Electrochemical deposition of co under the influence of high magnetic fields

Article abstract of DOI:10.1149/1.2073167

The effect of uniform, vertically oriented high magnetic fields up to 13 T on the electrodeposition of Co has been investigated in dependence on the cell and electrode geometry as well as the orientation and strength of the magnetic flux density by means of cyclic voltammetry, chronoamperometric measurements, and atomic force microscopy investigations. In the majority of cases, the limiting current density i_lim increases with increasing magnetic flux densities independent of the cell geometry and orientation. The current efficiency of Co increases with increasing magnetic flux densities only in magnetic fields aligned parallel to the electrodes due to the magnetohydrodynamic (MHD) effect. The morphology of the deposits exhibits randomly oriented round-shaped grains. The electrochemical behavior of horizontal electrodes with magnetic fields oriented perpendicular to the surface is strongly dependent on the electrode geometry. The current efficiency of the Co deposition on flat electrodes increases for low magnetic flux densities and keeps constant for high magnetic fields. In contrast, for wall electrodes the current efficiency decreases strongly even for low magnetic fields. These results are caused by overlapping effects of two types of convection, macro-MHD- and micro-magneto convection due to gradients of the concentration and the magnetic susceptibility. This leads to a modified morphology.

Full text of DOI:10.1149/1.2073167

Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
C817
0013-4651/2005/152͑12͒/C817/10/$7.00 © The Electrochemical Society, Inc.
Electrochemical Deposition of Co under the Influence of High
Magnetic Fields
M. Uhlemann,a,z A. Krause,a J. P. Chopart,b and A. Geberta
aLeibniz-Institute for Solid State and Materials Research, IFW-Dresden, 01171 Dresden, Germany
bDTI, EA 3083, UFR Sciences, 51687 Reims Cedex 2, France
The effect of uniform, vertically oriented high magnetic fields up to 13 T on the electrodeposition of Co has been investigated in
dependence on the cell and electrode geometry as well as the orientation and strength of the magnetic flux density by means of
cyclic voltammetry, chronoamperometric measurements, and atomic force microscopy investigations. In the majority of cases, the
limiting current density ilim increases with increasing magnetic flux densities independent of the cell geometry and orientation. The
current efficiency of Co increases with increasing magnetic flux densities only in magnetic fields aligned parallel to the electrodes
due to the magnetohydrodynamic ͑MHD͒ effect. The morphology of the deposits exhibits randomly oriented round-shaped grains.
The electrochemical behavior of horizontal electrodes with magnetic fields oriented perpendicular to the surface is strongly
dependent on the electrode geometry. The current efficiency of the Co deposition on flat electrodes increases for low magnetic flux
densities and keeps constant for high magnetic fields. In contrast, for wall electrodes the current efficiency decreases strongly even
for low magnetic fields. These results are caused by overlapping effects of two types of convection, macro-MHD- and micro-
magneto convection due to gradients of the concentration and the magnetic susceptibility. This leads to a modified morphology.
© 2005 The Electrochemical Society. ͓DOI: 10.1149/1.2073167͔ All rights reserved.
Manuscript submitted March 31, 2005; revised manuscript received June 8, 2005. Available electronically October 24, 2005.
1/3
ilim = 0.687nFcϱD2/3d5/3
␣
͓3͔
Magnetic field effects on electrochemical reactions and in par-
ticular on the deposition of metals are widely accepted and summa-
rized in reviews of Fahidy1,2 and Taken.3 Proved and established are
the convective magnetohydrodynamic effects ͑MHD͒ generated by
the magnetic field acting on the mass transport and their conse-
quence for the morphology of the deposits. Generally, hydrody-
namic electrodes and convective effects are extensively investigated
and semiempirically analyzed based on the fundamental equations
of Navier–Stokes and the convective diffusion equations. A laminar
flow close to the electrode surface increases the mass-transport rate
and therefore, the limiting current ͑Ilim͒ is enhanced as soon as an
inhibiting species is not favored by the magneto-induced
convection.4,5 According to the basic investigations discussed in
Ref. 6, Ilim is dependent on the flow rate in the vicinity of the
electrode. For stationary disk electrodes the following approxima-
tions based on the transport equations were obtained for a uniform
laminar or rotating flow of the electrolyte
Hence, it can be concluded from this relation ͑Eq. 3͒ and Eq. 1 and
