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On the growth kinetics of ferrite plates and allotriomorphs in high-nickel FeCNi alloys
Scripta
.XlETAI,I,UR(~ICA
V o l . 19, pp. 1 1 7 1 - 1 1 7 6 , 1985 P r i n t e d in the U.S.A.
Pergall/on P r e s s I, t d . AI', r i g h t s reserved
ON THE GROWTH KINETICS OF FERRITE PLATES AND ALLOTRIOMORPHS IN HIGH-NICKEL Fe-C-Ni ALLOYS
W.T. Reynolds, Jr. and H.I. A a r o n s o n Department o f Metallurgical Engineering and M a t e r i a l s Science Carnegie-Mellon University Pittsburgh, Pa. 15213 U.S.A.
(Received May 29, (Revised .July 3],
1985) 1985)
In 1967, Rao and Winchell (1) r e p o r t e d their careful m e a s u r e m e n t s of the lengthening kinetics o f bainite plates at 4 0 0 ° C in high-purity Fe~C-Ni a l l o y s (2). The e x p e r i m e n t a l g r o w t h rates w e r e compar ed with those calculated f r o m a c a p i l l a r i t y ( 3 ) - m o d i f i e d v e r s i o n o f the Horvay-Cahn (4) anal ysi s o f the d i f f u s i o n - c o n t r o l l e d g r o w t h kinetics o f elliptical p a r a b o l o i d s . The calculated lengthening rates were f ound to be about 100-fold greater than the measured rates. This important result has been r e p e a t e d l y cited in the phase t r a n s f o r m a t i o n literature. In a context of particular interest to the present authors, Hehemann (5) in 1972 and Christian and Edmonds (6) in 1984 have used this f i n d i n g as evidence against the existence o f a solute drag-like e f f e c t (SDLE) (7-10). Br i ef l y, this e f f e c t p o s t u l a t e s reduction in the paraequilibrium m i g r a t i o n kinetics o f d i s o r d e r e d areas o f austenite:ferrite b o u n d a r i e s by nonequilibrium a d s o r p t i o n thereat o f a s u b s t i t u t i o n a l solute which decreases the a c t i v i t y o f carbon in austenite and thus the carbon c o n c e n t r a t i o n gradient driving growth. Since Ni increases the a c t i v i t y o f carbon in austenite (11,12), the Rao-Winchell result is not explicable as a SDLE and has a c c o r d i n g l y been taken as indicative o f the general absence o f such an e f f e c t . The present authors w e r e m o t i v a t e d to r e - e x a m i n e the Rao-Winchell {RW) calculations p r i m a r i l y because their g r o w t h kinetics analysis was r e p o r t e d a f e w year s b e f o r e the highly s o p h i s t i c a t e d Trivedi (13} t r e a t m e n t o f plate lengthening kinetics became available. Taken in conj unct i on with earlier c o n s i d e r a t i o n s by T r i v e d i and Pound (14) on the n u m e r i c a l l y serious p r o b l e m arising f r o m the influence o f the exponential v a r i a t i o n o f the d i f f u s i v i t y o f carbon in austenite with carbon c o n c e n t r a t i o n upon the lengthening rate, the a v a i l a b i l i t y o f this t r e a t m e n t appeared to warrant further analysis o f the RW g r o w t h rate data. A further incentive f o r the present study was the RW calculation o f the radius o f plate edges y i e l d i n g the maximum g r o w t h rate as 0.03-0.043 nm (no m e a s u r e m e n t s o f these radii were reported); since these values are but a small f r a c t i o n o f one lattice parameter o f ferrite, they appear p h y s i c a l l y implausible. In an Fe-0.24 WlO C alloy, this radius is 6-6.5 nm in the v i c i n i t y o f 400° C (15). Three o m i s s i o n s or s i m p l i f i c a t i o n s utilized in the present analysis require comment. On the o b s e r v a t i o n of Speich and Cohen (16), f o r example, the leading edge of bainite plates is free o f carbide; h e n c e , p l a t e lengthening can be analyzed by cons i der i ng the bainite plates to be, o p e r a t i o n a l l y , plates o f p r o e u t e c t o i d f e r r i t e (17). The data of G o o d e n o w et. a/. (18) on bainite plate lengthening rates in 8.7 AIO Ni steels w i l l not be utilized. A l t h o u g h their measured rates were even s l o w e r than those of RW under c o m p a r a b l e c o n d i t i o n s , the presence o f n o n - n e g l i g i b l e a m o u n t s o f other s u b s t i t u t i o n a l a l l o y i n g elements in most o f their a l l o y s (particularly, o f 0.60-0.79 W/O Mn) gives rise to concern about the p o s s i b i l i t y o f at least additive, if not s y n e r g i s t i c e f f e c t s , o f such c o m p o n e n t s upon g r o w t h kinetics. Finally, the o f t raised, o f t disputed v i e w that shear may p o s s i b l y play s o m e role in the bainite reaction, which w o u l d of course alter d r a s t i c a l l y the c o n s i d e r a t i o n s o f this paper, is left ent i r el y to literature past and future f o r disputation. Trivedi A n a l y s i s of RW Plate Len t ~ n i n g Rates The RW lengthening rate data w e r e f i r s t r e p l o t t e d in Fig. 1 in a manner c o n s i s t e n t with the variables used by Trivedi. A s s u m i n g that Ni does not p a r t i t i o n b e t w e e n f e r r i t e and austenite during the reaction times used (19), the carbon c o n c e n t r a t i o n s c o r r e s p o n d i n g t o x~Y, the af(a+ 7) and to xY a, the yl(a+ 7} paraequilibrium phase b o u n d a r i e s in Fe-C-10.2 AIQ Ni a l l o y s were c o m p u t e d f r o m the H ~ l e r t - S t a f f a n s o n model (HS) (20,21) at 400°C. For x~Y, RW o b t a i n e d 4.3 x 10 .4 whereas HS y i e l d s 2.0 x 10-4; f o r xY a, the c o m p a r a b l e f i g u r e s are 0.128 and 0.108. The HS data w e r e used to calculate the sans~eai~illarity supersaturations show n in Fig. 1, i.e., ~ = (x7 ~ - x )/(x7 a - x~Y), where x is the atom f r a c t i o n o f carbon o y Y 7 Y
]171 0036 9748/85 $3.00 + .00 Copyright (c) 1985 Pergamon Press
Ltd.
1172
GROWTH KINETICS OF FERRITE
10-2
I
I
I
i
T
Vol.
I
19, No.
l0
I
I~ ~
u
E
,/
i0-~ I"
J I
f s"x
J
"
2 0 0 -~--~2
~
/.Lo= 6.0 xl 0 -
x= Rao and Winchell ExperimentoI Data
I
).95
L 0.95
I
I 0.97
I
I 0.99
I
XrTa -X 7 &"~'O =
(Rao and Winchell supersaturation.
(1))
yT~
~T
_ya-f
~a
Fig. 1: Variation o f calculated and o f experimental lengthening rates o f bainite plates at 4 0 0 ° C in F e - C - I O . 2
A/O
Ni
alloys
with
in the a l l o y . The l e n g t h e n i n g rate, V, and the radius o f curvature s i m u l t a n e o u s s o l u t i o n o f the f o l l o w i n g e q u a t i o n s (13): VOo
re
~o = I 1 +
Sl(p)
--
by
]
+ -:{}oS2(p)
#o(X;=.xy)
r
of the p l a t e edges, r, w e r e then c a l c u l a t e d
(1)
r
~o[S,(p)-
1 1 p(1 - ~ + ~)S,(p)
dS2(P) ] - p dp
=
(2)
rc
[( p
1 ~) I - T +
VOo +
1 1
V~'~ 0
dSI(P) ]
(1 - T + ~)S,(p) + " Fo(XY=-x7 ) y dp P ° ( x T7 a - x )7 Eq. (2) w a s here o b t a i n e d b y d i f f e r e n t i a t i n g Eq. (1) w i t h re sp e ct t o r and se tti n g dV/dr equal to zero. In these e q u a t i o n s , I = (~rp)'/'°exp(p)°erfc(p'/'), p = Vr/2D, /Jo = i n t e r f a c e k i n e t i c c o e f f i c i e n t , r¢ = critical
Vol.
