Nucleation Limitation and Hardenability*

R. C. SHARMA AND G. R. PURDY

The r e l a t i o n be tween nuc lea t ion t h e o r y and h a r d e n a b i l i t y of s t e e l s has been c r i t i c a l l y e x a m - ined. The effect on h a r d e n a b i l i t y of mos t e l e m e n t s with the excep t ion of boron and s t r o n g c a r b i d e fo rming a - s t a b i l i z e r s , is found to be s e miqua n t i t a t i ve ly cons i s t en t with c l a s s i c a l nuc lea t ion theo ry . The " a n o m a l o u s " ef fec ts of boron , c h r o m i u m and molybdenum, a r e d i s - cu s sed in t e r m s of p o s s i b l e p h y s i c a l i n t e r f e r e n c e of p r e c u r s o r r e a c t i o n s with f e r r i t e fo rma t ion .

T H E r e l a t i o n s h i p be tween nuc lea t ion t h e o r y and h a r d - enab i l i t y r e m a i n s a cha l lenging topic for sc i en t i f i c in - ve s t i ga t i on . The e a r l y r e v i e w s of Hobs te t t e r 1 and C h r i s t i a n 2 and the r e c e n t and c o m p r e h e n s i v e r ev iew by Russe l l a p rov ide much of the s o u r c e m a t e r i a l for th i s work. The p u r p o s e s of th is con t r ibu t ion a r e :

1) To use the gene ra l t h e o r y to d raw some b r o a d in- f e r e n c e s about nuclea t ion ef fec ts in ha rdenab i l i t y .

2) To f o r m u l a t e exp l i c i t l y the t h e r m o d y n a m i c s of nuc lea t ion in t h r e e component s y s t e m s (the min imum n u m b e r of components which p e r m i t s the t e r m " h a r d - e n a b i l i t y " to take i t s ful l meaning) .

3) To compute r e l a t i v e h a r d e n a b i l i t y e f fec ts of s e - l e c t ed a l loy ing e l emen t s .

4) To c o m p a r e the o r d e r s - o f - m a g n i t u d e of nuclea t ion t i m e s and a l loy ing e l emen t e f fec t s with those expec ted on the b a s i s of c l a s s i c a l he t e rogeneous nuc lea t ion the - o ry , and as a c o m p l e m e n t , to c o n s t r u c t a p l aus ib l e mode l for the c r i t i c a l nucleus for p r o e u t e c t o i d f e r r i t e in aus ten i t e .

5) To d raw a t tent ion to a l loy s y s t e m s which d e p a r t f r o m p r e d i c t i o n s of the e l e m e n t a r y t heo ry and to s p e c - u la te on the c a u s e s of t he se d e p a r t u r e s .

THERMODYNAMICS OF NUCLEATION

The theory of t h e r m a l l y ac t iva t ed nuc lea t ion f o c u s s e s on the (unstable) equ i l i b r i um be tween the c r i t i c a l nu- c l eus (of phase a) and the p a r e n t phase (/3). The i n t e r - face is a s s u m e d to be sha rp , and the p r e c i p i t a t e and m a t r i x a r e a s s u m e d to be un i fo rm in compos i t ion . The f r e e ene rgy of the nucleus is a m a x i m u m with r e s p e c t to growth o r decompos i t i on , and a m i n i m u m with r e - s p e c t to any o the r p r o c e s s , such as a change in shape o r compos i t ion . It is th is pos tu l a t ed uns tab le equ i l ib - r i u m which m a k e s t r a c t a b l e the d i s c u s s i o n of the e f - f ec t s of complex f luc tua t ions at the s u b m i c r o s c o p i c l eve l in t e r m s of m e a s u r a b l e m a c r o s c o p i c quant i t i es .

P r o v i d e d that the m a c r o s c o p i c quant i t i es a r e p r e - c i s e l y def ined, i t is p o s s i b l e to d r aw f r o m the t h e o r y

R. C. SHARMA and G. R. PURDYare Graduate Student and Pro- fessor, respectively, Department of Metallurgy and Materials Science, McMaster University, Hamilton, Ontario, Canada. This paper is based on a presentation made at a symposium on "Hardenability" held at the Cleveland Meeting of The Metallurgical Society of AIME, October 17, 1972, under the sponsorship of the IMD Heat Treatment Commit- tee. *This entire paper is published correctly in this issue since many paragraphs were out of sequence in the original publication. (Met. Trans., 1973, vol. 4, pp. 2303-11. October issue).

a number of i l lumina t ing s t a t e m e n t s about nuc lea t ion behav io r . R should be noted, however , that the a s s u m p - t ions d e s c r i b e d above have been cha l l enged by n e a r l y e v e r y w r i t e r in the f i e ld of nuclea t ion theo ry . While the a s sumpt ion that m a c r o s c o p i c e q u i l i b r i u m p r o p e r t i e s obta in at the f luc tuat ion s tage can be j u s t i f i ed by d e - t a i l ed a r g u m e n t s in many c a s e s , 4 in r e g i m e s where the f luc tua t ions a r e known to be coheren t , and the i n t e r - f aces a r e d i f fuse , c l a s s i c a l nuc lea t ion t h e o r y fa i l s con- c lu s ive ly . The r e a d e r is r e f e r r e d to the work of Cahn and H i l l i a r d a s r e c e n t l y r e v i e w e d by H i l l i a rd f l More r e l e v a n t to the p r e s e n t d i s c u s s i o n is the ca se where the m a c r o s c o p i c i n t e r f ace conta ins de fec t s which p e r i o d i c - a l ly i n t e r rup t cohe rency . If the spac ing be tween defec t s (e .g . , d i s loca t ions ) is g r e a t e r than the nucleus s i ze , then ' the a s s i g n m e n t of m a c r o s c o p i c i n t e r f ace p r o p e r - t i e s to the nucleus mus t be c r i t i c a l l y ana lyzed .

We wil l be conce rned with the d r i v ing f o r c e for nu- c lea t ion in mul t i component s y s t e m s , AGv, in ene rgy pe r unit vo lume. In b i n a r y s y s t e m s , th is quant i ty is ob - ta ined f r o m f r e e e n e r g y vs compos i t i on cu rves by con- s t ruc t ing a tangent to the p a r e n t phase f r ee ene rgy cu rve at the bulk compos i t ion , a s in F ig . 1, and d e t e r - mining the v e r t i c a l d i s t ance VaAG v to the p r e c i p i t a t e compos i t ion . This l a t t e r is obta ined by cons t ruc t ing a second tangent to the p r e c i p i t a t e f r e e ene rgy curve , such that Ap. 1 = - Kaa~V ~ and A~2 = -- Kaa/3V a , where K is c u r v a t u r e , aa~ the i n t e r f a c i a l f r e e ene rgy and V/a

�9 a

X~'Xa

I I I

x ~ �9 X z

Fig. 1--Illustrating the equilibrium construction for c~ nuclei of cri t ical size, i.e., with cri t ical curvature K*. The matrix composition is X and the most probable nucleus composition is that which maximizes AG. For comparison the infinite r a - dius equilibria X a and X/3 are shown (after Hillert6).

