Bi electrodeposition under magnetic field

Article abstract of DOI:10.1016/j.electacta.2005.05.059

Bi was galvanostatically electrodeposited in a hydrochloric acid solution in the presence and absence of a 0.5 T field. The effects of magnetohydrodynamics (MHD) convection were focused on the concentration overpotential as well as the current efficiency. The morphological and microstructural variation of electrodeposited Bi thin film was also investigated. Dendritic growth enhanced at higher current density was considerably suppressed by superimposition of a 0.5 T field, while the effect on the crystal microstructure was not confirmed.

Full text of DOI:10.1016/j.electacta.2005.05.059

Electrochimica Acta 51 (2005) 897–905
Bi electrodeposition under magnetic field
M. Motoyamaa, Y. Fukunakaa,∗, S. Kikuchib
a
Department of Energy Science and Technology, Kyoto University, Yoshida-honmachi, Sakyo, Kyoto 606-8501, Japan
Department of Materials Science, University of Shiga Prefecture, 2500 Hassaka-cho, Hikone, Shiga 522-8533, Japan
b
Received 19 February 2005; received in revised form 27 April 2005; accepted 8 May 2005
Available online 19 August 2005
Abstract
Bi was galvanostatically electrodeposited in a hydrochloric acid solution in the presence and absence of a 0.5 T field. The effects of mag-
netohydrodynamics (MHD) convection were focused on the concentration overpotential as well as the current efficiency. The morphological
and microstructural variation of electrodeposited Bi thin film was also investigated. Dendritic growth enhanced at higher current density was
considerably suppressed by superimposition of a 0.5 T field, while the effect on the crystal microstructure was not confirmed.
© 2005 Elsevier Ltd. All rights reserved.
Keywords: Bi; Electrodeposition; Magnetic field; Ionic mass transfer; Current efficiency
1. Introduction
of electrodeposited metal was determined by the direction of
MHD convection.
The introduction of magnetic field into the electrochem-
ical processing may open the large potential applications.
Enhanced mass transfer [1,2], better electrodeposit quality
[3–5] and control of corrosion [6,7] are just some of effects.
In addition, the magnetic field may offer a powerful scientific
tool in the research field on electrochemical reaction kinetics
[8].
A number of studies have been reported on metal elec-
trodeposition in a magnetic field [3–5,9–19]. They focused on
the morphology [3,4,16] and crystal microstructure of elec-
trodeposited thin film [9–15], and kinetics [19], for example.
Devos et al. studied the preferred orientation of electrode-
posited Ni thin film [12]. They concluded that magnetohydro-
dynamics (MHD) convection influenced the concentration
of competitive adsorption of various species (e.g. hydrogen
adatom), which determined the texture axis of electrode-
posited Ni. Kyoto university team engaged in the pole figure
measurement to find out the biaxial texture evolution of elec-
trodepositedNiandFethinfilmsinamagneticfieldparallelto
the substrate [14,15]. They deduced that the texture evolution
The characteristic morphological variation of electrode-
posited metal was often observed in a magnetic field. The
macroscopic dendrite shape of metals like Cu, Zn, Co, and Fe
was significantly influenced by a magnetic field at the higher
current density [3,4,17,18]. Under the mass transfer-limited
condition, MHD convection must reduce the contribution of
concentration overpotential to the morphological variations.
Fe dendrites electrodeposited in a magnetic field sometimes
show the extraordinary macroscopic shape variation [17].
When the thin film was electrodeposited, not only the size
but also the shape of crystallite was modified by the super-
imposition of a magnetic field, for example, Fe [15,16] and
ZnO [20]. Although the stirring effect of MHD convection
was surely confirmed in the many studies, the interest is still
remained on the macroscopic shape evolution.
We have examined the morphological and microstructual
variations of electrodeposited Cu and Ag films by discussing
the important contribution of concentration overpotential
measured with the interferometry technique [21,22]. It is
an interesting subject in the field of shape evolution to
investigate systematically the characteristic morphological
variations induced by the complicated interaction between
electric and magnetic fields near the cathode surface.
∗
Corresponding author. Tel.: +81 75 753 5415; fax: +81 75 753 4719.
E-mail address: fukunaka@energy.kyoto-u.ac.jp (Y. Fukunaka).