19,
No.
lV
GROW'Ell
radius ( s u f f i c i e n t t o p r e v e n t and P o u n d (14), the w e i g h t e d
KJN~!'['[CG
()I'
FliNRIII:
',! ,~
g r o w t h ) and S ( p ) and $2(p) are t r a n s c e n d e n t a l f u n c t i o n s o f p. a v e r a g e d i f f u s i v i t y o f c a r b o n in a u s t e n i t e , D, is u t i l i z e d in p:
With
Trivedi
x)` a
)`
D . . . . . . X )`a
)`
X
-
S
D{x)dx
(3
)` ×)`
w h e r e D(x), the c o m p o s i t i o n - d e p e n d e n t diffusivity o f c a r b o n in a u s t e n i t e , is d e s c r i b e d b y the e m p i r i c a l r e l a t i o n s h i p o f K a u f m a n et. a/, (17). Since Ni a p p e a r s to increase the d i f f u s i v i t y o f c a r b o n in a u s t e n i t e j u s t s l i g h t l y at 1 0 0 0 ° C and data are n o t a v a i l a b l e on the t e m p e r a t u r e - d e p e n d e n c e o f this e f f e c t (22), no a t t e m p t w a s m a d e to i n c o r p o r a t e it in the e q u a t i o n f o r D(x), N u m e r i c a l i n t e g r a t i o n o f Eq.(3) y i e l d s v a l u e s v a r y i n g o n l y f r o m 6.38 x 10 -~] t o 6.78 x 10 -~ cm2/sec as x is i n c r e a s e d f r o m 0.0012 to 0.0075. It is v e r y i m p o r t a n t to n o t e (in the c o n t e x t o f T r i v e d i - P o u n d ) that ~ v a l u a t i o n o f O at the m i n i m u m x = 0.0012 y i e l d s 2.08 x 10 ~ cm2/sec w h e r e a s at xY a = 0.108, D = 2.69 x 10 ~° cm2/see. This e n o r m o u S ' range of d i f f u s i v i t i e s o f c a r b o n in a u s t e n i t e w h i c h )'could be u t i l i z e d under the c i r c u m s t a n c e s o f the RW e x p e r i m e n t s indicate.~the crucial n u m e r i c a l i m p o r t a n c e o f this f a c t o r in c a l c u l a t i n g the l e n g t h e n i n g rate. The o t h e r p a r a m e t e r s n e e d e d to s o l v e Eqns. (1) and (2), S , S , dS /dp and d S j d p , w e r e approximated f r o m graphs o f t h e s e f u n c t i o n s p r e s e n t e d b y T r i v e d i (14). Eqns'. (1}2 and 2 w e r e s o l v e d using a m o d i f i e d N e w t o n m e t h o d in w h i c h the J a c o b i a n w a s a p p r o x i m a t e d b y f i n i t e d i f f e r e n c e s . A check on these s o l u t i o n s with a simplex algorithm supported their accuracy. Results o f C a l c u l a t i o n s F o l l o w i n g S i m o n e n et. el. (15), s o l u t i o n s w e r e f i r s t o b t a i n e d t a k i n g the i n t e r r a c i a l e n e r g y o f the p l a t e edges, 7, as 800 m J i m 2 (and u t i l i z i n g the T r i v e d i - P o u n d (14) e x p r e s s i o n f o r c a p i l l a r i t y at p l a t e edges), i.e., a s s u m i n g that the e d g e s h a v e a d i s o r d e r e d s t r u c t u r e . Hence Fo = oo. A s s h o w n on Table I, r c a l c u l a t e d on this basis v a r i e s w i t h s u p e r s a t u r a t i o n f r o m 20 to 33 nm. N o t e that the r e s u l t i n g p l o t o f V v a l u e s in Fig. 1 has a s u p e r s a t u r a t i o n d e p e n d e n c e q u i t e s i m i l a r to that f o u n d e x p e r i m e n t a l l y b y RVV and l y i n g at higher rates b y a f a c t o r o f o n l y 4.6. If one n o w uses an i n t e r f a c i a l e n e r g y o f 200 m J / m 2 ( w i t h RW and K a u f m a n et. a/.), on the a s s u m p t i o n that the p l a t e e d g e s are p a r t i a l l y c o h e r e n t , and also a c c e p t s the physically implausible assumption that l e n g t h e n i n g is d i f f u s i o n - c o n t r o l l e d rather than l e d g e - c o n t r o l l e d (15,23,24), Fig. 1 s h o w s that t h e s e c a l c u l a t e d V's lie a b o u t 2 0 - f o l d higher than t h o s e m e a s u r e d b y RW. The f i n a l set o f c a l c u l a t i o n s again t o o k 7 = 200 m Jim 2 and v a r i e d Ho to f i t the m e a s u r e d l e n g t h e n i n g rate at each s u p e r s a t u r a t i o n . Table I i n c l u d e s the v a l u e s o f r and Ho o b t a i n e d f o r each a l l o y . N o t i n g that ~o a p p e a r s t o v a r y a p p r e c i a b l y w i t h s u p e r s a t u r a t i o n , p l o t s o f c a l c u l a t e d V vs. ~ have been i n c l u d e d in Fig. 1 u t i l i z i n g the l a r g e s t and s m a l l e s t Fo'S o b t a i n e d . N a t u r a l l y , the s u p e r s a t u r a t i o n ? - d e p e n d e n c e of V no l o n g e r m a t c h e s that o b t a i n e d e x p e r i m e n t a l l y . Table I: Summary o f Calculations Atom fract, of C in a l l o y , x 7 C Supersaturation,
Qo
0.0012
0.0020
0.0027
0.0040
0.0075
0.991
0.983
0.977
0.965
0.932
7 ~ 800 m J / m : Fo = oo
V(cm/s) r(nm)
18.2 x 10 4 20.0
9.50 21.9
7 = 200 m J / m 2 = oo
V(cm/s) r(nm)
72.8 x 10 .4 5.0
37.9 x 104 5.5 2.80 x 10 .4 33.9
7 = 200 m J/m2: F0 = 4.0 x 10 .3 if0 = 1.5 X 1 0 .3
3.21 x 10 .4 V r 44.7 V
/l 0 =
V
X
6.43 23.4
1 0 .4
r 1.0
x
1 0 .3
3.71 x 10 4 26.0
1.42 x 10 4 32.9
25.6 x 10 .4 5.9
14.9 x 10 .4 6.5
5.68 x 10 ' 8.2
2.52 x 10 .4 29.0 1.06 x 1 0 .4 58.3
2.12 X 1 0 "4 24.2 0.930 x 10 ~ 45.2 0.645 ~ 10 ~ 60.5 0.399 x 10 4 88.1
X
10 4
r
Ho = 0 . 6
x
10 3
V
0.605 x 10 -4 95.0
0.481 x 10 -4 169.0
0.450 x 10 `4 124.0
1.43 × 10 .4 20.1
0,482 x 10 .4 42,7 0.307 x 10 4 59.4
Discussion With
the p h y s i c a l l y
acceptable
pair
of
conditions
that
7 = 800
m J / m 2 and
yo = oo, the
discrepancy
1174
GROWTH KINETICS OF FERRITE
Vol.
