, they concluded that at a p a r t i c u l a r s u l f u r activity in the gas phase fixed by a PH2S/PH2 r a t i o , the p a r a b o l i c rate constant kp for the f o r m a t i o n of a FeS l a y e r on i r o n i n c r e a s e s with i n c r e a s i n g pH z in the gas. They j u s t i f i e d t h e i r postulate by using some of the e x p e r i m e n t a l r e s u l t s of W o r r e l l arid T u r k d o g a n 1~ P a r t II. U n f o r t u n a t e l y , Zelouf and Simkovich m i s i n t e r p r e t e d our e x p e r i m e n t a l data which were i n t e n d e d to d e m o n s t r a t e , as stated c l e a r l y in the text, the slow approach to g a s - s u l f i d e s u r f a c e e q u i l i b r i u m d u r i n g the sulfidation of i r o n in H2S-H2-Ar m i x t u r e s . T h e i r und e r s t a n d i n g of our data and the i n t e r p r e t a t i o n t h e r e o f a r e c o m p l e t e l y e r r o n e o u s . The p u r p o s e of this c o r r e s p o n d e n c e is to c l a r i f y this m i s u n d e r s t a n d i n g . Our work on the F e - S s y s t e m was published s i m u l t a n e o u s l y in two c o n s e c u t i v e p a r t s . In P a r t I, ~' to which Zelouf and Simkovich make no r e f e r e n c e , the t h e r m o d y n a m i c s and the p a r a b o l i c rate of sulfidation were d i s c u s s e d . By m e a s u r i n g the t h i c k n e s s of the p y r r h o t i t e (FeS) l a y e r f o r m e d , it was shown that the p a r a b o l i c rate law was obeyed only a f t e r the i n i t i a l r e a c t i o n time of a few h o u r s or days, depending on gas composition and t e m p e r a t u r e , i n d i c a t i n g a slow approach to g a s - s u l f i d e e q u i l i b r i u m . This i m p o r t a n t point was f u r t h e r d e m o n s t r a t e d by the r e s u l t s in Fig. 1 of P a r t II, in which the s q u a r e of the weight gain per unit a r e a was plotted a g a i n s t t i m e for gas m i x t u r e s having pH2S/PH2 = 1.0 with 0, 25, 50, and 67 pet Ar for 800~ These plots gave S - s h a p e d c u r v e s ; the s l o p e s for the " p s e u d o l i n e a r " p a r t of the S - s h a p e d c u r v e s i n c r e a s e d with i n c r e a s i n g p a r t i a l p r e s s u r e of hydrogen, or hydrogen sulfide. Even in the a b s e n c e of a r g o n dilution, the true p a r a b o l i c r a t e ' o f sulfidation was not a p p r o a c h e d before a l l the i r o n , 0.5 m m thick s t r i p , was c o n v e r t e d to p y r r h o t i t e . It is i m p o r t a n t to r e c a l l the data given in P a r t I for 800~ and PHzs/PH2 = 1.0 using 5 - r a m - t h i c k i r o n s a m p l e s ; it was shown that the p a r a b o l i c rate s t a r t e d a f t e r the c o n v e r s i o n of about 1 - m m - t h i c k iron l a y e r to p y r r h o t i t e . Despite the fact that all these points were c l e a r l y stated in our p a p e r s , Zelouf and Simkovich took the slopes of *S. ZELOUF and G. SIMKOVICH,Trans. TMS-AIME, 1969, vol. 245, pp. 875-76. W. L. WORRELL is Professor, School of Metallurgyand Materials Science, University of Pennsylvania,Philadelphia, Pa. E.T. TURKDOGAN is with the Edgar C. Bain Laboratory for Fundamental Research, U. S. Steel Corporation, Research Center, Monroeville,Pa. Discussion submitted July 24, 1969. METALLURGICALTRANSACTIONS