METALLURGICAL TRANSACTIONS VOLUME 5, APRIL 1974-939

the pa r t i a l molar volume of i in the prec ip i ta te (a). This is the Gibbs-Thomson equil ibrium condition. The double tangent construction is due to Hil lert , 6 and p ro - vides a useful and general graphical method for de t e r - mining phase equi l ibr ia involving curved interfaces in sys tems where pa r t i a l molar volumes differ. This p ro - cedure is pa r t i cu l a r ly important when an in te rs t i t i a l solute is involved. The more usual construction, e.g. , Fig. 2, f rom Hobstetter, ~ assumes equal par t ia l molar volumes, and is approximate only.

For t e rna ry sys tems this construct ion is eas i ly ex- tended, as descr ibed below. The Gibbs-Thomson equa- tion is again:

--(~ a p i : - K c a ~ V i ; i = 1,2, 3. [11

The driving force for nucleation is proport ional to the ver t i ca l distance from the plane, which is tangent to the parent phase free energy surface at the bulk phase composition, to the prec ip i ta te free energy su r - face at the prec ip i ta te composition.

As suggested by this construction, the volume free energy change of nucleation of seve ra l phases (stable or metastable) in the t e rna ry field may be appreciable , thei r r a t e s of nucleation and order of appearance being determined by kinetic fac tors and surface energies as well as the re la t ive magnitudes of AGv.

The composit ion of the c r i t i ca l nucleus in a t e r n a r y sys tem is r ead i ly obtained from cap i l l a r i ty theory. For example, in the t e rmina l port ions of the t e rna ry i so- therm, which consis t of dilute (noninteracting) solutes with dis t r ibut ion coefficients k i = C~/C~, we have the approximate express ions

k~ =~,~ , [2]

and , 0 ~ -K* (Y V~ k a = k2v . [3]

where the supe r sc r ip t * r e f e r s to a dis tr ibut ion coeffi- cient under c r i t i ca l curvature K* and the supe r sc r ip t 0 r e f e r s to zero curvature . Since the matr ix composit ion now l ies on the phase boundary, as shown in Fig. 3, the c r i t i ca l equil ibr ium nucleus composit ion is uniquely de- t e rmined by these two express ions . Of course, other composit ions of nuclei may form, but with smal l p rob-

a Z Cm 1

Acm A~, X

--~- X c

.AGV

F%C Fig. 2--For undercooled austenite (y) of eutectoid composition the approximate driving forces for nucleation of ferrite and cementite are represented by the respective distances from tangent at X to the ferrite and cementite free energy curves (after Hobstetterl).

\ \ f~

• \XXk\

W " \ \\ i l i l "\XX\x\

X, Fig. 3--The composition of the equilibrium critical nucleus (0) in the ternary system containing solutes 1 and 2 is given by the capillarity-modified tie-line which terminates at the bulk par- ent phase composition X. For dilute solutions, the solute dis- tribution coefficients for critical curvature are independent, and related to the zero curvature solute distribution coefficients by Eqs. [2] and [3].

abi l i ty unless kinetic p a r a m e t e r s mi l i ta te in their favor (see below).

This is the local equi l ibr ium model for nucleation in three component sys tems . In the previous contribution, Coates 7 d i scusses two kinds of equi l ibr ium models which can obtain during unparti t ioned growth, including the local equil ibr ium no-par t i t ion (LE-NP) model. For nucleation, no pa ra l l e l model ex is t s ; par t i t ion of a l loy- ing e lements must accompany the formation of a true local equil ibr ium nucleus.

At large supersa tura t ions , the poss ib i l i ty exis ts that unparti t ioned nuclei may form, because of the grea t t ime requi red for alloying element redis t r ibut ion . In this case, a special kind of pa r t i a l equi l ibr ium t e rmed "pa r a e qu i l i b r i um " by Hultgren 8 and Hil ler t , ~ (or the s i m i l a r concept of "no-par t i t ion equ i l ib r ium" of Aaron- son, Domian, and Pound ~~ may apply. Fig. 4 shows the paraequi l ibr ium construct ion which a s s u r e s equal ac t iv- i t ies of carbon in parent and product phases . Here the t i e - l ine coincides with a component ray . A paraequi l ib - r ium d iagram as modified by cap i l l a r i t y is given in Fig. 5. A calculated paraequi l ib r ium phase d iagram is shown super imposed on a t rue t e r na r y i so therm for Fe- C-Ni in Fig. 6. n

Note that, at low supersa tura t ions , the host phase is not supersa tu ra ted with r e spec t to the paraequi l ibr ium boundaries , so that alloying element par t i t ion is neces- sa ry . At higher supersa tura t ions , the formation of un- par t i t ioned (or pa r t i a l ly part i t ioned) nuclei is possible . For unpart i t ioned nuclei, the appropr ia te form of the Gibbs-Thomson equation is that given by Gilmour et al. TM as

~t 7 - . ~ : - Kaa~Fg [4]

- + - = - § G c , d [ 5 ]

Here subscr ip ts 1, 2, and 3 r e fe r to carbon, the immo- bile solute and the solvent (iron), r e spec t ive ly . This express ion is seen to reduce to the paraequi l ib r ium condition for large radi i .

The cap i l l a r i ty conditions given above also apply to p rec ip i t a tes with nonisotropic in ter face p rope r t i e s . In this case, the condition that the c r i t i c a l nucleus pos-

940-VOLUME 5, APRIL 1974 METALLURGICAL TRANSACTIONS

~Plone tangent to the oustenite free energy surface, at m.

~'Plane tangent to the ferrite free energy surface ~pth..

/

~- Paraequilib'ium tie-line

Mn Fig. 4--Schematic free energy sur faces for fe r r i t e and aus ten- ite i l lustrat ing the paraequil ibr ium conditions (after Gilmour, Purdy, and Kirkaldyt2).