19, No.
l0
b e t w e e n calculated and measured lengthening rates is reduced to a f a c t o r o f ca. 4.6, with the calculated rates being higher. In Fe-C a l l o y s , Simonen et. al. (15) f ound the calculated rates under the same c o n d i t i o n s to be roughly 1.8-fold higher than the experimental ones at 450° C (and a s u p e r s a t u r a t i o n o f ca. 0.9, o n l y a little b e l o w those used by RW), the l o w e s t t emper at ur e they e m p l o y e d . This r at i o diminished to 1.2 at 550°C, 0.6 at 650°C and 0.2 at 700°C (the latter c o r r e s p o n d i n g to s u p e r s a t u r a t i o n s averaging ca. 0.5.). Particularly in v i e w o f the great s e n s i t i v i t y o f V to the precise choice o f the const ant averaged carbon d i f f u s i v i t y in austenite, one might aver, as did Purdy and Hillert (25) recently, that f e r r i t e and bainite plate lengthening in Fe-C alloys, and n o w perhaps even in Fe-C-Ni alloys, takes place at e s s e n t i a l l y the rates permitted by the v o l u m e d i f f u s i o n o f carbon in austenite under the applicable boundar y conditions. This o u t c o m e was, in fact, predicted a g e n e r a t i o n ago (23). However, this p r e d i c t i o n has not been borne out in several n o n - f e r r o u s a l l o y s y s t e m s in which the interfacial structure o f plate edges can be i n v e s t i g a t e d with TEM. The edges o f 8 ' AI-Cu (26,27) and y A I - A g (28,29) plates have been shown q u a n t i t a t i v e l y to have a s e s s i l e d i s l o c a t i o n structure, and g r o w t h ledges have been d i r e c t l y o b s e r v e d on plate edges during t r a n s f o r m a t i o n in 7 A I - A g (28). M o r e recently, indications o f a p a r t i a l l y coherent structure were found at the edges o f a 1 Cu-Zn plates, though this structure could not be s u f f i c i e n t l y r e s o l v e d f o r detailed characterization (30). However, both ), A I - A g (28) and 8 ' AI-Cu (27) plates (the latter p a r t i c u l a r l y when their broad faces are p a r t i a l l y coherent (27) ) lengthen with e s s e n t i a l l y v o l u m e i n t e r d i f f u s i o n c o n t r o l l e d kinetics. Those o f a 1 Cu-Zn appear to lengthen a little more r a p i d l y than predicted f o r d i s o r d e r e d (and also p a r t i a l l y coherent) plate edges (30); lack o f i n f o r m a t i o n on the l o c a t i o n o f the a /(a + ,8') phase boundary (31), h o w e v e r , makes exact c o m p a r i s o n b e t w e e n cal cul at i on and measurement s o m e w h a t uncertain. Optical m i c r o s c o p y p r o v i d e s limited support f o r the presence o f a ledge structure on the edges o f f e r r i t e plates (32,33). A det ai l ed t r e a t m e n t o f plate lengthening by the ledge mechanism is badly needed, even though this is surely a f o r m i d a b l e mathematical p r o b l e m (34,35). For the present, though, it appears that c o m p a r i s o n o f the measured ki net i cs o f plate lengthening with those calculated assuming v o l u m e d i f f u s i o n c o n t r o l is o f t e n not a useful independent means o f assessing the g r o w t h mechanism c o n t r o l l i n g the lengthening process. However , p r o v i d e d that the f o r e g o i n g 4 . 6 - f o l d discrepancy between calculated and measured V's is accepted as significant, in the case o f Fe-C-Ni a l l o y s a s o m e w h a t clearer result emerges when a t t e m p t s are made to bring the t w o sets o f V's in agreement by i n t e r p o s i n g a u n i f o r m barrier to interface m o v e m e n t through assigning a f i n i t e value to /~o" Such a value o f /Jo implies a p a r t i a l l y coherent structure at the plate edges. In this situation, a value o f 200 mJ/m 2 is usually assigned to the e n e r g y o f a u s t e n i t e : f e r r i t e boundaries (1,17,36). Whereas Simonen et al (15) f o u n d that ,~o varies f r o m 0.60 at 7 0 0 ° C and Q ~, 0.5 d o w n to 0.07 at 450° C and ~ o -,, 0.9, Table I s h o w s that those f o r Fe-C-Ni fall in the range 4 x °103 to 6 x 10 .4 at ~ o = 0.99-0.93. Hence, the T r i v e d i t r e a t m e n t indicates that there is a more e f f e c t i v e barrier to g r o w t h at the edges o f f e r r i t e o f bainite plates in Fe-CNi than in Fe-C alloys. We suggest, h o w e v e r , that this barrier is likely to be a larger inter-ledge spacing in Fe-C-Ni alloys, pehaps because Ni i m p r o v e s matching b e t w e e n austenite and f e r r i t e at plate edges. The p r i m a r y reason f o r p r o p o s i n g this rather than a solute drag-like e f f e c t as the e x p l a n a t i o n f o r the d i f f e r e n c e s between calculated and measured g r o w t h rates in Fe-C-10.2 A/O Ni a l l o y s derives f r o m a c o m p a r i s o n o f e x p e r i m e n t a l l y measured thickening kinetics o f grain boundar y f e r r i t e a l l o t r i o m o r p h s (corrected f o r faceting) w i t h those calculated assuming the paraequilibrium (37) g r o w t h model (9). Fig. 2 reproduces such evidence f o r several Fe-C-X alloys. In t hose a l l o y s containing 3.28 W/O and 7.51 W/O Ni the ratio o f these rates is seen to be e s s e n t i a l l y unity at all temperatures studied. Si gni f i cant departures, on the other hand, are o b s e r v e d at s o m e temperatures in the Fe-C-Mn and Fe-C-Cr alloys, and these have been ascribed to a SDLE (9). TEM studies have shown that carbide p r e c i p i t a t i o n cannot play a s i g n i f i c a n t role in these d e v i a t i o n s (38). The s t r o n g e s t SDLE so far r e p o r t e d is f ound in Fe-C-Mo alloys. In an Fe-0.11 W/O C-1.95 WlO Mo alloy, f o r example, at the temperature o f the bay in the TTT-curve f o r i n i t i a t i o n o f t r a n s f o r m a t i o n , 650°C, the calculated parabolic rate constant f o r thickening o f grain b o u n d a r y a l t o t r i o m o r p h s is ca. 4 0 - f o l d greater than the e x p e r i m e n t a l l y measured one, c o r r e s p o n d i n g to a d i s c r e p a n c y in the averaged d i f f u s i v i t i e s o f carbon in austenite o f ca. 1600 (24,39,40). A l t h o u g h the interphase b o u n d a r y structure o f grain boundar y a l l o t r i o m o r p h s is not well est abl i shed e x p e r i m e n t a l l y , it is p r o b a b l e that a larger p r o p o r t i o n o f this structure is o f the d i s o r d e r e d t y p e than at plate broad faces and edges, s i m p l y because the a l l o t r i o m o r p h s are const r ai ned to f o l l o w an average g r o w t h path usually not parallel to w e l l matched conjugate habit planes. Since the SDLE is expect ed t o d e v e l o p o n l y at d i s o r d e r e d - t y p e areas o f a u s t e n i t e : f e r r i t e boundaries (7,8), the g o o d agreement b e t w e e n calculated and measured thichening rates o f grain boundar y f e r r i t e a l l o t r i o m o r p h s in Fe-C-Ni a l l o y s (9) is thus p a r t i c u l a r l y g o o d evidence f o r the absence o f the SDLE in this system. A less decisive though still useful piece o f evidence against the presence o f at least a strong SDLE in Fe-C-Ni a l l o y s is the circumstance that RW w e r e e v i d e n t l y able to make their m e a s u r e m e n t s on w e l l f o r m e d plates. In the bay region o f Fe-C-Cr (39) and e s p e c i a l l y o f F e - C - M o a l l o y s (39,41), wher e the SDLE is c o n s i d e r e d to be m o s t e f f e c t i v e (7,8), the W i d m a n s t a t t e n structure o f the f e r r i t i c c o m p o n e n t o f bainite
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No.
[0
GROWTH KINETICS OF FERR~TE
I
1175
I
I
F¢-O.40%C-
1 . 7 3 % Si x
10
w
F¢ - O.43°/o~ C - 7.51°/o N i .,~ o f
.
