Diffusion-Limited Sulfidation of Wustite

SCOTT McCORMICK, M. A. DAYANANDA, AND R. E. GRACE

The sulf idat ion of wust i te in H2S-H20-Hz-Ar a tmospheres has been studied at t e m p e r a t u r e s of 700, 800, and 900~ with t h e r m o g r a v i m e t r i c techniques. Po lyc rys t a l l i ne wust i te wafers were equi l ib ra ted in a flowing H20-H2-Ar gas s t r e a m and then sulf idized in s i t u . During an in i t ia l t r a n s i e n t stage a protect ive l ayer of FeS formed on the sample , and an in t e rmed ia t e l ayer of FesO 4 fo rmed between the FeO and FeS l aye r s . Subsequently, the r eac t ion followed a parabol ic ra te law. The parabol ic r a t e constant va r i ed f rom 0.22 x 10 -2 mg 2 cm "~ mi n -~ at 700~ to 6.5 • 10 -2 mg 2 cm "~ min -~ at 900~ The reac t ion ra te was l imi ted by the diffusion of i ron through the in te rmedia te Fe304 l aye r which grew c o n c u r r e n t l y with the FeS l ayer and at the expense of the FeO core. After the FeO core was comple te ly conver ted to FesO4, the p rocess en te red a pass ive stage dur ing which no fur ther mass changes could be detected.

HIGH t e m p e r a t u r e gas - so l id reac t ions involving more than one gaseous species a re of cons iderab le e n g i n e e r - ing impor tance . Examples include the hot c o r r o s i o n of meta l s in oxygen and su l fur bea r ing gases , 1 the roas t ing

2 . . .

of sulf ide o res , the p r o c e s s i n g of omde and ca rb ide nuc l ea r fuels, 3 and the desu l fur iza t ion of gases with a lkal ine ear th oxides. 4-~

In many of these reac t ions , the reac t ion product fo rms an in te rmedia te protec t ive sca le between the r eac t an t s so that the r eac t ion ra te is l imi ted by the solid state diffusion of one or more of the r eac tan t s through this sca le . The f i r s t quant i ta t ive explanat ion of this type of reac t ion was given by Wagner who r e - la ted the growth ra te of the protect ive layer to the dif- fus iv i t i es and chemica l potent ia ls of the r eac t ing spe - c ies within the sca le .

Wagner expresses the r a t e of scale fo rmat ion (g-equiv. s - ' cm -2) as:

1 d n b r - [ 1 ]

A d t A X

where k r is the ra t iona l r a t e constant (g-equiv. s -1 cm -I) and AX is the ins tan taneous sca le th ickness (cm). For a meta l deficient , e l ec t ron ica l ly conducting oxide such as FeO or FezO 4 in which the diffusivi ty of the meta l cat ions is much g r ea t e r than that of the anions: 6

-- f cM d tn ao [2] a~ M

where I I

a o and ao = oxygen ac t iv i t i es at the meta l -ox ide and oxide-gas phase boundar ies , r espec t ive ly ,

C M = concen t ra t ion of metal cat ions in the scale , g-equiv, cm -a,

N o / N M = ra t io of mole f rac t ion of oxygen anions to that of me ta l cat ions in the scale ,

D~4 = se l f -d i f fus iv i ty of the metaI cat ion in the oxide, am z s-*.

In a b i n a r y meta l -oxygen sys t em where phase bound-

a r y reac t ions a re rapid enough so that the rmodynamic equ i l ib r ium is v i r t ua l l y es tab l i shed at each in terface , the l imi t s of in tegra t ion of Eq. [2] a re fixed. The d i s - socia t ion p r e s s u r e of the oxide in equ i l i b r ium with meta l f ixes a~ and the gas compos i t ion fixes a o. If ap- p ropr ia te average va lues a re ass igned to the other t e r m s within the in tegra l , the solut ion to Eq. [2] is s t ra igh t forward and re su l t s in the f ami l i a r parabol ic ra te law. If a sur face reac t ion at the oxide-gas phase boundary is pa r t i a l ly ra te cont ro l l ing , ao will no longer be fixed but will v a r y with t ime .

The addi t ional degree of f reedom int roduced by the p re sence of a th i rd component fu r the r compl ica tes the ana lys i s . With this addit ional degree of f reedom it can no longer be a s sumed that the ac t iv i t ies at the meta l - oxide phase boundary a re fixed. For example, dur ing the oxidation of a b i n a r y alloy, the l e s s noble metal may be oxidized and removed f rom the alloy at the a l - loy-oxide in ter face . Thus, the al loy composi t ion and the ac t iv i t ies of the components may change cont inu- ously with t ime.

S imi lar p rob lems can a r i se , for example, dur ing the sulf idat ion of an oxide. Even though the act ivi t ies at the su l f ide-gas phase boundary may be fixed by the gaseous phase, the act iv i t ies at the in te rna l ox ide - su l - fide phase boundary can s t i l l v a r y cont inuously as the r eac t ion proceeds . In o rder to fo rmula te a ra te equa- tion, this va r i a t ion must be known as a function of t ime.

Many inves t iga to rs have used the Wagner theory to analyze the p rob lem of the attack of meta l s and alloys by gases conta in ing one reac t ing species . Cons iderab ly less a t tent ion has been paid to the reac t ion of a meta l oxide, ca rb ide , n i t r ide , or sulfide with a th i rd compo- nent f rom a gas phase. This inves t igat ion of the su l f i - dation of wust i te was under taken to provide a f i r m e r the rmodynamic and mechanis t ic unders tand ing of this type of reac t ion . The i r on -oxygen - su l fu r sys t em was chosen because the the rmodynamic , s t ruc tu ra l , and t r a n spo r t p rope r t i e s of the F e - O and Fe-S b ina ry s y s - t ems a re r ea sonab ly well understood.