X 2

Xi Fig. 5--The equilibrium phase d iagram (heavy lines), and the paraequi l ibr ium phase diagram (light lines) are compared. The capi l lar i ty-modif ied paraequi l ibr ium boundaries for a cr i t ical nucleus (bulk parent phase composit ion X) are shown as broken l ines. The broken t ie- l ine joins the bulk matrix composition to the paraequi l ibr ium (unpartitioned) nucleus composition (0).

s e s s e s the equ i l i b r ium shape wil l a s s u r e that (~i /r i is a cons tant ,* which can be subs t i tu ted d i r e c t l y into the

*For interfaces in cusp orientations; r i must be measured perpendicular to the interface plane.

c a p i l l a r i t y equat ions . S t ra in energy , whether a s s o c i a t e d with volume change,

o r with the main tenance of cohe rency , should be added to the A G v t e r m in the nuc lea t ion equat ions whenever i t b e c o m e s s ign i f ican t , z

In any quant i ta t ive t e s t of the a p p l i c a b i l i t y of nuc l ea - t ion t heo ry to s t e e l s , the f r ee e n e r g i e s of t r a n s f o r m a - t ion mus t be known. F igs . 7 and 8 give our ca l cu l a t ed va lues of these f r ee e n e r g i e s for the a l loy s y s t e m s F e - C-Ni and F e - C - M n for p a r a e q u i l i b r i u m and loca l equ i - l i b r i u m modes . We c o n s i d e r that the t h e r m o d y n a m i c s

ffs.

~ c l 2 --

8

7 3 o o 0

SOACTIVITY LINE

~ ---.-~ARA- EQUILIBRIUM

/ r =CONBT. \

. . . . v , . \ 4 5 6

ATOMIC % C Fig. 6--Calculated i so therm of Fe -C-Ni at 730~ Also shown are the paraequi l ibr ium and no-par t i t ion boundaries for local equil ibrium growth.

o =E

J

v

<3

I I - - PARA-EQUILIBRIUM - - - EOUILIBRIUM

-(~) Fe-O.O05 C

( ~ Fe-O.O05 C-O.OI Mn

( ~ F'e -0 .005 C-O.051Ni

(~) F'e -0.005 C- 0031Mn

-I oc

800 700 600 500 400

TEMPERATURE ,~

Fig. 7 - -F ree energy for nucleation vs t empera tu re for four 0.1 wt pct C alloys.

of these s y s t e m s a r e among the mos t r e l i a b l e ava i l ab le . S i m i l a r va lue s of A G v have been given for t he se and o the r a l loy s y s t e m s by Aaronson , Domlan, and Pound. 1o

NUCLEATION KINETICS

In what fo l lows, we a r e conce rned p r i m a r i l y with the nuc lea t ion of p r o e u t e c t o i d cons t i tuen t s a t g r a in bounda- r i e s in aus t en i t e s ince f rom the o b s e r v a t i o n of s t r u c - t u r e s of p a r t i a l l y t r a n s f o r m e d s t e e l s we know that g r a i n bounda ry nuc lea t ion p r e d o m i n a t e s under a wide v a r i e t y of condi t ions . F u r t h e r m o r e , the me t i cu lous m e t a l l o - g raph ic work of Hi l l e r t 13 sugges t s that p e a r l i t e a t t a ins full coope ra t ion only a f t e r an extended p e r i o d of non- coope ra t i ve growth, and that the p r e c u r s o r of p e a r l i t e is a p roe u t e c to id cons t i tuent . If, a s is l ike ly , th is is g e n e r a l l y t rue , then the nuclea t ion of p roeu t ec to id f e r - r i t e o r c a r b i d e i s the p r o p e r foca l point for th is d i s c u s -

METALLURGICAL TRANSACTIONS VOLUME 5, APRIL 1974-941

I I I i

- - PARA-EQUILIBRIUM

- - - - - EQUILIBRIUM

( ~ Fe --0.017 C

( ~ Fe--O.OI7 C-0,0:51Mn

i - 2 0 0

r

-30~

A bJ

d ~=-2oo . J

~2

I J _ .,'t..~ I I 800 700 600 500

TEMPERATURE, *C.

(a)

I I I I

- - PARA- EQUILIBRIUM

- - - EQUILIBRIUM

( ~ Fe - 0,017 C

( ~ Fe - 0,017 C-0 .029 Ni j

I 400

800 700 600 500 400 TEMPERATURE, ~

(b) Fig . 8-- (a) The e f fec t of Mn on the f r e e e n e r g y for nuc l ea t i on of f e r r i t e . (b) The e f fec t of Ni on the f r e e e n e r g y fo r n u c l e a - t ion of f e r r i t e . Note tha t the u n p a r t i t i o n e d and p a r t i t i o n e d r e - ac t ion h a v e s i m i l a r d r i v i n g f o r c e s .

sion. Since we will be concerned with lower carbon s tee ls , what follows will deal with f e r r i t e .

The discuss ion of kinet ics requ i res that a detai led model be adopted. We will consider seve ra l approaches to this problem in the following section.

In the textbooks, ~4 and in the recent l i t e ra tu re ~s' 18 the poss ib i l i ty that nucleation of f e r r i t e is accomplished by the shear ing of a smal l volume of austenite has been discussed. Shewmon ~4 c lea r ly dist inguishes between a the rmal ly act ivated event, in which a sharp interface completely bounds the new par t ic le of a , and an event in which the or iginal s t ruc ture is sheared local ly into the product la t t ice . A theory for f e r r i t e nucleation by shear was put forward by Ryder and Pitsch ~6 who a s - sumed that the grain boundary plane remained unro-

tated during the nucleation event. The theory was shown to be consis tent with the exper imenta l s ca t t e r in o r i en- tation re la t ionships (near Kurdjumov-Sachs) found for f e r r i t e a l lo t r iomorphs in Fe-C a l loys . More recent ly , Kennon and Purdy 17 analyzed or ientat ion re la t ionships between a and/3 b r a s s using the Ryde r -P i t s ch analys is , and showed that this pa r t i cu l a r theory pred ic ted the exper imenta l sca t te r of thei r resu l t s , but fai led when it was applied to individual p rec ip i t a t e s . This obse rva - tion cas t s some doubt on the proposi t ion that f e r r i t e nucleates by a shear ing p r oc e s s of the type envisioned by Ryder and Pttsch.

