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Abstract
Nucleation and variant selection during the a–c–a phase
transformation in microalloyed steel
I. Lischewski, G. Gottstein ⇑
Institute of Physical Metallurgy and Metal Physics, RWTH Aachen University, 52056 Aachen, Germany
Received 19 August 2010; received in revised form 8 November 2010; accepted 8 November 2010
Available online 4 December 2010
This study addresses variant selection during the a–c–a phase transformation in recrystallized, low-carbon, microalloyed steel. Since
variant selection was found to occur during incipient stages of transformation, the investigation focused mainly on c-grain nucleation
from the a phase. To obtain comprehensive microstructure information, the sample was characterized by high-temperature electron
backscatter diffraction in a scanning electron microscope and additional three-dimensional serial sectioning. It is shown that preferred
nucleation at a grain boundary near a triple junction requires an orientation relationship close to the Kurdjumov–Sachs (K–S) correspondence
to both adjacent a grains (nucleation rule I). Furthermore, a low disorientation of a {1 1 0} bcc crystallographic plane to
the grain boundary plane favors nucleation (nucleation rule II). The results suggest that the nucleation of c grains is favored at triple
junctions by a low surface energy of the nucleus. A corresponding model is proposed. On this basis, variant selection of different ferrite
orientations and the product textures of the complete transformation cycle were successfully predicted for a random grain boundary
plane distribution.
Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Microalloyed steel; Phase transformation; Crystallographic texture; Variant selection
1. Introduction
Available online at www.sciencedirect.com
Acta Materialia 59 (2011) 1530–1541
The production of steel sheet involves many processing
steps which are accompanied by a change in phase composition,
texture and microstructure. These changes strongly
influence the material properties. Low-carbon, microalloyed
steel at high temperatures is usually hot-rolled in
the austenite (c) regime. This is commonly accompanied
by the formation of a pronounced crystallographic texture.
During subsequent cooling, the austenite–ferrite phase
transformation takes place. This reversible phase transformation
causes a change in crystal structure, but is also
associated with a dramatic change in microstructure and
texture. A review of transformation textures was given by
Ray et al. [1]. The crystallography of the phase transformation
reveals a specific orientation relationship between aus-
⇑ Corresponding author.
E-mail address: Gottstein@imm.rwth-aachen.de (G. Gottstein).
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2010.11.017
www.elsevier.com/locate/actamat
tenite (parent phase) and ferrite (product phase). For
carbon steels, this crystallographic correspondence typically
follows the Kurdjumov–Sachs (K–S) orientation relationship,
or close to it [2–5]. A specific orientation
relationship can be used to predict the product texture.
The same holds for the back transformation (a–c). However,
experiments show that not all crystallographic variants
are generated equally frequently, so that the
computed and measured transformation textures do not
coincide. This is attributed to variant selection, but the
rules and reasons for variant selection in recrystallized
materials are not known. As the material properties are
strongly influenced by microstructure and texture, a basic
understanding of the underlying principles of variant selection
is indispensable for texture control during processing.
Owing to experimental difficulties, variant selection has
been investigated mostly at room temperature in the ferritic
regime after previous deformation of the high-temperature
austenite phase. Therefore, respective models had to

assume a copper-type rolling or cube-type recrystallization
texture of austenite prior to transformation to ferrite. To
explain the variant selection of deformed steels, the activity
of slip systems [6,7], the Bain strain [2,8] or the elastic interaction
of transformation events [9] was considered. However,
variant selection is also observed for recrystallized
austenite (Fig. 1), which is less pronounced than in the
deformed state, but distinct and reproducible.
Brückner and Gottstein proposed associating the variant
selection in recrystallized steel with the Bain strain
and residual stresses in recovered areas [3], but because
of limitations in their experimental techniques, these
assumptions could not be confirmed. The development of
high-temperature orientation imaging, however, opened
new avenues for observing phase transformations with spatial
resolution and for obtaining information on local orientations.
This allowed the mechanisms of phase
transformations to be investigated and the underlying
physics of variant selection to be revealed.
Most previous investigations of variant selection phenomena
pertained to the c–a phase transformation,
whereas little attention was paid to forward transformation.
However, since the transformation may occur in both
directions during processing, the whole transformation
cycle must be investigated [3,10].
To acquire information on the location and orientation
of the product phase with respect to the parent phase, local
orientation measurements need to be conducted at the
transformation temperature. Therefore, for this study a
laser-powered heating stage for a scanning electron microscope
was developed which would allow rapid heating and
cooling as well as concurrent electron backscatter diffraction
(EBSD) measurements. With such a device the whole
transformation cycle a ? c and c ? a can be investigated
in situ. This study focuses on the a ? c transformation
which has been addressed only infrequently so far.
I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541 1531
Previous investigations on the same material revealed
that the newly developed c-phase texture did not significantly
change with progressing transformation [11].
Accordingly, variant selection must already occur during
the nucleation period. Furthermore, it was established that
the K–S relationship which was originally developed for
the martensitic transformation holds for the a–c–a phase
transformation as well. Typically, a small deviation from
the ideal K–S relationship is observed [12].
