Carbonitride Precipitate Growth in Titanium/Niobium Microalloyed Steels

HEILONG ZOU and J.S. KIRKALDY

Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) have been used to investigate the morphology, distribution, composition, particle size distri- butions, and growth kinetics of carbonitride precipitates in steels containing low levels of Ti, Nb, C, and N. During the aging, only the complex carbonilride precipitates of the form (TixNbl_x) ( C y N I _ y ) w e r e found in the newly nucleated and growing particles. The youngest of these par- ticles which approach the size of critical nuclei tends to be Ti-rich. Almost all of these particles are nearly spherical. The initial growth of the precipitates, which is very rapid, lasts less than 30 seconds followed by slow ripening. A model predicting the growth kinetics of carbonitrides and composition variation within the precipitates for the initial stage (before coarsening) has been developed based on equilibrium thermodynamics with the inclusion of capillarity and multicomponent diffusional kinetics. Satisfactory agreement with the experimental results has been demonstrated.

I. INTRODUCTION

IN the development of microalloying technology, much attention has been paid to the investigation of the com- bined effect of several microalloying elements forming a multicomponent precipitate. Thermodynamic struc- tures for the multicomponent phase diagram Fe-EMi-EX~ of dilute iron alloys containing any number of solutes have been developed by a number of authors for quite general cases [1-6] (here, M is the substitutional transition metal Ti, Nb, and V; X is the interstitial element C and N). Many experimental studies on complex carbonitride precipitation during various thermomechanical treat- ments t3-1~ have been carded out in the past decade. It has been reported tT] that in (TixNbl-x) ( C y N I - y ) precip- itates, internal composition gradients exist and specific patterns of composition are correlated with different morphologies and alloy compositions. However, theo- retical understanding of the kinetic process for this kind of compound precipitates is limited.

While multicomponent diffusion theory was devel- oped in the late 1940s and the 1 9 5 0 S , [1Ll2'13] very few applications to more than three components have been reported. This is due, in part, to the complications of the theoretical treatment and the difficulty of finding the "ideal" practical case to which the theory can be directly applied. However, we will demonstrate that subject to some reasonable simplifications and machine computa- tion, the multicomponent diffusion theory may be ap- plied to the kinetics of complex carbonitride precipitation in microalloyed steels..

The objectives of this study are to obtain complete ex- perimental kinetic information about the multi- component carbonitride precipitates in austenite alloyed with titanium and niobium and comparative theoretical predictions with the inclusion of both thermodynamic and

HEILONG ZOU and J.S. KIR KAL DY are with the Department of Materials Science and Engineering and the Institute for Materials Research, respectively, McMaster University, Hamilton, ON, Canada L8S 4M1.

Manuscript submitted June 6, 1990.

kinetic effects. In the present study, a model has been developed to describe the kinetic processes of precipi- tation pertaining to carbonitride in the initial growth stages (before coarsening). The present experimental work has been carded out on the characteristics and the growth kinetics of (TixNbl_x) (CyNl-y) precipitates via trans- mission electron microscopy (TEM) and scanning trans- mission electron microscopy (STEM).

II. EXPERIMENTAL PROCEDURES

The general experimental procedures are described elsewhere, t141 We mention here only some modifica- tions. The chemical compositions of the alloys studied are given in Table I. The encapsulated specimens were given a solution treatment at 1390 ~ for 2 hours and quenched rapidly in agitated iced brine. They were then reencapsulated and up-quenched to 1000 ~ or 1100 ~ and held for various times. However, for aging times less than 10 minutes, specimens ranging from 0.5 to 2 mm in thickness were up-quenched in a salt bath to reduce the heat-transfer time. Another treatment was ex- plored for application to the precipitation transformation. In this approach, the specimens were rapidly transferred to the aging temperature after the solution treatment. This process was achieved by sliding the encapsulated spec- imens from one hot zone to the other in a two-zone hor- izontal cylindrical furnace and holding at 1000 ~ for various times. Optical metallography was used to ex- amine the general microstructure of the quenched specimens.

The carbon replica technique was employed to extract the carbonitride precipitates from the specimens. Ana- lytical electron microscopy was then used to investigate the characteristics of the precipitates. To determine the chemical content of the precipitates in each specimen, X-ray microanalysis was performed with a Vacuum Generator HB5-dedicated STEM equipped with a TRACOR NORTHERN TN200/4000* energy disper-

*TRACOR NORTHERN TN 200/4000 is a trademark of Tracor Northern, Inc. , Middleton, WI.

METALLURGICAL TRANSACTIONS A VOLUME 22A, JULY 1991 - - 1511

Table I. Compositions in Weight Percent of the Alloys Studied*

Steel Number Ti Nb C N O Mn

1 0.0956 0.0965 0.087 0.0010 0.0007 0.0170 2 0.0370 0.0756 0.075 0.0088 0.0015 0.0159 3 0.0206 0.0246 0.022 0.0027 0.0030 0.0165

*All o~er elements are negligible or undetected.

sive spectrum X-ray system. The unique capabilities of the STEM microscopy allow the quantitative micro- analysis of isolated particles down to 1.5 nm using an electron beam diameter of approximately 1 nm. The quantification of X-ray data was performed using the Cliff- Lorimer k factor with the adoption of the thin film cri- terion; that is, CTi/CNb = kTi~ITi/Ir~, where the CM are the weight percentages of M, the IM are the intensities of the characteristic X-ray peaks of M, and k is the Cliff- Lorimer factor. In this work, thin foil standards of nio- bium and titanium alloy were employed to determine the k factor and to enable a high degree of accuracy in microanalysis of precipitate compositions. The average value of k T ~ for Ti K~ and Nb L~ was determined to be 0.56 - 0.025, and this compares favorably with the theoretical value of 0.58Y 5j The use of a windowless EDS detector in the STEM has enabled C and N to be detected qualitatively for particles larger than 20 nm.