Thermal ly act ivated incoherent gra in boundary nu- cleation has been d iscussed by Clemm and Fisher . ~a They assumed that a l lo t r iomorphs nucleate as double symmet r i c spher ica l caps at grain boundaries , the con- tact angle being determined by the balance of in terfacia l f ree energies at the nucleus edge. They showed that grain boundaries can act as ve ry effective nucleation ca ta lys ts . Recently, Russell 19 cons idered the nucleation of severa l types of grain boundary p rec ip i ta tes , includ- ing incoherent a l lo t r iomorphs , coherent (on one side) a l lo t r iomorphs and d iscs . He assumed that the coher - ent a l lo t r iomorph possessed one interface which was isotropic and of low energy (hence the equi l ibr ium nu- cleus bulges into the gra in with which the nucleus shares a favorable or ientat ion re la t ionship as shown in Fig. 9). The energet ics of nucleation of these f igures are developed by s t ra ight forward methods of c l a s s i ca l nucleation theory, and are tabulated in Table L Russell a lso obtained express ions for the incubation t imes , and these a re also l is ted in Table L To determine the incu- bation t ime the pr inciple of mic roscop ic r eve r s ib i l i t y 2~ is invoked, and the dissolution of the subcr i t i ca l c lus ter studied. For incoherent a l lo t r iomorphs , Russel l con- s ide r s that in terfacla l solute diffusion controls d i s so - lution, and the frequency factor/3k is es t imated as the boundary jump frequency Dbeff/a z multipl ied by the num-

/

/ Y SEMI-COHERENT

INTERFACE

INCOHERENT~ ' ' ' ~ ' ~ AUSTENITE INTERFACE y GRAIN BOUNDARY

Fig . 9 - -A s c h e m a t i c s e m i c o h e r e n t a l l o t r i o m o r p h a t the n u c l e a - t ion s t a g e . The n u c l e u s b u l g e s into the p a r e n t c r y s t a l wi th wh ich it s h a r e s a s e m i c o h e r e n t ( lower e n e r g y ) i n t e r f a c e .

Table I. Quantities Relevant to the Nucleation of Incoherent and Coherent AIIotriomorphs, after Russell 19

Incoherent Coherent Allotriomorpks Atlotriomorphs

r* (radius of critical nucleus)

nk(number of solute atoms) 3AGv a 3AGv 3

32Hoc~3 f(O) 1611~3f(0) AG* energy/critical nucleus

3AGv ~ 3AGv 2

6k Tn k T 6 kTn k T r(incubation time) a b 3 - - a

AGv~ k DeffAGv AGv~ k DAGv 2

-2a~/A G v -20~/A G v

64[1(~a#' C f(O) 321"Ioor 3 C f(O)

942-VOLUME 5, APRIL 1974 METALLURGICAL TRANSACTIONS

be r of solute a toms within one jump d is tance of the a l - lo t r tomorph edge, i . e . ,

IIr*Dbff s in 0C [6] ~ k = a 3

where a is the jump dis tance and C is the solute con- cen t ra t ion in the mat r ix .

Now for coherent a l lo t r iomorphs , m a t e r i a l is sup- posed to be able to add to the en t i re curved sur face ; hence the volume diffusivt ty gives the jump f requency f f /a 2 and

flk _ ~.n~ r . ~ C ( l _ cos 0) [7] t/4

Thus, /3 b for coherent a l lo t r iomorphs is found to de- pend on the volume diffustvtty and/3 k for incoherent a n o t r i o m o r p h s on the boundary diffusivity. Both incu- ba t ion t imes and nuclea t ion r a t e s will be s t rongly in - f luenced since

Tn~

AG% and the steady state ra te of nucleat ion

[9]

where C~, the concent ra t ion of c r i t i ca l nuclei , is

No C

and N o a ry .

[10]

is the number of a toms per unit a r ea of bound-

ESTIMATION OF THE RELATIVE HARDENABILITY EFFECTS OF ALLOYING ELEMENTS

The equat ions of the prev ious sec t ion p e r m i t us to catalog the fundamenta l quant i t ies needed to calcula ted incubat ion t imes and nuclea t ion r a t e s : these a re the In te r rac ia l f ree energy, an/3, the effect ive diffusion coeff icient , Deft, and the volume f ree energy for nuc l e - at ion, AG v . We begin this d i s cus s ion with an a s sumed knowledge of AG v only.

The quant i t ies predic ted by the theory (the incubat ion t ime 7, and s teady state nuclea t ion ra te J) a re a c c e s - s ible to exper iment , but we a re aware of no such m e a - s u r e m e n t s for s imple b i n a r y or t e r n a r y s tee l s . The re - fore, we will focus on the pred ic t ion of ce r t a in aspects of exper imen ta l T T T curves , taking cognizance of ava i l - able exper imenta l growth data and theore t ica l models for f e r r i t e growth. It is recognized that, at the ve ry leas t , the posi t ion of the f e r r i t e - s t a r t l ine on a TTT di- a g r a m places an upper l imi t on the incubat ion t ime, 7, and r e q u i r e s a co r respond ing lower l im i t on the s teady s ta te nucleat ion ra te , J .

We will begin by a s suming that the f ree energy for nuclea t ion , at l a rge supe r sa tu ra t i on AG v is that ca lcu- la ted on the pa r aequ i l i b r i um model. Therefore , the nuc leus and its p rope r t i e s a re not apprec iab ly changed by the addition of al loying e l emen t s .

Next, we cons ider the a s s ignmen t of an opt imum value to %~fl. This quanti ty is unknown, so is adjusted such that sens ib le nuclea t ion r a t e s a re obtained for a wide range of Fe -C and F e - C - X al loys over the t e m p e r a t u r e range of in t e re s t . For tunate ly , this p rocedure is com-

pa ra t ive ly insens i t ive to the model chosen ( e . g . , coher - ent or incoherent nucleat ion, cont ro l led by in t e r s t i t i a l or subs t i tu t ional volume or boundary diffusion) but is v e r y sens i t ive to ~ f l , e spec ia l ly at Iow s u p e r s a t u r a - t ions . We have chosen to keep ~ f l as high as poss ible , to be cons i s ten t with p r i o r kinet ic work 21 which placed the energy of a f e r r i t e boundary (at a Widmanst~/tten plate tip, and a s sume d pa r t i a l ly coherent) in the neigh- borhood of 200 e rgs per sq cm. Thus we a r r i v e at a " b e s t " value of ~afl of about 75 ergs per sq cm. Fig. 10 shows seve ra l f ami l i e s of r a t e s calcula ted using this value in our p r e f e r r e d model.