the "pseudolinear" p a r t of the S-shaped c u r v e s in Fig. 1 of P a r t II to r e p r e s e n t the p a r a b o l i c rate of sulfidation of i r o n . One can speak of the p a r a b o l i c rate of oxidation or sulfidation of m e t a l s only when the c h e m i c a l potential on each side of the growing l a y e r , oxide, sulfide, and so forth, is fixed. T h i s a r g u m e n t is i l l u s t r a t e d s c h e m a t i c a l l y in Fig. 2(a) where the flux of s u l f u r (Js) from the gas to the p y r r h o t i t e is plotted a g a i n s t t i m e . The dotted c u r v e is for the p a r a b o l i c growth rate of the p y r r h o t i t e l a y e r at fixed s u l f u r a c t i v i t i e s on each side of the sulfide l a y e r . When the sulfide l a y e r is thin, the diffusional flux in the p y r r h o t i t e would be v e r y g r e a t for such diffusion c o n t r o l , and hence the rate would be c o n t r o l l e d e s s e n t i a l l y by a c h e m i c a l r e action at the g a s - s u l f i d e i n t e r f a c e . As shown in Fig. 2(b), the sulfur activity at the s u r f a c e of the sulfide l a y e r will i n c r e a s e with r e a c t i o n t i m e . When the s u l f u r activity at the s u r f a c e is in e q u i l i b r i u m with the gas phase, (aS)e, the s u b s e q u e n t rate of s u l f i d a tion i s c o n t r o l l e d p r i m a r i l y by the diffusion p r o c e s s and obeys the p a r a b o l i c - r a t e law. It follows from the foregoing d i s c u s s i o n that the m i s u s e of our data by Zelouf and Simkovich i s not an e x p e r i m e n t a l proof of t h e i r postulate c o n c e r n i n g the effect of hydrogen on the cation v a c a n c y c o n c e n t r a t i o n in p y r r h o t i t e . Another b a s i c objection to the a n a l y s i s of Zelouf and Simkovich is t h e i r a s s u m p t i o n of the p a r a b o l i c rate c o n s t a n t kp b e i n g p r o p o r t i o n a l to the n u m b e r of cationic v a c a n c i e s in ' F e S ' , t h e i r Eq. [6]. As d e m o n s t r a t e d c l e a r l y in P a r t I of our study, 1' the c h e m i c a l diffusivity of i r o n in p y r r h o t i t e , and hence Jep, is not d i r e c t l y p r o p o r t i o n a l to the n u m b e r of i r o n v a c a n c i e s , Fig. 13 of Ref. 2. However. the s e l f - d i f f u s i v i t y of i r o n is d i r e c t l y p r o p o r t i o n a l to the n u m b e r of i r o n

\ DIFFUSION CONTROL (PARABOLIC RATE)

',i./ \\

",

Js

(o1

cREA:/#(~)~-RATE MIXED CONTROL

(%)e

(hi IN EQUILIBRIUM WITH IRON TIME Fig. 2---Schematic diagram showing (a) mixed reaction-rate and diffusion controlled flux of sulfur from gas to pyrrhotite compared to parabolic rate of sulfidation, (b) activity of sulfur on the pyrrhotite surface as function of time. VOLUME 1,JANUARY 1970- 299

v a c a n c i e s in p y r r h o t i t e , Fig. 11 of Ref. 2. Zelouf and Simkovich have confused c h e m i c a l diffusivity with s e l f - d i f f u s i v i t y , and t h e r e f o r e t h e i r Eq. [6] has no validity.