III. T H E O R E T I C A L P R E C I P I T A T I O N M O D E L

The intention is to establish a model predicting the growth kinetics of carbonitrides and composition varia- tion within the precipitates for Ti and Nb microalloyed steels. That is, for a given thermomechanical processing and steel composition, we would like to estimate th~ course of the precipitate growth process and the com- position distribution within the particles.

A. The Austenite-Carbonitride Equilibrium

Based on the assumption of perfect compound stoi- chiometry, the carbonitride may be expressed by the chemical formula (TixNbl_x) ( C y N l - y ) , where 0 --< x <-- 1 a n d 0 - < y - < 1.

To express the free energy of the (TixNb~_,) ( C y N l - y ) phase in terms of the free energies of the binary com- pounds, Hillert and Staffansson tl61 proposed that the molar free energy of the precipitate be written as

GTi.Nbt_.CrNt_~ = x y a ~ i c + (1 -- x)yG~bc

+ (1 -- x) (1 -- Y)G~oN

+ X(1 - y ) G ~ i N - TIs m + EGm [1 ]

where the G~c are the molar free energies of the pure I m binary coml~ounds, S is the integral ideal molar entropy

of mixing, ~G m is the integral excess molar free energy of mixing, and T is the absolute temperature. According to Temkin, ~ assuming that Nb and Ti and C and N mix independently on two different sublattices in the inter-

stitial compound, the ideal entropy of mixing is

IS" = - R [ x l n x + (1 - x) In (1 - x)

+ y l n y + ( 1 - y ) l n ( 1 - y ) ] [2]

where R is the universal gas constant. The integral excess molar free energy of mixing is ex-

pressed using a regular solution model, allowing for C-N and Nb-Ti interactions. The expression is

EGm = x(1 - x)y~riNb + x(1 - x) (1 - Y)~-'~iNb

+ xy(1 - y ) l ) ~ + (1 - x ) y ( l - Y)flc~ [31

where l~XTi and f~cMN are the four regular sOlution parameters. [16]

The influence of curvature on the interface composi- tion is significant for the tiny spherical particles that exist in the initial stage of precipitation. Therefore, the effect of curvature must be taken into account for the calcu- lation of chemical potential. Including capillarity for spherical precipitates, the partial molar free energies of the individual compounds in the (Ti~Nbl_x) (CrNI_ r) precipitate solution are given by

GTiC = G~ic + R T l n [xy] + (1 - x) (1 - y ) A G

4~rV~ + EGTiC + - - [4a]

r

GNbC = G~bc + R T l n [(1 - x)y]

- x(1 - y )AG + e(~Nb c + - -

GTiN = G~iN + RT In [x(1 - y)]

4O'Vc [4b]

r

4trVr - (1 - x ) y A G + EGTi N + - - [4cl

r

GNbN = G~bN + R T l n [(1 - x) (1 - y)]

4o'Vc + xyAG + EGNb N + - - [4d]

r

where AG is defined by

AG o o o GTiN GNbN a T i C [5 ] = GNbC + -- ~ --

the eGMx are the partial excess molar free energies, or is the specific interfacial free energy of the precipitate/matrix interface, Vc is the molar volume of carbonitride, and r is the radius of the particle.

Since the regular solution parameters are not well known ~NbTi and will be taken to be for this system, the c N ~'~NbTi

zero following Speer et alJ 41 for the Nb-V-C-N system,

1512-- VOLUME 22A, JULY 1991 METALLURGICAL TRANSACTIONS A

and it will also be assumed that 11cr~ = ~cr~ = 11. The partial excess molar free energies are then given by

eGNbc = eGTic = f~(1 -- y)Z [6a]

E~NbN = E~TiN = ~'~y2 [6b]

The austenite/carbonitride equilibrium condition can be satisfied when the partial molar free energies of each ele- ment in both phases are equal; that is,

[7a]

[7b]

[7c]

[7d] GTiN = dT~i q- a~q

where G? are the partial molar free energies of each ele- ment in austenite, and the GMc are given by Eqs. [4a] through [4d]. The solutes in the austenite are assumed to obey Henry's law, since the solution is very dilute. Thus, the partial molar free energies of Ti, Nb, C, and N in austenite can he written as

G7 = ~ + R T l n [X~] + Ee~Xj [8]

where i refers to the solutes, X~ is the mole fraction of the ith element in austenite at the precipitate interface at equilibrium with the spherical particle, ~ refers to the infinitely dilute standard state in austenite, and e~ is the constant Wagner interaction parameter defmed by the linear Taylor expansion of In y~ (3'~ is the Henry's law coefficient). Since the compositions of steels studied are very dilute, the effect of the last terms in Eq. [8] on the thermodynamics can be neglected; but this may not be the case for diffusional kinetics discussed later. Substi- tuting Eq. [8] and Eqs. [4a] through [4d] into Eqs. [7a] through [7d], we obtain the following four chemical po- tential equalities in terms of the composition of the two phases:

R T l n [XcXTi ] = AG~ic + R T l n [xy] + AGO - x)

4o-V~ �9 ( 1 - y ) + 1 1 ( 1 - y ) 2 + _ _ [9a]

r

R T l n [XcXwo] = AG~bc + R T l n [(1 - x)y]

- AG(x) (1 - y) + ~(1 - y)2

4o-V~ + - - [9b]

r

RT In [XNXTi] = AGaiN + RT In [x(1 - y)]

- AGO - x) (y) + ~ y 2

4~V~ + - - [9c]

r

R Tln [XNXNb] = AG~bN + R T l n [(1 - x) (1 - y)]

4o-V~ + AG(x) (y ) + O y : + - - [9d]

r

where the AG~x terms refer to the free energy of for- mation of the respective compounds from austenite with infinite dilution as the reference state. Note that when

the terms to the right of AG~x become zero, the expres- sion corresponds to the binary compound solubility. It can be shown that only three of the equations are in- dependent. For example, addition of Eqs. [9a] and [9b] is equal to the sum of the other two equations.

