Thermodynamic Calculation and
Experimental Verification of the CarbonitrideAustenite Equilibrium in Ti-Nb Microalloyed Steels
HEILONG ZOU and J.S. KIRKALDY
The sublattice-regular solution model has been adapted to describe the thermodynamics of
complex carbonitrides. This model has been applied to titanium- and niobium-bearing microalloyed steels for calculation of the mole fraction and composition of the carbonitride precipitates
and the residual solute levels in the austenite. Both experimental results and calculations show
that titanium nitride predominantly forms at very high temperatures and titanium-niobium carbides go to completion at low temperatures. Quantitative agreement between the experimental
measurements and the predictions for carbonitride compositions as a function of temperature is
demonstrated.
I.
INTRODUCTION
IT is well known that the carbonitrides of transition
metals play an important role in improving the overall
properties of microalloyed steels. Thermodynamic analysis is an important method for optimizing both the
chemistry and process design of microalloyed steels for
thermomechanical processing. Thermodynamic representations of the multicomponent phase diagram Fe-~MiEXj of dilute iron alloys containing any number of
solutes have been developed by a number of
authors [1-121 (here, M is the substitutional transition metal
Ti, Nb, and V and X is the interstitial element C and
N). None of these models has taken capillarity into account. The surface tension effect can be significant as a
consequence of the typically tiny particle sizes (5 to 10
nm), which raises the matrix composition at the interface
in equilibrium with the precipitates and thereby reduces
the mole fraction of precipitates. Many experimental
studies [5-1sl on the multicomponent carbonitride compositions have been carried out in the past decade. Almost all of them were restricted to measurements of
metallic compositions (e.g., the x in Ti~Nb~_x) (CyNl_y)*
in terms of binary compounds at a given temperature,
and the residual solute contents in microalloyed steels.
The compositions of the extracted particles (both the x
and y in (TixNbl_x) (CyNl-y)) w e r e determined by two
complementary techniques: energy dispersive X-ray
spectrometry (EDX) and electron energy loss spectrum
(EELS).
II.
With the inclusion of the capillarity term for spherical
particles, the following four chemical potential equalities
in terms of the composition of the two phases define the
austenite-carbonitride equilibrium: ~12J
RT In [XcXTi] = AG~ic + RT In [xy] + AG(1 - x)
4o-V~
9 ( l - y ) + 1)(1 - y ) 2 + _ _
r
[la]
RTIn [XcXNb] = AG~bc + RTln [(1 - x)y] - AG(x)
9 (1 - y )
*In this article, (Ti~Nb~ x) (CyNl--y) is frequently simplified as (TiNb)
(CN). The complete formula will be used only in the case when precise knowledge of the compositions of the precipitates is required.
in the complex compounds.
In the present study, the sublattice-regular solution
model proposed by Hillert and Staffansson tl61 has been
modified with the inclusion of the capillarity effect and
applied to Fe-Ti-Nb-C-N alloys. The purposes of the
thermodynamic analysis are to calculate the effective
contents of Ti, Nb, C, and N available for the formation
of the complex carbonitride precipitates during aging,
the compositions and mole fractions of these precipitates
THE AUSTENITE-Ti-Nb
EQUILIBRIUM
CARBONITRIDE
4o'V~
+ f~(1 _ y ) 2 + _ _
r
[lbl
RTIn [XNXTi ] = m a g i N -1- RTIn Ix(1 - y)]
4o-Vc
- AG(1 - x) (y) + ~y2 + __
F
[lc]
J
RTln [Xrogwo] = AG~br~+ RTln [(1 - x) (1 - y)]
4o'Vc
+ AG(x)(y) + OAy 2 + - -
[1 d]
F
HEILONG ZOU, formerly Research Associate, with the Institute
for Materials Research, McMaster University, is Research Scientist,
with Atomic Energy of Canada, Limited, Chalk River, ON, Canada.
J.S. KIRKALDY, Emeritus Professor, is with the Institute for Materials
Research, McMaster University, Hamilton, ON, Canada L8S 4M1.