0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2005.05.059

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M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
This paper deals with Bi electrodeposition in the pres-
ence and absence of a magnetic field. Bi is a semimetal
and has the most diamagnetic property among all elements.
The unique electronic properties like enormous magnetore-
sistance (MR) effects in thin films [23] and nanowire arrays
[24,25] have been demonstrated. Bi is the most promising
candidate to examine the evidence of magnetic field effect
on diamagnetism during electrodeposition as contrasted with
the ferromagnetic elements, Fe, Co, and Ni. The present work
focuses on the magnetic field effects on the electrochemical
processing of Bi thin film.
2. Experimental
The composition of electrolyte was adjusted to 0.32 M
BiCl3–4.9 M HCl. Au sheet (1 cm × 1 cm) with a thick-
ness of 100 ␮m was used as the cathode. A conventional
three-electrode cell was employed with a Ag/AgCl, KCl
sat. (E = +0.20 V versus SHE) reference electrode through
using a Luggin capillary. The electrolytic cell is schemati-
cally illustrated in Fig. 1. The working electrode was installed
vertically and fixed to the inner wall of 3 cm long duct
type of cell as well as a Bi counter electrode. They were
faced to each other with 1 cm distance at the center of
duct cell [26]. Electrodeposition was carried out galvano-
statically in the range of 1.0–150 mA cm−2. The anode
stripping method measured current efficiency. The mag-
netic field of 0.5 T was applied to the electrolysis with
a permanent magnet of Nd–Fe–B alloy. All experiments
were performed at room temperature. Electrodeposited Bi
thin film was rinsed carefully by ethanol and dried out.
The crystal microstructure of electrodeposited Bi thin film
was determined by X-ray diffraction using Co K␣ radiation
(λ = 1.78897 nm).
Fig. 2. Transient variation of electrode potential during Bi electrodeposition
at 75 mA cm−2 in the presence and absence of a 0.5 T field. (a) Transient
variation over 600 s and (b) over initial 30 s.
3. Results and discussion
Transient variation of electrode potential during Bi elec-
trodeposition at 75 mA cm−2 is shown in Fig. 2. When the
electrolysis started without magnetic field, the electrode
potential suddenly jumped up by 0.1 V from E = −0.3 V
around several seconds after starting the electrolysis as
clearly demonstrated in Fig. 2(b). This duration period, τ (s),
was significantly influenced by the applied current density.
The potential then started gradually shifting to more negative
direction to attain −0.4 V around t = 150 s (see Fig. 2(a)).
Maintaining a constant potential of −0.4 V over 100 s, it was
gradually recovered to −0.3 V at t = 600 s.
The superimposition of magnetic field, on the other hand,
introduced a remarkable fluctuation of potential. It varied
between−0.2and−0.3 Vwithafrequencyof3 Hz. Itwasdif-
ficulttoreducesuchasignificantfluctuationevenifleadwires
were completely sealed with Al foil. Kim and Fahidy found
the current oscillation phenomenon during the magnetoelec-
trolysis [27]. They investigated the effect of the migration on
it when Cu2+ was electrodeposited in CuSO4–H2SO4 solu-
tion. The smaller ratio of the supporting electrolyte to the
metallic ion tended to induce the oscillation. The current
oscillation was observed at the ratio <40. In the present work,
the electrode potential oscillation are noticed in the galvano-
static condition when [HCl]/[Bi3+] is 15. Another possibility
is described in Appendix A, although this value is within their
criterion.
Fig. 1. Schematic illustration of the duct type of electrolytic cell. (A 0.5 T
field was applied perpendicularly).

M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
899
The polarization curve was determined by selecting an
electrode potential recorded around 20–60 s after an abrupt
potential jump at a particular current density. If it did not
appear, the steady state potential was selected. The reason
why such an abrupt electrode potential jump appears will be
described later.
3.1. Solution chemistry
The present composition of electrolyte is 0.32 M
BiCl3–4.9 M HCl. The following chemical reactions ((1)–(5)
[28] and (6))are considered to estimate the pH value of the
electrolyte
Bi3+ + Cl− = BiCl2+ (K1 = 102.44
)
(1)
(2)
(3)
(4)
(5)
(6)
+
BiCl2+ + Cl− = BiCl2
(K2 = 100.66
)
Fig. 3. Concentration distribution of chemical species in 0.32 M BiCl3–HCl.