The goal of this work was to reveal and to analyze all
factors that cause a texture change and variant selection
during the reversible a–c–a phase transformation in recrystallized
microalloyed steel. The required local information
of the parent and product orientation was obtained by
high-temperature in situ EBSD and three-dimensional
(3D) serial sectioning. These results were analyzed with
respect to the underlying mechanisms of variant selection.
The relations derived were used to predict the transformation
texture. A model is presented to rationalize the
observed preference of nucleus orientations.
2. Experimental
2.1. Material
The material investigated was a commercial hot band of
a microalloyed low-carbon steel. The chemical composition
is shown in Table 1. Initially, the samples of this material
were cold rolled in a reversing manner to 50% thickness
reduction. The cold-rolled samples were annealed at
700 °C for 5 h in a vacuum furnace, in order to obtain a
stable microstructure for transformation annealing. Grain
growth was suppressed during transformation annealing
by the presence of stable micro carbo-nitrides. The sample
size was 10 7mm 2 with thickness 1 mm and average
grain size 7 lm.
Fig. 1. Variant selection for the orientation u 1 = 75, U = 58, u 2 = 50 (allowed scattering of 5° disorientation): (a) corresponding 24 K–S variants in a
{2 0 0}-pole figure; (b) experimental variant distribution in a {2 0 0}-pole figure.

1532 I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541
Table 1
Chemical composition of the microalloyed low-carbon steel (wt.%).
C Si Mn P S Al N Cu Cr Ni Sn Mo Ti Nb
0.05 0.28 0.82 0.014 0.001 0.039 0.006 0.03 0.05 0.03 0.003 0.01 0.08 0.034
After stabilization annealing, the metallographic preparation
was carried out. The samples were mechanically polished
and finally electropolished (A2 Struers, U =50V,
t = 12 s). Details of sample preparation procedures are
given elsewhere [13].
2.2. High-temperature in situ EBSD
To obtain all the necessary local information during the
a–c–a phase transformation, EBSD measurements at elevated
temperatures had to be carried out. For this purpose,
a laser-powered heating stage was developed at the Institute
of Physical Metallurgy and Metal Physics of RWTH
Aachen University. Details of its setup and operation are
given elsewhere [14]. The basic features are summarized
below.
The hot stage was mounted on a JEOL JSM-6100 scanning
electron microscope. Attached to the microscope was
a standard EBSD-Detector System Nordlys by HKL with a
70° tilted specimen stage for EBSD analysis. The EBSDdetector
contained a four-quadrant forward scatter detector
framing the phosphor-screen, which provided the orientation
contrast (OC) images for enhancement of the
microstructure information by EBSD.
The hot stage consisted of three basic components
(Fig. 2a and b). A SiC sample holder comprised the main
body, which was illuminated by a commercial continuous
diode IR laser with wavelength 810 nm and maximum
power output 100 W. The incident IR laser light was emitted
from an optical fiber. The specimen was attached to the
SiC sample holder by a tungsten clamp (Fig. 2(4)).
The temperature of various attachments (EBSD-detector,
secondary electron-detector, hot stage) in the microscope
chamber was recorded by thermocouples. Three
thermocouples monitored the hot stage temperature (heating
shield, sample holder) and controlled temperature and
(a) rear outer heating (b)
incoming
4
1
3
shield
4
cooling
conduit
5
front outer heating shield
(copper, passive cooled)
4
outgoing cooling
conduit
heating rate. The laser power output was controlled by an
external computer linked via an RS232 interface using Labview
8.0. The hot stage could be operated at any tilting
angle and at a working distance as low as 15 mm. Typically,
6–8 bands were used to determine the crystal orientation
from the EBSD patterns. The orientation imaging of
an area 250 180 lm 2 took 45 min.
2.3. 3D analysis of grain boundary plane
Exact information on the grain boundary plane (GBP)
orientation can only be achieved from 3D images. Such
measurements were conducted by serial sectioning with
the following procedure. A ferrite sample was marked at
several locations of the sample surface with a Vickers micro
hardness indenter. The microstructure of the surface was
measured by EBSD and OC imaging. After this first measurement,
the sample surface was carefully mechanically
polished. Three polishing steps were performed by using
a Buehler/Phoenix 4000 polishing wheel at very low contact
pressure. The embedded sample was polished for
2 min with 1 lm diamond paste and 5 min with 0.25 lm
diamond paste. The total thickness reduction after each
polishing step was 0.6 lm, 1.3 lm and 2.4 lm. These values
were easily obtained from the change in the indent shape
with each polishing step. The use of several micro hardness
markers allowed precise measurement of the thickness
reduction and of the planarity of the sample surface.
After each polishing step, the sample was placed back
into the sample holder of the scanning electron microscope
in the same position as before, and an OC image (step size
0.1 lm) was generated. The different OC maps were superimposed
(Fig. 3) using commercial image editing software
(Paint Shop Pro7) to determine the position of the grain
boundary traces. The different microhardness markers
served as reference points and allowed matching of the
Fig. 2. Design of the hot stage: (a) front view to reveal the basic outer parts (b) cross section of the stage interior: (1) copper shield (water cooled); (2)
tantalum shield (not cooled); (3) SiC sample holder; (4) specimen mount–tungsten clamp; (5) heating stage copper base (active water cooled); (6) optical
fiber guidance; (7) goniometer stage adapter. Overall dimensions 8.2 3.5 3.6 cm 3 .
