Materials Transactions, Vol. 52, No. 2 (2011) pp. 139 to 141
#2011 The Japan Institute of Metals
Effect of a High Magnetic Field on Carbon Diffusion in -Iron
Shou-Jing Wang1;2 , Yan Wu1 , Xiang Zhao1; * and Liang Zuo1
1
Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), Northeastern University,
Shenyang 110004, Liaoning Province, P. R. China
2
Mechanical Engineering Institute, Liaoning Shihua University, Fushun 113001, Liaoning Province, P. R. China
The effect of 12-Tesla high magnetic field on carbon diffusion in -Fe at 1273 K has been investigated using a diffusion couple made by
pure Fe and high purity Fe-0.76%C alloy. The results show that the high magnetic field obviously hinders carbon diffusion in the direction
perpendicular to the magnetic field direction; while it only slightly enhances the carbon diffusion in the direction parallel/antiparallel to the
magnetic field direction. [doi:10.2320/matertrans.M2010327]
(Received September 17, 2010; Accepted November 11, 2010; Published January 25, 2011)
Keywords: high magnetic field, carbon, diffusion, iron-carbon alloys
1.
Introduction
The diffusion is a very important process in diffusional
transformations in steels, but so far, only a few papers have
been published to show the effects of a magnetic field on
diffusion in metallic materials. Youdelis et al.1) reported that
a 3 T magnetic field retarded the diffusion of copper in
aluminium. Nakajima et al.2) observed no magnetic effects on
the diffusion of nickel in titanium. Pokoev et al.3,4) measured
the diffusivity of nickel in -Fe and Fe-1.94%Si alloy and
the magnetic effect on diffusivity were not monotonic as a
function of applied magnetic field. Nakamichi et al.5) studied
the effects of magnetic field and magnetic field gradient on
the diffusion of carbon and titanium in -Fe and found that
the carbon diffusion in -Fe was retarded by the application
of a 6 T magnetic field. However, the diffusion of carbon in
-Fe can be enhanced in a magnetic field gradient when
carbon atoms move towards the direction with a higher
magnetic field strength. The higher the magnetic field
gradient strength becomes, the more the carbon diffusion is
enhanced. Nevertheless, a magnetic field gradient causes a
decrease in diffusivity of carbon in -Fe when the opposite
magnetic field gradient is applied. Ohtsuka6,7) studied the
influence of 10 T magnetic field on carbon diffusion by using
a diffusion couple made by pure Fe and Fe-0.8C alloy.
The results showed that the high magnetic field retarded the
carbon diffusion along the magnetic field direction after
isothermal annealing at 1073 K for 24 h. While after
isothermal annealing at 1203 K for 5 h, the influence of high
magnetic field on carbon diffusion is unnoticeable. The above
two studies have great importance on elucidating the
mechanism and the influence rule of high magnetic field on
carbon diffusion in Fe-C alloy. However, till now, the study
about the carbon diffusion in the direction perpendicular to
the magnetic field direction is rarely mentioned. In this study,
we further studied the effect of high magnetic field on carbon
diffusion in -Fe using a diffusion couple made by pure Fe
and high purity Fe-0.76%C alloy.
*Corresponding
author, E-mail: zhaox@mail.neu.edu.cn
2.
Experiment
The diffusion couple used in this study was made by pure
Fe (99.99%) and high-purity Fe-0.76C alloy (Besides Fe and
C, the total content of other elements is below 0.01%), they
were subjected to isothermal annealing at 1273 K for 5 h
with and without a 12 T magnetic field, and then cooled to
473 K with a cooling rate of 20 K/min. The vacuum degree
during the heat treatment is 103 Pa. During the magnetic
field annealing, the magnetic field was applied in the
direction parallel and perpendicular to the interface between
pure Fe and high-purity Fe-0.76C alloy, respectively. Specimen was fixed at the center of the applied field, therefore
the magnetic field gradient and the magnetic force to the
specimens are negligible.
3.
Results and Discussion
Figure 1 shows the microstructures of the specimens at
room temperature after isothermal annealing at 1273 K for
5 h with and without high magnetic field. The line between
the pure Fe in the right part and the Fe-0.76C alloy in the left
part is the diffusion interface. In the figure, Jc presents the
carbon diffusion direction, and H presents the magnetic
field direction, both of them are shown by the white arrows.