Authors' Reply S. Z E L O U F AND G. SIMKOVICH We welcome the a n t i c i p a t e d r e m a r k s by W o r r e i l and T u r k d o g a n . In our t e c h n i c a l note we have a s s u m e d that the " p s e u d o p a r a b o l i c " r e g i o n given in Fig. 1 of the paper by the d i s c u s s e r s lz i s g o v e r n e d p r i m a r i l y by solid state diffusion. The s l o p e s of these r e g i o n s have b e e n taken as a m e a s u r e of this diffusion p r o c e s s and, a s such, have b e e n d e s i g n a t e d as kp. The difference in slopes at a c o n s t a n t s u l f u r p o t e n t i a l , a c o n s t a n t r a t i o of H2/HzS, has b e e n a t t r i b u t e d by us to be due to the d i s s o l u t i o n of h y d r o g e n a s an i n t e r s t i t i a l proton which c r e a t e s additional cation v a c a n c i e s in the FeS b e i n g formed. We have not given c o n s i d e r a t i o n to P a r t I of the d i s c u s s e r s ' work 13 b e c a u s e , in the thick FeS l a y e r s d e s c r i b e d , n u m e r o u s c r a c k s and p o r e s a p p e a r e d , see Fig. 4 and the d i s c u s s i o n c o n c e r n i n g this figure in Ref. 2 where p o r o s i t i e s as high as 9 pct a r e given. F o r the benefit of the d i s c u s s e r s W a g n e r ' s p a r a b o l i c r e l a t i o n s h i p ~4 a p p l i e s to a d h e r e n t , p o r e f r e e l a y e r s and not to porous and c r a c k e d l a y e r s . Such m a c r o s c o p i c defects lead to high v a l u e s of sulfidation which a r e not n e c e s s a r i l y in a c c o r d with the o v e r a l l t h i c k n e s s of the FeS l a y e r , that i s , s h o r t c i r c u i t i n g paths a r e a v a i l able and the t r u e k i n e t i c s m a y be v a s t l y d i f f e r e n t f r o m that p r e s e n t e d . T h u s , o u r choice of the " p s e u d o p a r a b o l i c " region which although p o s s i b l y in the m i x e d c o n t r o l r e g i o n a r e p r o b a b l y c l o s e r to true p a r a b o l i c k i n e t i c s than that shown by the c r a c k e d , porous s c a l e s given in P a r t I. T h i s is in a c c o r d with the findings of Mrowec and e o w o r k e r s . ' S No confusion e x i s t s on o u r p a r t c o n c e r n i n g v a r i o u s diffusion c o e f f i c i e n t s r a t h e r the d i s c u s s e r s s e e m to be confused as to the o r i g i n of our Eq. [6]. T h u s , we d e r i v e this r e l a t i o n s h i p below. W a g n e r ' s p a r a b o l i c equation ~4 for the case of oxidation of pure m e t a l s to a p o r e - f r e e , a d h e r e n t , s i n g l e phase compound m a y be a p p r o x i m a t e d by the equation

aO

kp = const 4' DMed * In a s

a~

[1]

when the m e t a l ion m o v e m e n t is rate d e t e r m i n i n g and the compound f o r m e d is an e l e c t r i c conductor. D ~ e is the s e l f - d i f f u s i o n coefficient of the m e t a l i o n s , a s i s the a c t i v i t y of the s u l f u r , and the 0 and i s u p e r s c r i p t s r e p r e s e n t q u a n t i t i e s at the g a s - c o m p o u n d and the metal-compound interfaces, respectively. For most compounds the s e l f - d i f f u s i o n coefficient i s given a s D ~ e = eonst p~/n S2

--

const [ ( P ~ n ) ~ - ( P s1/n 2)] i

[3]

F o r the benefit of the d i s c u s s e r s , we should like to note that Eq. [3] was p r e s e n t e d in the A m e r i c a n l i t e r a t u r e some 18 y e a r s ago. 16 F u r t h e r m o r e , in FeS, the c o n c e n t r a t i o n of cation v a c a n c i e s , Fe[],, where the double dash i n d i c a t e s a dual negative charge in c o m p a r i s o n to the u n d i s t u r b e d l a t t i c e , i s given as XFeD,, = const p ls2 /n

[4]

and s u b s t i t u t i o n in Eq. [3] gives kp = const [ (XFec3,,)~ - (XFeD,,)]i

[ 5]

