Materials Transactions, Vol. 48, No. 2 (2007) pp. 234 to 238
#2007 The Japan Institute of Metals
The Effect of Frequency of Electromagnetic Vibrations on Vibrational Motion
in Fe-Co-B-Si-Nb Bulk Metallic Glasses
Takuya Tamura* , Daisuke Kamikihara, Yuuki Maehara, Naoki Omura and Kenji Miwa
Solidification Processing Group, Materials Research Institute for Sustainable Development, National Institute
of Advanced Industrial Science and Technology (AIST), Nagoya 463-8560, Japan
The method for producing Fe-Co-B-Si-Nb bulk metallic glasses using electromagnetic vibrations is effective in forming the metallic glass
phase. The purpose of this study was to investigate the effects of the frequency of electromagnetic vibrations on the vibrational motion in Fe-CoB-Si-Nb bulk metallic glasses. The amplitudes of the electromagnetic vibrations at 5 kHz were calculated to be on the order of micrometers, but
those at higher frequencies were on the order of nanometers. It was found that the nanometer-sized amplitudes resulted in the disappearance of
the increased cooling rate caused by electromagnetic vibrations observed at lower frequencies. When particles in the sample have lower electric
resistance than the molten sample, these particles are considered to vibrate vigorously in the molten sample by Lorentz force because the electric
current concentrates in those. It is suggested that this phenomenon is the reason electromagnetic vibrations decrease the number of crystal
nuclei. [doi:10.2320/matertrans.48.234]
(Received September 21, 2006; Accepted November 30, 2006; Published January 25, 2007)
Keywords: bulk metallic glass, electromagnetic vibration, vibrational motion, amplitude, crystal nuclei
1.
Introduction
Different combinations of stationary and/or alternating
electric and magnetic fields have been used for a wide range
of purposes, including stirring, shaping, etc.1) Among these
combinations, it was reported that electromagnetic vibrations
induced by the interaction between alternating electric and
stationary magnetic fields can act as a powerful vibrating
force in melts and affect microstructural refinements in the
usual crystalline alloys.2–9) The simultaneous imposition of a
stationary magnetic field with a magnetic flux density B and
an alternating electric field with a current density J and a
frequency f on a conducting liquid results in the induction of
a vibrating electromagnetic body force with a density of F ¼
J B inside the liquid. This force, which has a frequency
equal to that of the applied electric field, vibrates in a
direction perpendicular to the plane of the two fields and
results in vibrational motion of the constituent particles of the
conducting liquid.
The present authors reported that a new method for
producing Mg-Cu-Y bulk metallic glasses using electromagnetic vibrations is effective in forming the metallic glass
phase, and that disappearance or decrement of clusters by the
electromagnetic vibrations applied to the liquid state is
presumed to cause suppression of crystal nucleation.10,11)
Moreover, the present authors reported that the glass-forming
ability of Fe-Co-B-Si-Nb alloys also increases with increasing intensity of electromagnetic vibrations. The effects of the
electromagnetic vibrations were found to be two-fold. The
first effect was the increase in the cooling rate. However, this
increase in the cooling rate disappears with electromagnetic
vibrational frequencies of more than 10 kHz. It was considered that the absence of macroscopic stirring resulted in the
disappearance of the increase in the cooling rate. The second
effect was the decrease in the number of crystal nuclei.12–14) It
was found that the reactants of a Mo electrode that were solid
*Corresponding
author, E-mail: [email protected]
at 1573 K moved into an Fe-based alloy sample with the
application of the electromagnetic vibrations and caused the
nuclei of crystal particles which composed the round lines.13)
This phenomenon is considered to be caused by the vibrational motion of the electromagnetic vibrations. However,
vibrational motion of the electromagnetic vibrations is not
fully investigated so far. Thus, the purpose of this study is to
investigate the effects of the frequency of these electromagnetic vibrations on the vibrational motions in Fe-Co-BSi-Nb bulk metallic glasses in order to clarify the effects of
these electromagnetic vibrations.
2.
Experimental Apparatus
The experimental apparatus is based on a superconducting
magnet, which is able to deliver a magnetic field of up to 10
Tesla at the center of a bore 150 mm in diameter. It was
designed and assembled to hold the sample by stainless-steel
cylinders as firmly as possible against the mechanical
vibrations of the system when electromagnetic vibrations
are applied, and prevent the vibrations from being transferred
to the magnet.
The cylindrical sample is placed between two tungsten
electrodes in an alumina tube and set in the experimental
apparatus (Fig. 1). The electrodes are firmly fixed in the
tube to prevent leakage of the molten liquid when vibrations
are applied. The electric current for the electromagnetic
vibrations is supplied to the sample through the two
electrodes on both ends of the sample. The temperature is
measured by a K-type thermocouple on the exterior of the
tube. Two nozzles are positioned to spray the tube with
water. An electric heating furnace is used to heat and melt
the sample, and is removed when water is sprayed. It is
important to note the temperature of the sample was known
when the sample was heated, but when the sample was
cooled, the temperature was unknown as water is sprayed
onto the thermocouple directly.