1
3
6
7
2
1
5
4

image position for each OC map. From this experimental
procedure, the GBP orientation near the sample surface
was obtained.
3. Results
Fig. 3. Correlation of two OC maps.
3.1. Transformation texture development
The texture development in the course of the a–c phase
transformation was measured to determine the essential
period where variant selection occurred.
To obtain good statistics for texture calculation, especially
for the low transformed volume fractions, many samples
were investigated by high-temperature in situ EBSD.
The c-phase orientations were binned with respect to their
f(g)
~ {112}
8
6
4
2
0
45 o
~ {123}
60 o
75 o
(a) -fibre (max. density)
I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541 1533
~ {011}
90 o
2
90 o
/
1
55 o
45 o
20 o
60 o
75 o
(b) -fibre orientation
volume fraction (1–10% = 5%, 15–25% = 20%, 35–
45% = 40%), and the texture was calculated (Fig. 4).
The results demonstrate that no significant texture
change occurred with progressing a–c phase transformation.
The small deviations were attributed to slight variations
in the ferrite microstructure and texture of different
specimens. Hence, the product texture and therefore also
variant selection were essentially controlled by nucleation.
Further investigations into variant selection phenomena
therefore concentrated on the nucleation stage.
3.2. Nucleation
The ferrite (a) to austenite (c) phase transformation in
steel proceeds by nucleation of the new phase and its
growth. Partially transformed microstructures were
recorded at 907 °C by orientation imaging via EBSD.
The early stage of transformation allowed the nucleation
sites of c nuclei to be located exactly in the a microstructure,
and thus to establish the orientation relationship of
a nucleus to its parent phase. An investigation of the early
stages of transformation (17,000 austenite grains) showed
that nucleation of the c phase occurred predominantly at
grain boundary triple junctions (Table 2).
Furthermore, it can be seen (Fig. 5) that the K–S orientation
relationship was quite often met. Previous
detailed investigations on a similar steel rendered the
information that slight deviations from the exact K–S
relationship were usually found [12,15]; this was also confirmed
in the current study. A spread of the K–S toward
Table 2
Fraction of nucleation sites of c grains (%).
Triple junction Grain boundary Inner grain
90.3 9.6 0.1
90 o
2
{011}
8
6
4
2
0
0 o
{011} {011}
Fig. 4. Texture development during progressing a–c phase transformation in terms of fcc fiber plots: austenite volume fraction 5% (s), 20% (h), 40% (D),
100% ( ).
f(g)
30 o
-fibre
60 o
{011}
=45 o
= 0
2
o
90 o
1

1534 I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541
907°C Austenite:4%
=50 µm; Map1; Step=0.8 µm; Grid180x160
Fig. 5. EBSD map of partially transformed microstructure during a–c
phase transformation (4% austenite at 907 °C): ferrite, gray; austenite, red;
high-angle grain boundaries, black lines, 60° h111i twins, blue lines; phase
boundaries (colored according to deviation from ideal K–S relationship):
0–5° (white), 5–10° (yellow), 10–15° (green), 15–20° (purple), >20° (black).
the Nishiyama–Wassermann relationship was usually
observed. Reasons for this deviation have been discussed
elsewhere [16,17]. For the sake of simplicity, the results
were associated with a K–S relationship. If a deviation
from the ideal K–S relationship of up to 15° was allowed,
many c grains had a K–S relationship to more than one a
mother grain. Usually, two a mother grains were
observed. To find out whether this was a systematic effect
or just incidental, the experimental results were compared
with a simulated nucleus distribution. For this, the experimental
data were evaluated from the EBSD measurements
with an in-house developed computer code. The
maximum allowed deviation from the K–S relationship
was set to 15°. A statistical nucleus distribution was
generated by distributing 2000 experimental c grains randomly
in a representative measured ferrite microstructure.
This rendered the information that the actual measured
nucleation frequency with two K–S mother grains was
twice as high as that in the statistical distribution
(Fig. 6). Also, the measured frequency of three mother
grains was significantly higher than predicted by statistics.
It is noted that the real number of nuclei with two or
three a mother grains might have been even higher than
measured, because potential ferrite mother grains might
have been located below the sample surface. The results
illustrate that the nucleation of c grains during the a–c
phase transformation preferentially occurs with two a
mother grains, each of which has a K–S orientation relationship
to the nucleus. This will be called nucleation rule
I in the following. These experimental results actually
confirm the hypothesis of Tomida et al. [18], who were
the first to propose that a product grain needs more than
one parent grain. On this basis, they were able to compute
the transformation texture adequately.
frequency [%]
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
40.8
71.7
3.3. Grain boundary plane
The experimental procedure to determine the GBP orientation
was described in Section 2.3. The main problem
was to obtain the combined information of the GBP orientation
and the nucleation site of the c grains during the
reversible a–c phase transformation. Because in situ 3D
measurements at elevated temperatures were not possible,
a different strategy was used. A ferrite sample was annealed
for a long time (35 h/780 °C vacuum) in order to establish a
stable microstructure. This sample was then annealed to a
partly transformed state and, to avoid microstructural
changes, a fast (10 min map time) EBSD measurement
was conducted at constant temperature (907 °C). After
the measurement, the sample was rapidly cooled to room
temperature to conserve the general features of the hightemperature
microstructure. At room temperature, a second
EBSD measurement was conducted. This EBSD map
served as reference for the 3D measurements and contained
information on how the microstructure had changed from
the two-phase high-temperature microstructure (Fig. 7).