Manuscript submitted May 31, 1991.
METALLURGICAL TRANSACTIONS A
where AG can be calculated by
AG = AG~oc + AG~-iN- AG~N - AG~ic
[le]
and where the AG~x refer to the free energies of formation of the respective MX carbides and nitrides from
VOLUME 23A, FEBRUARY 1992--651
austenite with infinite dilution as the reference state, ois the specific interfacial free energy of precipitate/ma~ix
interface, Vc is the molar volume of carbonitride, r is the
radius of the particle, ~ is the regular solution parameters, Xi is the mole fraction of the ith element in austenite at the precipitate interface at equilibrium with the
spherical precipitate, and the factor 4 instead of 2 in the
capillarity term results from our definition of Vc.
The mass balance equations can be written as
V
~ c = Xc(1 - Z) + =-Z
2
)~N = XN(1 -- Z) +
[2a]
Y)Z
(1 -
[2c]
2
(1 - x)
[2d]
~XNb : XNb(1 -- Z ) + - - Z
2
where the X~ refer to the overall (or initial) composition
of steel and Z refers to the mole fraction of the carbonitride. Equations [la] through [2d] can be solved numerically to determine the austenite/carbonitride equilibrium,
and this effectively defines the Fe-rich comer of the
Fe-Ti-Nb-C-N phase diagram, including tie-lines to the
precipitate phase plane.
RESULTS OF THE COMPUTATIONS
In this section, we illustrate the evolution of the mole
fractions and compositions of complex carbonitrides and
matrix compositions with temperature. These quantities
are reassessed using the concept of effective compositions for the newly formed carbonitride precipitates and
then compared with the experimental results obtained in
this study.
Numerical methods must be used to solve the
nonlinear simultaneous equations which represent the
equilibrium and mass balance pertaining to the austenite(TixNbl-x) (CyNl_y) system, and we chose to use the
Newton-Raphson technique. Considerable care in the
choice of the numerical method and initial guesses was
required in the search for real positive roots to ensure
convergence. Only one selfconsistent set of solution parameters was found to simultaneously satisfy the thermodynamic equilibrium and mass balance relations for
a given temperature and alloy composition.
The composition of microalloyed steels studied experimentally is given in Table I. The adopted free energies of formation in austenite are presented in Table II.
Table I.
Steel Number
1
2
3
Ti
0.0956
0.0370
0.0206
Compound
AG~x (J/mole)
Reference
NbC
TiC
NbN
AG~,c = -176,335 + 8.6T*
AG~ic = -166,923 + 14.64T*
AG~br~ = -147,010 - 247.7T
+ 30.3T In T
A G ~ i N = -221,560 - 238.2T
+ 30.3T In T
**
19
20
TiN
20
*These are the best estimates from available observations. Theoretically, one expects the entropic coefficients to have the same sign
as the nitrides.
**Estimated using the data of Johansen e t a l . tl7j and Smith. t'sj
[2b]
2
X
~Ti : STi(1 -- Z ) ~- - Z
IIl.