The Effect of Frequency of Electromagnetic Vibrations on Vibrational Motion in Fe-Co-B-Si-Nb Bulk Metallic Glasses
3.
Experimental Procedures
Samples of (Fe0:6 Co0:4 )72 Si4 B20 Nb4 alloys with a diameter
of 2 mm were provided by RIMCOF Japan. Alloy ingots were
prepared by induction melting of pure metal mixtures under
an argon atmosphere. The cylindrical samples were produced
by casting into a copper mold.
The (Fe0:6 Co0:4 )72 Si4 B20 Nb4 alloy, which was cylindrical
with a diameter of 2 mm and a length of 7.8 mm, was placed
in an alumina tube of almost the same inner diameter and an
outer diameter of 4 mm. Argon was passed through the inside
of the stainless-steel cylinders. The sample was heated at a
rate of 20 K/min to 1573 K using the heating furnace set
around the sample in the center of the magnet. The molten
sample was kept at this temperature for 2 minutes and then
water was sprayed on the alumina tube. The flow rate of the
cooling water was fixed at 3 L/min. The electromagnetic
Fig. 1
A schematic illustration of the experimental apparatus.
235
vibrations were applied by passing the alternating electric
current through the sample in a preset magnetic field. The
applied time of the electromagnetic vibrations for the alloys
is shown in Fig. 2. The electromagnetic vibrations were
applied for 10 seconds before the onset of the water spray,
and 10 seconds after the spray.
The metallic glass and/or crystalline structures were
examined using optical microscopy and SEM. For the optical
microscopy observations, a 10% nitric acid-ethanol solution
was used for etching the sample surface.
4.
Results and Discussion
4.1
Effect of the frequency of the electromagnetic
vibrations
Figure 3 shows optical micrographs of the alloys with
electromagnetic vibrations at various frequencies: (a) 1 kHz,
(b) 5 kHz, (c) 50 kHz and (d) 200 kHz. These micrographs
were taken in the boundary area of the W electrodes. The
Fig. 2 Applied time of the electromagnetic vibrations.
Fig. 3 Optical micrographs for the alloys with electromagnetic vibrations at various frequencies: (a) 1 kHz, (b) 5 kHz, (c) 50 kHz and (d)
200 kHz. These micrographs were observed in the boundary area of the W electrodes. The frequency of the electromagnetic vibrations
was varied with that of the alternating electric current. The magnetic field and the alternating electric current were fixed at 10 T and 5 A,
respectively. The left side is the W electrode side.
236
T. Tamura, D. Kamikihara, Y. Maehara, N. Omura and K. Miwa
Fig. 4
An SEM composition image of the same alloy with electromagnetic vibrations as shown in Fig. 3 at a frequency of 50 kHz.
frequency of the electromagnetic vibrations was varied by
varying that of the alternating electric current. The magnetic
field and the alternating electric current were fixed at 10 T
and 5 A, respectively. The left side is the W electrode side in
Fig. 3. Round lines consisting of crystal particles in a glassy
phase were observed in the samples with electromagnetic
vibrations at frequencies of 1 and 5 kHz. Moreover, these
round lines were observed in the center area of the sample
with electromagnetic vibrations at a frequency of 1 kHz. It
was previously reported that the reactants of a W electrode
that were solid at 1573 K moved into the sample with the
application of the electromagnetic vibrations and caused the
nuclei of crystal particles that appeared as round lines.13)
However, other lines were also observed for the samples with
electromagnetic vibrations at frequencies of 50 and 200 kHz.
Figure 4 shows an SEM composition image of the same
alloy with electromagnetic vibrations at a frequency of
50 kHz shown in Fig. 3. The lines observed by the optical
micrograph were again present. A composition analysis of
the gray and white areas of the SEM image was carried out
using EDS. Boron was excluded from the detection elements
because boron cannot be detected precisely by SEM-EDS.
Table 1 shows the W content from the SEM-EDS analysis
corresponding to the SEM image shown in Fig. 4. The
difference between the gray and white areas was found to be
due to differences in W content. The gray and white areas in
the SEM image have lower and higher W content, respectively. However, both areas are a glassy phase.
Table 1 W content by SEM-EDS corresponding to the SEM image shown
in Fig. 4. Boron was excluded from detection elements.
(a)
W content
in Gray parts (at%)
W content
in White parts (at%)
(b)
0.02
(c)
(d)
0.15
0.34
(e)
(f)
0.05
0.25
(g)
(h)
0.00
0.21
(i)
0.15
0.23
The electromagnetic vibrations at low frequencies result in
a migration of the reactants of the W electrode. However, the
electromagnetic vibrations at high frequencies were found to
move the W atoms directly.
4.2 Motion of the electromagnetic vibrations
If we assume that only the alloy sample exists in free
space, and that the electric current is passed through the
sample uniformly, two equations hold. One is the Lorentz
force:
F ¼ iBl
ð1Þ
where F (N) is force, i (A) is electric current, B (T) is
magnetic-flux density, and l (m) is the length of the sample.