We next inquire into l imi t s on the f requency factor, /3b, as cons t ra ined by fundamenta l p r o c e s s e s and by e mp i r i c a l r e s u l t s . As noted above, the reac t ion s t a r t t ime on a TTT curve is de t e rmined by the incubation t ime , T, and by the t ime r equ i r ed for the p rec ip i ta tes to reach obse rvab le s ize. At higher t e m p e r a t u r e s , r a t e s of nuclea t ion and growth may be low and so both contr ibute to the t ime for observab le t r ans fo rma t ion . At 450 to 500~ however, our ca lcula ted ra tes of nu- c leat ion a re la rge for al l a l loys studied (except the high Mn alloy, number 7) and for all models cons idered (as noted above). Reference to expe r imen t and to the the- o ry of proeutectoid growth 22'z3 suggests that high ra tes of growth will a lso exist for this t empe ra tu r e , such that the t imes for in i t ia t ion of r eac t ion on TTT d iag rams will be a guide to the magnitude of the incubation t ime, 7. This was ver i f ied by ca lcula t ions based on the John- son-Mehl z4 equation as modified by Dub6fl 5

Thus we have, for a l imi ted range of t e m p e r a t u r e and al loying e lement levels , an es t imate of T which c o r r e - sponds to exper imen ta l TTT curves . Without inqui r ing fur ther into the r a t e - l i m i t i n g p rocess , we can es t imate the i so the rma l a l loy ing -e l emen t effect on the TTT dia- g r a ms using the fact that T oc 1/(AGv) 3 for boundary dif- fus ion l imi ted nuclea t ion . Fig. 11 shows the r e s u l t of compar i son with expe r imen ta l T T T curves . 2z'37 For the a l loys l i s ted in Table II. Here we have taken T = 1 S for the b i n a r y Fe-0.005 C alloy. The a g r e e me n t is seen to be gene ra l l y quite good, and poores t for the high m a n -

I i I

6OO

O @ ~ .~C)O

i |

t | \ \ / I / I | r \ I I I I I / \ I I I I I

300t (~)Fe-O017C-OO31 Mn I I 1 I I ,

' ,o,~ ,b, i0 5 i0 ~~ NUCLEI / CM 2

Fig. 10--Nucleation rates calculated for o~/3 = 75 ergs/cm 2. /3/~ is assumed to be determined by boundary diffusion with D~ff = e -30,600/RT. If a~fl is taken as 100 ergs/cm 2 similar rates are obtained at temperatures about 75~ lower than those shown here.

METALLURGICAL TRANSACTIONS VOLUME 5, APRIL 1974-943

20

I0

4 X

/ / x

/ / 6

a / x / /

L ," / /

/ x 5 /

/ I 2

i i I / ,

x 7 / / "

/ /

/ / /

/ / /

/ /

/ /

/

I I I 5 I0 20

"CcoL F i g . l l - - C o m p a r i s o n of c a l c u l a t e d r e l a t i v e i n c u b a t i o n t i m e s (Tcalc) and incubation times estimated from the reaction start times (rapp) on TTT diagrams at 450~ For this calculation the Tap p and rcalc were taken as 1 s for alloy 1 and we have assumed roz(1/AG3v) (see Table I).

Table II. Fe-C-X Systems Studies

Alloy No. At. Pct C At. Pct Ni At. Pct Mn

1 0 . 5 - -

2 0.5 - 1 3 0.5 3 - 4 0.5 - 3 5 1.7 6 1.7 3 - 7 1.7 - 3

ganese a l loy , no. 7, which is expec ted to p o s s e s s the lowes t r a t e s of nuc lea t ion and growth.

In the absence of a c c u r a t e nuc lea t ion data , and of a c - c u r a t e ac t iva t ion e n e r g i e s for a l l p o s s i b l e r a t e - d e t e r - min ing p r o c e s s e s , i t is dif f icul t to a t tach a f i r m value to the ac t iva t ion e n e r g y for nuc lea t ion . However , us ing the fac t that the incubat ion t ime T mus t be no l a r g e r than the r e a c t i o n - s t a r t t i m e s at a l l t e m p e r a t u r e s , a t h e o r e t i c a l f i t to the TTT c u r v e s a l lowed us to p l ace an upper l imi t of 35,000 cal p e r mol on this quanti ty. Higher ac t iva t ion e n e r g i e s would y ie ld too g r e a t an in- cubat ion t ime at some t e m p e r a t u r e s .

Austeni te g r a i n s i ze is not c o n s i d e r e d a m a j o r f ac to r in d e t e r m i n i n g r e a c t i o n s t a r t t i m e s at lower t e m p e r a - t u r e s . However , s ince our nuc lea t ion r a t e s a r e given in nuc le i p e r unit a r e a of g ra in bounda ry pe r unit t ime , a comple t e TTT d i a g r a m ca l cu l a t ed us ing these da ta would show a g r a i n - s i z e dependence of f r ac t ion t r a n s - fo rmed .

The d i s c u s s i o n thus fa r has been l imi t ed to the a l l o y - ing e l e m e n t s Mn and Ni. However , we submi t that the app roach taken so f a r is qua l i t a t i ve ly cons i s t en t with the known b e h a v i o r of such e l e m e n t s a s Co and Si: as s u p e r s a t u r a t i o n is changed by a l loy ing e l emen t a d d i - t ions , both nuc lea t ion and growth should be inf luenced in the s a m e way, i .e. , a c c e l e r a t e d for i n c r e a s e d s u p e r - s a tu r a t i ons , and r e t a r d e d for d e c r e a s e d s u p e r s a t u r a - t tons . Hence the r educ t i on of the r e a c t i o n s t a r t t ime a s s o c i a t e d with coba l t addi t ions is unde r s t andab le .

The ca l cu la t ion p r o c e d u r e s used h e r e wil l only y ie ld

h a r d e n a b i l i t y e f fec ts which r e s u l t in a shi f t of the TTT d i a g r a m to the r igh t o r lef t , with l i t t l e change in the shape of the curve . Also, the magni tude of the shi f t wil l be s i m p l y r e l a t e d to t h e change in s u p e r s a t u r a t i o n , a s r e f l e c t e d in AGv. It is i m m e d i a t e l y appa ren t , on th is b a s i s , that the b a y - f o r m i n g e l e m e n t s Mo and Cr a r e anomalous . The effect of a m o d e s t add i t ion (say 1 pct of Mo) is to de l ay s e l e c t i v e l y the r e a c t i o n at i n t e r m e - d ia te t e m p e r a t u r e s . While the c a l c u l a t e d e q u i l i b r i a a r e a dmi t t e d ly not as c e r t a i n a s those for Ni and Mn, they give no indica t ion of a c o r r e s p o n d i n g m a j o r d e - c r e a s e in s u p e r s a t u r a t i o n at t e m p e r a t u r e s where , ex - p e r i m e n t a l l y , nuclea t ion a n d / o r growth a r e inhibi ted. Thus, our ca l cu l a t ed nuc lea t ion r a t e s r e m a i n l a r g e for s t e e l s conta in ing these e l e m e n t s th rough the t e m p e r a - tu re r ange included by the bay , jus t a s the ca l cu l a t ed growth r a t e s of Kinsman and Aaronson 22 (based on a p a r a e q u t l i b r i u m model) f a i l ed to r e f l e c t the m a j o r in- h ibi t ion o b s e r v e d in F e - C - M o . We have t h e r e f o r e not been s u c c e s s f u l in r a t i o n a l i z i n g the behav io r of the c a r b l d e - f o r m i n g f e r r i t e s t a b i l i z e r s Mo and Cr , nor have we managed to account for the ef fec t of boron on any r e a s o n a b l e m a c r o s c o p i c t h e r m o d y n a m i c model .