The mass balance equations can be written as

X X~i = XTi(1 -- Z) + - Z [10a]

2

(1 - x ) X~I b - - XNb(1 -- Z ) + - - Z [10b]

2

X~: -- Xc(1 - Z) + Y-Z [10c] 2

(1 - Y) z X~ = XN(1 -- Z) + - - [10d] 2

where the X~ terms refer to the overall (or initial) com- position of the steel, and Z refers to the mole fraction of the carbonitride. Equation [9] through [10] can be solved numerically to determine the austenite/carbonitride equilibrium.

B. Diffusion in a Multicomponent System

The irreversible phenomena of multicomponent dif- fusion are described by phenomenological equations out- lined completely by OnsagerY ~1 In a volume-fixed reference frame, the general linear phenomenological equations of the molar fluxes of component i in an n-component system are given by

n--1

Ji = -- E D ikV fk [11] k=l

where the Di~ are diffusion coefficients, and the Ck are concentrations. The off-diagonal diffusion coefficients specify the diffusivity of one component on the concen- tration gradient of the other component.

In the dilute austenite containing strong carbonitride- forming alloying elements (Ti, Nb), the on-diagonal diffusion coefficients, DMM and Dxx, can be assumed to be constant, and the off-diagonal D ' s (DxM and DMX) are approximately proportional to Cx and CM, respectively.

For dilute Fe-M-X ternary systems, it has been shown 081 that

Dxu - eMXx [12a]

Dxx

DMX ------- EXXM [12b]

DMM

It is a very good approximation to extend this formula to dilute the Fe-Ti-Nb-C-N pentenary system. In this system, the fact that Dxx )> DMM assures that the effect of DMX on the corresponding component fluxes can be neglected, and the same holds for DCN, DNC, DNbTi, and DTi~- Then the fluxes in the austenite can be approxi- mately represented in one dimension as

[ OCc cgC-n OCNb'~ Jc I = l - - + e~'Xc + ecNbXc [13a]

- ~ ox ox ox :

METALLURGICAL TRANSACTIONS A VOLUME 22A, JULY 1991-- 1513

/0CN OCTi 0CNb t + 8NNbXN

= - D % W + ox ox / [13b]

0 CTi JTi = --Owi - - [13cl

Ox

OC~ JNb = --DNb - - [13d1

Ox

C. Computer Modeling

The proposed model in this paper is based on the fol- lowing assumptions.

(1) The rate of the precipitation process is controlled by volume diffusion of the Ti, Nb, C, and N atoms in austenite. (2) Local equilibrium, including the effect of capillarity, holds at the interface. (3) The particles are spherical. (4) The interfacial energy, or, is a constant. (5) There is no diffusion within the particle.

We further assume that all of the nuclei form imme- diately after the up-quenching and are uniformly distrib- uted. The matrix is then divided into equisized cells with the radius R0 of equivalent spheres. Following the method of Voice and Faulkner tlgJ for carbide dissolution, in one cell the matrix is theoretically divided into shells of equal thickness radiating from the center of the particle (usu- ally of the order of 2-nm thickness). Each shell is then assigned an initial concentration of solute M and X.

Diffusion is assumed to occur from one shell (i + 1) to i across the spherical interface of area Ai. Based on the general mass-transfer equation, the solute transferred through the interface Ai can be approximately presented by

ith solute transferred/At =

AiDi i i j -- - - [(Xi+ 1 -- Xl ) -{- ~.r 1 -- XJ)],

V,.Ax

( j # i) [141

X~ is the mole fraction of the j th solute in the ith shell, At is the time interval, Ax is the thickness of the shell, and V~ is the molar volume of the austenite matrix. The transferred solutes are subtracted uniformly from the (i + 1)th shell and added to the ith shell when its atoms transfer to the (i - 1)th shell in a similar way, and fi- nally, the diffused solutes are added to the particle sur- face. When the ultimate shell is reached, this shell is given the same atom density as the penultimate shell of the cell according to the principle that there is no net flux into or out of each cell.

The fluxes of M and X at the austenite/precipitate interface can be written approximately in accord with Eqs. [13a1 through [13d] as

Dc (Xc - X* XTi - - XT~i Jc -- V m \ ~ x + EcTiXc AX

+ e~Xc XNb z X * ~ [15al Ax /

n N ( i N ~ X~ X T i - X~i JN-- V,,\ Ax +e~ixN Ax

+ x b: Ax ] [15b]

JTi-- DTi (XTi--XT*iX~ Vm \ Ax ] [15c1

&~= vm \ Ax /

where the local equilibrium compositions Xi are as- signed to the shell next to the particle and the X* terms are the compositions of solutes in the second shell next to the austenite/precipitate interface.

Applying the stoichiometry restrictions in (TixNbl_x) (CyNl_y) to diffusional fluxes at the precipitate/matrix interface creates three more equations

(1 - x) (JTi -1- vC~i) = X(JNb "4- vC~,lb) [16a]

(1 - y) (Jc + vC~c) = Y(JN + vC~) [16b]

(JTi + vC~i) "~- (JNb -~- vC~qb) = (Jc + vCec)

+ (JN+ VCN) [16C]

where v is the velocity of interface motion, and the C~ terms are the local equilibrium concentrations of solutes. However, for microalloyed steels, the vC~ terms make a much smaller contribution compared with the Ji and can be neglected. Furthermore, in the dilute solution range, the general expressions can be simplified to

(1 - X)JTi = XJsb [17a]

(1 - Y)Jc = YJN [17b]

Jwi + JNu = Jc + JN [17c]

Equations [9a] through [9c] and [17a] through [17c] are six equations in six unknowns (x, y, and four Xi) which can be solved numerically. By applying the conservation of M solutes to the whole particle, the velocity of growth of a spherical precipitate will be

v(CPi + C~!b) = (JTi "4- vC~i ) "~ (JNb "4- vC~Ib) [18]

where CPi -- x/Vc and C p = (1 - x)/Vc; and neglecting the vC e terms gives

v = dr /d t = Vc(JTi -~ JNb) [191

Eqs. [9] and [17] are solved at the beginning of each time increment At, and at the same time, the fluxes are calculated by Eq. [15]. After the solution of the equilib- rium and diffusion equations, the position of the inter- face is updated via Eq. [19], simply by adding vAt to the previous value; thus, the precipitate size with time is obtained. Simultaneously, the internal composition parameters, x and y, at a certain position r in the particle are recorded.