SCOTT McCORMICK, formerly Graduate Student, Purdue Univer- sity is currently Assistant Professor, Department of Metallurgical and Materials Engineering, Illinois Institute of Technology, Chicago, Illinois 60616. M. A. DAYANANDA and R. E. GRACE are Associate Professor and Professor, respectively, School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907.

Manuscript submitted April 25, 1974.

THE IRON-OXYGEN-SULFUR SYSTEM

Wusti te (FeO)* has the NaC1 c r y s t a l s t ruc tu re and

*In this paper, the symbols FeO, Fe304, and FeS represent wustite, magnetite, and pyrrhotite phases, respectively, and do not imply stoichiometry.

METALLURGICAL TRANSACTIONS B VOLUME 6B,MARCH 1975-55

is s table over a wide r ange of composi t ions on the oxy- gen - r i ch side of s to ich iomet r i c FeO. 7 This nons to ich i - omet ry , which can be accounted for by vacanc i e s on the i ron cation subla t t ice , is a function of t e m p e r a t u r e and oxygen par t ia l p r e s s u r e , a-~a The t r a c e r diffusion coef- f ic ient of i ron in FeO i n c r e a s e s with t e m p e r a t u r e and deviat ion f rom s to ich iomet ry . ~4-~7 The i ron d i f fus iv i - t ies found by Himmel , Mehl, and Bi rchena l l ~4 for FeO,.lo a re shown in Fig. 1. It is gene ra l l y agreed that i ron diffusion takes place by a vacancy mechan i sm

FeO and that D Fe is v e r y much l a rge r than D FeO Magnetite (FeaO 4) has a s t r uc tu r e v e r y s i m i l a r to

that of FeO but with d i f fe rences in the n u m b e r and lo- cat ion of Fe § cat ions . FeaO 4 has a wide range of com- posi t ions at e levated t e m p e r a t u r e s that is be l i eved to be due to the p r e sence of vacant i ron cat ion s i tes . ~8 Schmalzr ied m studied the t r a c e r diffusivi ty of i ron in

4.1-, o,'- r~Fe304 FesO 4 and found . . . . . . Fe inc reased over two o r d e r s of magnitude with d e c r e a s i n g i ron content at 1115~ The range of these r e s u l t s and the r e s u l t s of H immel et al . ~4 are shown in Fig. 1. Cast le and Surman ~9 have

Fe304 shown that D Fe304 is v e r y much l a r g e r than p O . Pyr rho t i t e (FeS) is s tab le over a wide range of com-

posi t ions 2~ between s to ich iomet r i c FeS and FeS~.~. This nons to ich iomet ry is due to the p r e s e n c e of i ron vacanc ies and is a funct ion of t e m p e r a t u r e and sulfur pa r t i a l p r e s s u r e f i ~-~5 The diffusivi ty of i ron in FeS is v e r y high and o rde r s of magnitude g rea te r than that of

~6-~8 sul fur . The se l f -d i f fus ion coefficient of i ron in FeS as calcula ted by M e u s s n e r and Bi rchena l l ~a f rom sul f i - dation exper iments is shown in Fig. 1.

Fe -O-S T e r n a r y System. Most expe r imen ta l i nves t i - gat ions of the F e - O - S s y s t e m have been pe r fo rmed at t e m p e r a t u r e s above 900~ to be t t e r unders tand the fo r - marion of nonmeta l l i c inc lus ions in s teel . ~a-a2 These inves t iga t ions have es tab l i shed that a t e r n a r y eutect ic point exis ts at about 915~ where solid i ron, FeO, and FeS coexist with a l iquid oxysulfide. Below this t e m - pe ra tu re , in the Fe-FeaO~-FeS region of the sys tem, only solid phases a re s table .

TEMPERATURE ~ iO-S I100 I000 900 800 700

h i ~

t~ l ; IO-r "o .

t.J

t _~ .

~ 10 "10

(n

U- U- i0- H

~ Fe304 n,'

~ 10 -i=

t-.-

i0 -13 7.0 7'8 ' 80 ,'5 ,'o ,5' ,o'o ,o5

TEMPERATURE -I, eK-I Fig. 1--Tracer diffusion coefficients of iron in FeOl.t0, Fe304 and FeS. �9 - Himmel, Mehl, and Birchenall, i4 �9 - Meussner and Birchenall, 28 �9 - Schmalzried. ~a

I i i i /

/ G e- . . . . . . . . . . . . . . . . F

~J i II

O.~ -I FeS

D C / H /! o - . . . . . . . . . I I

I I I I o . J I I / /

-3 Fe

-I I 2 3

LOG PHtO/PNt Fig. 2--Pourbaix equilibrium diagram of the iron-oxygen-sul- far system at 900~ showing possible reaet~on paths during the sulfidation of FeO.

Kor and Turkdogan ss have r epor t ed the solid so lub i l - ity of su l fur in FeO to be 140 ppm at 1250~ and sug- gest that su l fur may fo rm a subs t i tu t iona l solut ion r e l - ative to the oxygen s i tes . Leonard and St. P i e r r e ~ have repor ted the so lubi l i ty of sul fur in FeO in equ i l ib r ium with FesO 4 to be 420 ppm at 1100~ There is appa r - ent ly no in fo rmat ion avai lable on the solubi l i ty of su l fur in FesO 4 or oxygen in FeS, although the s t ruc tu r a l s i m - i l a r i t i e s between FeO and FesO 4 sugges t that the i r su l - fur so lub i l i t i e s might be s i m i l a r .