Table II. Free Energies of Formation
of TiC, NbC, TiN, and NbN in Austenite
The regular solution parameter 1~ is taken as - 4 2 6 0
J / m o l e following Roberts and Sandberg, Izu ~r is taken
as 0.3 j/m2, t22~ and Vc is estimated via the law of
mixing.I~2J
In the present experiment, the microalloyed steels were
solution-treated at 1390 ~ for 2 hours, quenched, and
then aged at different isothermal temperatures for various times. The EDX and EELS techniques were carried
out to measure the compositions of the carbonitride precipitates. The general experimental procedures are described elsewhere, t12'23 25~
A. Mole Fractions and Compositions of the
(TiNb) (CN) Precipitates
In this part of the calculation, the overall equilibrium
between carbonitride-austenite is considered. The capillarity effect here is irrelevant. Figure 1 shows the calculated mole fractions of (TixNb~_x) ( C y N I - y ) in terms of
the accumulation of binary compounds in the temperature range 800 ~ to 1500 ~ for steels 1 through 3. The
overall mole fraction of carbonitride (as defined by the
TiC solid contour line) and proportions of each type of
binary carbide/nitride in the multicomponent compound
strongly depend on the composition of the steels and the
temperature. It can be seen that none of the three steels
are completely free from precipitates in the austenite phase
field (910 ~ to 1395 ~
At very high temperature, the
precipitates are mainly (TixNb,_x)N (TiN and NbN) and
their amount increases slowly with decreasing temperature because of rapid depletion of N. Steel 2 with both
relatively higher Ti and N contents is expected to contain
the larger fraction of undissolved (TiNb)N at 1390 ~
However, with further cooling along the abscissa of
Figure 1 through the typical thermomechanical processing temperature (1200 ~ to 900 ~
the compound
Compositions in Weight Percent of the Alloys Studied*
Nb
0.0965
0.0756
0.0246
C
0.087
0.075
0.022
N
0.0010
0.0088
0.0027
O
Mn
0.0007
0.0015
0.0030
0.0170
0.0159
0.0165
*Allotherelements me negligible orundetected. These span atypicalrange of microalloyed steels.
652--VOLUME 23A, FEBRUARY 1992
METALLURGICAL TRANSACTIONS A
4,
I
I
I
I
I
tion and grain growth in austenite during thermomechanical processing.
It is worth noting that with cooling below 1300 ~
the amount of (TiNb)N is almost unchanged due to the
matrix depletion of N. Figure 1 also shows the repartitioning of TiN and NbN resulting from the strongly preferential entry of Nb into the carbonitride at low
temperature.
The particle composition changes ( i . e . , x and y in
(TixNbl_x) (CyNl_y)) with temperattLre for steels 1 through
3 are presented in Figure 2. It is evident that for all three
steels near the solution temperature, the x values approach unity and the y values zero. Thus, the precipitates
are chemically close to TiN, as already indicated in
Figure 1. Therefore, Ti and N are the dominant elements
in the quaternary carbonitride at higher temperature. By
contrast, as temperature decreases, the x decreases and
y goes the opposite way; i . e . , the proportions of Nb and
C in the compound increase. The inversion of the x value
in steel 1 occurs at around 1220 ~ and this is due to
the sharp increase in TiC in steel 1. The precipitate may
be considered as Ti-Nb carbide.
I
x
(-
Steel 1
3,
o
...-1
O 2.
D
1._
LL.
J
....
NbN
. NbC
o
Z
%
....,__
__.,,
_
TiN
+ _ _ _
I
%
"\\
"\\
,
I
I
I
I
x
,
I
Steel 2
.
c
o
1.S
0
o
1.
ii
J
9
0.S
o
TiN
,
I
,
I
I
I
,
I
i
I
I
,
I
I
I
i
I
,
],
1
'
'
'
'
'
I
0.8
~"
0.0
-
Steel 3
;~0.6
~J
c
i -
..--i
.-o
o
• 0.,--..
\
0.4
0.2
Steel 1
o
Z
O.
-_iS"bN.N._ _- . . . . .
a
I
1.
0.
"
,Ti.l.r~
800.
g00.
,
,
1000.
,
I
,
ll00.
Temperature
i
1200.
,
,
i
I
,
,
I
~
1
i
,
i
i
,
f
, ~'~."x,~
1300.
1400.
1500.
0.8
X
[ ~
Fig. 1 - - T h e cumulative mole fraction of (TiNb) (CN) precipitates as
a function of temperature in three steels.
0.6
-(3
c
o 0.4
0.2
(TiNb)C consisting of a mixture of TiC and NbC, although intimately mixed with (Ti~Nbl x)N, dominates the
precipitation reaction, and this results in a sharp increase
of the mole fraction of carbonitride particles in such steels
due to the rapid precipitation of TiC and NbC.