The solubility data expressed in the form of free ener- gies of formation of TiC, NbC, TiN, and NbN in aus- tenite are given in Table II. The diffusion coefficients and the interaction parameters in C, N, Ti, and Nb in austenite are given in Tables III and IV.

1514--VOLUME 22A, JULY 1991 METALLURGICAL TRANSACTIONS A

Table II. Free Energies of Formation Table IV. Wagner Interaction of TiC, NbC, TiN, and NbN in Austenite Parameters Adopted in the Calculation

Compound. AGhx (J/mole) Reference

NbC TiC , NbN

TiN '

AG~c = -176,335 + 8.6T * AG~'ic = -166,923 + 14.64T 22 AG~N = -147,010 - 247.7T 23

+ 30.3T In T AGaiN = -221,560 - 238.2T 23

+ 30.3T In T

*Estimated using the data of Johansen et al. and Smith in Refs. 20 and 21, respectively.

IV. R ESULTS A N D D I S C U S S I O N

Optical metallography was used to reveal the general features of the microstructure. Figure 1 shows a perfect lath martensite microstructure of steel 2 quenched after solution treatment. This structure has a relatively uni- form and very high density of dislocations which act as nucleation sites for the precipitates.

For the alternative treatment, wherein the samples were transferred from a solution treatment direct to the aging temperature (1000 ~ and held from 5 to 15 minutes in a two-zone furnace, electron microscopic study shows no newly nucleated particles in anstenite in accord with expectations. This is reasonable, since after the high- temperature homogenization, the microstructure and compositions of alloy become much more uniform, the defects (especially dislocations) which are the favored nucleation sites become depleted, and nucleation inhi- bition is encountered. Accordingly, the rest of our work is focused on the alloys that were homogenized, quenched, and aged, with further justification in the fact that high defect densities are characteristic of thermomechanical processing..

After the 1390 ~ solution treatment, some of the quenched specimens were checked for undissolved par- ticles. High magnification images showed no evidence of newly nucleated precipitate during quenching. How- ever, quite a few remaining cubic particles were found in steels 2 and 3, as shown in Figure 2(a). On the other hand, no undissolved particles were found in steel 1, which was much more dilute in N, although thermo- dynamically expected. This discrepancy can be under- stood within the uncertainty of the solubility data and the insufficiency of the area examined. Figure 2(b) shows the energy dispersive X-ray (EDX) from the undissolved particles, and the sharp nitrogen peaks can be seen clearly. They were identified as (Tio.91Nb0.o9)N in steel 2 and as (Ti0.95Nb0.05)N in steel 3. The theoretically predicted equilibrium composition for precipitates at this temper- ature is (Tio.9oNb0a0) (C0.07N0.93) in steel 2 and (Tio.97Nbo.03)

Wagner Interaction Parameter Reference

66,257 Nb ec = - - - 28 T

79,150 Ti ec. 29 T

406,240 e ~ = - - + 206 30

T 705,000 Ti e~ = - - + 385 30

T

(C0.02N0.98) in steel 3. The EDX is insufficiently sensitive for a quantitative determination of C and N.

While it has been reported tsa~ that Nb-rich precipi- tates nucleate and grow on the undissolved Ti-rich cu- boids, in this study, we found no micrographic evidence of this effect. Although these undissolved cuboids play no direct role in the precipitation behavior, they effec- tively tie up Ti and N. Hence, the solutes in the austenite must be corrected for the undissolved part. Accordingly, the effective concentrations of the precipitate-forming solutes are defined as the dissolved concentrations of solutes in austenite at the solution temperature 1390 ~ The undissolved particles at 1390 ~ were thus elimi- nated from further consideration. It is assumed that fol- lowing solution treatment, the equilibrium between aus- tenite and carbonitride is sufficiently approached, where the concentrations of dissolved solutes are calculated from the thermodynamic analysis presented above and re- corded in Table V.

A. Precipitate Morphologies and Distributions

Figures 3 and 4 shows the course of development of the typically very fine dispersion of carbonitride precip- itates appearing in the aged Fe-Ti-Nb-C-N alloys at 1000 ~ and 1100 ~ respectively, for various times. Quite fine particles are visible in each steel almost im- mediately after aging.

Table III. Diffusion Coefficients of C, N, Ti, and Nb in Austenite

Solute Do (mm 2) Q (kJ/mol) Reference

C 67 157 24 N 91 169 25 Ti 15 250 26 Nb 75 264 27 Fig. 1 - -Op t i ca l micrograph of typical lath martensite structure after

quenching from homogenization in steel 2.

METALLURGICAL TRANSACTIONS A VOLUME 22A, JULY 1991--1515

AL

(a) (b)

Fig. 2--(a) STEM dark-field micrograph of undissolved cuboid (TiNb)N in steel 3. (b) EDX X-rays obtained from the undissolved particle in (a).

The precipitates visible in the replicas reveal only two shapes: spherical and cuboidal. Nearly all of the newly formed particles approach sphericity, suggesting that the growth of carbonitrides is mainly diffusion controlled. Only the undissolved particles have the cubic shape, as shown in Figure 2(a).