Kor and Turkdogan ss have e s t ima ted the diffusivi ty of su l fur in FeO to be about 1 x 10 -7 cm 2 s -1 at 1300~ No in fo rmat ion is avai lable on the diffusivi t ies of oxy- gen in FeS or su l fur in FesO 4.

To fac i l i ta te the in t e rp re ta t ion of the r e su l t s of this study, equ i l i b r i a in the F e - O - S s y s t e m are r e p r e s e n t e d by a fo rm of Pourbaix d i ag ram in which the range of t he rmodynamic s tab i l i ty of each sol id phase is mapped as a funct ion of oxygen and su l fur pa r t i a l p r e s s u r e s as m e a s u r e d by H20/H 2 and H2S/H 2 p r e s s u r e ra t ios as shown in Fig. 2. The oxygen and su l fur pa r t i a l p r e s - su r e s in this d i ag ram are below those r equ i r ed for the p r e sence of Fe~Os, FeS2, FeSO4, or Fe~(SO4) S.

This d i ag ram was cons t ruc ted f rom the t he rmody- namic data for the F e - O and Fe -S b i n a r y sy s t e ms 7,s' x~,13,2,,~3 and the assumpt ion that the so lubi l i t ies of ox- ygen in FeS and of sul fur in FeO and Fe304 are neg l i - gible. A consequence of this a s sumpt ion is that each oxide or sulf ide phase may be t r ea t ed t h e r m o d y n a m i c - al ly as par t of a b i n a r y sys tem. There fore , within the oxide phase f ie lds in Fig. 2, the i so -ac t iv i ty l ines for i ron a re v e r t i c a l ; within the FeS phase field they a re hor izonta l . The H20/H 2 and H2S/H 2 p r e s s u r e ra t ios for the four phase equ i l ib r i a ( F e - F e O - F e S - g a s and FeO- Fe304-FeS-gas) at 700, 800, and 900~ are shown in Table L

Scaling React ions . During the oxidat ion of i ron to FeO in CO s / C O and H 2 0 / H 2 a tmosphe re s between 570 and 1200~ a protec t ive FeO layer f o r ms and grows between the i ron and the gas. For s m a l l oxide th ick- n e s s e s the p r i m a r y r a t e - d e t e r m i n i n g step is a phase boundary r eac t ion at the FeO-gas in ter face . 3~-s7 For l a rge r oxide th icknesses the oxidation of i ron obeys Wagner ' s parabol ic ra te law with the diffusion of i ron cat ions through the sca le be ing the ra t e de t e rmin ing step.SS-S7

56-VOLUME 6B, MARCH 1975 METALLURGICAL TRANSACTIONS B

Table I. H2S/H2 and H20/H2 Pressure Ratios at Fe-FeO-FeS-Gas and FeO-FeaO4-FeS-Gas Equilibria at 700, 800, and 900~

Fe-FeO-FeS-Gas FeO-FeaO4-FeS-Gas

T,~ log (P~H-~-S ~ log (PH~o~ logiC2 S ) 1 og(P~H-~-O~ krH2 / XrH~ ] krH, ]

700 -3.054 -0.373 -2.575 0.072 800 -2.754 -0.300 -2.021 0.381 900 -2.501 -0.225 -1.552 0.663

Davies e t a ! . ~ s tud ied the growth of FesO a on i ron at t e m p e r a t u r e s be low 570~ and the growth of FesO 4 on FeO be tween 850 and 950~ They o b s e r v e d that the r e a c t i o n s obeyed W a g n e r ' s p a r a b o l i c r a t e law with the r e a c t i o n r a t e l im i t ed by the di f fus ion of i ron th rough the Fe304 l a y e r . Hauffe and Rahme139 and M e u s s n e r and B i r c h e n a l l s8 s tud ied the su l f ida t ion of i ron to FeS in su l fur vapor . The r e a c t i o n obeyed W a g n e r ' s p a r a - bo l ic r a t e law with the r a t e - d e t e r m i n i n g s t ep be ing the di f fus ion of i ron through the FeS l a y e r . Turkdogan and Worrel125'4~ s tud ied the su l f ida t ion of i ron in HsS-Hs-Ar a t m o s p h e r e s at 670, 800, and 900~ They found tha t th i s p r o c e s s was con t ro l l ed in i t i a l l y by a phase bound- a r y r e a c t i o n at the F e S - g a s in t e r face . Af ter p e r i o d s r ang ing f rom s e v e r a l hours to s e v e r a l days , the r e a c - t ion obeyed W a g n e r ' s p a r a b o l i c r a t e law with the r a t e - l i m i t i n g s t ep be ing the d i f fus ion of i ron through the FeS.