Figure 1(a) shows the microstructure of the specimen
annealed without magnetic field. And Fig. 1(b)(c)(d) show
the microstructures of specimens annealed with magnetic
field. In the left region of pure Fe, there are some phase
transition product formed in the cooling process—pearlite
(black regions) and Widmanstaten structure ferrite like
needle and plate (white regions). Along the carbon diffusion
direction, with the increase of the distance to the diffusion
interface, the area percentage of black pearlite of per unit
area reduces gradually; and the carbon content decreases
gradually, too. The far right side where carbon didn’t diffuse
is the equiaxed ferrite grains. As shown in Fig. 1(d), when the
direction of carbon diffusion perpendicular to the magnetic
field direction, the few transformation amount of the black
pearlite in the right side of the interface indirectly indicates
that the number of the carbon atoms passed through the unit
S.-J. Wang, Y. Wu, X. Zhao and L. Zuo
(a) 0T
Fe-0.76C
Jc
Pure Fe
(b) 12T
H
Jc
Fe-0.76C
Pure Fe
(c) 12T
Fe-0.76C
H
Jc
Pure Fe
(d) 12T
H
Fe-0.76C
Jc
Pure Fe
200µm
Fig. 1 Microstructures of the specimens isothermally annealed at 1273 K
for 5 h: (a) 0 T; (b) 12 T, Jc parallel to H; (c) 12 T, Jc antiparallel to H; (d)
12 T, Jc perpendicular to H.
diffusion interface area is smaller, and the carbon diffusion
distance is short. But, when the carbon diffusion direction
parallel/antiparallel to the magnetic field direction, the high
magnetic field only slightly promotes the carbon diffusion,
compared to the non-field annealed specimen.
Figure 2 shows the carbon diffusion distance in specimens
annealed with and without the high magnetic field. The
measurement of the carbon diffusion distance is as follows:
when measuring the area percentage of pearlite, the measurement starts from the point 1500 mm away from the diffusion
interface on the side of pure Fe along the direction opposite
to Jc with a step size of 5 mm (The measuring width
perpendicular to Jc is 1000 mm). When the measured area
percentage of the pearlite is greater than 1%, the distance
between this point to the diffusion interface is defined as
‘‘carbon diffusion distance’’. It can be seen from Fig. 2 that,
in the direction perpendicular to the magnetic field, the
carbon diffusion distance is the shortest, which is far below
the carbon diffusion distance in the non-field annealed
specimen. While in the direction parallel and antiparallel
to the magnetic field, the carbon diffusion distance is a bit
longer, which is slightly higher than that of the non-field
annealed one. Among them, the carbon diffusion distance
of the field annealed specimen with the carbon diffusion
direction parallel to the magnetic field direction is the
longest.
Ohtsuka6,7) attributed the retardation of diffusivity of
carbon in a magnetic field to two factors, (1) retardation of
carbon diffusivity and (2) shift of Fe-C diagram. Concerning
(1), it is known that the Arrhenius plot of the self-diffusion
coefficients in ferromagnetic -Fe below the Curie temperature deviates downwards from the extrapolated Arrhenius
plots from the paramagnetic state above the Curie temper-
Carbon Diffusion Distance (µm)
140
1600
1400
1200
0T
12T Jc parallel to H
12T Jc antiparallel to H
12T Jc perpendicular to H
1000
800
600
400
200
0
Fig. 2 Carbon diffusion distance in annealed specimens with and without
the magnetic field.
ature. Therefore it is expected that the carbon diffusion is
retarded in a the magnetic field. As for (2), the A3 line of an
Fe-C phase diagram is shifted to higher temperature and
higher carbon content in a magnetic field. That is, at the same
temperature, the carbon content of = phase equilibrium
point is increased by the high magnetic field, resulting in the
decline of carbon diffusion driving force. The above theories
successfully explain the mechanism of high magnetic field on
carbon diffusion in = two-phase coexistence temperature
range. When in single-phase region, Ohtsuka observed
that the high magnetic field almost had no effect on carbon
diffusion, but he didn’t give clear theory explanation, since in
this region there is not only no slope change of Arrhenius
plots but also no carbon content change of the = phase
equilibrium point.
From Fig. 1 and Fig. 2, it can be seen that, compared with
the carbon diffusion in the non-field annealed specimen,
the 12 T high magnetic field obviously hinders the carbon
diffusion in the direction perpendicular to the magnetic field;
while it only slightly enhances the carbon diffusion
in the direction parallel/antiparallel to the magnetic field.
The above experimental phenomena adequately demonstrate
that the high magnetic field has strong anisotropic effect on
the carbon diffusion in -Fe. Ono et al.8) measured the
magnetic susceptibility curve of -Fe with different carbon
content in 2 T magnetic field at high temperature, the results
showed that at the same temperature, the magnetic susceptibility of -Fe increased with the increasing of its carbon
content. According to the experimental results of Ono
et al.,8) we extrapolated the magnetic susceptibility of
Fe-0.76C and pure iron at 1273 K, and they are about
0:38 106 Kg/m3 and 0:35 106 Kg/m3 , respectively.