Figures 3 and 4 also indicate that newly formed pre- cipitate nuclei have appeared at 1 second for 1100 ~ and this aging time is extended to 2.5 seconds for 1000 ~ in steel 3. These are evidently upper limits on the incubation times. Such short incubation times (com- pared with other treatments and predictions t31'32]) are pre- sumably a consequence of the very high supersaturation which is the driving force for precipitation. Besides, high dislocation densities can accelerate nucleation by short circuit solute diffusion. A high density of quenched-in vacancies can also assist nucleation by increasing dif- fusion rates and by relieving misfit energies.

Figure 5 illustrates that the distribution of particles ap- proaches randomness, which may be attributed to the relatively uniform high density of dislocations in the quenched specimens. However, in a few cases, the ex- tracted particles were in clusters (Figure 5(b)), possibly a consequence of overetching and settling.

B. Precipitate Size Analysis

The recording of particle sizes for the 1- and 2.5-second aging samples was carried out directly on the STEM screen, thus avoiding micrography, which is subject to vibration, drift, and contamination at the highest mag- nification of 10 M. Even so, there exists a large residual error in this measurement due to the limitations of equip- ment and our inability to detect nuclei with a size less than 1 nm.

The average of maximum and minimum measured lin- ear dimensions of particles was recorded as the diameter

of the particles. The particle size distribution, arithmetic means, and standard deviation have been deduced from the size measurements on typically 200 to 250 particles (about 100 particles for 1- and 2.5-second agings). Figure 6 shows the particle size distributions for various aging times at 1000 ~ and 1100 ~ in steel 3. The par- ticle size trends as a function of aging time indicate that the distribution shifts to the right very rapidly (within 10 seconds) and then changes very slowly as it widens. The carbonitrides apparently increase their average sizes in a monotone way with aging time, growing quite rapidly to an average size of about 5 nm within 30 seconds with further growth (coarsening) being slow.

C. Comparison between Predicted and Observed Growth Rates

The parameters used in the computations are estimated in the following ways. The matrix concentration is es- timated as the equilibrium value at 1390 ~ based on the assumption that the large undissolved particles ( - 4 0 nm) are equilibrated. As already noted, the regular solution parameters ~ have not been previously determined for C-N mixing in the Ti-Nb-C-N system. The value l] = - 4 2 6 0 J /mole deduced for a C-N mixing in the Ti-C-N system has been adopted following Roberts and Sandberg ~33] on the grounds that the C and N mixing have

Table V. Predicted Concentrations in Weight Percent of Dissolved Ti, Nb, C, and N in Austenite at 1390 ~

Steel Number Ti Nb C N

1 0.091 0.095 0.087 0.00057 2 0.013 0.070 0.075 0.0016 3 0.016 0.024 0.022 0.0014

1516-- VOLUME 22A, JULY 1991 METALLURGICAL TRANSACTIONS A

(a) (bY

(c) (d)

(e) Fig. 3 - - S T E M dark-field micrographs of (TiNb) (CN) precipitates showing the particle growth, morphology, and distribution in steel 3 for various aging times at 1000 ~ (a) 2.5 seconds, (b) 5 seconds, (c) 10 seconds, (d) 15 seconds, and (e) 60 seconds.

a similar sublattice chemical effect in the carbonitrides. The general outcome is not very sensitive to these as- sumptions for our conditions. The molar volume of the matrix Vm = 7.31 x 10 -6 m3/mole was calculated from the lattice parameter of austenite, a = 0.365 nm, and

the molar volume of carbonitride, Vc, was calculated from the lattice parameter which varies with the com- position of the particle. To accommodate this variation, it is assumed that the lattice parameter of mixed carbo- nitride proportionates as the mole fraction of each binary

METALLURGICAL TRANSACTIONS A VOLUME 22A, JULY 1991--1517

(a) (b)

(c) (d)

(e)

Fig. 4 - - S T E M dark-field micrographs of (TiNb) (CN) precipitates showing the particle growth, morphology, and distribution in steel 3 for various aging times at 1100 ~ (a) 1 second, (b) 5 seconds, (c) 10 seconds, (d) 20 seconds, and (e) 60 seconds.

compound according to the law of mixing; that is

a(TiNb)(CN) = x y a x l c + (1 - x)yaNbC + x(1 - y)aTiN

+ (1 - x) (1 - y)awoN [20]

where the aMx terms are the lattice parameters of MX.

Here, x and y are calculated from the isothermal equi- librium model. The lattice parameters for the binary car- bides and nitrides are given in Table VI. The corrected Ti, Nb, C, and N concentrations in austenite at 1390 ~ (Table V) are employed as the initial compositions X ~ The interfacial energy was taken to be 0.3 J / m 2 (with

1518 - - VOLUME 22A, JULY 1991 METALLURGICAL TRANSACTIONS A

m

~m

.r I

Q

4 -

f

O

(a) (b)

Fig. 5 - - T E M bright-field micrographs of (TiNb) (CN) precipitates in steels 1 and 2 illustrating the spatial distributions of particles in steels 1 and 2: (a) at 1100 ~ 60 seconds in steel 1 and (b) at 1000 ~ 20 seconds in steel 2. Note the particle clusters in steel 2.

reference to data on the austenite/Cr23C6 interface[37]). An integration shell spacing of 2 nm was used through- out the calculations, and a different time interval of 10 -6

to l 0 -4 seconds was used depending on the stability of the computation. It is assumed that for our very thin samples ( - 0 . 5 mm), the aging temperature is achieved instantaneously and the kinetic barrier for nucleation is negligible (site saturation). The half spacing, R0, be- tween particles is estimated to be 40 nm at 1000 ~ and 50 nm at 1100 ~ according to the following self-consistent method. Considering one cell, we have

(v,/v~) Z - [21]

(V~o./Vm) where Vp is the average precipitate volume in one cell, Vcen is the volume of a single cell. Rearranging gives

= ( V,n ~ l/3 r R0 \ ~ ] [22]

where the equilibrium mole fraction of carbonitride, Z, is calculated from Eqs. [9a] through [9c] and [10] and ~- is assigned the value of the average particle radius for 1-minute aging at 1000 ~ and 20-second aging at 1100 ~ obtained in this study. The critical radius of precipitate, re, is calculated from Eqs. [9a] through [9c] by substituting the initial compositions X~. We then set r = 1.01 rc to start the computation.