Rahme141'~2 has s tud ied the s ca l i ng of i ron in N2-O 2- SO s and CO-COs-COS m i x t u r e s be tween 700 and 900~ He found that if the r a t e - l i m i t i n g p r o c e s s was d i f fus ion th rough a gas bounda ry l a y e r o r a r e a c t i o n at the s c a l e - gas phase boundary , su l f ide and oxide phase s could f o r m s imu l t aneous ly . When the p r o c e s s was l i m i t e d b y the di f fus ion of i ron th rough the s ca l e , the t h e r m o - d y n a m i c a l l y s t ab le phase (oxide o r sulf ide) was f o r m e d e x c l u s i v e l y and the p r e s e n c e of a second oxidant did not inf luence the s ca l i ng r a t e

B i r k s 43 has examined the a t t ack of a m e t a l by oxygen and su l fur and r e l a t e d the t h e r m o d y n a m i c s and k ine t i c s of the p r o c e s s to the r e s u l t i n g s c a l e morphology . He out l ined condi t ions under which both su l f ide and oxide p h a s e s could grow s i m u l t a n e o u s l y and c o n f i r m e d t h e s e condi t ions for i ron, copper and n ickel .

THE SULFIDATION OF FeO

In th i s inves t iga t ion of the su l f ida t ion of FeO the b o u n d a r y condi t ions we re se t by the fol lowing e x p e r i - ment . A wust i te wafer was equ i l i b r a t ed at a c o m p o s i - t ion FeO x with a gas of a f ixed oxygen poten t ia l and v e r y low, but unknown, su l fur po ten t ia l r e p r e s e n t e d by point A in Fig . 2. The gas compos i t i on was then changed to one r e p r e s e n t e d by points D o r G so that FeS was the s ing le s t ab le so l id phase . The subsequent growth of a l a y e r of FeS on the oxide wafer was fo l - lowed by mon i to r ing the m a s s change of the s a m p l e .

In a d e s c r i p t i o n of th is p r o c e s s , t h r e e s imp l i fy ing a s s u m p t i o n s a r e made in addi t ion to those made by Wagner f l These a s s u m p t i o n s a r e that t h e r e is neg l i - g ible so l id so lub i l i t y of oxygen in FeS, that t h e r e is neg l ig ib le so l id so lub i l i t y of su l fur in FeO and Fe3Oa, and that the d i f fus iv i t i e s of oxygen and su l fur anions in each phase a r e o r d e r s of magni tude l e s s than the d i f fus iv i ty of i ron .

METALLURGICAL TRANSACTIONS B

These a s s u m p t i o n s , while c o n s i s t e n t with what is known about the i r o n - o x y g e n - s u l f u r s y s t e m , he lp c h a r - a c t e r i z e the n a t u r e of the r eac t i on . The FeS l a y e r is a s s u m e d to be i m p e r m e a b l e to oxygen; oxygen is t h e r e - f o r e c o n s e r v e d in the s a mp le , and t h e r e is v i r t u a l l y no net oxygen t r a n s f e r to o r f r o m the gas phase wha tever i t s oxygen poten t ia l . The growth of the FeS l a y e r p r o - ceeds by the d i f fus ion of i ron f rom the FeO c o r e to the F e S - g a s i n t e r f a c e where i t r e a c t s with sul fur f rom the gas phase to f o r m FeS. The d r iv ing f o r c e for th is i ron dif fus ion i s the d rop in i ron ac t i v i t y f r o m the oxide c o r e to the F e S - g a s phase boundary . Since no oxygen is los t f r o m the oxide co re , the oxygen ac t iv i ty in the c o r e i n c r e a s e s con t inuous ly as the i r on is r e m o v e d . This i n c r e a s e in oxygen ac t i v i t y and c o r r e s p o n d i n g d e - c r e a s e in i ron ac t i v i t y in the oxide c o r e cont inues as long as a ne t t r a n s f e r of i ron a c r o s s the ox ide / su l f i de i n t e r f ace o c c u r s .

When the H2S/H 2 p r e s s u r e r a t i o , point D in Fig . 2, for example , i s l e s s than that at the F e O - F e s O 4 - F e S - gas e qu i l i b r i um, point H, the c o m p o s i t i o n of the FeO c o r e tends to shi f t f r om point A to tha t r e p r e s e n t e d by point B. When the H2S/H 2 p r e s s u r e r a t i o , point G, for example , i s g r e a t e r than that at the F e O - F % O 4 - F e S - gas e qu i l i b r i um, a l a y e r of Fe30 a f o r m s be tween FeO and FeS and grows at the expense of FeO. This is i l - l u s t r a t e d by path A E F G in Fig . 2. Along this path the oxygen a c t i v i t y in the s a m p l e con t inuous ly i n c r e a s e s f r o m the F e O c e n t e r to the Fe304-FeS in t e r f ace and then d rops to that at point G.

AN ANALYSIS OF SULFIDATION KIN E TIC S

The r a t e of su l f ida t ion of an i r on oxide wafer can be d e s c r i b e d by the r a t e of m a s s gain, d m / d t , due to the f o r m a t i o n of FeS z. Since i ron and oxygen a r e a s s u m e d to be c o n s e r v e d in the s a m p l e du r ing the p r o c e s s

dnFeSz d m - z M s [3] d t d t

where

nFeSz = number of m o l e s of FeS z at t ime t, z be ing the a v e r a g e va lue for the l a y e r

M s = g a tomic weight of su l fu r , 32.064 g mole -1.

If ~x is the t h i cknes s of the FeS z l a y e r at t ime t, A is the c r o s s - s e c t i o n a l a r e a of the l a y e r and PFeS z is the m o l a r dens i ty of FeSz,

dm d ~ [4] d t - z M s A P F e S z d t

F o r the c a s e where FesO 4 is f o r m e d as an i n t e r m e d i - ate l a y e r be tween FeO and FeS pha se s ,

d A x d t = I ~I -- ~bIII [5]

where

@I = v e l o c i t y of F e 3 0 4 / F e S z i n t e r f ace I ~bli = v e l o c i t y of F e S z / g a s i n t e r f ace II.