For steel 1 with high Ti, Nb, and C and very low N,
the TiC and NbC start to rapidly increase their proportion around 1275 ~ for steel 2, they start to proportionate around 1200 ~ However, for steel 3 with low
Ti, Nb, and C and relatively higher N levels, it is not
until about 1000 ~ that the amount of carbides begins
to significantly increase. As a result, the mole fraction
of precipitates (mainly TiC and NbC) in steel 1 with the
higher levels of total solutes is highest in the aforementioned rolling temperature range and is least in steel 3
due to its relatively lower total amount of solutes. The
(TiNb)C precipitates of this kind are considered to be
the major contributor to the retardation of recrystallizaMETALLURGICAL
TRANSACTIONS A
Steel
0.
1.
~
I
~
I
i
I
,
I
I
1
I
'
I
'
I
'
t
t
I
X
0.8
>'~' 0 . 6
-13
C
O 0.4
0.2
0.
,
000
~
,
900
I
,
1000
i
,-"--r--,
1100
1200
TemperaLure
i
, Yl
,
1300
1400
1000
[ ~
Fig. 2--Predicted carbonitride composition (i.e., x and y in (TixNbl x)
( C r N , _ y ) ) as a fugction of temperature in three steels.
V O L U M E 23A, F E B R U A R Y 1 9 9 2 - - 6 5 3
0.1
Since at the temperature of complete dissolution of the
particles, the composition in the equilibrium case will be
strongly biased toward the most stable compound TiN,
the ultimate dissolution temperature should not be significantly affected by the mixing effects; i.e., it can be
estimated at the point of complete dissolution of TiN
(which is slightly underestimated). At lower temperatures, however, calculations tl] showed that mixing effects give rise to an increase in precipitate mole fraction.
3:
o
C
o
o
C
O
i
'
I
-
-
Steel
'
-
= Steel
0.0S . . . . .
'
i
i
i
0.08
0.06
0.04
0.02
0,
0,006
,
I
~
I
l
I
,
]
I
,
t
I
Steel 1
Steel 2
= Steel 3
=
0.005
c
o
.....
/i
0.004
-S
-p
C
o
0
0.003
/
0.002
C
0
u
800
I
I
/
I
I
I
./
0.001
O,
i
i
LJ
z
'
i
1
(3
g.
~J
u
0.1
i
Steel
=
-
E
B. Concentrations of Residual Solutes in the Austenite
The concentrations of the remaining Ti, Nb, C, and
N in the steels as a function of temperature were also
calculated, and these are presented in Figures 3 and 4.
Mass balance equations indicate that the concentrations
of the remaining solutes depend directly on the mole
fractions of the precipitates and on the overall concentrations of the steels. Therefore, the solute concentration
changes with temperature are consistent with the inverse
trend of the mole fraction change. It may be noted that
N is almost depleted at very high temperature as most
of the TiN comes out at above 1300 ~ The temperature
for the onset of the rapid decrease of Ti, Nb, and C content in austenite corresponds directly to the temperature
at which TiC and NbC start to precipitate rapidly, as can
be seen in Figure 1.
i
-
900
1000
1100
1200
1300
1400
1500
Temperature ( ~ )
1
2
/
Ste
F i g . 4 - - C a l c u l a t e d v a r i a t i o n o f the r e m a i n i n g C a n d N c o m p o s i t i o n s
in the a u s t e n i t e w i t h t e m p e r a t u r e in t h r e e steels.
C
2 o.o6
C. Mole Fractions and Compositions of the Newly
Formed (TiNb) (CN) Precipitates Taking Account
of Capillarity
o
c
m
0.04
o
co
u 0.02
0.1
'
[
/
-~ [0.08
0.04
i
/
i
'
i
. .:-:- J
'
i
-
:
Steel
1
"
-
= Steel
2
"
-
= Steel
3
-
'
I
'
i
I
J~---~
/
-
F y
Iii
/
i ~
O.
800
l ' ~ ~ ,
900
i
,
. . . .
t
,
I
,
I
I
I
,
1000 1100 1200 1300 1400 1500
Temperature ( ~
Fig. 3--Calculated variation of the remaining Ti and Nb compositions in the austenite with temperature in three steels.