Only those triple junctions and grain boundaries were
investigated where c-phase nucleation was found during
the high-temperature anneal, and the surrounding a grains
did not show a significant change after cooling to room
temperature. This allowed the orientation of the observed
c nuclei to be associated with the orientation of the GBP.
The influence of the GBP on nucleation was investigated
by considering three grain boundaries and nine triple junctions
where nucleation of a c grain at high temperatures
was found. Fig. 8 shows a typical example of an OC
map. It is a part of the EBSD map in Fig. 7b, which was
measured at RT. In this example, a c grain had nucleated
at a triple junction and revealed a K–S relationship to both
a grains A and B. It can be seen that all necessary information,
such as grain orientations (from EBSD), nucleation
site, inclination and position of the GBP is available. From
this information, it was derived that all GBPs at the triple
junction were associated with close-packed planes with
48.9
25.8
Experimental values
Calculated values
1
2
3
number of α-grains at a triple junction with a K-S relationship
Fig. 6. Frequency of statistically expected and experimentally measured
K–S relationships of c grains at triple junctions.
10.3
2.5

50 µm
RD
respect to the K–S relationship {1 1 0}a//{1 1 1}c of each
a–c grain combination. Because of the typical deviation
from the ideal K–S relationship, the crystallographic
{1 1 0} planes of the ferrite were taken as reference for
the disorientation to the GBP. Presumably, this plane
was the location from where the c grain nucleated.
The results of the analysis of grain boundaries and triple
junctions are summarized in Table 3, where the orientations
of a grains with a K–S relationship to the c grain
are shown. The c-grain orientation and the related crystallographic
variant according to K–S are listed. The crystallographic
{1 1 0} plane for this variant and the calculated
disorientation to the GBP is also indicated. As a result,
I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541 1535
(a) (b)
Fig. 7. EBSD maps of (a) a partially transformed ferrite sample at 907 °C and (b) the ferrite sample (same position) at room temperature (coloring as in
Fig. 5); white circle indicates the triple junction of the example in Fig. 8.
grain C
10µm
~70°
~60°
~50°
14° from TD
25° from TD
grain A
grain B
6° from RD
Fig. 8. OC map of an investigated triple junction with A–C as adjacent grains (the position of this example is marked in Fig. 7b): angles 50°, 60° and 70°
define the inclination of the three GBPs (arrows indicate direction of inclination); angles 25°, 6° and 14° define the position of each grain boundary trace
related to TD and RD.
50 µm
RD
RD
in general one of the two K–S mother grains had a small
disorientation of its {1 1 0} plane to the GBP. This
{1 1 0} plane was defined by the calculated variant. Hence,
it is concluded that the preferred nucleation at a triple junction
proceeds by nucleation at a GBP with a K–S relationship
to two adjoining grains. This hypothesis is supported
by the measurements. The observed disorientation of the
close-packed planes and the GBP was in the range 0–15°
(GB1–GB3 in Table 3); 15° was used as the cut-off because,
in this range, crystallographic deviations from the ideal lattice
can be compensated by dislocation arrangements such
as low-angle grain boundaries. The required alignment of
the GBP with a {1 1 0} plane is termed nucleation rule II.

1536 I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541
Table 3
Results of the investigated triple junctions and grain boundaries.
TJ/GB a mother grain orientation Euler
angles (°)
The disorientations determined between the f110g a planes
and the GBP may contain some uncertainty because, especially
at high inclination of the GBP, only a rough definition
of the disorientation angle was possible.
Nevertheless, the results obtained confirmed the expected
tendency. At TJ8 in Table 3, three mother grains were
observed with a K–S relation to the c nucleus. Also for this
case, the aforementioned correlation held true. TJ9 represents
a c-grain nucleation only with one mother grain. This
case, as an exception, violates nucleation rule I, but may be
specially promoted by only a small disorientation of the
f110g a plane to the GBP.
It is noted that the condition of a specific GBP orientation
does not define a variant selection rule by itself. However,
in combination with the requirement that this {1 1 0}
plane is selected as the coherent phase boundary, nucleation
rule II imposes another restriction on potential crystallographic
variants and thus also constitutes a variant
selection rule.