~bi and qSii a r e c o n s i d e r e d to be oppos i t e in d i r ec t i on to each o the r . In t e r m s of m o l a r concen t r a t i ons (CFe) and f luxes ( JFe ) of i ron in the ad jacen t phases at the two i n t e r f a c e s , I and II, @I and qSii a r e given by

VOLUME 6B,MARCH 1975-57

j F e 3 0 4 FeSz Fe -- JFe

r = [6] C FeaOr ..= cFeSz

Fe Fe I

FeS z J F e

= - - [ 7 ] FeS~

CFe ~ II

Subst i tut ing Eqs. [5], [6] and [7] in Eq. [4] and r e a r - ranging , one gets

I / - F e S z X / _FeSz\ [ dm I "riFe " ~ - ( J F e -~ [ d---~ = zMsAOFeSz " Q" /p---F~eSz ] ~P--~--eSz ] [ [81

\ ~ F e I I \ ~ F e I I I l

whe re

FeaO 4 . FeS z [ JFe / J F e -- 1_ [9]

q = 7 ~ 1 Fe / ~ Fe I

If the Fe g rad ien t in the sul f ide l a y e r is a s s u m e d l i nea r

j F e S z/,~FeSz ~ / rFeSz /~ feS z "~ [1 0] Fe /WFe ] I = \OFe /~Fe ]II

Eqs. [8], [9] and [10] y ie ld

drn JFF: Sz [111 dt - ZMsAPFeSz (Q -- 1)

UFe

The Fe flux through the sulf ide l a y e r a long the x - coord ina te may be def ined by 44

FeS z FeS z FeS z _FeS z 3 In aFe [12]

J F e = - -CFe DFe 31

FeS z where DFe is the di f fuai~i ty of Fe , a s s u m e d constant ,

~e~z " "t in the FeS z l aye r , and aFe r e f e r s to the a c h w y of i ron . On the b a s i s of the Gibbs -Duhem re l a t i on , Eq. [12] can be wr i t t en as

FeSz ~FeS z ~FeS z 3 In aFs esz [13] J F e = Z ~ F e UFe 31

FeS z where a s r e f e r s to the ac t iv i ty of su l fur . F o r l i nea r su l fur ac t iv i ty g r ad i en t s

3 ln aFs esz In a Fesz II -- In asFeSz I - [14 ]

Ox Ax

On e x p r e s s i n g a s at i n t e r f a c e s I and II in t e r m s of PH2S/PH2 r a t i o s and not ing Ax = m / P F e S z Z M s A , Eqs. [11], [13], and [14] y ie ld :

s~.2~2 2 DFeSz dm 2.303z lVisi4 PFeS z (Q - 1) Fe

dt m

�9 (A log H2S/H 2) [15]

where A log H2S/H2 is the d i f fe rence in the l o g a r i t h m of the PH2 S/PH2 r a t i o s at the F e S z / g a s and FeaO 4 / F e S z i n t e r f a c e s . Eq. [15] can be in t eg ra t ed ove r the su l f ida - t ion t ime t to get

rn z a ~ 2 (V nFeSz A----- ~ = 2 . 2 . 3 0 2 z MsPFeSz - 1) ~ F e

�9 (A log HzS/H2) t [161

The pa rabo l i c k ine t i c s impl i ed in Eq. [16] m a y b e -

come va l id only a f t e r some t i m e t o of sul f idat ion. This is b e c a u s e of the fact that an i n t e r m e d i a t e Fe304 l a y e r has to f o r m and the in i t i a l FeO c o r e has to shif t f r o m i ts o r i g i n a l compos i t ion FeO x to FeOy in equ i l i b r ium with FesO 4. If t o is the t ime r e q u i r e d to e s t ab l i sh the equ i l i b r ium compos i t i ons at the i n t e r f a c e s I and II, the su l f ida t ion k ine t i c s for t > to can be d e s c r i b e d by

-- rrt0)2 a 2 " t l~]rl FeSz (m A 2 = 4.604z MsPFeSz . (Q - ~, i~Fe

�9 (A log H2S/H2) (t - t o) [ 1 7 ]

where m o is the m a s s of s a m p l e at t o. The p a r a b o l i c r a t e cons tan t , kp, is given by:

t - f e S z kp = 4.604z3M2sP~ZeSz l (q - 1) " F e

�9 (A log H2S/H2) [ 1 8 ]

With the a id of Eqs. [9] and [12], Eq. [18] can be a l t e r - na t ive ly w r i t t e n as :

/ Fe304 3 2 ~ [. CFe

kp = 4.604z MsPFeSz ~ ~Fe3~44 7 7 F e S z \~Fe ~Fe I

D ~[nFeaO4 �9 I (R G - I "D, I~Fe (A log HzS/H,) [19]

where RG is the r a t i o

Fe30 ' /ax] / [3 In feSz '^ " R G = [a In aFe aFe /VXJI [ 2 0 ]

and

nFeSz /nFe304 [21] RD = ~'Fe /~'Fe

During the s t age of p a r a b o l i c k ine t i c s of sul f idat ion, (R G - RD) is a constant . If the m a s s change is e x - p r e s s e d in m i l l i g r a m s and if a v e r a g e n u m e r i c a l va lues of the known cons tan t s a r e subs t i tu ted in Eq. [19], kp e x p r e s s e d in mg 2 cm -4 min -I is given by

Fe304 . kp = 4.73 x 109zZ(R G - R D ) D E e ( a log H2S/H,)

[221

The a v e r a g e va lues of the cons tan t s employed he re a r e :

M s = 32.064 g / m o l e ; PFeS z = 0.055 moles / cm-S ;

Fe304 CFe = 0.0672 moles /cm-3 ; -FeSz CFe = 0.055 m o l e s / c m -3.