The broken line indicates the pH.
BiCl2+ + Cl− = BiCl3 (K3 = 100.64
)
−
BiCl3 + Cl− = BiCl4
(K4 = 100.03
)
ically starts once the cathodic potential has been shifted to
negative versus Ag/AgCl reference electrode. The cathodic
current starts to flow around −0.18 V versus Ag/AgCl ref-
erence electrode. A large cathodic overpotential for Bi3+
reduction reaction is expected onto Au substrate.
The pH value of the present electrolyte is about −0.7
as the solution chemistry indicates. Thus, the equilibrium
potential of hydrogen gas evolution may be shifted to
about −40 mV versus SHE. Because the potential difference
between Bi3+/Bi and H+/H2 becomes smaller, the hydrogen
gas evolves more easily than expected from the noble char-
acteristics of Bi metal.
HCl = H+ + Cl− (K5 = 106)
H+ + OH− = H2O (K6 = 1014)
The mass balance equations and the electroneutrality equa-
tions are expressed as follows:
−
[Bi3+] + [BiCl2+] + [BiCl2+] + [BiCl3] + [BiCl4
]
= 0.32 (mol l−1
)
(7)
−
[Cl−] + [BiCl2+] + 2[BiCl2+] + 3[BiCl3] + 4[BiCl4
]
Polarization curve and current efficiency are shown in
Fig. 4. The limiting current behavior is noticed around
60 mA cm−2 from −0.23 to −0.32 V versus Ag/AgCl ref-
erence electrode. The current density starts to increase again
above −0.35 V.
+ [HCl] = 5.86 (mol l−1
)
(8)
3[Bi3+] + 2[BiCl2+] + [BiCl2+] + [H+]
= [BiCl4−] + [Cl−] + [OH−]
The electrode potential decreases about 0.1 V by intro-
duction of a 0.5 T field. The current density linearly increases
with electrode potential under a magnetic field. 150 mA cm−2
(9)
The concentration of each ion is calculated combining
with these stability constants (Kn, n = 1–6). The calculated
resultsareillustratedinFig. 3. Bi3+ ionsmustbetransferredin
the forms of complex ions like BiCl4− to the cathode surface
because HCl concentration is so high.
The pH value was calculated to be −0.7. It was quite
difficult to directly measure such a low value with a con-
ventional pH meter. This negative value of pH shifts the
equilibrium electrode reduction potential of the reaction:
H+ + e− = (1/2)H2 toward a more positive direction. It indi-
cates that the electrode potential difference between both
reduction reaction of Bi3+ to Bi and H2 evolution becomes
smaller.
3.2. Polarization curve and current efficiency
The standard electrode potential of E0 (Bi3+/Bi) is +0.20 V
Fig. 4. Polarization curve and current efficiency for 0.32 M BiCl3–4.9 M
HCl in the presence and absence of a 0.5 T field.
versus SHE. Thus, the reduction of Bi3+ ion thermodynam-

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M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
is attained at −0.35 V while about a half value is recorded at
0 T. MHDconvectionsignificantlyenhancesthemasstransfer
rate at higher current density. Moreover, the limiting current
density is not noticed under the magnetic field.
Current efficiency was measured by the anode stripping
method. Only Bi dissolution reaction takes place at first when
Bi thin film on Au substrate is polarized to be anodic at a con-
stant current. Gas evolution, which is supposed to be Cl2, is
followed immediately after the deposited Bi is almost com-
pletely dissolved from the substrate. Because of the large
potential difference between Bi dissolution and gas evolu-
tion, we can easily identify the start of gas evolution in the
transient variation of electrode potential.
At low current density below 1.0 mA cm−2 or higher
electrode potential above −0.2 V, the measurement error of
current efficiency becomes significant. Bi metal was not uni-
formly electrodeposited all over the Au substrate. Bi elec-
trodeposition progressed mainly on the particular location
where Bi was originally nucleated. Moreover, the transient
variation of electrode potential was not stable. That is, the
nucleation overpotential of Bi onto Au substrate is rather
high.