6 5 4 - - VOLUME 23A, FEBRUARY 1992
In Section B, we calculated the equilibrium mole fraction of precipitates using the overall compositions. The
calculated results show that there exist undissolved carbonitrides at the solution temperature in steels 1 through
3, and this was also proved by experimental observations. 111}Since these undissolved cuboids play no role in
the precipitation behavior, the solutes in the austenite
must be corrected for this undissolved part. Therefore,
we subtract out the solute amount in the cuboids and
calculate the mole fraction of the solutes in the matrix
using the remainder. These are now regarded as the effective concentrations of the solutes. For this calculation, the radius of the large undissolved particles is
estimated ag'40 nm based on the micrographs, with the
final result as shown in Table III. The effective concentrations of the precipitate-forming elements were used in
further calculations of the mole fractions and compositions of the newly formed precipitates which come out
during isothermal aging below the solution temperature.
The average particle size of 5 nm is assigned to r in the
capillarity term.
The predicted mole fraction of new particles is plotted
in Figure 5. The total amount of newly formed precipitates is less than that in Figure 1 at a given temperature,
METALLURGICAL TRANSACTIONS A
Table IIl.
P r e d i c t e d C o n c e n t r a t i o n s in W e i g h t P e r c e n t
o f D i s s o l v e d T i , N b , C , a n d N in A u s t e n i t e at 1 3 9 0 *C
S~el
Number
Ti
Nb
C
N
1
2
3
0.091
0.013
0.016
0.095
0.070
0.024
0.087
0.075
0.022
0.00057
0.0016
0.0014
since the u a d i s s o l v e d c a r b o n i t r i d e at the s o l u t i o n t e m p e r a t u r e is e ~ c l u d e d . S t e e l 2 is a f f e c t e d the m o s t b e c a u s e
o f its highest u n d i s s o l v e d a m o u n t o f ( T i N b ) N at 1390 ~
H o w e v e r , in all three a l l o y s , the g e n e r a l t r e n d and s h a p e
r e m a i n s i m i l a r . T h e results o f the c a l c u l a t i o n also s h o w
that the solute c o m p o s i t i o n changes with temperature k e e p
to the s a m e trend as in Figures 3 and 4. T h e figure s h o w s
that the carbonitride precipitated in steel 1 is almost T i - N b
c a r b i d e . H o w e v e r , c o m p a r e d w i t h steels 1 and 2, steel
4.
I
%
I
I
I
I
3 has an extended (TiNb)N range. Another factor that
results in the decrease of mole fraction is the capillarity
effect. The repeated calculation for r = oo shows that the
mole fraction of carbonitride is reduced by about 10 pct
(i.e., the total amount of solutes in the matrix increases
by - 10 pct).
So far it has not been possible to obtain estimates of
the volume fraction of the precipitates from carbon replicas in microalloyed steels because of grain-to-grain
variability in the etching response of the steel and the
sensitivity of the extraction process to the etching time
of the specimen. Furthermore, after etching, the exposed
particles are sitting on a very rough surface, and as a
result, the electron micrographs pertain to the projection
of particles from this surface which implies a density
greater than the true two-dimensional value.
The experimental and predicted compositions of the
reprecipitated (TiNb) (CN) as a function of aging temperature and effective steel compositions are presented
in Figure 6. In comparison with Figure 2, the general
trend remains similar but a significant shift of the curves
I
Steel 1
x
.
3.
c
o
0.8
-3
O 2.
O
Ii
J
0.6
"O
C
O 0.4
Q) 1.
o
Z
NbC
9
1.%
NI,,~N--,~X,x
. . . .
.t
~/_
TiN
,_".~
/.
o
0.2
,
Steel 1
I
I
I
I
I
I
0.
x
d
,
I
I
I
I
I
I
I
I
I
I
I
I
Steel 2
1.
_Z_
u_ 0.5 _
ID
J
o
Z
"1".