EXPERIMENTAL PROCEDURE

FeO s a m p l e s were p r e p a r e d f r o m zone re f ined i ron ingots p r e p a r e d for the AISI by Ba t t e l l e M e m o r i a l In- s t i tu te . I ron wa fe r s (2 mm • 1 c m ~) we re ox id ized to FeO at 900~ in an HzO-Hz-Ar gas mix tu re . The r e - sul t ing FeO s a m p l e s cons i s t ed of an FeO she l l with a l a rge gap be tween the two oxide l a y e r s . The oxide had a l a r g e g r a i n s i ze (~ 1 mm) and a s t r o n g p r e f e r r e d o r i en t a t i on with (100) p lanes p a r a l l e l to the su r f ace . Each FeO she l l was sp l i t with a knife edge and a b raded to a t h i cknes s of about 0.25 m m and an a r e a of about 1 cm 2 with the f inal gr inding done on 4 /0 pape r . An u l t r a son ic cut t ing device was used to cut a 0.01 inch hole in each s a m p l e for subsequent suspens ion .

58-VOLUME 6B, MARCH 1975 METALLURGICAL TRANSACTIONS B

|

L]

L_~

Fig. 3--Schematic diagram of sulfidation apparatus: 1) pre- mixed HaS-Ha-At gas. 2) premixed Ha-Ar gas. 3) Matheson 701 PBV flowmeter. 4) Matheson 621 PBI flowmeter. 5) mix- ing chamber. 6) heated flask for water saturation of HaS- bearing gas. 7) refrigeration unit. 8) washing bottle for water saturation of equilibration gas. 9) quartz furnace tube. 10) pyrex microbalance housing. 11) movable Marshall furnace. 12) chromel-ahimel thermocouples. 13) vacuum pump. 14) gas sampling jar.

A schemat ic drawing of the sulf idat ion appara tus is shown in Fig. 3. P r e - m i x e d cy l inders of p repur i f i ed hydrogen-a rgon and hydrogen su l f ide -hydrogen-a rgon were used with hydrogen contents between 1.8 pct and 3.8 pct and hydrogen sulf ide contents between 0.18 pct and 23.4 pct. Gas flows were regula ted with Matheson 701 and 621 f lowmeters with ca l ib ra ted ranges of 50 to 700 and 20 to 90 cm 3 min -z, r espec t ive ly .

Dur ing the equi l ib ra t ion of an FeO sample gas f rom the hydrogen-a rgon cy l inder was sa tura ted with water vapor to room t e m p e r a t u r e dew point by bubbl ing the gas through a washing bott le f i l led with d is t i l led water . During the sulf idat ion segment of an exper iment the dew point of the hydrogen sulfide bea r ing gas was fixed by sa tu ra t ing the gas with water and condensing excess water in a pyrex coil within a r e f r i ge r a t ed bath. Dew points between room t e m p e r a t u r e and - 40~ could be achieved. These gases were passed through a p r ehea t - ing coil into a quar tz fu rnace tube within a movable Marshal l furnace with a 5 cm •176 reac t ion zone. The t e m p e r a t u r e in the reac t ion zone was moni tored with a c h r o m e l - a l u m e l thermocouple .

Mass changes were m e a s u r e d with a quartz grav i ty mic roba lance s i m i l a r in des ign to that of Gulbransen and Andrew. ~ Deflect ions were measu red with a cath- e tomete r and mass changes of about 0.001 mg a s s o c i - ated with a ba lance a r m deflect ion of 0.001 mm could be detected.

In the course of a typical exper iment an FeO wafer was suspended f rom a 0.1 mm diam 50 cm long quar tz f iber which in t u rn was suspended f rom a chromel wire and the mic roba lance a rm. The reac t ion chamber was evacuated and the equ i l ib ra t ing w a t e r - h y d r o g e n - a r g o n mix ture was allowed to flow through the sys t em at a flow ra te of 600 cm s min -z. The sys t em was brought to t empe ra tu r e , and the sample equi l ibra ted unt i l no mass change could be detected for a per iod of s ev e r a l hours .

The sul f id iz ing gas was then admit ted to the sys t em at a flow ra te of 600 cm 3 min -z. At 700, 800, and 900~ this flow ra te r e su l t ed in bulk gas ve loc i t ies of 2.8, 3.1, and 3.4 cm s- ' past the sample . Sulfidizing gas compo-

6 , , i

%8,%~ 5F PH S~PH "0"0 ~ " -

2 2

N, ~ 4 9 ~ o

~ 3 �9 800"

2

I

0 I00 2 0 0 300 4 0 0 500

t, MIN Fig. 4--Representative plots of mass gain/area versus time.

s i t ions had hydrogen sulfide pa r t i a l p r e s s u r e s between 0.33 and 34.75 mm Hg and hydrogen pa r t i a l p r e s s u r e s between 0.002 and 24.70 mm Hg. Upper l imi t s on the HzS/H 2 p r e s s u r e ra t io of the su l f id iz ing gases were set at each t e m p e r a t u r e by the ra t io above which sulfur would condense on the g lassware and support wire in the cooler reg ions of the sys tem.