Another is the equation of motion:
F ¼ ma
ð2Þ
where m (kg) is the weight of the sample, and a (m/s2 ) is
The Effect of Frequency of Electromagnetic Vibrations on Vibrational Motion in Fe-Co-B-Si-Nb Bulk Metallic Glasses
237
Table 2 Effects of the frequency of the electromagnetic vibrations on the
calculated amplitude of the vibrational motion.
Frequency
1 kHz
5 kHz
50 kHz
200 kHz
Amplitude
140 mm
5.6 mm
56 nm
3.5 nm
acceleration. The sine curve for alternating electric current
was used:
i ¼ ð2Þ0:5 ie sinð2 ftÞ
ð3Þ
where ie (A) is the effective sine curve current, f (Hz) is
frequency, and t (s) is time. The Fe based alloys were
experimented at a magnetic density of 10 T, a sample length
of 7.8 mm, an effective sine curve current of 5 A and a weight
of 0.20 g. The integral of the acceleration of the sample is the
velocity of the sample, and the integral of the velocity of the
sample is the displacement of the sample. Thus, the
amplitude of the vibrational motion was calculated from
the acceleration. The effect of the frequency of the electromagnetic vibrations on the calculated amplitude of the
vibrational motion is shown in Table 2. It was calculated that
the amplitudes of the electromagnetic vibrations at 1 and
5 kHz are on the order of micrometers, but those at high
frequencies are on the order of nanometers. It was previously
reported that one of the effects of the electromagnetic
vibrations is the increase in the cooling rate. However, the
increase in the cooling rate caused by the electromagnetic
vibrations disappears with the frequency exceeds 10 kHz.12)
The micrometer-sized amplitudes result in macroscopic
stirring which caused the increase in the cooling rate because
of the restraint of a container. However, the nanometer-sized
amplitudes at high frequencies don’t cause macroscopic
stirring. Thus, it was found that the absence of macroscopic
stirring resulted in the disappearance of the increase in the
cooling rate at frequencies of more than 10 kHz. Moreover, it
is considered that the nanometer-sized amplitudes at high
frequencies are one of causes of the migration of W atoms by
the electromagnetic vibrations.
Given the assumptions that only the alloy sample exists in
free space and that the electric current is passed through the
sample uniformly, the electromagnetic vibrations result in
vibrational motion rather than ultrasonic-like waves because
the entire sample shifts in the same direction at the same
time. In reality, this vibrational motion is affected by the
restraint of the container and the non-uniform electric
current. However, the restraint of a container does not affect
this vibrational motion at high frequencies because the
amplitudes are on the order of nanometers. The electromagnetic vibrations at high frequencies have been reported to
decrease the number of crystal nuclei.12,14) It is then
presumed that the non-uniform electric current causes the
decrease in the number of crystal nuclei. If particles having
different electric resistance exist in the molten sample, the
electric current will concentrate in or avoid these particles
depending on the resistance. When particles have lower
electric resistance than the molten sample, these particles are
considered to vibrate vigorously in the molten sample due to
the Lorentz force because the electric current concentrates in
those. Figure 5 shows a schematic illustration of this
Fig. 5 A schematic illustration of the non-uniform electric current when
particles have lower electric resistance than the molten sample.
phenomenon. This phenomenon is considered to result in
not only the migration of the reactants of the electrode into
the sample, but also the migration of W atoms at high
frequencies. Moreover, it is suggested that this phenomenon
is the reason electromagnetic vibrations decrease the number
of crystal nuclei because the clusters of crystals in the liquid
state, which have lower electric resistance than the melt,
vibrate vigorously and disappear.
5.
Summary
The effects of the frequency of electromagnetic vibrations
on vibrational motion in Fe-Co-B-Si-Nb bulk metallic
glasses has been investigated, and the following summaries
have been made.
(1) Electromagnetic vibrations at low frequencies result in
a migration of the reactants of the W electrode.
However, the electromagnetic vibrations at high frequencies were found to move the W atoms directly. It is
considered that the nanometer-sized amplitudes at high
frequencies are one of causes of this W atom migration.
Moreover, it was found that the nanometer-sized
amplitudes resulted in the disappearance of the increased cooling rate caused by electromagnetic vibrations
observed at lower frequencies.
(2) Under the assumptions that only the alloy sample exists
in free space and that the electric current is passed
through the sample uniformly, the electromagnetic
vibrations result in vibrational motion and not ultrasonic-like waves.
(3) Particles in the sample having lower electric resistance
than the molten sample vibrate vigorously in the molten
sample due to the Lorentz force because the electric
current concentrates in these particles. This phenomenon is considered to result in not only the migration of
W atoms or the reactants of the electrode into the
sample, but also the decrease in the number of crystal
nuclei.
Acknowledgments
This work has been supported by a grant for the Metallic
Glasses Project of the Material Industrial Competitiveness
Strengthening Program from the New Energy and Industrial
Technology Development Organization (NEDO). The authors are grateful to Dr. N. Nishiyama, Mr. K. Amiya and
Mr. A. Urata for providing the Fe-based alloys and numerous
helpful discussions. The authors also thank Dr. K. Yasue,
Mr. Y. Sakaguchi and Mr. H. Matsubara for technical
assistance.
238
T. Tamura, D. Kamikihara, Y. Maehara, N. Omura and K. Miwa
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