3.4. Prediction of variant selection in ferrite
c-grain orientation Euler angles
(°)
The information obtained, outlined in Section 3.3, can be
used to predict the preferred K–S variants during transformation,
and therefore also the product textures during a–c
phase transformation. The procedure is demonstrated here,
K–S var Crystallographic {1 1 0}
plane
Disorientation to
GBP
GB1 A: 184.1 8.8 33.2 290.9 43.6 9.3 3 ( 110) 60°
B: 2.0 44.8 67.3 8 ( 1 10) 15°
GB2 A: 228.4 33.4 45.2 253.6 18.3 65.2 13 (1 0 1) 16°
B: 165.2 45.4 79.3 5 (1 10) 62°
GB3 A: 331.2 44.6 50.0 36.0 36.9 80.1 5 (1 10) 9°
B: 318.5 53.0 42.8 20 (0 11) 69°
TJ1 A: 192.3 41.6 38.3 106.6 38.0 28.8 3 ( 110) 18°
B: 11.6 36.9 29.9 17 (0 1 1) 53°
TJ2 A: 185.9 8.6 31.4 56.3 44.0 68.7 12 ( 101) 20°
B: 289.6 49.9 49.2 12 ( 101) 90°
TJ3 A: 312.8 42.0 51.5 43.0 44.8 74.2 20 (0 11) 42°
B: 117.5 25.3 82.8 9 (1 0 1) 80°
TJ4 A: 157.0 37.4 50.3 139.5 32.8 17.4 21 (0 1 1) 7°
B: 357.8 17.8 54.9 2 (1 1 0) 5°
TJ5 A: 193.9 43.8 51.4 280.8 21.6 56.8 14 (1 0 1) 73°
B: 20.5 46.4 59 21 (0 1 1) 8°
TJ6 A: 55.7 49.4 45.4 174.6 38.1 3.6 12 ( 101) 16°
B: 8.1 32.1 40.2 16 ( 10 1) 63°
TJ7 A: 8.3 31.7 40.1 239.4 23.1 63.9 1 (1 1 0) 10°
B: 157.6 22.7 57.3 5 (1 10) 73°
TJ8 A: 180.3 23.3 40.9 266.4 24.8 62.8 19 (0 11) 44° (A–B)/18° (A–C)
B: 30.5 36.3 32.7 6 (1 10) 40° (B–A)/43° (B–C)
C: 183.2 35.6 50.6 18 (0 1 1) 60° (C–A)/52° (C–B)
TJ9 A: 346.1 20.0 43.5 113.1 24.2 28.8 2 (1 1 0) 6
as an example, for the variant selection of two a-phase orientations.
To obtain the transformation texture, this procedure
is applied to the entire ferrite texture. From the abcc
fiber, orientations with Euler angles u1 =0°, U =30°,
u2 =45° and u1 =60°, U =55°, u2 =45° from the cbcc
fiber were taken. Nucleation rule I requires that, for nucleation
near a triple junction, two a grains with a K–S relationship
to the new c grain are necessary, in general. For
the calculation, a typical ferrite microstructure measured
by EBSD was taken. This microstructure contained
3000 triple junctions.
For each of the three a grains at a triple junction, the 24
variants (Table 4) of the K–S relationship were calculated.
Thereafter, the misorientation of all 24 variants to the three
a grains was calculated. If the misorientation between two
variants of two a grains was

educed to one variant in the majority of cases. Hence, for
selection of the actual variant, the influence of the GBP
between two a grains is also important. For the computation
of the transformation texture, it was assumed in the
first approximation that the GBP distribution in the investigated
steel was random, and therefore did not influence
the product texture. The calculation and prediction of variant
selection of different a orientations is then reduced to
nucleation rule I. Since nucleation rule II was neglected, at
some triple junctions several possible c orientations would
meet the required correlation. In these cases, all such variants
were taken into account.
The product was filtered with regard to any a orientation
of interest. For better statistics of the variant distribution
for the two selected orientations, a small deviation (7°)
about the ideal position was allowed. The experimental
data were obtained in a similar way. Several hundred partly
transformed microstructures were imaged using high-temperature
in situ EBSD, and the newly developed c grains
were assigned (K–S 10° dev.) to their a-mother orientations.
In this way, a product list was generated which contained
information on the distribution of the selected
variants to all a orientations and also the texture information
on the austenite phase. This list was then filtered with
respect to the above specified a orientations (7° dev.).
The results (Fig. 9) demonstrate overall good agreement
of the measured and predicted variant distributions.
Apparently, the variant selection is already well predicted
using only nucleation rule I. However, some of the predicted
variants show some conspicuous deviations from
the experimental data. This may be caused by a slightly
non-random GBP distribution. Also, other factors, such
I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541 1537
Table 4
Correlation of the crystallographic planes and directions of the 24 K–S variants.