The subsequent sulf idat ion reac t ion was followed by moni to r ing the deflect ion of the mic roba lance a r m with the ca the tometer . Because of some ins tab i l i ty of the mic roba lance at the high expe r imen ta l gas flow ra tes , the accu racy of any one read ing is e s t ima ted to be =~0.02 mg. A typical exper iment las ted about eight hours . At the end of a run the fu rnace was lowered, the furnace tube f lushed with argon, and the sample removed, weighed, polished, and etched in methyl alcohol-20 pct HC1.

The sulf idat ion of FeO was studied at 700, 800, and 900~ in gases with HaS/H 2 p r e s s u r e ra t ios between 0.025 and 2.55 and H20/H 2 p r e s s u r e ra t ios between 0.002 and 1.79.

RESULTS

For each run a plot of mass gain/sample area versus t ime was made. Data f rom two runs at each t e m p e r a - tu re are plotted in Fig. 4. These plots a re typical and show an in i t i a l ly rapid sulf idat ion ra te that dec reases cont inuously with t ime. In some 900~ runs a pass ive stage was eventua l ly reached dur ing which no fur ther mass gain was observed.

In o rder to compare the expe r imen ta l r e su l t s to Eq. [17], plots of [(m - mo)/A] 2 vs (t - to) were made for each run. The data f rom runs shown in Fig. 4 a re plotted in this manne r in Fig. 5.

The r e su l t s of all exper iments conducted in a tmo- spheres with HaS/H 2 p r e s s u r e ra t ios above those of the FeO-Fe304-FeS-gas equ i l ib r ia were s i m i l a r to those shown in Fig. 5. After a per iod of 10 to 100 min. the k inet ics obeyed a parabol ic ra te law as shown by the l inear region of each curve. The s lopes of these l in - ear regions a re the exper imenta l parabol ic ra te con- s tants , kp, and a re l i s ted in Table II.

According to Eq. [18] the parabol ic ra te constant should be an i n c r e a s i n g function of the log HaS/H 2 p r e s s u r e ra t io of the sulf idiz ing gas. This r e l a t ion -

METALLURGICAL TRANSACTIONS B VOLUME 6B, MARCH 1975-59

18

t6

14

0

04 " a

I 00 2 0 0 300 4 0 0 500

( t - to), MIN

Fig. 5--Representative plots of [ (m- m0)/A] 2 vs ( t - to).

Table II. Summary of Experimental Conditions and Values of kp Calculated from Plots of [(m - mo)/A] 2 Vs (t - t o)

T'~ 1~ ~ ! k, A~ log{ ,-~- | (mg2cm -4 rain -I) X 10 2

900 -0.148 -1.600 -0.036 900 -0.107 -0.522 1.042 4.51 900 0.253 -0.417 1.147 4.38 900 -0.013 -0.308 1.256 4.72 900 -0.087 -1.000 0.564 4.19 900 -1.704 -0.308 1.256 5.78 900 -2.440 -0.308 1.256 6.51 900 -1.704 -0.308 1.256 5.92 900 -2.440 -1.000 0.564 3.28 900 -2.440 -0.308 1.256 5.33 900 -1.555 -0.614 0.950 5.67 900 -2.660 0.091 1.656 6.18 900 -2.476 -0.991 0.573 2.89 800 -2.219 --0.308 1.717 2.11 800 -1.151 -0.308 1.717 2.12 800 -0.226 -0.308 1.717 2.73 800 -0.564 -0.308 1.717 2.67 800 -1.121 -0.164 1.411 2.19 800 -1.576 0.407 2.432 3.15 800 -1.576 0.091 2.116 3.03 800 -2.617 -0.996 1.029 1.39 800 -2.481 -1.298 0.727 1.26 700 -2.218 -0.308 2.271 0.58 700 -2.443 -0.308 2.271 0.67 700 - 1.548 -0.407 2.985 0.76 700 -1.194 -0.616 1.963 0.24 700 -2.660 0.091 2.671 0.56 700 -2.653 -0.985 1.594 0.22

ship is shown for t e m p e r a t u r e s of 700, 800, and 900~ in Fig. 6, where kp is plot ted against (A log H2S/H3); a common d i f fe rence , for example , be tween points G and H in Fig. 2, has been used for compa r i son of a l l expe r imen t a l data. These plots show a l inea r depen- dence of kp on (A log H3S/H3); the s lopes of the plots a r e a m e a s u r e of this dependence. These s lopes a r e 0.25 X 10 -2, 1.40 • 10 -3, and 4.43 x 10 -2 mg 2 cm -4 min -I at 700, 800, and 900~ respectively.

The independence of kp with the H20/H 2 pressure ratio can be seen in Table II for runs conducted at 800 and 900~ with log (PH2 s/PH2) = --0.308. These runs were conducted with H30/H 3 pressure ratios between

8 I ' I I ' I , I , I

=o , : / T �9

�9 $

o 0

- 700 *

e0 0 .5 1.0 1.5 3 . 0 2 . 5 3 .0

ALOG H=S/H z Fig. 6--Parabolic rate constant, kp, as a function of (A log H2S/H2). �9 700, C) 800~149 900~

0.004 and 0.97. There was v i r t u a l l y no dependence of kp on PH20/PH2 at any given t e m p e r a t u r e .