F~z-O.1 - 2°•° C - 3.28°/o Ni
_
_
./
N
"~J
--*-----
_
O1 Fe-O.12%C-3.O8 001 500
,
/oMn I
\ J
600
I
700 Tempcroture,
=
I
800
°C
Fig. 2: Variation with reaction temperature o f the ratio o f the corrected experimental to the calculated parabolic rate constants f o r thickening o f grain boundary allotriomorphs in Fe-C-X alloys, when calculations are performed on the basis of the paraequilibrium growth model (9). is v e r y degenerate, and can even vanish e n t i r e l y at s u f f i c i e n t l y high carbon and X concentrations. At l o w e r t e m p e r a t u r e s , it should f i n a l l y be noted, the normal W i d m a n s t a t t e n m o r p h o l o g i e s are r e c o v e r e d and g r o w t h kinetics tend to rise t o w a r d the values which they w o u l d have had in the absence o f a SDLE. C oncl usi ons Recalculation o f the data reported by Rao and Winchell (1) on the lengthening kinetics o f f e r r i t e / b a i n i t e plates at 400°C in Fe-C-10.2 A/O Ni a l l o y s using the subsequently d e v e l o p e d Trivedi (13) t r e a t m e n t and the T r i v e d i - P o u n d (14) approach to handling the c o m p o s i t i o n dependence o f the d i f f u s i v i t y o f carbon in austenite reduces the ratio o f calculated to measured lengthening rates f r o m 100 to less than 5 p r o v i d e d the interfacial energy f o r d i s o r d e r e d a u s t e n i t e : f e r r i t e boundaries (ca. 800 mJ/m 2) and an i n f i n i t e i n t e r f a c e kinetic c o e f f i c i e n t , Fo, are utilized. To obtain exact agreement b e t w e e n the RW measurements and the calculations, it is necessary to set ), = 200 mJ/m 2 (appropriate to p a r t i a l l y coherent boundaries) and introduce f i n i t e values o f /~o' which are f r o m one to t w o orders o f magnitude smaller than their c o u n t e r p a r t s in Fe-C a l l o y s (15). This d i f f e r e n c e is suggested to arise f r o m a marked increase in the inter-ledge spacing at the edges o f f e r r i t e / b a i n i t e plates in Fe-C-Ni alloys. That this d i f f e r e n c e is not due to a solute drag-like e f f e c t (SDLE) is indicated by the g o o d agreement obt ai ned between e x p e r i m e n t a l l y measured thickening kinetics of grain boundar y allotriomorphs and t hose calculated assuming paraequilibrium and carbon d i f f u s i o n - c o n t r o l in Fe-C-Ni a l l o y s (9). This conclusion is in agreement with current v i e w s o f the SDLE (8,10) but is in o p p o s i t i o n to suggest i ons that the s l o w e r - t h a n - c a l c u l a t e d lengthening rates o f f e r r i t e / b a i n i t e plates in Fe-C-Ni a l l o y s f o u n d by Rao and Winchell (1) tend to d i s p r o v e the existence o f a SDLE (4-6). Acknowledgements A p p r e c i a t i o n is e x p r e s s e d by WTR, Jr. f o r support f r o m the Amer i can Iron and Steel Institute and the Electric P o w e r Research Institute and by HIA f o r support f r o m the NSF-funded Center f o r the Study o f M a t e r i a l s through Grant DMR-81-19507. References 1. 2. 3, 4. 5. 6.
M.M, Rao and P,G. Winchell, Trans. T M S - A I M E 239, 956 (1967). M.M. Rao, n.J. Russell and P.G. Winchell, Trans. T M S - A I M E 239, 634 (1967). M. Hillert, J e r n k o n t o r e t s Ann. 140, 757 (1957). G. H o r v a y and J.W. Cahn, A c t a Met. 9, 695 (1961). R.F. Hehemann, K.R. Kinsman and H.I. A a r o n s o n , Met. Trans. 3, 1077 (1972). J.W. Christian and D.V. Edmonds, Phase T r a n s f o r m a t i o n s in Ferrous A l l o y s , p.293, T M S - A I M E , Warrendale, PA (1984). 7. K.R. Kinsman and H.I. A a r o n s o n , T r a n s f o r m a t i o n and H a r d e n a b i l i t y in Steel, p.39, Climax M o l y b d e n u m Co., Ann Arbor, MI (1967). 8. H.I. A a r o n s o n , The Mechanism o f Phase T r a n s f o r m a t i o n s in Crystalline Solids, p.270, Institute o f
1176
GROWTH KINETICS OF FERRITE
Vol.
19, No.
Metals, London, UK (1969). 9. J.R. Bradley and H.I. Aaronson, Met. Trans. 12A, 1729 (1981). 10. W.T. Reynolds, Jr., M. Enomoto and H.I, Aaronson, Phase Transformations in Ferrous A l l o y s , p.155, TMS-AIME, Warrendale, PA (1984). 11. R.P. Smith, Trans. TMS-AIME 218, 62 (1960). 12. A.J. Heckler and P.G. Winchell, TMS-AIME 227, 732 (1963). 13. R. Trivedi, Met. Trans. 1, 921 (1970). 14. R. Trivedi and G.M. Pound, J. App. Phys. 38, 3569 (1967). 15. E.P. Simonen, H.I. Aaronson and R. Trivedi, Met. Trans. 4, 1239 (1973). 16. G.R. Speich and M. Cohen, Trans. TMS-AIME 218, 1050 (1960). 17. L. Kaufman, S.V. Radcliffe and M. Cohen, D e c o m p o s i t i o n of Austenite by Diffusional Processes, p.313, Interscience, NY (1962). 18. R.H. Goodenow, S.J. Matas and R.F. Hehemann, Trans. TMS-AIME 227, 651 (1963). 19. H.L Aaronson and H.A. Domian, TMS-AIME 236, 781 (1966). 20. M. Hillert and L.I. Staffansson, Acta Chem. Scand. 24, 3618 (1970). 21. B. Uhrenius, Hardenability Concepts with A p p l i c a t i o n s to Steel, p.5, TMS-AIME, Warrendale, PA (1978). 22. C. Wells and R.F. Mehl, Trans. AIME 140, 279 (1940). 23. H.I. Aaronson, D e c o m p o s i t i o n of Austenite by Diffusional Processes, p.387, lnterscience, NY (1962). 24. H.I. Aaronson, C. Laird and K.R. Kinsman, Phase Transformations, p.313, ASM, Metals Park, OH (1970). 25. G.R. Purdy and M. Hillert, Acta Met. 32, 823 (1984). 26. C. Laird and H.I. Aaronson, Trans. TMS-AIME 242, 591 (1968). 27. R. Sankaran and C. Laird, Acta Met. 22, 957 (1974). 28. C. Laird and H.I. Aaronson, Acta Met. 15, 73 (1967). 29. J.M. Howe, H.I. Aaronson and R. Gronsky, Acta Met., in press. 30. K. Chattopadhyay and H.I. Aaronson, Acta Met., in press. 31. K. Chattopadhyay, Proceedings of an International Conference on Solid-Solid Phase Transformations, p.990, TMS-AIME, Warrendale, PA (1983). 32. R.F. Mehl, C.S. Barrett and D.W. Smith, Trans. AIME 105 215 (1933). 33. E. Eichen, H.I. Aaronson, G.M. Pound and R. Trivedi, Acta Met. 12, 219 (1963). 34. W.P. Bosze and R. Trivedi, Acta Met. 23, 713 (t975). 35. C. Atkinson, private communication, U. of Pittsburgh, 1983. 36. L. Kaufman and M. Cohen, Progress in Metal Physics 7, 165 (1958). 37. J.B. Gilmour, G.R. Purdy and J.S. Kirkaldy, Met. Trans. 3, 1455 (1972). 38. G.J. Shiflet, H.I. Aaronson and J.R. Bradley, Met. Trans. 3, 1743 (1981). 39. P.G, Boswell, K.R. Kinsman, G.J. Shiflet and H.I. Aaronson, unpublished research. 40. H.I. Aaronson, S.K. Liu, W.T. Reynolds, Jr and G.J. Shiflet, J. Mat. Sci., in press. 41. H. Tsubakino and H.t. Aaronson, unpublished research, Carnegie-Mellon Univ., (1982).
i0
.XlETAI,I,UR(~ICA
V o l . 19, pp. 1 1 7 1 - 1 1 7 6 , 1985 P r i n t e d in the U.S.A.