Figure 7 shows a plot of the mean particle size against aging time in the fast growing stage for the two experi- mental temperatures (the error bars denote the standard deviation of the mean on about 200 particles). The pre- dicted growth rate is close to that observed. A sensitivity analysis [38] shows that there is a small but significant ef- fect of multicomponent diffusion interactions on the interstitial concentration profiles both in matrix and par- ticle, but a negligible effect on the interface motion due to such low solute concentrations. As another sensitivity test for the effect of surface tension, we have repeated the calculation setting ~ = 0 and rc = 0.1 nm, yielding

the dashed line in Figure 7(b) at 1000 ~ This calcu- lation demonstrates that the inclusion of surface tension decreases the particle size by about 10 pct for the same aging time. After trying a shell thickness of 0.5 and 1 nm, it was found that the particle growth rate is not very sensitive to the shell thickness (-<2 nm). Both the experimental and predicted results have proven that the rapid growth of (TiNb) (CN) particles at the expense of matrix solute (i.e., before coarsening) lasts only about a minute and that the equilibrium volume fraction can be approached in a short aging time. It should be noted here that the equilibrium is between austenite and newly precipitated particles with the exclusion of undissolved particles. Since the (TiNb) (CN) is the only stable pre- cipitation phase with austenite at the aging temperature, the equilibrium here is actually the quasiequilibrium de- fined by the very slow kinetic process of composition and volume fraction change of undissolved large (TiNb)N particles.

In the calculations for all three steels, the same pre- cipitate spacing, R0, has been assumed for the same aging temperatures; i.e., the density of nucleation sites which is directly related to the dislocation density is assumed to be the same in the quenched specimens. This as- sumption is born out by the fact that after approaching equilibrium after aging for about 60 seconds, the average size of particles is larger in proportion to the concentra- tion of the dissolved solutes (in the sequence of steels 1, 2, and 3). Of course, the ratio of M to X is also an important factor affecting the molar fraction of precipitate.

There are a number of reasons why the predicted growth rate is slightly deviated from that observed in some cases. For one thing, the incubation time should not be ignored in the model. Experimental results show that the incu- bation time of precipitation at 1100 ~ is less than 1 second and is larger than 1 second at 1000 ~ Second, we have not made a correction for the gradual heating to the aging temperature. However, heat-transfer data of iron suggest that it should take less than 1 second to reach the aging temperature for up-quenching in a salt

METALLURGICAL TRANSACTIONS A VOLUME 22A, JULY 1991 - - 1519

40-

�9 ~ 3O w

>,, o c 20 - (I)

13- a)

10- i i

30

>,, 0 c 20 ID

0 - (I) ~- 10

LI-

0

30 w

0 c 20

13" (I) ~- 10

U_

0

30 w

2.5 sec

I i i I

40

7 I I

I

I I

I

5 sec

3O

0 c 20 ID

D - a)

~- 10 LL

0

30 - w

0 c 20-- ID :3

|

10,- I,

.

7 30

15 sec >. o

] ~ c 20

13-

10 i i

0 �9 ~ 30

"-"I I

I

I I

60 sec o

c 20 i (D

~- 10 u_

0 0 I 2 3 4

P a r L l c t e

5 6 7 8 9 10 Slze Into}

1 sec

7

I i

5 sec

2 0 sec

>,, o c 20 60 sec

O- II! ~- 10 LL

0 0 1 2 3 4 5 6 7 8 9 10

P a r s S l z e (nmJ

(a) (b)

Fig. 6 - -Hi s tog rams of actual carbonitride precipitate size distributions in steel 3: (a) at 1000 ~ and (b) at 1100 ~

bath. On the other hand, these errors are offset by the fact that dislocation densities and quenched-in excess va- cancies are very high in the quenched specimens so that the nucleation and growth of precipitates may be enhanced.

D. Compositions of Particles

The compositions of individual extracted particles were measured by STEM-EDX quantitative microanalysis, with an accuracy of about 5 pct for fairly large particles. The

1520--VOLUME 22A, JULY 1991 METALLURGICAL TRANSACTIONS A

Table VI. Lattice Parameters of MX

Lattice MX Parameters (~) Reference

NbC 4.470 34 TiC 4.326 34 NbN 4.392 35 TiN 4.244 36

EDX output indicated that no Fe or other residual ele- ments exist in the particles analyzed (Figure 8; note that the A1 peak comes from the A1 bars o f the grids). Figure 9 shows the (TiNb) (CN) particle composit ions measured in steels 2 and 3 at 1000 ~ aging temperature as a function of particle size. Although the scatter is fairly large, a particle size dependence of composit ion is

12. 11.

10.

8. ~ 7 .

~ 6.

~ S. o

~ 3 .

~ ~ 1000~ ~0

9

~ 7 ~u N g

m 5

O ~ 3

2 2 1

0

i r i T

1000~

I~. 2 .

I .

0. 0.

1 2 . - -

lt. ~ 10. E c 9.

8. ~ 7. m 6.

..o ~ 3.

1.

0.

I I 10. 20,

1100~

10 2LO 310 r 5LO 610 L I I I

30. 40. 50. 60. 70. A g t n g t l m e ( s

'1 1 T 1 1 't r tO.

9.

"~ a. c

o

at- 2.

70

1.

0 . ~ 10. 20. 30. 40, 50. 60. 70. O. 10. 20. 30. 40. 50. 60. 70.

A91n 9 t l m e [ s e c ) A91n 9 t i m e ( s e c l

(b)

lO00~

10, 20. 30. 40. SO, 60. 70.

i i I i i I 10. 20. 30. 40, 50. 60. 70.