If the H2S/H 3 p r e s s u r e ra t io was below that at the F e O - F e 3 0 4 - F e S - g a s equ i l ib r ium, the sulfidation was v e r y slow and ceased af te r a s m a l l weight gain and a per iod of about th ree hours . No i n t e rm ed ia t e l aye r of Fe304 f o r m e d upon subsequent me ta l log raph ic e x a m i - nation. In c a s e s where the H3S/H 2 p r e s s u r e ra t io was g r e a t e r than point H in Fig. 2, a continuous Fe304 l a y e r f o r m e d dur ing the f i r s t few minutes of sulf idat ion; this l aye r r e m a i n e d throughout the e n t i r e p r o c e s s .

DISCUSSION

The e x p e r i m e n t a l r e su l t s as p r e s e n t e d in Figs . 4 and 5 r e f l e c t parabol ic sulf idat ion k ine t ics except for an in i t ia l pe r iod of nonparabol ic sulf idat ion. During this in i t ia l pe r iod an i n t e rmed ia t e l aye r of FesO 4 is f o r m e d be tween the FeO c o r e and the ex te rna l FeS l aye r s . Af ter the compos i t ions of the va r i ous phases at the FeO/Fe304 and F e 3 0 4 / F e S in t e r f aces become invar iant , the parabo l ic r a t e law b e c o m e s opera t ive .

The pa rabo l i c nature of the sulf idat ion p r o c e s s is cons i s t en t with the model employed in the de r iva t ion of Eq. [17]. This equation has been de r ived under the assumpt ion that i ron is the only mobi le spec ies in the s y s t e m and that the r eac t ion p r o c e e d s by the diffusion of i ron f r o m the FeO co re to the F e S / g a s phase bound- ary. Accord ing to the model f luxes of i ron in the ad- jacent Fe304 and FeS z phases d ic ta te the t r a n s f e r of i ron a c r o s s the F e 3 0 4 / F e S z in t e r f ace and the su l f ida- tion k ine t i cs . F r o m the r e l a t ion for kp given in Eq. [19], it is apparent that the pa rabo l i c r a t e constant is p ropor t iona l to the d i f fe rence be tween the ra t io , RD, of Fe d i f fus iv i t i e s and the ra t io , RG, of Fe ac t iv i ty g rad ien t s in the Fe304 and FeS z phases as defined in

Eqs. [20] and [21]. Since D F%O~ is at l ea s t two to t h r ee Fe _FeS z

o r d e r s of magnitude s m a l l e r t h a n / ) F e , the Fe ac t i v - ity grad ien t in the Fe304 l aye r is expec ted to be v e r y l a rge c o m p a r e d to that in the FeS z l aye r , and the l i m - i t ing flux would be the Fe flux in the FeaO 4 phase. ](R D - RG)I is a constant dur ing pa rabo l i c sulf idat ion and is found to be quite sma l l (< 1) on the bas i s of the m e a s u r e d kp va lues and the r e p o r t e d Fe d i f fus iv i t ies (Fig. 1).

F o r some e x p e r i m e n t s c a r r i e d out at 900~ the pe - r iod of pa rabo l i c sulf idat ion was fol lowed by a pa s s ive s tage with negl ig ib le r a t e of sulf idat ion. Such v i r tua l ending of the sulf idat ion p r o c e s s was found to occur a f te r the growing Fe304 l aye r c o m p l e t e l y r ep laced the

60-VOLUME 6B, MARCH 1975 METALLURGICAL TRANSACTIONS B

FeO core , as ver i f i ed by meta l lographic examinat ion. During this pass ive stage the l imi t ing flux, rFe304 de- ~ F e ' c rease s , as the FesO 4 layer undergoes composit ional changes to reach uniform iron act iv i ty a c r o s s the s a m - ple . At this point the reac t ion c e a s e s . This observat ion i s cons i s t en t with the as sumpt ion that the FeS z l ayer is v i r tua l ly i m p e r m e a b l e to oxygen.

SUMMARY

The sulf idation of FeO in HaS-HzO-H2-Ar a t m o s - p h e r e s has been studied by t h e r m o g r a v i m e t r i c m e t h - ods at t e m p e r a t u r e s of 700, 800, and 900~ During the init ial s tage of sulf idation (ca. 10 to 100 min.) , a pro tec t ive layer of FeS f o r m e d on the sample , and an in termedia te layer of Fe304 formed between the FeO and the FeS l a y e r s . With the e s tab l i shment of constant c o m p o s i t i o n s in the adjacent phases at the var ious in- t erphase boundaries , the sulf idation react ion obeyed a parabol ic rate law. The parabol ic rate constant var ied f r o m 0.22 • 10 -2 m g z c m -~ min -1 at 700~ to 6.5 • 10 -2 m g 2 c m -~ min -1 at 900~ These k inet i c s w e r e c o n s i s - tent with a sulf idation mode l based on f luxes of Fe in the FeaO 4 and FeS phases . Some 900~ e x p e r i m e n t s entered a p a s s i v e s tage after the comple te c o n v e r s i o n of the FeO core to Fe304. This p a s s i v i t y sugges ted that the FeS layer was v ir tua l ly i m p e r m e a b l e to oxygen dur- ing the ent ire sulf idation p r o c e s s .

ACKNOWLEDGMENTS

This manuscr ipt is based on a d i s ser ta t ion submit ted by Scott M c C o r m i c k in part ial ful f i l lment of the r e - qu irements for the Ph.D. degree at Purdue Univers i ty . The r e s e a r c h was supported by USAEC Contract AT (11-1) -1436 and a fe l lowship awarded by the Inland S t e e l - R y e r s o n Foundation, Inc.

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M E T A L L U R G I C A L TRANSACTIONS B VOLUME 6B, MARCH 1 9 7 5 - 6 1