The current efficiency becomes smaller with decreasing in
electrode potential, while it is over 90% at −0.2 V. It varies
from 95 to 70% without a magnetic field. The superimposi-
tion of a 0.5 T field decreased the current efficiency by 5–10%
and its difference between 0 and 0.5 T becomes more evident
at negative potential. Furthermore, it must be mentioned that
the measured current efficiency appreciably decreased in a
magnetic field even at a more positive potential larger than
−0.2 V, though no effect was noticed on the measured cur-
rent density itself. H2 gas evolution may be enhanced. Further
careful measurement is necessary on this subject.
The measured current efficiencies in Fig. 4 may be a little
smaller than the real values at a high current density. Little
dendrite tips of deposited Bi sometimes mechanically falls
down to the bottom of electrolytic cell during anode strip-
ping. It is caused by the faster dissolution rate realized near
the substrate. Actually, the sample of electrodeposited Bi
at 75 mA cm−2 for the amount of electricity of 50 C cm−2
without a magnetic field was so fragile that it could not be
picked up from the electrolyte solution without any collapse
of deposits.
Fig. 5. Relationship between density of BiCl3–4.9 M HCl electrolyte solu-
tion and concentration of BiCl3.
cathode. Many data have been accumulated on the ionic mass
transfer rate under the condition of the limiting current den-
sity especially in CuSO4–H2SO4 aqueous solution. They are
summarized as [29,30],
Shx = 0.499(Rax)1/4
(10)
It is questionable if this correlation equation can be appli-
cable to the present electrolytic cell design or not, because
all experimental data were measured at the cathode immersed
in an infinitely large volume of electrolyte. The existence of
top wall of duct cell above a vertical cathode may disturb the
development of upward natural convection. Nevertheless, the
correlation equation provides a convenient way to predict the
limiting current density as the first order approximation.
Eq. (10) predicts the limiting current density of
63 mA cm−2 for 1 cm cathode immersed in 0.32 M
BiCl3–4.9 M HCl aqueous solution. The numerical values
necessaryforthecalculationarelistedinTable1. Itcanberea-
sonably compared with the measured value of 60 mA cm−2
.
3.4. Evaluation of τ based on transient natural
convection theory
3.3. Limiting current density
When the transient variation of electrode potential was
measured at a constant current density, the electrode potential
jumped by the order of 100 mV several seconds after the
electrolytic circuit was closed.
When Bi3+ ion is electrodeposited without H2 gas evo-
lution, the concentration profile of Bi3+ ion is formed along
a vertical plane. The density of electrolyte with higher con-
centration of Bi3+ ion is much higher than that with lower
concentration as demonstrated in Fig. 5. Although the con-
centration dependence of electrolyte density is not perfectly
constant as noticed in Fig. 5, the linearity was assumed for the
simplicityofdiscussion. Becausethedensificationcoefficient
(α = 1/ρ(∂ρ/∂C)) is positive (α = 2.13 × 102 cm3 mol−1), the
upward natural convection is induced along a vertical plane
Table 1
Numerical values used in the calculation
D (cm2 s−1
)
8 × 10−6 [31]
0.0
t
µ (g cm−1 s−1
)
1.13 × 10−2 [32]
ρ (g cm−3
α (cm3 mol−1
)
1.16
2.13 × 102
)

M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
901
The duration period, τ, varied with the current density. The
present phenomenon must be deeply relating to the hydro-
gen gas evolution. Once Bi3+ ion is depleted at the cathode
surface under the galvanostatic electrodeposition, the elec-
trode potential must be shifted to more negative direction
to maintain the constant current density. The pH value of
present electrolyte is about −0.7. The equilibrium potential
of H+/H2 must be around −59 mV × −0.7 = 40 mV versus
SHE. It reasonably corresponds to the measured value of
−0.16 V versus Ag/AgCl reference electrode. Moreover, it
must be taken into account that the ionic mass transfer rate
of Bi3+ ion is accompanied by the transient natural convec-
tion developing along a vertical cathode till H2 gas starts to
evolve.
It was tried to calculate the instance, τ, when Bi3+ ion
concentration reached to zero by simultaneously solving the
partial differential equations of ionic mass and momentum
transfer rate. The detail analysis on the transient natural
convection induced by the electrochemical reaction along a
vertical plane electrode should be referred to the ref. [33].