No. Ferrite plane/direction Austenite plane/direction Rotation axis
1 (1 1 0) [ 1 1 1] (1 1 1) [1 1 0] [1 12]
2 (1 1 0) [1 11] ( 11 1) [1 1 0] [1 1 2]
3 ( 110)[ 1 11] (11 1) [ 1 1 0] [1 1 2]
4 ( 110)[111] ( 1 1 1) [ 1 1 0] [1 1 2]
5 (1 1 0) [1 1 1] ( 1 1 1) [1 10] [ 1 12]
6 (1 10)[ 1 11] (11 1) [1 10] [ 1 1 2]
7 ( 1 10)[ 1 1 1] (1 1 1) [ 1 10] [ 11 2]
8 ( 1 10) [1 11] ( 11 1) [ 1 10] [ 112]
9 (1 0 1) [ 1 11] (11 1) [1 0 1] [1 2 1]
10 (1 0 1) [ 1 1 1] (1 1 1) [1 0 1] [ 1 21]
11 ( 101)[1 11] ( 11 1) [ 1 0 1] [1 2 1]
12 ( 101)[111] ( 1 1 1) [ 1 0 1] [ 12 1]
13 (1 0 1) [1 1 1] ( 1 1 1) [1 0 1] [1 21]
14 (1 0 1) [1 11] ( 11 1) [1 0 1] [ 1 2 1]
15 ( 10 1) [ 1 1 1] (1 1 1) [ 10 1] [1 2 1]
16 ( 10 1) [ 1 11] (11 1) [ 10 1] [ 121]
17 (0 1 1) [1 11] ( 11 1) [0 1 1] [2 1 1]
18 (0 1 1) [1 11] (11 1) [0 1 1] [2 11]
19 (0 11)[ 1 1 1] (1 1 1) [0 11] [ 2 1 1]
20 (0 1 1) [1 1 1] ( 1 1 1) [0 11] [ 211]
21 (0 1 1) [1 1 1] ( 1 1 1) [0 1 1] [2 1 1]
22 (0 1 1) [ 1 1 1] (1 1 1) [0 1 1] [2 1 1]
23 (0 1 1) [1 11] ( 11 1) [0 1 1] [ 2 11]
24 (0 1 1) [ 1 11] (11 1) [0 1 1] [ 21 1]
as inhomogeneities or the different statistical base of the
experimental and predicted data, could be important. This
exercise was also extended to other orientations. Again, the
predicted variant distributions showed good agreement
with experiments.
3.5. Texture prediction of the a–c–a phase transformation
3.5.1. General procedure
With the analysis presented above, one can scan the ferrite
microstructure for triple junctions that comply with
nucleation rule I to determine the orientation spectrum of
the c nuclei. Since nucleation rule II was neglected, several
triple junctions allowed for more than one possible c orientation.
For calculation of the transformation texture, all
possible variants at a triple junction were taken into
account. For simplicity, the orientations of the different
variants were averaged. This reflects the assumption that
each possible product orientation will actually be created
in a real sample, because triple junctions with a defined
combination of three a orientations (allowing for some
scatter) were found to appear quite often in a real microstructure
of a sample with several hundreds of thousands
of grains. For a random GBP distribution, any possible
product orientation according to nucleation rule I will be
preferred at some triple junction.
The c- and a-phase textures were measured on completely
transformed samples by EBSD. The predicted and
measured c-phase textures are compared in Fig. 10 in terms
of the face-centered cubic (fcc) a and b fibers. The texture
prediction was accomplished under the assumption that
each product grain had the same volume. This assumption

1538 I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541
(a)
norm. frequency
(b)
norm. frequency
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
0-30-45
60-55-45
Prediction
Experiment
2 4 6 8 10 12 14 16 18 20 22 24
K-S variants
Prediction
Experiment
2 4 6 8 10 12 14 16 18 20 22 24
K-S variants
Fig. 9. (a, b) Measured and predicted variant distribution of two ferrite
orientations normalized to a maximum frequency of 1.
was substantiated by the fact that the transformation texture
did not change much with progressing transformation
so that growth selection could be ruled out. For comparison,
the product texture without variant selection was also
calculated.
3.5.2. a–c phase transformation
The ferrite texture of a 50% cold-rolled and recrystallization
annealed sample is shown in Fig. 10a. The c fiber
is weakly developed with a maximum intensity close to
the inverse brass component {1 1 2} h1 10i. The measured
c-phase texture is composed of a uniformly developed b
fiber with slight preference of the copper component
{1 1 2} h 111i (Fig. 10b). The maximum intensity on the
a fiber of austenite was found at the Goss {0 1 1} h1 00i
and brass {0 1 1} h 211i components. Altogether, the austenite
transformation texture was weaker than the ferrite
starting texture. The predicted c-phase texture with variant
selection showed excellent agreement with the experimental
results. The texture prediction without variant selection led
to a much weaker product texture.
3.5.3. c–a phase transformation
The measured c-phase texture (Fig. 10) was used as the
starting texture for a computation of the back transformation
texture. Again, the product texture revealed typical
body-centered cubic (bcc) fibers (Fig. 11). The experimental
ferrite product texture after a complete transformation
cycle was relatively weak. But, good prediction of the
experimental texture was also possible in this case. Because
of the weak product texture, prediction without variant
selection also yielded a reasonable fit. The slight deviation
from experimental texture was probably due to insufficient
grain statistics of the back transformed sample.
4. Discussion
4.1. Nucleation
From previous investigations, it is known [11] that variant
selection takes place already during nucleation. The
product texture is therefore essentially determined by the
nucleation texture. As detailed in this study, the c grains
typically comprised a K–S relationship (with some scatter)
to both a grains at a grain boundary next to a triple junction.
The allowed deviation from the ideal K–S relationship
was commonly in the range 10–15°. Furthermore, in
one of the two a grains, a close-packed {1 1 0}bcc plane
was parallel to the GBP. This suggests that each c grain
had only one real mother grain from which nucleation
started. It is proposed to associate the preference of such
nucleation sites with minimization of the nucleus surface
energy, which reduces the critical nucleus size and thus
strongly increases its nucleation rate. An exact K–S orientation
relationship is accompanied by a coherent interface
between the two phases and thus a low interfacial energy
[20–23]. If a grain boundary is parallel to the close-packed
crystallographic planes {1 1 0}bcc//{1 1 1}fcc, it already
resembles a configuration of low interfacial energy [24].