This d i s c u s s i o n c o m p r i s e s the m a x i m u m in quan t i t a - t ive in fe rence in the a bse nc e of e x p e r i m e n t a l m e a s u r e - men t s for s i m p l e b i n a r y and t e r n a r y s t e e l s . It a p p e a r s that the ca lcu la t ions of bulk t h e r m o d y n a m i c ef fec ts of a l loy ing e l e m e n t s is suf f ic ien t fo r the s emiquan t i t a t i ve unde r s t and ing of the e f fec t s of a number of e l e m e n t s but even th is s i m p l e t e s t of r e l a t i v e e f f e c t i v e n e s s f a i l s c onc lu s ive ly in the ca se of s t r o n g c a r b i d e - f o r m i n g e l e - men t s .

A MODEL FOR THE CRITICAL NUCLEUS

Let us now cons ide r a p o s s i b l e f o r m of f e r r i t e nu- c l eus ( s emicohe ren t ) a t a h igh -ang le aus t en i t e g r a i n boundary . We expec t that the K - S r e l a t e d s ide wi l l be of low a v e r a g e i n t e r f a c i a l f r e e e ne rgy . The d i r e c t i o n s p e r p e n d i c u l a r to (111>~ should have an e n e r g y s i m i l a r to that e s t i m a t e d for Widmans t~ t t en p la te t ips by T r i - ved i et a l . , 21 i .e . , 200 e r g s p e r sq cm. This is about one q u a r t e r of that thought r e a s o n a b l e for aus t en i t e g r a i n b o u n d a r i e s ~750 e r g s p e r sq cm. Now it is known that Wtdmanst~t ten p l a t e s do not tend to s p h e r - o id ize on p ro longed holding at t e m p e r a t u r e ; hence the i n t e r f ace ene rgy is l i ke ly to be s t r o n g l y a n i s o t r o p i c , with the Wtdmanst~itten habi t p l anes p o s s e s s i n g v e r y low e n e r g i e s , s ay o n e - s i x t h of the t ip ene rgy , o r about 30 e r g s p e r sq cm. The c h a r a c t e r of the i n t e r f ace in th is cusp o r i en ta t ion has been the sub j e c t of con j ec tu re by a number of w r i t e r s .

Paxton 26 s u p e r i m p o s e d ( l l 0 ) a and ( l l l ) y p l a n a r mod- e l s and noted that i so l a t ed r e g i o n s of good f i t were s e p - a r a t e d by ex tens ive r e g ions of m i s m a t c h . More r e - cent ly , Malco lm 27 o b s e r v e d what a p p e a r e d to be c o h e r - ent s e g m e n t s of a - ~ i n t e r f ace in b r a s s , and Hall et al. 28 found that Cr p r e c i p i t a t e s in Cu were bounded by d i s l o - ca ted i n t e r f a c e s . They showed that , by t i l t ing the i n t e r - face p lane f rom <lll>~,, the r e g i o n s of good f i t could be made to include i n c r e a s i n g l y l a r g e f r a c t i o n s of the bounda ry a r e a , al though p e r i o d i c de fec t ive r eg ions a r e s t i l l r e q u i r e d . Now the d i m e n s i o n s of the c r i t i c a l nu- c leus m a y wel l be l e s s than the d i s t a n c e be tween i m - p e r f e c t r eg ions , so that we might expec t the i n t e r f ace

9 4 4 - V O L U M E 5, A P RIL 1974 M E T A L L U R G I C A L T R A N S A C T I O N S

n e a r ( l l l ) v to be a l m o s t c o m p l e t e l y cohe ren t and to p o s s e s s a v e r y low ene rgy .

Thus, our model for the nucleus involves a half d i sc , ly ing in one g ra in , with i t s h a l f - t h i c k n e s s to r ad iu s r a t i o given by a e ~ / a a ~ ~ 0.2 as r e q u i r e d by the equi - l i b r i u m condit ion d i s c u s s e d p r e v i o u s l y . The incoheren t bounda ry e n e r g y i s expec ted to be s i m i l a r to that of the g r a i n boundary ~/3/~ (Fig . 12). E l e m e n t a r y g e o m e t r y then g ives the d i sc r a d i u s

r * = - 2 a 2 / A G v [11]

and

AG*cc t ~ l [12] (AGv) 2

Thus the a v e r a g e o r ef fec t ive gab i s of o r d e r 75 e r g s p e r sq cm, the va lue which was found to be r e q u i r e d to g e n e r a t e o b s e r v a b l e nuc lea t ion r a t e s in the p rev ious sec t ion . The i n t e r p r e t a t i o n of the f r equency fac to r f3 k p o s e s a m o r e di f f icul t p r o b l e m . We mus t i m m e d i a t e l y ru l e out vo lume diffusion of subs t i tu t iona l e l e m e n t s a s a r a t e - d e t e r m i n i n g s tep, b e c a u s e the ac t iva t ion ene rgy for th is p r o c e s s is too high. (We r e q u i r e d < 35,000 cal p e r mol for the r a t e - d e t e r m i n i n g s tep in the p rev ious sec t ion) .

Carbon volume dif fus ion i s a p o s s i b l e r a t e - d e t e r m i n - ing f a c t o r . However , when we cons ide r the number of ca rbon a t o m s that mus t be r e j e c t e d f rom a volume of aus t en i t e which c o r r e s p o n d s to a t yp i ca l f e r r i t e c r i t i c a l nuc leus conta ining, say, 200 i ron a toms , we find this number is about unity. It t h e r e f o r e s e e m s mos t un l ike ly that ca rbon dif fus ion wil l d e t e r m i n e nuc lea t ion r a t e s . In addi t ion i t wi l l g e n e r a l l y be p o s s i b l e to f ind c r i t i c a l n u c l e u s - s i z e d vo lumes in aus ten i t e which a r e c o m - p l e t e l y f r e e of ca rbon .

We a r e thus led to fu r the r c o n s i d e r a t i o n of the model shown in Fig. 12. The equ i l i b r i um condi t ion is expec ted to hold ove r the growth of the c r i t i c a l nucleus to the s u p e r c r i t i c a l s t a t e . This r e q u i r e s tha t the shape in Fig. 12 be ma in ta ined dur ing growth, which then r e - qu i r e s d i s p l a c e m e n t of the p l a n a r cohe ren t i n t e r f a c e s . We wil l pos tu la te that th is n o r m a l d i s p l a c e m e n t t akes p l a c e he t e rogeneous ly , involving l a t e r a l p ropaga t ion of an incoheren t ledge, emana t ing f rom the incoheren t g r a i n boundary .