\\\X~X
NbC
\~
.
,
I
I
,
I
I
,
TiN
0.2
_--_I
I
,
I
I
,
I " ~
I
Steel 2
I
0.
I
1.1
O.a
X
~'~ 0.6
c
o 0.4-
o
o
0.
_I.
0.8
X
I
I
I
I
I
'
I
'
I
'
I
l
I
I
I
I
I
'
i
'
I
~x'
I
Steel 3
d
o 0.6
o
o
~- 0.4
LL
ID
J 0.2
O
Z
0.
800. 900. 1000. 1100. 1200. 1300. 1400. 1500.
Temperature
{~
Fig. 5--Calculated equilibrium mole fraction of newly formed (TiNb)
(CN) in three steels.
METALLURGICALTRANSACTIONSA
>,..
o
x
9
800
I
900
I000
II00
1200
Temperature
1300
•
I i
1400
1500
[ *C]
Fig. 6--Comparison of experimental and predicted compositions (solid
lines) of reprecipi.lztted panicles in three steels: A = x and x = y.
VOLUME 23A, FEBRUARY 1992--655
is evident, unlike the mole fractions and matrix compositions. All of the alloys showed the expected increase
in Ti content of the particles with increasing aging temperature. Although the experimental results are limited,
they show very good agreement with the prediction for
steels 1 and 2 and reasonable agreement for steel 3. Furthermore, for steel 1, the results obtained confirm the
reversion of x as calculated.
Most of the experimental results are based on the EDX
measurements of about 15 particles in specimens aged
60 seconds, which have accordingly not reached quasiequilibrit]rn. Detailed microanalysis has been made on
the specimens of steel 3 aged 100 hours (Figure 7) which
should have nearly reached equilibrium. The measured
average x values from cubic particles are higher for
100 hours at 1000 ~ than those from spherical particles,
while both values are greater than those for aging
60 seconds. On the other hand, the deduced trends of y
values are opposite for cubic and spherical particles. The
time dependence of the particle compositions could be
an indication that the transfer of Ti and Nb from the
undissolved particles to the newly formed particles is occurring so as to attain the true equilibrium over such a
long holding time at 1000 ~ Overall equilibrium, including the undissolved (TiNb)N, may not be reached
by holding even for 100 hours, since only about half of
the particles are cuboids.1241 On the other hand, the overall equilibrium at 1100 ~
including the undissolved
(TiNb)N, may be reached by holding for 100 hours, since
almost all of the particles are cuboids. Therefore, one
should be aware that the measured compositions at
1390 ~ for 2 hours and 1100 ~ for 100 hours well represent the overall equilibrium compositions and should
be compared with the curves in Figure 2.
IV.
DISCUSSION
In the thermodynamic calculation, it has been assumed that the newly formed carbonitrides are in complete equilibrium with microalloyed steels. However, all
of the results obtained in this study with aging at various
temperatures show that the attainment of true (overall)
1.
.
,
.
~
i
'
i
9
i
,
0.6
r
o
z
0.4
0.2
X
X
1000
1100
O,
800
,
900
1200
I
1300
I
1r
1S00
Temperature (*C)
Fig. 7--Comparison of experimentaland predicted compositions (solid
lines) of reprecipitated particles in steel 3 for 100 hours: A = x for
cuboids and ,6, = x for spheroids; • = y for cuboids and • = y for
spheroids; and 9 = y for cuboids from EELS.
6 5 6 - - V O L U M E 23A, FEBRUARY 1992
equilibrium, particularly at low temperatures, cannot obtain for short aging times. Indeed, in the experiments, it
was found that the coexistence of coarse TiN and fine
(TiNb) (CN) particles cannot correspond to a true equilibrium situation. On the other hand, the undissolved TiN
cuboids are sufficiently coarse and widely dispersed that
local equilibrium between the fine carbonitride precipitates and austenite can be completely dictated by the
remaining solutes in matrix.