Based on these facts, the following model is proposed for
the observed nucleation geometry (Fig. 12). A nucleus with
semi-spherical shape is considered for geometrical simplicity.
Various studies report an interfacial energy of K–S
phase boundaries in the range 0.27-0.56 J m 2 [25,26].
The interfacial energy of a random ferrite grain boundary
is 0.8 J m 2 [25].
The energy DG GB
het of a nucleus of a new phase is given by
[27].
DG ¼ V ðDGl eÞþrS ð1Þ
where DGl is the chemical driving force, V is the volume of
the nucleus, r is the specific interfacial energy, e is the
strain energy density, and S is the interfacial area.
For heterogeneous nucleation
DG GB
het ¼
4
3 pr3 ðDGl eÞþ4pr 2 r SK
a c SðhÞ ð2Þ
where SðhÞ is the so-called shape factor, which is defined
for a spherical cap geometry by

(a)
(b)
f(g)
{001}
0 o
-fibre
30 o
ð2 þ cos hÞ ð1 cos hÞ2
SðhÞ ¼
4
8
6
4
2
0
f(g)
~{112}
8
6
4
2
0
(a)
45 o
{112}
~{123}
60 o
{111}
60 o
75 o
-fibre (max. density)
{110}
90 o
~{011}
90 o
2
f(g)
{111}
8
6
4
2
60 o 75 o 90 o
0
90 o
/
1
55 o
45 o
20 o
(b)
-fibre
ð3Þ
{111}
1
60 o
-fibre orientation
Fig. 10. (a) a bcc fiber and c bcc fiber of the ferrite starting texture; (b) b fcc fiber and a fcc fiber presentation of austenite-textures: s, experimental; h, with
variant selection predicted; D, without variant selection predicted.
{001}
8
6
4
2
0
0 o
{112}
30 o
{111}
60 o
{110}
f(g) f(g)
90 o
{111}
60 o 75 o 90 o
0
-fibre -fibre
8
6
4
2
{111}
Fig. 11. abcc fiber and cbcc fiber presentation of a-textures: s, experimental;
h, with variant selection predicted; D, without variant selection
predicted.
I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541 1539
1
α 3
75 o
90 o
The wetting angle h results from the surface energy
balance
h ¼ arccos ðra a r HC
a c Þ
r LC
a c
2
f(g)
{011}
8
6
4
2
0
0 o
-fibre
γ
{011}
30 o
{011}
60 o
{011}
90 o
Less coherent phase
boundary
(only K-S)
Better coherent phase boundary (K-
S+GBP)
Fig. 12. Schematic illustration of nucleation of an austenite (c) grain at a
ferrite (a) grain boundary near a triple junction.
1
α 1
α 2
ð4Þ

1540 I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541
ΔG [J]
ΔG *
ΔG
TP
*
GB
where ra a is the interfacial energy of the a grain boundary,
rHC a c is the interfacial energy of the coherent a–c phase
boundary (K–S + GBP), and rLC a c is the interfacial energy
of the less coherent a–c phase boundary (only K–S).
The dependency of DG GB
het is plotted in Fig. 13. Evidently,
the work of nucleation DGGB and therefore the nucleation
rate strongly depend on the interfacial energy of the phase
boundaries. Thus, for preferential nucleation, a low interfacial
energy, i.e., high coherency, is required.
While this nucleation model can account for preferred
nucleation of c-phase grains at ferrite grain boundaries,
experimental results demonstrate that nucleation actually
starts at triple junctions. This was repeatedly confirmed
by high-resolution, high-temperature in situ EBSD measurements.
It is proposed that this behavior is associated
with the line tension rl a of the triple junction. Nucleation
at a triple junction can also use the triple line energy as a
driving force, which further promotes nucleation at such
locations. This modifies Eq. (2) to
DG TP
het ¼
r *
1
4
3 pr3 ðDGl eÞþ4pr 2 r SK
a c 2r r l
a
The functional dependences DG TP
het
given in Fig. 13.
Function DG TP
het
~r 2
-r 3 +r 2 -r
~r 3
SðhÞ
ð5Þ
ðrÞ and DGGB
het ðrÞ are
ðrÞ reveals, besides the maximum pre-
dicted by Eq. (2), also a relative minimum at a small
nucleus size r 1 . Although the corresponding free energy
gain is very small (10 20 J), it proves that the triple line tension
favors the new phase, but of course the nucleus is too
small to grow. A viable nucleus has to attain size r2 .
If one assumes that rl a is independent of h the critical
nucleus size follows from
@DG TP
het
@r ¼ 4pr2 ðDGl eÞþ8pr r SK
a c 2r l
a ¼ 0 ð6Þ
or
ð8p rSK
r c
r1;2 ¼ Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð8p rSK r cÞ2 16p ðDGl eÞ 2rl q
8p ðDGl eÞ
a
ð7Þ
r *
2
~r
r *
3
-r 3 +r 2
r [nm]
Fig. 13. Dependency of free energy DG on nucleus size r for nucleation at
a grain boundary (DGGB) and at a triple junction (DGTP ).