A91n 9 t i m e ( g e c l

(r

(a)

8.

7.

ce6.

m 4.

o 3.

1.

0. 0.

8.

7.

N

O 3,

~ 2 . 13_

I.

0. 0.

F i g . 7 - - V a r i a t i o n o f a v e r a g e c a r b o n i t r i d e particle s izes with heating time (precoarsening), sol id line predicted f r o m m o d e l , u p r i g h t t r i a n g l e

experimental data. ( a ) ( T i N b ) C in s t ee l 1; (b ) ( T i N b ) ( C N ) in s t ee l 2 , s h o w i n g the effect o f zero surface tension at 1 0 0 0 ~ (dashed line predicted b y setting tr = 0 ) , a n d (c) ( T i N b ) ( C N ) in s t ee l 3.

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 A V O L U M E 22A, J U L Y 1 9 9 1 - 1 5 2 1

L i J l l i , , l . . . . I , , LL I . . . . I . . . . I j , , , I k , t , i , , , , l , , , ~ r , ,

Nb-L

T I - K

AL

ty-T, , , , I , , , , I , , , , I , , , , i , , , , i , , , , i , , , , i , , , , i , , , , i , , , r l , ,

Fig. 8- - (a) EDX (X-ray spectrum) obtained from a q TiNb) (CN) par- ticle with size of 3 nm in steel 3.

apparent. Figure 9 indicates that the youngest smaller particles have a higher average Ti content than the larger ones for aging 1 second and 2.5 seconds; it also shows that the differences in compositions between the smaller precipitates and the larger ones are reduced for the longer holding times. This can be considered to be a true and significant result since the theory also suggests it. The same trend is observed for aging at 1100 ~ in steels 2 and 3 but not in steel 1 because it has very low nitrogen. The small particles have a higher Ti composition which, to some extent, indirectly supports the predicted Ti and Nb composition profdes in the particle (Figure 10). These conclusions depend on the assumption that diffusion of the Ti and Nb in the carbonitride is negligible at the aging temperature.

During nucleation, the composition of newly formed carbonitride precipitate is determined by both the thermodynamics and kinetics of the solutes (i.e., local equilibrium and diffusion). Depending on the tempera- ture at which a given panicle has nucleated, its com- position is the result of the balance of equilibrium thermodynamics that determine the composition as a

1

0.9

0.8

�9 0.7 -o

3 o.61

o.s Z

+. 0.4

0,3 C

0.2

0.I

O. O.

I.

0.9

0.8

�9 0.7

0.6

7 ~ 0.5

t 0.4

0.3

0.2

0.1

O. O.

' I ' I l ' f l l ' l ' l l ' f

0

@

@ @ < > ~ 4> {>

o o <)

<>

i i I , i i i

2. 3. 4. 5. 6.

I i I I I

e 8 e o

I l l l i l I I

1. 2. 3. 4. 5. 6.

P a r t ! c L e s i z e [ n m ]

(a)

1 sec

I J I I I I

7. 8. 9. 10.

1 w I ' I I

60 sec

<>

o 8

I * I I I I

7. 8. 9. 10.

I.

0.9

0.8 .q

�9 0.7

0 0.6

-~ o.s Z

t 0.,

"~ 0.3

0.2

0.1

O. O.

1.

0.9

0.8

�9 0.7 0

~ 0.6

_a 0,5 Z

t,~ 0.4

~ 0.3 .,..~

0.2

0.1

O. 0.

, ~ e ~ , , , , , , , ,

e 8 e <> ~ 2.5 sec

<> <~ <> <> <>

I I I I I t I I I I "I i I I

1. 2 , 3 . 4 . 5 , 6 . 7 . 8 . 9 , t O ,

I l ~ i l ' I I l v

. 8 60 sec

<)

I i I I I t I I I I i I I I I

1. 2, 3. 4. 5. 6. 7. 8. 9. 10.

P a r t l c L e slze ( n m )

Fig. 9--Composition of individual (TiNb) (CN) panicles at 1000 ~ (a) in steel 2 and (b) in steel 3.

(b)

1 5 2 2 - - V O L U M E 22A, JULY 1991 METALLURGICAL TRANSACTIONS A

] .

0.9

0.8

0.7

0.6 >-

i 0.5

x 0.r

0 . 3

0.2"

0.1

I

X

' I I i

,Y / I

/I I

i / / / I l l

/ l I

I !

/I I i I i I I

I. 2. 3.

Distance from particle center (nm)

q j~ ].

0.9

0.8

0.7

0.6

0.5

0.4.

0.3

0.2

0.1

O. O.

I !

I I

/ J

O. - - - t I t I i I t

O. 4.." 1. 2. 3. 4.

Distance from particle center (nm)

(a) (b)

Fig. 10--Predicted composition profiles in the complex particles (i.e., x and y) in (Ti,Nbl_x) (CrNI_y) at 1000 ~ (a) in steel 2 and (b) in steel 3.

function of temperature and the diffusional kinetics of 4. the process that change the composition as a function of time. This can be understood qualitatively by noting that TiN has the highest supersaturation and that Ti diffuses faster than Nb. Therefore, the nuclei of precipitates or 5. the core of the precipitates should have high Ti and N contents and low Nb and C, but after Ti is depleted in the matrix, Nb becomes the major diffusion element and the particles have a Nb-rich shell.

V . S U M M A R Y

A detailed study of the morphology, distribution, composition, particle size distributions, and growth ki- netics of complex carbonitride particles in microalloyed steels has been carried out using TEM- and STEM-based high-magnification micrographs and microanalysis. A model of precipitate growth at the precoarsening stages has been developed based on thermodynamics and ki- netics to predict the precipitation behavior of carbo- nitrides and the composition distribution in the particles. The main conclusions from this work are the following.