Fig. 6 shows the dependence of τ on the current density,
i. The calculated duration period, τ, reasonably agrees with
the observed value especially at higher current densities than
65 mA cm−2, and below this value, τ did not appear in the
transient variation of electrode potential. That is because the
limiting current density, iL, is 63 mA cm−2, and it is rea-
sonable that the concentration of Bi3+ ion did not reach to
zero if the current density lower than iL was applied. In
spite of the existence of duct cell enclosure roof above the
vertical cathode, the agreement of the calculated limiting cur-
rent density with the observed values is acceptable for the
present discussion. It supports the soundness of the proposed
electrochemicalinterfacialphenomenaaccompaniedwiththe
simultaneous mass transfer of Bi3+ and H+ ion toward Au
cathode.
Fig. 7. Variation of partial current density for Bi electrodeposition and H2
evolution.
3.5. Partial current density
Partial current densities for Bi electrodeposition and H2
evolution were calculated from Fig. 4. They are shown in
Fig. 7. Current density for Bi electrodeposition, iBi, linearly
increases with increasing in total current density, iT, in the
absence of magnetic field. No substantial effect due to the
magnetic field appears in Bi electrodeposition current at iT
<100 mA cm−2. The superimposition of a 0.5 T field reduces
H2 evolution above iT = 75 mA cm−2. It is interesting to see
that iBi is maintained at 90 mA cm−2 in spite of significant
increase in iH when iT >100 mA cm−2
.
2
MHD convection is driven by Lorentz force as defined by
the following equation:
F = j × B
(11)
where F, j, and B are Lorentz force vector, current density
vector, and magnetic flux density vector, respectively. MHD
convection is generated in the electrolyte solution when the
lines of electric field are not parallel to the magnetic flux. It
results in enhanced ionic mass transfer rate [34].
The concentration overpotential increases as Bi3+ ion is
consumed at the cathode surface. Bi3+ concentration would
become eventually zero when the applied current density
is above the limiting current density of about 60 mA cm−2
under a conventional electrolysis. However, an abrupt elec-
trode potential jump was not observed in a magnetic field as
described previously. Once hydrogen gas bubble is generated
on the cathode surface, it distorts the lines of electric field
around a growing gas bubble. The interaction between the
electric and the magnetic field becomes so complicated that
the microscopic MHD convection enhances the ionic mass
transfer inside a concentration boundary layer. It might be
highly turbulent enough not to induce the steady state deple-
tion condition of Bi3+ at the cathode surface to make the
opportunity toward the abrupt potential jump.
Fig. 6. Variation of transition time with current density. The broken line
indicates the calculated result.

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M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
Fig. 8. SEM images of electrodeposited Bi thin film at 75 mA cm−2 in the presence and absence of a 0.5 T field: (a) 133 s and (b) 400 s.
3.6. Time variation of macroscopic morphology at
higher current density
3.7. Morphological variation with current density
The left row in Fig. 9 shows the SEM images of electrode-
posited Bi thin films at 1.0–50 mA cm−2 without a magnetic
field. The amount of electricity of 50 C cm−2 corresponds
to the Bi film thickness more than 37 ␮m if the film would
be perfectly compact and uniformly electrodeposited on Au
substrate.
Fig. 8(a) shows the SEM images of Bi thin films elec-
trodeposited for 133 s at 75 mA cm−2, that is 10 C cm−2. Bi
dendrites composed of aggregated few ␮m-sized rods are
observed all over the surface. Bi dendrites were easily swept
away and bare Au substrate appeared when the electrode-
posited film was rinsed by ethanol. Because of significant
growth of dendrite, the effective electrode surface area was
enlarged with the progress of electrodeposition. Therefore,
the overpotential under galvanostatic condition gradually
decreases after t = 200 s as demonstrated in Fig. 2(a). The
surface roughness of electrodeposited Bi thin film rapidly
developed with time. It was clearly illustrated in Fig. 8(b),
which was obtained 400 s at the same current density. Note
that the magnification is one-tenth of Fig. 8(a). The dis-
tance between the Luggin capillary and the cathode surface
becomes closer. It results in the decrease of IR drop.
The surface morphology of Bi thin film electrodeposited
in a 0.5 T field is shown in the right row in Fig. 8. The macro-
scopic surface roughness is drastically improved. No den-
drites were noticed at the amount of electricity of 30 C cm−2
(see the size scale in Fig. 8(b)).