Pergall/on P r e s s I, t d . AI', r i g h t s reserved
ON THE GROWTH KINETICS OF FERRITE PLATES AND ALLOTRIOMORPHS IN HIGH-NICKEL Fe-C-Ni ALLOYS
W.T. Reynolds, Jr. and H.I. A a r o n s o n Department o f Metallurgical Engineering and M a t e r i a l s Science Carnegie-Mellon University Pittsburgh, Pa. 15213 U.S.A.
(Received May 29, (Revised .July 3],
1985) 1985)
In 1967, Rao and Winchell (1) r e p o r t e d their careful m e a s u r e m e n t s of the lengthening kinetics o f bainite plates at 4 0 0 ° C in high-purity Fe~C-Ni a l l o y s (2). The e x p e r i m e n t a l g r o w t h rates w e r e compar ed with those calculated f r o m a c a p i l l a r i t y ( 3 ) - m o d i f i e d v e r s i o n o f the Horvay-Cahn (4) anal ysi s o f the d i f f u s i o n - c o n t r o l l e d g r o w t h kinetics o f elliptical p a r a b o l o i d s . The calculated lengthening rates were f ound to be about 100-fold greater than the measured rates. This important result has been r e p e a t e d l y cited in the phase t r a n s f o r m a t i o n literature. In a context of particular interest to the present authors, Hehemann (5) in 1972 and Christian and Edmonds (6) in 1984 have used this f i n d i n g as evidence against the existence o f a solute drag-like e f f e c t (SDLE) (7-10). Br i ef l y, this e f f e c t p o s t u l a t e s reduction in the paraequilibrium m i g r a t i o n kinetics o f d i s o r d e r e d areas o f austenite:ferrite b o u n d a r i e s by nonequilibrium a d s o r p t i o n thereat o f a s u b s t i t u t i o n a l solute which decreases the a c t i v i t y o f carbon in austenite and thus the carbon c o n c e n t r a t i o n gradient driving growth. Since Ni increases the a c t i v i t y o f carbon in austenite (11,12), the Rao-Winchell result is not explicable as a SDLE and has a c c o r d i n g l y been taken as indicative o f the general absence o f such an e f f e c t . The present authors w e r e m o t i v a t e d to r e - e x a m i n e the Rao-Winchell {RW) calculations p r i m a r i l y because their g r o w t h kinetics analysis was r e p o r t e d a f e w year s b e f o r e the highly s o p h i s t i c a t e d Trivedi (13} t r e a t m e n t o f plate lengthening kinetics became available. Taken in conj unct i on with earlier c o n s i d e r a t i o n s by T r i v e d i and Pound (14) on the n u m e r i c a l l y serious p r o b l e m arising f r o m the influence o f the exponential v a r i a t i o n o f the d i f f u s i v i t y o f carbon in austenite with carbon c o n c e n t r a t i o n upon the lengthening rate, the a v a i l a b i l i t y o f this t r e a t m e n t appeared to warrant further analysis o f the RW g r o w t h rate data. A further incentive f o r the present study was the RW calculation o f the radius o f plate edges y i e l d i n g the maximum g r o w t h rate as 0.03-0.043 nm (no m e a s u r e m e n t s o f these radii were reported); since these values are but a small f r a c t i o n o f one lattice parameter o f ferrite, they appear p h y s i c a l l y implausible. In an Fe-0.24 WlO C alloy, this radius is 6-6.5 nm in the v i c i n i t y o f 400° C (15). Three o m i s s i o n s or s i m p l i f i c a t i o n s utilized in the present analysis require comment. On the o b s e r v a t i o n of Speich and Cohen (16), f o r example, the leading edge of bainite plates is free o f carbide; h e n c e , p l a t e lengthening can be analyzed by cons i der i ng the bainite plates to be, o p e r a t i o n a l l y , plates o f p r o e u t e c t o i d f e r r i t e (17). The data of G o o d e n o w et. a/. (18) on bainite plate lengthening rates in 8.7 AIO Ni steels w i l l not be utilized. A l t h o u g h their measured rates were even s l o w e r than those of RW under c o m p a r a b l e c o n d i t i o n s , the presence o f n o n - n e g l i g i b l e a m o u n t s o f other s u b s t i t u t i o n a l a l l o y i n g elements in most o f their a l l o y s (particularly, o f 0.60-0.79 W/O Mn) gives rise to concern about the p o s s i b i l i t y o f at least additive, if not s y n e r g i s t i c e f f e c t s , o f such c o m p o n e n t s upon g r o w t h kinetics. Finally, the o f t raised, o f t disputed v i e w that shear may p o s s i b l y play s o m e role in the bainite reaction, which w o u l d of course alter d r a s t i c a l l y the c o n s i d e r a t i o n s o f this paper, is left ent i r el y to literature past and future f o r disputation. Trivedi A n a l y s i s of RW Plate Len t ~ n i n g Rates The RW lengthening rate data w e r e f i r s t r e p l o t t e d in Fig. 1 in a manner c o n s i s t e n t with the variables used by Trivedi. A s s u m i n g that Ni does not p a r t i t i o n b e t w e e n f e r r i t e and austenite during the reaction times used (19), the carbon c o n c e n t r a t i o n s c o r r e s p o n d i n g t o x~Y, the af(a+ 7) and to xY a, the yl(a+ 7} paraequilibrium phase b o u n d a r i e s in Fe-C-10.2 AIQ Ni a l l o y s were c o m p u t e d f r o m the H ~ l e r t - S t a f f a n s o n model (HS) (20,21) at 400°C. For x~Y, RW o b t a i n e d 4.3 x 10 .4 whereas HS y i e l d s 2.0 x 10-4; f o r xY a, the c o m p a r a b l e f i g u r e s are 0.128 and 0.108. The HS data w e r e used to calculate the sans~eai~illarity supersaturations show n in Fig. 1, i.e., ~ = (x7 ~ - x )/(x7 a - x~Y), where x is the atom f r a c t i o n o f carbon o y Y 7 Y
]171 0036 9748/85 $3.00 + .00 Copyright (c) 1985 Pergamon Press
Ltd.
1172
GROWTH KINETICS OF FERRITE
10-2
I
I
I
i
T
Vol.
I
19, No.
l0
I
I~ ~
u
E
,/
i0-~ I"
J I
f s"x
J
"
2 0 0 -~--~2
~
/.Lo= 6.0 xl 0 -
x= Rao and Winchell ExperimentoI Data
I
).95
L 0.95
I
I 0.97
I
I 0.99
I
XrTa -X 7 &"~'O =
(Rao and Winchell supersaturation.
(1))
yT~
~T
_ya-f
~a
Fig. 1: Variation o f calculated and o f experimental lengthening rates o f bainite plates at 4 0 0 ° C in F e - C - I O . 2
A/O
Ni
alloys
with
in the a l l o y . The l e n g t h e n i n g rate, V, and the radius o f curvature s i m u l t a n e o u s s o l u t i o n o f the f o l l o w i n g e q u a t i o n s (13): VOo
re
~o = I 1 +
Sl(p)
--
by
]
+ -:{}oS2(p)
#o(X;=.xy)
r
of the p l a t e edges, r, w e r e then c a l c u l a t e d
(1)
r
~o[S,(p)-
1 1 p(1 - ~ + ~)S,(p)
dS2(P) ] - p dp
=
(2)
rc
[( p
1 ~) I - T +
VOo +
1 1
V~'~ 0
dSI(P) ]
(1 - T + ~)S,(p) + " Fo(XY=-x7 ) y dp P ° ( x T7 a - x )7 Eq. (2) w a s here o b t a i n e d b y d i f f e r e n t i a t i n g Eq. (1) w i t h re sp e ct t o r and se tti n g dV/dr equal to zero. In these e q u a t i o n s , I = (~rp)'/'°exp(p)°erfc(p'/'), p = Vr/2D, /Jo = i n t e r f a c e k i n e t i c c o e f f i c i e n t , r¢ = critical
Vol.