1. The undissolved cubic particles were identified as (Tio.91Nb0.09)N in steel 2 and as (Ti0.95Nb0.05)N in steel 3 which are in good agreement with the pre- dicted equilibrium composition for precipitates at this temperature.

2. The morphologies of the newly formed fine precip- itates are roughly spherical, which indicates that dif- fusion control of growth dominates. The distribution of precipitates was nearly random in space and in size.

3. The growth of (TiNb) (CN) particles before coars- ening can be adequately predicted using the model proposed in this study. Both experimental and pre- dicted results suggest that the rapid growth of (TiNb) (CN) at the expense of matrix solutes lasts less than 1 minute before slow coarsening occurs.

During aging, only the complex carbonitride precip- itates of the form (TixNbl_x) (CyNl-y) were found in the newly nucleated and growing particles due to the mutual solid solubility of carbides and nitrides. The composition profiles of Ti and Nb within the par- ticles were calculated using the model presented in this study and found to be in qualitative accord with the experimental observations. Both calculated and measured results show that the youngest nuclei tend to be Ti-rich, but as they grow, the Ti/Nb ratio decreases.

R E F E R E N C E S

1. D.C. Houghton: McMaster University, ON, Canada, unpublished research, 1983.

2. M. Grujicic, I. Wang, and W.S. Owen: CALPHAD, 1986, vol. 10, pp. 117-28.

3. S.V. Subramanian, S. Shima, G. Ocampo, T. Castillo, J.D. Embury, and G.R. Purdy: Proc. CSM Conf., HSLA 1985, Beijing, China, 1986.

4. J.G. Speer, J.R. Michael, and S.S. Hansen: Metall. Trans. A, 1987, vol. 18A, pp. 211-22.

5. S. Suzuki, G.C. Weatherly, and D.C. Houghton: Acta Metall., 1987, vol. 35, pp. 341-52.

6. J. Strid and K.E. Easterling: Acta Metall., 1985, vol. 33, pp. 2057-74.

7. G. Ocampo: M. Eng. Thesis, McMaster University, ON, Canada, 1984.

8. M. Grujicic, I.J. Wang, and W.S. Owen: CALPHAD, 1988, vol. 12, pp. 261-75.

9. D.C. Houghton, G.C. Weatherly, and J.D. Embury: in Thermomechanical Processing of Microalloyed Austenite, TMS- AIME, Warrendale, PA, 1981, pp. 267-92.

10. D.C. Houghton, G.C. Weatherly, and J.D. Embury: Advances in the Physical Metallurgy and Applications of Steels, Book 284, Metals Society, London, 1982, pp. 136-46.

11. L. Onsager: Ann. NYAcad. Sci., 1945, vol. 46, p. 241. 12. G.J. Hooyman, S.R. DeGroot, and P. Mazur: Physica, 1955,

vol. 21, p. 360. 13. J.S. Kirkaldy, D.H. Weichert, and Zia-ul Haq: Can. J. Phys.,

1963, vol. 41, p. 2166.

METALLURGICAL TRANSACTIONS A VOLUME 22A, JULY 1991-- 1523

14. H. Zou and J.S. Kirkaldy: Can. MetaU. Q., 1989, vol. 28, pp. 171-77.

15. D.C. Houghton, G.C. Weatherly, and J.D. Embury: McMaster University, ON, Canada, unpublished research, 1981.

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17. M. Temkin: Acta Physicochem. URSS, 1945, vol. 20, pp. 411-20. 18. J.S. Kirkaldy: Energetics in Metallurgical Phenomena, W.M.

Mueller, ed., Gordon and Breach Science Publishers, New York, NY, 1968, vol. 4, pp. 242-64.

19. W.E. Voice and R.G. Faulkner: Met. Sci., 1984, vol. 18, pp. 411-18.

20. T.H. Johansen, N. Christensen, and B. Augland: Trans. TMS-AIME, 1967, vol. 239, p. 1651.

21. R.P. Smith: Trans. TMS-AIME, 1966, vol. 236, pp. 220-21. 22. T. Sharaiwa, N. Fujino, and J. Murrayama: Trans. Iron Steel

Inst. Jpn., 1970, vol. 10, p. 406. 23. K. Balasubramanian and J.S. Kirkaldy: McMaster University,

Hamilton, ON, Canada, unpublished research, 1989. 24. R.P. Smith: Trans. TMS-AIME, 1964, vol. 230, p. 476. 25. L.S. Darken, R.P. Smith, and E.W. Filer: Trans. Am. Inst. Min.

Eng., 1951, vol. 191, p. 1174. 26. S.J. Moll and R.W. Ogilvie: Trans. Metall. Soc. AIME, 1959,

vol. 215, p. 613.

27. S. Kurokawa, J.E. Ruzzante, A.M. Hey, and F. Dyment: Met. Sci., 1983, vol. 17, pp. 433-38.

28. J.C. Greenband: J. Iron Steel Inst., 1971, vol. 208, p. 986. 29. K. Balasubramanian and J.S. Kirkaldy: CALPHAD, 1986, vol. 10,

p. 187. 30. K. Balasubramanian and J.S. Kirkaldy: Can. Met. Q., 1989,

vol. 28, pp. 301-15. 31. W.J. Liu and J.J. Jonas: Metall. Trans. A, 1989, vol. 20A,

pp. 689-97. 32. B. Dutta and C.M. Sellars: Mater. Sci. Technol., 1987, vol. 3,

pp. 197-206. 33. W. Roberts and A. Sandberg: Swedish Institute for Metals Research

Report No. IM-1489, Stockholm, 1980, p. 301. 34. S. Nagakura and S. Oketani: Trans. ISIJ, 1968, vol. 8, p. 265. 35. H.J. Goldschmidt: Interstitial Alloys, Plenum Press, New York,

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of Ternary Diffusion, G.R. Purdy, ed., Pergamon Press, New York, NY, 1990, pp. 184-95.

1524--VOLUME 22A, JULY 1991 METALLURGICAL TRANSACTIONS A