The r a t e of nuc lea t ion wi l l then depend on the f r e - quency with which subs t i tu t iona l a toms on the ledge r e - gion join the p a r e n t c r y s t a l . If we a s s u m e that th is is s i m i l a r to the bounda ry jump f r equency then the a c t i v a - t ion ene rgy r e q u i r e m e n t of the p r e v i o u s sec t ion can be met .

While the p r e c e d i n g d i s c u s s i o n i s h ighly con jec tu ra l , the model has the advantage of be ing cons i s t en t with what is known or g e n e r a l l y i n f e r r e d about i n t e r f a c e s of the kind be l i eved to ex i s t at the K - S o r i e n t e d s ide of the nuc leus , and the ~k e x t r a c t e d is in o r d e r - o f - m a g n i t u d e a g r e e m e n t with the o b s e r v e d k ine t i c s of f e r r i t e f o r m a - t ion.

THE ROLE OF CARBIDE-FORMING ELEMENTS

In the p rev ious sec t ions , a s i m p l e t h e r m o d y n a m i c model was used to e s t i m a t e incubat ion t i m e s , and to show tha t c a r b i d e - f o r m i n g e l e m e n t s a r e not " w e l l - b e h a v e d . " We wil l include bo ron in th is group, s ince

!

o- a

Fig. 12--A model for the disc-shaped semieoherent grain boundary nucleus. The planar sides, of energy el, lie on low energy habit planes in the lower grain and may therefore be inclined to the grain boundary normal. The upper (shaded) boundary is considered to be incoherent, and bulges slightly into the upper grain. The shape of the disc is determined by the relative edge and facet free energies, el and e2, and the effective free energy for the nucleus becomes approximately (~lal) m �9

i t is c l e a r that boron addi t ions at the l eve l commonly used in s t e e l s a r e un l ike ly to g e n e r a t e the eno rmous changes in AG v r e q u i r e d for the h a r d e n a b i l i t y obta ined . We might con j ec tu re that bo ron (or Cr , o r Mo) inf lu- ence the i n t e r r a c i a l e n e r g i e s enough to make th i s d i f - f e r e n c e . However , it s e e m s unl ike ly that a s u r f a c e - ac t ive e l e me n t would r educe the cohe ren t i n t e r r a c i a l e n e r g y s ign i f i can t ly ; and t h e r e is some e x p e r i m e n t a l ev idence that boron r e d u c e s the g r a i n - b o u n d a r y e n e r g y by a few p e r c e n t onlyf l ~

We wil l thus c o n s i d e r the p o s s i b i l i t y (o r ig ina l ly sug - ge s t ed by Z e n e r 3~ that these e l e m e n t s , when added to s t e e l s , r e s u l t in copious nuc lea t ion of a l loy c a r b i d e s , which grow e x t r e m e l y s lowly and i n t e r f e r e with f e r r i t e nuclea t ion .

Let us f i r s t c o n s i d e r the e l e m e n t boron, which is known to fo rm a b o r o c a r b i d e , of the type M23C3B 3. T h i s phase is cubic and a d m i t s of an o r i en ta t ion r e l a t i o n s h i p with aus ten i t e which y ie lds a coheren t , n e a r l y i s o t r o p i c i n t e r f ace , v e r y p robab ly of low ene rgy . T h e r e is a m p l e ev idence that th is phase f o r m s at the g r a i n b o u n d a r i e s v e r y e a r l y in i s o t h e r m a l t r e a t m e n t (as would be e x - pec ted f rom the high di f fus ion r a t e s of the i n t e r s t i t i a l so lu tes , bo ron and carbon) , and thus should ac t as a he t e rogeneous nuc lea t ion s i t e for p r o e u t e c t o i d f e r r i t e . 31 At f i r s t s ight one would not look t ow a rds a d e m o n s t r a t e d he te rogeneous nuc lea t ion c a t a l y s t for a nuc lea t ion inhi - b i t ion m e c h a n i s m . However , we note that by the t ime the b o r o c a r b i d e is o b s e r v e d (no rma l ly by op t ica l m i - c roscopy) c o n s i d e r a b l e c o a r s e n i n g m u s t have o c c u r r e d , so that a l a r g e amount of c o n t i n u o u s incoheren t b o r o - c a r b i d e / a u s t e n i t e i n t e r f ace is ava i l ab l e to ac t a s a l e t - r i t e nuc lea t ion s i t e . Thus i t is not un reasonab le to sug - ge s t that , in e a r l y s t a ge s , the boron cons t i tuent ac t s to inhibi t f e r r i t e - n u c l e a t i o n , by cover ing the g ra in bound- a r y with cohe ren t p a r t i c l e s , a s shown in Fig . 13.

The c r e d i b i l i t y of th is m e c h a n i s m can be r e i n f o r c e d by e s t i m a t i o n s of nuc lea t ion r a t e s and incubat ion t i m e s for the boron cons t i tuent . F o r an i n t e r r a c i a l ene rgy (coherent ) of about 30 e r g s p e r sq cm, and AG v of 0 to 200 cal p e r mol , we find incubat ion t i m e s of l e s s than 10 -2 s, and nuc lea t ion r a t e s of > 10 +~s p e r sq cm p e r s fo r mos t of the t e m p e r a t u r e r a n g e of i n t e r e s t , i m p l y - ing that b o r o c a r b i d e p a r t i c l e s wi l l nuc lea te quickly and

Fig. 13--A schematic side view of an array of semicoherent grain boundary allotriomorplm (say M23BaC3) which acts to prevent nucleation of a subsequent reaction product.

METALLURGICAL TRANSACTIONS VOLUME 5, APRIL 1974-945

copiously to cover the grain boundary a rea . In a s i tua- tion like this the grain boundary prec ip i ta tes cover and rep lace with coherent interphase boundary segments the high-energy austenite grain boundaries, and so inhibit f e r r i t e or cementi te nucleation. Once the per iod of ini- t ia l growth is rep laced by coarsening, or coarsening combined with growth, the configuration will rap id ly change to give la rge a r eas of continuous incoherent grain or phase boundary (depleted in carbon) where f e r r i t e can read i ly nucleate. Hence, we have a ra t ion- ale which accepts the nucleation catalyt ic effect of the boron constituent at late s tages, but which never theless invokes the presence of this phase, as coherent a l lo- t r imorphs , as a nucleation-inhibit ing agent at ea r ly t imes . This hypothesis can, and should be tes ted by high resolut ion metal lographic observat ions of boron- containing s tee ls af ter b r ie f heat t rea tment .