For an evaluation of r1=2 , the various thermodynamic
quantities of Eq. (7) have to be known. According to the
literature, ra a = 0.8 J m 2 , rHC a c =0.27 J m 2 , rLC a c = 0.56
Jm 2 [25,26] and DGl ¼ 1:4 10 7 J=m3 [28].
The only existing value for a triple line energy was measured
by Zhao et al. on copper [29]. In lieu of any such data
on Fe, it is assumed that the triple line energy of ferrite is of
the same order of magnitude, i.e.,
r l
a ¼ 6 10 9 Jm 1
With these values, if the elastic energy contribution is neglected,
one obtains from Eq. (7) r 1 ¼ 1 nm and r 2 ¼
79 nm, with the corresponding free energies DG TP ðr 1 Þ¼
10 20 J and DG TP ðr 2 Þ¼2:95 10 17 J. This compares with
DG GB
het ðr 3 Þ¼3:15 10 17 J (r 3 ¼ 80 nm) and DGhomðr 0 Þ¼
1:5 10 14 J.
These results are interpreted as follows. Above the
a ! c transformation temperature, the new phase spontaneously
forms an embryo at the triple line, but this
embryo is unable to grow. By thermal fluctuations, the critical
nucleus size r 2 is obtained with a rate
_N exp
DG TP
het ðr 2 Þ
kT
If nucleation of the new phase is supported by the triple
line tension, the nucleation barrier DG TP
hetðr2Þ is smaller than
the nucleation barrier at grain boundaries. This favors nucleation
of the new phase at triple junctions, while variant selection
remains controlled by grain orientation and GBP.
It is noted that triple junctions are also often preferred
in diffusion-controlled phase transformations because they
constitute high-diffusivity pathways. In the current case,
this aspect is of no importance, because the composition
does not change during the phase transformation in this
microalloyed steel.
4.2. Origin of variant selection
The variant selection during the a ! c ! a phase
transformation of recrystallized low-carbon steel is not very
pronounced, but noticeable. As substantiated in this study, it
is due to preferential nucleation of particular variants
because of low interfacial energies at triple junctions, which
essentially requires that the viable variant has a reasonable
K–S relationship to two grains at a triple junction and that
the GBP matches a {1 1 0} plane of one of the grains. The
frequency of occurrence of such configurations with a high
propensity for nucleation depends, of course, on the distribution
of orientations and grain boundary character. For
a completely random crystallographic texture, variant selection
during the phase transformation is unlikely to occur,
since all misorientations across grain boundaries would be
equally likely and, therefore, equally favorable for all
24 K–S variants. As a conclusion, the variant selection during
the phase transformation in recrystallized microalloyed
steel is actually a consequence of the crystallographic texture
prior to transformation.
ð8Þ

Nucleation rule II, i.e., a specific GBP, serves as an
amplification of the texture-induced preference of a particular
variant. It favors a specific among several possible
variants, and thus conveys a larger weight to that particular
variant in the orientation distribution. Hence, the grain
boundary character distribution as well as the crystallographic
texture will affect the selection of variants. In
essence, both nucleation rules are important for a prediction
of the transformation texture.
It is finally noted that this study was conducted on
recrystallized material, where variant selection is obvious,
but not as conspicuous as in deformed material or during
the martensitic phase transformation in steels. In the latter
cases, other energetic contributions and physical principles
may also play a role in the selection and preference of particular
variants, as outlined in the pertinent literature
[6,30–35].
5. Summary
Variant selection during a ! c ! a phase transformation
was investigated in recrystallized low-carbon
microalloyed steel. High-temperature orientation imaging
by EBSD was applied to determine the location of transformation
nuclei and their orientation relationship to the environment.
The following results were obtained.
1. The preferred selection of variants occurs during the
nucleation stage of the phase transformation.
2. Nucleation of the new phase occurs predominantly at
triple junctions.
3. The new phase was always observed to be related to the
mother phase by an approximate K–S relationship.
4. Among the 24 crystallographically equivalent variants,
only that orientation was observed that complied with
two basic requirements:
a. the selected variant must have an approximate K–S
relationship to two adjacent grains (nucleation rule I)
b. a variant is particularly preferred over others in addition
to nucleation rule I, if its {1 1 1} c plane was parallel
to a {1 1 0} a grain boundary (nucleation rule II).
5. The computed variant selection based on these principles
showed excellent agreement with experimental
results and allowed an adequate prediction of the transformation
texture.
6. A model is proposed to account for the observed preferences.
It is based on a low surface energy of the nucleus.
It was demonstrated that the triple line energy promotes
nucleation of the new phase at triple junctions. The
observed nucleation rules can be associated with a higher
nucleation frequency of variants with low surface energy.
7. It is stressed that these results pertain to the a !
c ! a phase transformation of recrystallized microalloyed
steel, where no compositional changes accompany
the transformation. In deformed materials, complex
steels or for martensitic transformations, other principles
may predominate.
I. Lischewski, G. Gottstein / Acta Materialia 59 (2011) 1530–1541 1541
Acknowledgements
The authors wish to thank Professors Lasar S. Shvindlerman
and John J. Jonas for stimulating discussions.
Financial support by the Deutsche Forschungsgemeinschaft
(DFG) through grant Go 335/33 is gratefully
acknowledged.
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