In the present model, as in others, 1Hi] it has been assumed that in microalloyed steels, there is complete mutual solid solubility of Ti, Nb, C, and N in a single
carbonitride precipitate species of the form (TixNbl-x)
(CyNI_y). The fact that binary carbides and nitrides precipitated in steels have a similar fcc lattice structure suggests that such mutual solid solubility is likely. The present
study has again confirmed this belief. It has been found
from direct measurement of a large number of particles
from different microalloyed steels that not only do the
particle compositions strongly reflect the compositions
of the steels, but the average composition can be predicted from the thermodynamic model. In Figure 6, it
has been shown that these models provide a very good
description of the particle compositions in steels 1 and
2 and these particles turn out to be close to Ti-Nb carbides. For the precipitates in steel 3, the predicted particle compositions deviate somewhat from the
experimentally determined particle compositions at some
of the aging temperatures. The experimental results show
that the measurement scatter of particle compositions (i.e.,
the error bars in Figure 6) in steel 3 is fairly large, in
sharp contrast to the situation in steels 1 and 2. For long
aging times, this scatter is to be associated with the partial transformation of spherical and polyhedral particles
to cubic particles in steel 3. The nonuniform composition within the particles, and particularly for plate-shaped
particles, 125]is another contributor to the scatter. The cuboids and the centers of plate particles are strongly Ti
and N rich, while the spheroids and the two ends of plate
particles contain less Ti and N. These observations may
indicate that a partial phase separation ( i . e . , carbide rich
in spheroids and nitride rich in cuboids) is happening.
This was also suggested by Houghton et al. [131 and supported by a theoretical calculation. 12~
It is concluded that for the complex particles in the
size range studied here, the diffusion rate within particles may not be high enough to bring about homogenization of Ti and Nb within particles for very short times.
However, some homogenization within particles may be
reached and/or solute exchange between particles and
matrix may occur for very long aging times. If this were
to go to completion, then the carbonitride particles of
the size raprge analyzed should not exhibit significant
concentration gradients and all of the particles should
have similar compositions. In contrast, the experimental
observations do not show this uniformity. This could be
explained by the existence of phase separation which implies the coexistence of different morphological and
compositional particles. Any future attempt to model the
complex carbonitride precipitation reactions in microalloyed steels should account for this feature.
For Ti- and Nb-bearing high-strength low-alloy steels,
the carbonitride is typically described in the form of
METALLURGICAL TRANSACTIONS A
(TixNb~_x) (CyNl_y). The
variation of mole fraction and
composition of the newly formed complex compounds
with temperature has been theoretically predicted and
experimentally measured, as shown in Figure 6. One of
the important features of the complex carbonitride is the
temperature windows for the precipitation sequence of
various compounds. This, in turn, is dependent on the
overall chemistry and the solubility of the compounds.
It evidently can be seen that titanium nitride tends to
form at high temperatures and titanium and niobium carbide go t o completion at low temperatures. The advantages of th~ use of several microalloying elements are
that Ti is effective as a nitride former during reheat cycles
and high-temperature thermal cycling, as in welding, while
the carbides of Ti and Nb both contribute at low temperatures (below 1200 ~ to stopping austenite grain
growth and retarding recrystallization during thermomechanical processing.
V.
SUMMARY
The variations of the compositions and mole fractions
of the (TiNb) (CN) precipitates and the matrix compositions as a function of aging temperature and steel compositions have been predicted on the basis of a regular
solution thermodynamic model involving the four elements Ti, Nb, C, and N in iron. The calculated average
particle composition as a function of temperature is in
satisfactory agreement with measured compositions of
the newly formed particles. In particular, the thermodynamic model gives very good agreement with experiment for steels 1 and 2. The composition of the complex
carbonitride depends strongly on both the temperature
and the steel composition. The x value decreases with
temperature and the y goes in the opposite direction. Both
experimental results and prediction show that titanium
nitride tends to form at very high temperatures and
titanium-niobium carbides go to completion at low
temperatures.
METALLURGICAL TRANSACTIONS A
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