It is noteworthy to describe that MHD convection to
enhance the ionic mass transfer rate improves the macro-
scopic surface morphology more than 10 ␮m in size rather
than the microscopic scale less than a few ␮m as illustrated
in Fig. 8. Such a morphological variations may be character-
ized by the concentration boundary layer thickness and the
smaller H2 gas evolution rate under MHD convection.
The surface morphology becomes smoother with pref-
erentially growth of flat surface at 5.0 mA cm−2 than at
1.0 mA cm−2 in Fig. 9(b). The poorer nucleation rate at lower
current density may be participating to this morphological
variation. With further increase in the current density, the evo-
lution of H2 gas becomes evident as demonstrated in Fig. 7.
The current efficiency of 90% is recorded at 50 mA cm−2 and
iH thus reaches about 5 mA cm−2. Spherical dendrite forma-
2
tion appears at 50 mA cm−2 as demonstrated in Fig. 9(c). The
finer precipitates coagulate each other to form the spherical
deposits with 50 ␮m in diameter. The appearance of spher-
ical dendrite deposit accompanying with H2 gas evolution
was also observed in the electrodeposition of copper whose
crystal structure is completely different [22].
The right row of Fig. 9 corresponds to SEM in the presence
of magnetic field. It is rather difficult to clarify the morpho-
logical variations due to the magnetic field effect, especially
at lower current density. The surface roughness of electrode-
posited film is slightly improved in the magnetic field. The
effect of MHD on the macroscopic surface roughness has
been accepted. In order to further examine the morphologi-
cal variations, the sample of deposited film was observed in
a high magnification.

M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
903
Fig. 9. SEM images of electrodeposited Bi thin film: (a) 1.0 mA cm−2, (b) 5.0 mA cm−2, (c) 50 mA cm−2 and (d) 1.0 mA cm−2 (with 10 times higher
magnification).
Fig. 9(d) illustrates the 10 times-magnified image of
Fig. 9(a). Finer plate-like Bi crystallites were observed when
the current density was <5.0 mA cm−2. The thickness of plate
crystal was about 0.1–1 ␮m in diameter. The morphology like
a stack of flakes rather than a film is noticed.
duces a preferential growth of plate-like precipitates. Such a
morphological variation due to magnetic field effect is seen
even in such a low current density far below the limiting cur-
rent density. As already pointed out in Fig. 4, the current
efficiency decreases in this region due to superimposition of
magnetic field. It is interesting to point out the duplex effects
under the superimposition of magnetic field on the surface
roughness improvement at higher current density as well as
on the crystal growth variation of each precipitate at lower
A better crystallinity is seen at 1.0 mA cm−2 in a magnetic
field of 0.5 T as demonstrated in Fig. 9(d). The precipitate
diameter grows to about a few ␮m. The superimposition of a
magnetic field to the electrodeposition of Bi film surely intro-

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M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
electrode potential was observed, which was referred to the
depletion of Bi3+ and evaluation of H2 gas. At the lower cur-
rent density, the morphology like a stack of flakes appeared.
At the higher current density, Bi was dendritically electrode-
posited.
Current efficiency significantly decreased above −0.2 V
versus Ag/AgCl. Superimposition of the magnetic field
increased the current density, while slightly decreased the
current efficiency. MHD convection enhanced the mass trans-
fer rate of Bi3+ ion, and resulted in the suppression of the
dendrite growth and enhanced H2 evolution rate. The surface
morphology in a macroscopic scale was quite improved at
higher current density, while the preferential growth of plate-
like precipitates appeared at lower current density for below
the limiting current density. Preferred orientation of Bi film
was not noticed under the present experimental condition.
Acknowledgements
Part of this work was supported by financial aids from the
21st century COE program and the Ministry of Education,
Science and Culture (Giant-in-Aid for Exploration Research
No. 15360402), for which the authors are grateful.
Fig. 10. X-ray diffraction pattern of electrodeposited Bi thin film in (a) 0 T
and (b) 0.5 T. (Applied current densities: 1.0, 5.0, 10, 30, and 50 mA cm−2
from the bottom.)