19,
No.
lV
GROW'Ell
radius ( s u f f i c i e n t t o p r e v e n t and P o u n d (14), the w e i g h t e d
KJN~!'['[CG
()I'
FliNRIII:
',! ,~
g r o w t h ) and S ( p ) and $2(p) are t r a n s c e n d e n t a l f u n c t i o n s o f p. a v e r a g e d i f f u s i v i t y o f c a r b o n in a u s t e n i t e , D, is u t i l i z e d in p:
With
Trivedi
x)` a
)`
D . . . . . . X )`a
)`
X
-
S
D{x)dx
(3
)` ×)`
w h e r e D(x), the c o m p o s i t i o n - d e p e n d e n t diffusivity o f c a r b o n in a u s t e n i t e , is d e s c r i b e d b y the e m p i r i c a l r e l a t i o n s h i p o f K a u f m a n et. a/, (17). Since Ni a p p e a r s to increase the d i f f u s i v i t y o f c a r b o n in a u s t e n i t e j u s t s l i g h t l y at 1 0 0 0 ° C and data are n o t a v a i l a b l e on the t e m p e r a t u r e - d e p e n d e n c e o f this e f f e c t (22), no a t t e m p t w a s m a d e to i n c o r p o r a t e it in the e q u a t i o n f o r D(x), N u m e r i c a l i n t e g r a t i o n o f Eq.(3) y i e l d s v a l u e s v a r y i n g o n l y f r o m 6.38 x 10 -~] t o 6.78 x 10 -~ cm2/sec as x is i n c r e a s e d f r o m 0.0012 to 0.0075. It is v e r y i m p o r t a n t to n o t e (in the c o n t e x t o f T r i v e d i - P o u n d ) that ~ v a l u a t i o n o f O at the m i n i m u m x = 0.0012 y i e l d s 2.08 x 10 ~ cm2/sec w h e r e a s at xY a = 0.108, D = 2.69 x 10 ~° cm2/see. This e n o r m o u S ' range of d i f f u s i v i t i e s o f c a r b o n in a u s t e n i t e w h i c h )'could be u t i l i z e d under the c i r c u m s t a n c e s o f the RW e x p e r i m e n t s indicate.~the crucial n u m e r i c a l i m p o r t a n c e o f this f a c t o r in c a l c u l a t i n g the l e n g t h e n i n g rate. The o t h e r p a r a m e t e r s n e e d e d to s o l v e Eqns. (1) and (2), S , S , dS /dp and d S j d p , w e r e approximated f r o m graphs o f t h e s e f u n c t i o n s p r e s e n t e d b y T r i v e d i (14). Eqns'. (1}2 and 2 w e r e s o l v e d using a m o d i f i e d N e w t o n m e t h o d in w h i c h the J a c o b i a n w a s a p p r o x i m a t e d b y f i n i t e d i f f e r e n c e s . A check on these s o l u t i o n s with a simplex algorithm supported their accuracy. Results o f C a l c u l a t i o n s F o l l o w i n g S i m o n e n et. el. (15), s o l u t i o n s w e r e f i r s t o b t a i n e d t a k i n g the i n t e r r a c i a l e n e r g y o f the p l a t e edges, 7, as 800 m J i m 2 (and u t i l i z i n g the T r i v e d i - P o u n d (14) e x p r e s s i o n f o r c a p i l l a r i t y at p l a t e edges), i.e., a s s u m i n g that the e d g e s h a v e a d i s o r d e r e d s t r u c t u r e . Hence Fo = oo. A s s h o w n on Table I, r c a l c u l a t e d on this basis v a r i e s w i t h s u p e r s a t u r a t i o n f r o m 20 to 33 nm. N o t e that the r e s u l t i n g p l o t o f V v a l u e s in Fig. 1 has a s u p e r s a t u r a t i o n d e p e n d e n c e q u i t e s i m i l a r to that f o u n d e x p e r i m e n t a l l y b y RVV and l y i n g at higher rates b y a f a c t o r o f o n l y 4.6. If one n o w uses an i n t e r f a c i a l e n e r g y o f 200 m J / m 2 ( w i t h RW and K a u f m a n et. a/.), on the a s s u m p t i o n that the p l a t e e d g e s are p a r t i a l l y c o h e r e n t , and also a c c e p t s the physically implausible assumption that l e n g t h e n i n g is d i f f u s i o n - c o n t r o l l e d rather than l e d g e - c o n t r o l l e d (15,23,24), Fig. 1 s h o w s that t h e s e c a l c u l a t e d V's lie a b o u t 2 0 - f o l d higher than t h o s e m e a s u r e d b y RW. The f i n a l set o f c a l c u l a t i o n s again t o o k 7 = 200 m Jim 2 and v a r i e d Ho to f i t the m e a s u r e d l e n g t h e n i n g rate at each s u p e r s a t u r a t i o n . Table I i n c l u d e s the v a l u e s o f r and Ho o b t a i n e d f o r each a l l o y . N o t i n g that ~o a p p e a r s t o v a r y a p p r e c i a b l y w i t h s u p e r s a t u r a t i o n , p l o t s o f c a l c u l a t e d V vs. ~ have been i n c l u d e d in Fig. 1 u t i l i z i n g the l a r g e s t and s m a l l e s t Fo'S o b t a i n e d . N a t u r a l l y , the s u p e r s a t u r a t i o n ? - d e p e n d e n c e of V no l o n g e r m a t c h e s that o b t a i n e d e x p e r i m e n t a l l y . Table I: Summary o f Calculations Atom fract, of C in a l l o y , x 7 C Supersaturation,
Qo
0.0012
0.0020
0.0027
0.0040
0.0075
0.991
0.983
0.977
0.965
0.932
7 ~ 800 m J / m : Fo = oo
V(cm/s) r(nm)
18.2 x 10 4 20.0
9.50 21.9
7 = 200 m J / m 2 = oo
V(cm/s) r(nm)
72.8 x 10 .4 5.0
37.9 x 104 5.5 2.80 x 10 .4 33.9
7 = 200 m J/m2: F0 = 4.0 x 10 .3 if0 = 1.5 X 1 0 .3
3.21 x 10 .4 V r 44.7 V
/l 0 =
V
X
6.43 23.4
1 0 .4
r 1.0
x
1 0 .3
3.71 x 10 4 26.0
1.42 x 10 4 32.9
25.6 x 10 .4 5.9
14.9 x 10 .4 6.5
5.68 x 10 ' 8.2
2.52 x 10 .4 29.0 1.06 x 1 0 .4 58.3
2.12 X 1 0 "4 24.2 0.930 x 10 ~ 45.2 0.645 ~ 10 ~ 60.5 0.399 x 10 4 88.1
X
10 4
r
Ho = 0 . 6
x
10 3
V
0.605 x 10 -4 95.0
0.481 x 10 -4 169.0
0.450 x 10 `4 124.0
1.43 × 10 .4 20.1
0,482 x 10 .4 42,7 0.307 x 10 4 59.4
Discussion With
the p h y s i c a l l y
acceptable
pair
of
conditions
that
7 = 800
m J / m 2 and
yo = oo, the
discrepancy
1174
GROWTH KINETICS OF FERRITE
Vol.