The magnetic susceptibility is the intrinsic properties of
materials, while the change of magnetic free energy
GM ðT; HÞ of paramagnetic materials under the magnetic
field can be shown as
1
GM ðT; HÞ ¼ H 2
2
ð1Þ
Where H is the magnetic field intensity, is the magnetic
susceptibility. Then we can calculate that the change of the
magnetic free energy of Fe-0.76C is 0.215 J/m3 , and that
of Fe is 0.198 J/m3 . The magnetic free energy difference
of Fe-0.76C and Fe is about 0.017 J/m3 .
Effect of a High Magnetic Field on Carbon Diffusion in -Iron
(a)
(b)
Fig. 3 (a) Schemati of the alignment of atomic magnetic moments under
the magnetic field applied; (b) Position between two neighboring atomic
moments correlated in a coordinate system.9)
Therefore, it can be inferred that the magnetic free energy
of -Fe with higher carbon content formed by the Fe-0.76C
alloy in diffusion couple decreased much more than the
magnetic free energy of -Fe with lower carbon content
formed by the pure Fe in diffusion couple at 1273 K in 12 T
magnetic field. That is, the magnetic free energy of Fe-0.76C
alloy side is lower in the diffusion couple, and it is more
stable in the high magnetic field, which inhibits the carbon
diffusion to some extent. However, the magnetic free energy
of the austenite lowered by the field is dependent on its
carbon content, and there is no relationship with the diffusion
direction.
On the other hand, under the 12 T magnetic field, the
atomic magnetic moment of iron atoms in paramagnetic -Fe
tend to align along the magnetic field direction, as schematically illustrated in Fig. 3(a). Then there exists a dipolar
interaction between neighbouring atoms. Let the magnetic
moment of each atom be m and the distance between two
neighbouring atoms r. The magnetic moments align along the
magnetic field direction, as shown in Fig. 3(b). The dipolar
interaction energy ED between neighboring atoms can be
expressed as:9)
ED ¼ 0 m2 3 cos2 1
r3
4
ð2Þ
where 0 is the vacuum magnetic permeability and is the
included angle between r and magnetic field direction. It can
be seen that when ¼ 0 or 180 , i.e., the pairs of moments
2
0m
aligned are parallel to the field direction, ED ¼ 2r
3 , ED is
negative; when ¼ 90 or 270 , i.e., the pairs of moments
aligned are perpendicular to the magnetic field direction,
2
0m
ED ¼ 4r
3 , ED is positive. Therefore, the atoms attract each
other along the magnetic field direction, but repel each other
in the direction perpendicular to the magnetic field direction.
Correlatively, the distance between neighbouring atoms
tends to decrease along the magnetic field direction and
increase in the direction perpendicular to the magnetic field.
So, the carbon diffusion activation energy in the direction
perpendicular to the magnetic field direction increases, which
results in the decrease of the carbon diffusion coefficient,
while the carbon diffusion activation energy in the magnetic
field direction decreases, which results in the increase of the
carbon diffusion coefficient.
141
So, in the direction perpendicular to the magnetic field,
the joint action of the above two field effects result in the
obvious retardation of carbon diffusion in the magnetic field.
In the direction parallel/antiparallel to the magnetic field, the
counteraction of the above two field effects result in the
slightly promotion of the carbon diffusion in the magnetic
field, compared with that of the non-field annealed diffusion
couple. Besides, the effect of high magnetic field on atomic
magnetic moment of the diamagnetic carbon atoms may be
one reason that attribute to the different carbon diffusion
distance in the direction parallel/antiparallel to the magnetic
field.
4.
Conclusion
The high magnetic field obviously hinders the carbon
diffusion in the direction perpendicular to the magnetic field
direction; while it only slightly enhances the carbon diffusion
in the direction parallel/antiparallel to the magnetic field.
This may be attributed to two field effects. One is that the
magnetic free energy of the austenite lowered by the
magnetic field is dependent on its carbon content and the
other one is that the intensities of the magnetic dipolar
interaction between iron atoms in the magnetic field direction
and in the direction perpendicular to the magnetic field is
different. The joint influence of the two effect results in the
anisotropy of the carbon diffusion coefficient in these
directions.
Acknowledgements
Acknowledegments to the Projects 50801010, 50971034
and 50911130365 supported by NSFC, Program for Changjiang Scholars and Innovative Research Team in University
(Grant No. IRT0713), and the ‘‘111’’ Project (Grant
No. B07015).
The authors would like to express appreciation to the High
Magnetic Field Laboratory of Northeastern University for
providing the facilities.
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