T h u s , kp i s p r o p o r t i o n a l to the g r a d i e n t of cation v a c a n c i e s in FeS. Since the c o n c e n t r a t i o n of v a c a n c i e s in FeS in e q u i l i b r i u m with i r o n i s quite s m a l l , FeS is a l m o s t s t o i c h i o m e t r i c u n d e r t h e s e c o n d i t i o n s , while that u n d e r most sulfidizing a t m o s p h e r e s is quite l a r g e , we drop the second t e r m in the b r a c k e t s on the right hand side of Eq. [5] and obtain kp = const (XFe[3,,)0

[ 6]

which is i d e n t i c a l with Eq. [6] of our note. It should be noted that Eq. [6] is dependent upon 1) A l a r g e c o n c e n t r a t i o n of v a c a n c i e s at the g a s compound i n t e r f a c e in c o m p a r i s o n to the c o n c e n t r a t i o n at the m e t a l - c o m p o u n d i n t e r f a c e , and 2) The point defects r e s p o n s i b l e for motion should follow the r e l a t i o n s h i p given in Eq. [4] over the e n t i r e t h i c k n e s s of the s c a l e , that i s , over the e n t i r e s u l f u r a c t i v i t i e s f r o m the m e t a l - c o m p o u n d i n t e r f a c e to the compound-gas interface. F r o m some of our own data 6 point 2 above i s s o m e what in doubt for the case of FeS. We b e l i e v e that the above a n s w e r s adequately the d i s c u s s i o n s u b m i t t e d . However, we should a l s o note that one has r e c o u r s e to a v a r i e t y of e x p e r i m e n t s which would e i t h e r prove or d i s p r o v e our a s s u m p t i o n of hydrogen d i s s o l u t i o n in FeS. Among these a r e 1) D e t e r m i n a t i o n of p a r a b o l i c rate c o n s t a n t s u n d e r pure s u l f u r vapor and u n d e r an H2/H2S gas m i x t u r e having the s a m e s u l f u r potential a s the pure s u l f u r v a p o r . We a n t i c i p a t e a f a s t e r rate u n d e r the H2/HzS gas m i x t u r e due to the d i s s o l u t i o n of hydrogen. 2) M e a s u r e m e n t of weight g a i n s or l o s s e s of FeS under a c o n s t a n t HJH2S r a t i o diluted with v a r i o u s a m o u n t s of an i n e r t gas. We have made some m e a s u r e m e n t s of type 2 and have found that FeS g a i n s weight a s an i n e r t gas is r e m o v e d from the gas m i x t u r e i n d i c a t i n g that h y d r o gen d i s s o l u t i o n does o c c u r in the FeS.17 T h i s work further raises questions concerning stoichiometric s t u d i e s on FeS utilizing H2/H2S a t m o s p h e r e s s i n c e the defects p r e s e n t a r e p r o b a b l y a product of both s u l f u r and hydrogen d i s s o l u t i o n in the FeS and not of s u l f u r alone.

[2]

where n i s u s u a l l y an i n t e g e r of the o r d e r of 4, 6, or 8 for a p - t y p e c o n d u c t o r and i s dependent upon the p a r t i c u l a r point defect s t r u c t u r e of the compound b e ing f o r m e d . I n s e r t i o n of Eq. [2] into Eq. [1], utilizing the p a r tial p r e s s u r e of s u l f u r as the s u l f u r activity, and i n t e g r a t i n g , one o b t a i n s 300-VOLUME 1, JANUARY 1970

kp

10. W.L. WorreUand E. T. Turkdogan:Trans. TMS-AIME, 1968,vol. 242, pp. 1673-78. 11. E. T. Turkdogan:Trans. TMS-AIME, 1968,vol. 242, pp. 1665-72. 12. W.L. Worrelland E. T. Turkdogan:Trans. TMS-AIME, 1968,vol. 242, pp. 1673-78. 13. E. T. Turkdogan:Trans. TMS-AIME, 1968,vol.242, pp. 1665-72. 14. C. Wagner:AtomMovements, pp. 153-73,ASM,Cleveland,Ohio, 1951. METALLURGICALTRANSACTIONS