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b e t w e e n calculated and measured lengthening rates is reduced to a f a c t o r o f ca. 4.6, with the calculated rates being higher. In Fe-C a l l o y s , Simonen et. al. (15) f ound the calculated rates under the same c o n d i t i o n s to be roughly 1.8-fold higher than the experimental ones at 450° C (and a s u p e r s a t u r a t i o n o f ca. 0.9, o n l y a little b e l o w those used by RW), the l o w e s t t emper at ur e they e m p l o y e d . This r at i o diminished to 1.2 at 550°C, 0.6 at 650°C and 0.2 at 700°C (the latter c o r r e s p o n d i n g to s u p e r s a t u r a t i o n s averaging ca. 0.5.). Particularly in v i e w o f the great s e n s i t i v i t y o f V to the precise choice o f the const ant averaged carbon d i f f u s i v i t y in austenite, one might aver, as did Purdy and Hillert (25) recently, that f e r r i t e and bainite plate lengthening in Fe-C alloys, and n o w perhaps even in Fe-C-Ni alloys, takes place at e s s e n t i a l l y the rates permitted by the v o l u m e d i f f u s i o n o f carbon in austenite under the applicable boundar y conditions. This o u t c o m e was, in fact, predicted a g e n e r a t i o n ago (23). However, this p r e d i c t i o n has not been borne out in several n o n - f e r r o u s a l l o y s y s t e m s in which the interfacial structure o f plate edges can be i n v e s t i g a t e d with TEM. The edges o f 8 ' AI-Cu (26,27) and y A I - A g (28,29) plates have been shown q u a n t i t a t i v e l y to have a s e s s i l e d i s l o c a t i o n structure, and g r o w t h ledges have been d i r e c t l y o b s e r v e d on plate edges during t r a n s f o r m a t i o n in 7 A I - A g (28). M o r e recently, indications o f a p a r t i a l l y coherent structure were found at the edges o f a 1 Cu-Zn plates, though this structure could not be s u f f i c i e n t l y r e s o l v e d f o r detailed characterization (30). However, both ), A I - A g (28) and 8 ' AI-Cu (27) plates (the latter p a r t i c u l a r l y when their broad faces are p a r t i a l l y coherent (27) ) lengthen with e s s e n t i a l l y v o l u m e i n t e r d i f f u s i o n c o n t r o l l e d kinetics. Those o f a 1 Cu-Zn appear to lengthen a little more r a p i d l y than predicted f o r d i s o r d e r e d (and also p a r t i a l l y coherent) plate edges (30); lack o f i n f o r m a t i o n on the l o c a t i o n o f the a /(a + ,8') phase boundary (31), h o w e v e r , makes exact c o m p a r i s o n b e t w e e n cal cul at i on and measurement s o m e w h a t uncertain. Optical m i c r o s c o p y p r o v i d e s limited support f o r the presence o f a ledge structure on the edges o f f e r r i t e plates (32,33). A det ai l ed t r e a t m e n t o f plate lengthening by the ledge mechanism is badly needed, even though this is surely a f o r m i d a b l e mathematical p r o b l e m (34,35). For the present, though, it appears that c o m p a r i s o n o f the measured ki net i cs o f plate lengthening with those calculated assuming v o l u m e d i f f u s i o n c o n t r o l is o f t e n not a useful independent means o f assessing the g r o w t h mechanism c o n t r o l l i n g the lengthening process. However , p r o v i d e d that the f o r e g o i n g 4 . 6 - f o l d discrepancy between calculated and measured V's is accepted as significant, in the case o f Fe-C-Ni a l l o y s a s o m e w h a t clearer result emerges when a t t e m p t s are made to bring the t w o sets o f V's in agreement by i n t e r p o s i n g a u n i f o r m barrier to interface m o v e m e n t through assigning a f i n i t e value to /~o" Such a value o f /Jo implies a p a r t i a l l y coherent structure at the plate edges. In this situation, a value o f 200 mJ/m 2 is usually assigned to the e n e r g y o f a u s t e n i t e : f e r r i t e boundaries (1,17,36). Whereas Simonen et al (15) f o u n d that ,~o varies f r o m 0.60 at 7 0 0 ° C and Q ~, 0.5 d o w n to 0.07 at 450° C and ~ o -,, 0.9, Table I s h o w s that those f o r Fe-C-Ni fall in the range 4 x °103 to 6 x 10 .4 at ~ o = 0.99-0.93. Hence, the T r i v e d i t r e a t m e n t indicates that there is a more e f f e c t i v e barrier to g r o w t h at the edges o f f e r r i t e o f bainite plates in Fe-CNi than in Fe-C alloys. We suggest, h o w e v e r , that this barrier is likely to be a larger inter-ledge spacing in Fe-C-Ni alloys, pehaps because Ni i m p r o v e s matching b e t w e e n austenite and f e r r i t e at plate edges. The p r i m a r y reason f o r p r o p o s i n g this rather than a solute drag-like e f f e c t as the e x p l a n a t i o n f o r the d i f f e r e n c e s between calculated and measured g r o w t h rates in Fe-C-10.2 A/O Ni a l l o y s derives f r o m a c o m p a r i s o n o f e x p e r i m e n t a l l y measured thickening kinetics o f grain boundar y f e r r i t e a l l o t r i o m o r p h s (corrected f o r faceting) w i t h those calculated assuming the paraequilibrium (37) g r o w t h model (9). Fig. 2 reproduces such evidence f o r several Fe-C-X alloys. In t hose a l l o y s containing 3.28 W/O and 7.51 W/O Ni the ratio o f these rates is seen to be e s s e n t i a l l y unity at all temperatures studied. Si gni f i cant departures, on the other hand, are o b s e r v e d at s o m e temperatures in the Fe-C-Mn and Fe-C-Cr alloys, and these have been ascribed to a SDLE (9). TEM studies have shown that carbide p r e c i p i t a t i o n cannot play a s i g n i f i c a n t role in these d e v i a t i o n s (38). The s t r o n g e s t SDLE so far r e p o r t e d is f ound in Fe-C-Mo alloys. In an Fe-0.11 W/O C-1.95 WlO Mo alloy, f o r example, at the temperature o f the bay in the TTT-curve f o r i n i t i a t i o n o f t r a n s f o r m a t i o n , 650°C, the calculated parabolic rate constant f o r thickening o f grain b o u n d a r y a l t o t r i o m o r p h s is ca. 4 0 - f o l d greater than the e x p e r i m e n t a l l y measured one, c o r r e s p o n d i n g to a d i s c r e p a n c y in the averaged d i f f u s i v i t i e s o f carbon in austenite o f ca. 1600 (24,39,40). A l t h o u g h the interphase b o u n d a r y structure o f grain boundar y a l l o t r i o m o r p h s is not well est abl i shed e x p e r i m e n t a l l y , it is p r o b a b l e that a larger p r o p o r t i o n o f this structure is o f the d i s o r d e r e d t y p e than at plate broad faces and edges, s i m p l y because the a l l o t r i o m o r p h s are const r ai ned to f o l l o w an average g r o w t h path usually not parallel to w e l l matched conjugate habit planes. Since the SDLE is expect ed t o d e v e l o p o n l y at d i s o r d e r e d - t y p e areas o f a u s t e n i t e : f e r r i t e boundaries (7,8), the g o o d agreement b e t w e e n calculated and measured thichening rates o f grain boundar y f e r r i t e a l l o t r i o m o r p h s in Fe-C-Ni a l l o y s (9) is thus p a r t i c u l a r l y g o o d evidence f o r the absence o f the SDLE in this system. A less decisive though still useful piece o f evidence against the presence o f at least a strong SDLE in Fe-C-Ni a l l o y s is the circumstance that RW w e r e e v i d e n t l y able to make their m e a s u r e m e n t s on w e l l f o r m e d plates. In the bay region o f Fe-C-Cr (39) and e s p e c i a l l y o f F e - C - M o a l l o y s (39,41), wher e the SDLE is c o n s i d e r e d to be m o s t e f f e c t i v e (7,8), the W i d m a n s t a t t e n structure o f the f e r r i t i c c o m p o n e n t o f bainite