Appendix A
There are a number of papers to discuss the ionic mass
transfer accompanying the gas evolution along a vertical
plane cathode [36,37]. The ionic mass transfer rate is gov-
erned by the macroscopic natural convection caused by
upward moving gas bubbles along a vertical cathode. It is
also influenced by the microconvection caused by growing
or coalescing gas bubbles on the electrode surface. Alkire and
Lu introduced the concept of the overall mass transfer coef-
ficient km defined as the sum of the mass transfer coefficient
calculated by the macroscopic natural convection kn and that
by the microconvection due to growing gas bubble kb [36]
current density. Anomalous scaling analysis with AFM is
necessary to further discuss the phenomena [35].
3.8. Microstructural variation
Bi has an arsenic structure in rhombohedral system.
Fig. 10 shows X-ray diffraction pattern of electrodeposited
Bi thin film. The pattern does not remarkably show the
microstructural variation due to current density. The mag-
netic field effect on the microstructual variation is not noticed
as long as the present experimental conditions concern. The
relative intensities are always similar to those for the powder
pattern and the preferred orientations of any crystal planes are
not found. A similar experiment was conducted for Cu elec-
trodeposition confined in a quasi-two-dimensional electrode
cell 200 ␮m thick horizontally installed [4]. Preferred orien-
tation of electrodeposited copper was not observed, though
macroscopic morphology was drastically changed from den-
drite growth to the compact precipitate by superimposition
of a 0.5 T field.
km = kn + kb
(A1)
The applicability of Eq. (A1) was experimentally examined
to the ionic mass transfer rate of Cu2+ ion accompanying H2
gas evolution along a vertical Cu cathode in CuSO4–H2SO4
solution [37]. The former mass transfer rate of kn is primarily
governed by the density difference between the cathode
surface and the bulk electrolyte, that is, the body force.
The superimposition of magnetic field to the electrolytic
process introduces MHD flow. It diminishes the concentra-
tion boundary layer thickness to enhance the ionic mass
transfer rate. Under such a circumstance, the surface con-
centration of Bi3+ is high to induce the smaller concentration
overpotential. With the progress of electrodeposition, the sur-
face concentration of Bi3+ starts to deplete. The concentration
overpotential rises. H+ ion reduction is then driven to evolve
H2 gas in order to maintain the galvanostatic current. Once H2
4. Summary
Bi was galvanostatically electrodeposited in a concen-
trated hydrochloric acid solution in a duct type cell in the
presence and absence of a 0.5 T field. An abrupt jump of

M. Motoyama et al. / Electrochimica Acta 51 (2005) 897–905
[9] L. Yang, J. Electrochem. Soc. 101 (1954) 456.
905
gas bubble begins to grow, it distorts the electric field near the
cathode surface. The magnetic field then starts to couple the
electricfielddistortedaroundH2 gasbubble. ThemicroMHD
convection is then induced near H2 gas bubble. The depletion
of Bi3+ ion is quickly recovered to decrease the concentration
overpotential. The repetition of such a process may also intro-
duce the electrode potential oscillation phenomenon. Further
experiments are necessary to understand it.
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(2004) C81.
Appendix B. List of symbols
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[20] M. Nambu, T. Iida, E. Kusaka, Y. Fukunaka, R. Ishii, in press.
[21] Y. Fukunaka, T. Yamamoto, Y. Kondo, J. Electrochem. Soc. 136
(1989) 3630.
c
D
g
Rax
Shx
t
bulk concentration (mol cm−3
)
diffusivity of Bi3+ ion (cm2 s−1
)
gravitational acceleration (cm s−2
)
Rayleigh number (=gαcx3/νD)
Sherwood number (= i(1 − t)x/zFDΘ)
transference number (−)
x
vertical distance from the lower edge of cathode
(cm)
[22] Y. Fukunaka, H. Doi, Y. Kondo, J. Electrochem. Soc. 137 (1990)
88.
[23] F.Y. Yang, K. Liu, K. Hong, D.H. Reich, P.C. Searson, C.L. Chien,
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Inorganic Ligands, Pergamon Press, Oxford, 1982.
[29] K. Denpo, S. Teruta, Y. Fukunaka, Y. Kondo, Metall. Trans. B 14B
(1983) 633.
Greek letters
α
densification coefficeint (cm3 mol−1
kinematic viscosity (cm2 s−1
concentration difference at the cathode surface from
the concentration of bulk electrolyte (mol cm−3
)
ν
)
Θ
)
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