A s imi l a r approach to the explanation of the effects of other " r enegade" elements , here typified by chro- mium and molybdenum, will now be considered. These elements , in sufficient concentrations, produce a " b a y " in the TTT diagram. Until the presen t work, the bay has been postulated to resu l t f rom a t ransi t ion from part i t ioned to unparti t ioned growth, a2 or to an impuri ty drag mechanism 2z'za in which the carbon content at the aus t en i t e / f e r r i t e boundary is reduced to that in equi- l ibr ium with an a l loy ing-e lement -enr iched boundary region. The f i r s t hypothesis, while a t t rac t ive , has been disproven by microanalyt ic techniques. 34 The second is current , and remains to be tested. We believe, how- ever , that the impuri ty (alloying element) will be equally concentrated at the boundary in both the impuri ty drag and local equil ibr ium 2a'a5 cases . Since, in both models , the activity of carbon is taken to vary slowly through the interface, we consider that tlae impuri ty drag mecha- nism exis ts as an approximate l imit ing case of the local equil ibrium growth model, which always pred ic t s slower growth than the paraequi l ibr ium model, lz,3a but which appears to be inadequate to account for the grea t inhibi- tion of f e r r i t e formation found here.* [We say "appea r s

*The reader is referred to the previous contribution, by Coates, 7 where these models are explored in detail.

to be inadequate" because of rea l uncer ta int ies in the per t inent equi l ibr ia for these 7-loop ca rb ide- fo rming elements] . While we agree with Aaronson et a l . l~ that the absorption of su r face-ac t ive elements can indeed a l te r in terracia l energies , and so affect r a t e s of nucle- ation, we do not bel ieve that most coherent in terracia l energies will be much influenced in this way. A reduc- tion of the incoherent grain boundary energy attending impuri ty absorption would have a smal l effect on nucle- ation if the incoherent interphase boundary energy is s i m i l a r l y affected.

In summary, our cur ren t percept ion is that the im- pur i ty drag effect exis ts , but that it is probably insuf- ficient to account for the nucleation and growth r e t a r d - ing effects of the s t rong ca rb ide- fo rming f e r r i t e s t a - b i l i ze r s . Thus we are led to presen t an a l ternat ive hy- pothesis , which is consistent with the ca rb ide- forming tendency of these e lements , and which like the impuri ty drag hypothesis, r emains to be tes ted exper imental ly .

Coherent gra in-boundary carb ides containing excess Mo or Cr cannot nucleate in t ime to in ter fere with f e r - r i te nucleation, since these e lements diffuse much too slowly. It is quite possible , however, that the growth

(and to a l e s se r extent the nucleation) of f e r r i t e in these sys tems is inhibited at higher t e m pe r a t u r e s by the fo r - mation of p r ecu r so r c lus te r s , which a re enr iched in alloying elements (Cr or Mo) and in carbon. Nucleation theory does not apply to the formation of such coherent c lus te r s , but the minimum t ime for c lus t e r s to grow to a s ize sufficient to hinder f e r r i t e format ion can be crudely es t imated from self -dif fusion data for subs t i - tutional e lements in austenite using a s imple ~ argu- ment. Indeed, it is found that the t imes for growth to 20.~ radius become large at a t empera tu re which coin- cides with the bay on al l such TTT curves , as i l lus t ra ted in Fig. 14. This would pe rmi t the format ion of fe r r i t e , at lower t empera tu res , at r a t e s uninhibited by the c lus te r s .

The drag, or inhibition of f e r r i t e formation, is sup- posed to a r i s e because carbon must be d issoc ia ted from the alloying element c lus t e r s if f e r r i t e is to form. Hence an in terracia l react ion component is effect ively in t ro- duced into what was previous ly a volume diffusion con- t ro l led p rocess , and the carbon diffusion potential (and gradient) will be accordingly reduced and growth inhib- ited. One can think of a number of exper iments which can be designed to c red i t or d i s c red i t this idea. It is offered here as a plausible a l te rna t ive to the impuri ty drag model, and one which mer i t s fur ther cons idera - tion.

CONCLUSION

In p repar ing this paper , we have become aware of the paucity of exper imenta l information avai lable on such fundamental quantities as nucleation ra t e s and in- cubation t imes in high-pur i ty b inary and t e r na ry s tee l s . Also, we are just beginning to gain an understanding of the deta i l s of the s t ruc ture of fcc-bcc in ter faces . Ac- cordingly, much of what has been put forward here awaits confirmation by careful ly designed exper iments on appropr ia te alloy sys tems .

We can nonetheless conclude that: I) Class ica l nucleation theory is sufficiently wel l -

developed for the ra t ional iza t ion of the re la t ive effects of such alloying e lements as Mn, Ni, Co on nucleation of f e r r i t e in s tee ls . In the p r oc e s s of ra t ional iza t ion of observed t ransformat ion data, we have been led to

I000

.O aoo [ / / / ~ ' - [

~ e o o

40C

I I I I I , 1o ,o' Io 3 ,o'

TIME (SEC.)

Fig. 14--Illustrating the possible effect of prior clustering of substitutional alloying elements and carbon on a TTT diagram. The time for a cluster growth to a 20.~ radius is estimated from t ~- a2/D, and shown as a shaded curve. Without the pre- cursor clustering reaction the broken line could be obtained. The full curve schematically incorporates the retarding effect of the clustering reaction.

946-VOLUME 5, APRIL 1974 METALLURGICAL TRANSACTIONS

place l imits on the effective tnterfacial free energy for ferrite nucleation, and on the activation energy of the rate- l imit ing process . The model proposed here for the ferrite nucleus is not inconsistent with these l imits .

2) In the case of carbide-forming ferrite s tabi l izers , the observed hardenability cannot be attributed s imply to thermodynamic factors, and we propose, instead, that precursor reactions interfere with the formation of proeutectotd constituents. Boron additions are con- jectured to yield numerous coherent borocarbide grain- boundary precipitates , which interfere with ferrite nu- cleation when they are f irst formed (but which catalyze the ferri te reaction after they have coarsened). On the other hand, chromium and molybdenum additions may lead at higher temperatures to the formation of c lus- t ers , to which carbon atoms are bound. This suggestion is put forward as a possible reason for the bay in TTT curves , of s tee l s containing these e lements . It is to be considered as an alternative to the impurity drag hy- pothesis .

ACKNOWLEDGMENTS

We are grateful to our colleague, Professor J. S. Ktrkaldy, for a cri t ical reading of this manuscript, and to Professor H. I. Aaronson, for valuable d i scus- s ions . This work was supported by the National Re- search Council of Canada.

REFERENCES

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