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GROWTH KINETICS OF FERR~TE
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Fig. 2: Variation with reaction temperature o f the ratio o f the corrected experimental to the calculated parabolic rate constants f o r thickening o f grain boundary allotriomorphs in Fe-C-X alloys, when calculations are performed on the basis of the paraequilibrium growth model (9). is v e r y degenerate, and can even vanish e n t i r e l y at s u f f i c i e n t l y high carbon and X concentrations. At l o w e r t e m p e r a t u r e s , it should f i n a l l y be noted, the normal W i d m a n s t a t t e n m o r p h o l o g i e s are r e c o v e r e d and g r o w t h kinetics tend to rise t o w a r d the values which they w o u l d have had in the absence o f a SDLE. C oncl usi ons Recalculation o f the data reported by Rao and Winchell (1) on the lengthening kinetics o f f e r r i t e / b a i n i t e plates at 400°C in Fe-C-10.2 A/O Ni a l l o y s using the subsequently d e v e l o p e d Trivedi (13) t r e a t m e n t and the T r i v e d i - P o u n d (14) approach to handling the c o m p o s i t i o n dependence o f the d i f f u s i v i t y o f carbon in austenite reduces the ratio o f calculated to measured lengthening rates f r o m 100 to less than 5 p r o v i d e d the interfacial energy f o r d i s o r d e r e d a u s t e n i t e : f e r r i t e boundaries (ca. 800 mJ/m 2) and an i n f i n i t e i n t e r f a c e kinetic c o e f f i c i e n t , Fo, are utilized. To obtain exact agreement b e t w e e n the RW measurements and the calculations, it is necessary to set ), = 200 mJ/m 2 (appropriate to p a r t i a l l y coherent boundaries) and introduce f i n i t e values o f /~o' which are f r o m one to t w o orders o f magnitude smaller than their c o u n t e r p a r t s in Fe-C a l l o y s (15). This d i f f e r e n c e is suggested to arise f r o m a marked increase in the inter-ledge spacing at the edges o f f e r r i t e / b a i n i t e plates in Fe-C-Ni alloys. That this d i f f e r e n c e is not due to a solute drag-like e f f e c t (SDLE) is indicated by the g o o d agreement obt ai ned between e x p e r i m e n t a l l y measured thickening kinetics of grain boundar y allotriomorphs and t hose calculated assuming paraequilibrium and carbon d i f f u s i o n - c o n t r o l in Fe-C-Ni a l l o y s (9). This conclusion is in agreement with current v i e w s o f the SDLE (8,10) but is in o p p o s i t i o n to suggest i ons that the s l o w e r - t h a n - c a l c u l a t e d lengthening rates o f f e r r i t e / b a i n i t e plates in Fe-C-Ni a l l o y s f o u n d by Rao and Winchell (1) tend to d i s p r o v e the existence o f a SDLE (4-6). Acknowledgements A p p r e c i a t i o n is e x p r e s s e d by WTR, Jr. f o r support f r o m the Amer i can Iron and Steel Institute and the Electric P o w e r Research Institute and by HIA f o r support f r o m the NSF-funded Center f o r the Study o f M a t e r i a l s through Grant DMR-81-19507. References 1. 2. 3, 4. 5. 6.
M.M, Rao and P,G. Winchell, Trans. T M S - A I M E 239, 956 (1967). M.M. Rao, n.J. Russell and P.G. Winchell, Trans. T M S - A I M E 239, 634 (1967). M. Hillert, J e r n k o n t o r e t s Ann. 140, 757 (1957). G. H o r v a y and J.W. Cahn, A c t a Met. 9, 695 (1961). R.F. Hehemann, K.R. Kinsman and H.I. A a r o n s o n , Met. Trans. 3, 1077 (1972). J.W. Christian and D.V. Edmonds, Phase T r a n s f o r m a t i o n s in Ferrous A l l o y s , p.293, T M S - A I M E , Warrendale, PA (1984). 7. K.R. Kinsman and H.I. A a r o n s o n , T r a n s f o r m a t i o n and H a r d e n a b i l i t y in Steel, p.39, Climax M o l y b d e n u m Co., Ann Arbor, MI (1967). 8. H.I. A a r o n s o n , The Mechanism o f Phase T r a n s f o r m a t i o n s in Crystalline Solids, p.270, Institute o f
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Metals, London, UK (1969). 9. J.R. Bradley and H.I. Aaronson, Met. Trans. 12A, 1729 (1981). 10. W.T. Reynolds, Jr., M. Enomoto and H.I, Aaronson, Phase Transformations in Ferrous A l l o y s , p.155, TMS-AIME, Warrendale, PA (1984). 11. R.P. Smith, Trans. TMS-AIME 218, 62 (1960). 12. A.J. Heckler and P.G. Winchell, TMS-AIME 227, 732 (1963). 13. R. Trivedi, Met. Trans. 1, 921 (1970). 14. R. Trivedi and G.M. Pound, J. App. Phys. 38, 3569 (1967). 15. E.P. Simonen, H.I. Aaronson and R. Trivedi, Met. Trans. 4, 1239 (1973). 16. G.R. Speich and M. Cohen, Trans. TMS-AIME 218, 1050 (1960). 17. L. Kaufman, S.V. Radcliffe and M. Cohen, D e c o m p o s i t i o n of Austenite by Diffusional Processes, p.313, Interscience, NY (1962). 18. R.H. Goodenow, S.J. Matas and R.F. Hehemann, Trans. TMS-AIME 227, 651 (1963). 19. H.L Aaronson and H.A. Domian, TMS-AIME 236, 781 (1966). 20. M. Hillert and L.I. Staffansson, Acta Chem. Scand. 24, 3618 (1970). 21. B. Uhrenius, Hardenability Concepts with A p p l i c a t i o n s to Steel, p.5, TMS-AIME, Warrendale, PA (1978). 22. C. Wells and R.F. Mehl, Trans. AIME 140, 279 (1940). 23. H.I. Aaronson, D e c o m p o s i t i o n of Austenite by Diffusional Processes, p.387, lnterscience, NY (1962). 24. H.I. Aaronson, C. Laird and K.R. Kinsman, Phase Transformations, p.313, ASM, Metals Park, OH (1970). 25. G.R. Purdy and M. Hillert, Acta Met. 32, 823 (1984). 26. C. Laird and H.I. Aaronson, Trans. TMS-AIME 242, 591 (1968). 27. R. Sankaran and C. Laird, Acta Met. 22, 957 (1974). 28. C. Laird and H.I. Aaronson, Acta Met. 15, 73 (1967). 29. J.M. Howe, H.I. Aaronson and R. Gronsky, Acta Met., in press. 30. K. Chattopadhyay and H.I. Aaronson, Acta Met., in press. 31. K. Chattopadhyay, Proceedings of an International Conference on Solid-Solid Phase Transformations, p.990, TMS-AIME, Warrendale, PA (1983). 32. R.F. Mehl, C.S. Barrett and D.W. Smith, Trans. AIME 105 215 (1933). 33. E. Eichen, H.I. Aaronson, G.M. Pound and R. Trivedi, Acta Met. 12, 219 (1963). 34. W.P. Bosze and R. Trivedi, Acta Met. 23, 713 (t975). 35. C. Atkinson, private communication, U. of Pittsburgh, 1983. 36. L. Kaufman and M. Cohen, Progress in Metal Physics 7, 165 (1958). 37. J.B. Gilmour, G.R. Purdy and J.S. Kirkaldy, Met. Trans. 3, 1455 (1972). 38. G.J. Shiflet, H.I. Aaronson and J.R. Bradley, Met. Trans. 3, 1743 (1981). 39. P.G, Boswell, K.R. Kinsman, G.J. Shiflet and H.I. Aaronson, unpublished research. 40. H.I. Aaronson, S.K. Liu, W.T. Reynolds, Jr and G.J. Shiflet, J. Mat. Sci., in press. 41. H. Tsubakino and H.t. Aaronson, unpublished research, Carnegie-Mellon Univ., (1982).
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