2, that ilim ϰ B1/3 ϰ u1/2 or ␻1/2. Therefore, the velocity at the inter-
face diffusion layer/bulk electrolyte should be proportional to B2/3
.
Based on the semiquantitative solution of hydrodynamic equations
and the known magnetically induced convection, some authors13-15
found a dependency of ilim on the number of electrons involved in
the electrochemical mass-transport-controlled process under the ef-
fect of external magnetic fields on stationary disk millielectrodes.
The theory of the hydrodynamic electrodes assumes that the dif-
fusion layer is not moved and the transport of the electroactive spe-
cies is only controlled by the diffusion. Therefore, mechanical stir-
ring or magnetically induced convection takes place only outside of
the diffusion layer. A convective flow inside the diffusion layer of
electrodes with magnetic fields parallel to the surface is proposed by
Olivier et al.16 This motion is attributed to electrokinetic effects
caused by the tangential component of the electric field and is not
necessarily related to the presence of a magnetic field.17 Especially
the assumption that the motion of ions inside the double layer is
only determined by diffusion is not sustainable for systems with
magnetic fields oriented perpendicular to the surface. Additional
fluid motions have also been predicted for these electrode configu-
rations. Until now only a few studies are published for this case and
the results are still controversial. With respect to this magnetic field
configuration, Aogaki et al.18-20 analyzed symmetrical and nonsym-
metrical fluctuations forming micro- and macroscopic vortexes
which yield characteristic morphologies consisting of regular micro-
holes. In the magnetic field the macroscopic fluctuations are attrib-
uted to local breaks of the electrostatic equilibrium in the electric
double layer, and the microvortexes are generated by the thermal
motion inside the diffusion layer. This assumption predicts that the
surface has an effect on the nucleation process during the deposition
in an applied magnetic field. Recently, investigations of the
authors21,22 regarding the deposition of Co have shown that for the
configuration of B perpendicular to the electrode surface the mag-
netic field increases ilim but decreases the current efficiency for the
Co deposition. High-magnetic-field investigations of the Cu deposi-
␲
−1/6
1/2
Ilim = knFcϱD2/3
␯
d2͑u/d͒
͓1͔
͓2͔
4
␲
−1/6
1/2
Ilim = knFcϱD2/3
␯
d2␻
4
where k is 0.753–0.780, n is the number of electrons, c is the elec-
troactive species concentration in the bulk electrolyte, D is the dif-
fusion coefficient, ␯ = 10−6 m2/s is the kinematic viscosity, F is the
Faraday constant, d is the diameter of the disk electrode, u is the
laminar velocity, and ␻ is the rotating velocity of the solution close
to the electrode. First Aogaki et al.7,8 investigated and quantified the
convective effect of an applied magnetic field oriented parallel to the
electrode surface on the limiting current density for the electrodepo-
sition of Cu. From the experimental data and the analysis of the
basic transport equations ͑Eq. 1 and 2͒ it has been found that the
limiting current density ͑ilim͒ is proportional to c4ϱ/3 and Bb. The
exponential dependency of ilim from cϱ and B is widely established
and proved by numerous groups.9-12 The exponent b varies between
0.3 and 0.5, depending on the cell and electrode geometry and on
the electroactive species in the solution. Aaboubi et al.9 introduced a
velocity gradient ␣ = kBcϱ for steady-state conditions and found the
following relation considering the velocity gradient to be constant
tion refer to an oscillating behavior of ilim.
23 This behavior could be
caused by the Lorentz force generating a rotating flow at the edge of
the electrode due to nonparallel electric field lines. The motion of
the ions at the vicinity of the surface could also be affected by other
magnetically induced forces. For ions with high magnetic suscepti-
bilities the interaction of the external field with the magnetic prop-
erties of the ions can lead to an additional driving force toward, or
away from, the electrode, depending on the magnetic properties of
z E-mail: m.uhlemann@ifw-dresden.de
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C818
Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
Figure 1. Electrochemical cells: ͑a͒ embedded Cu disk ͑d = 11.3 mm͒ ar-
ranged in a glass cylinder; ͑b͒ quartz crystal ͑d = 14.05 mm͒ fixed with
O-rings forming a wall in a Teflon cell. The cells are placed horizontally and
vertically in a vertical magnetic field.
the electroactive species and on the concentration gradient in the
electrochemical double layer. This paramagnetic gradient force
Figure 3. Cyclic voltammograms recorded in 0.01 M CoSO4
+ 0.1 M Na2SO4, pH 3, on flat embedded vertical Cu electrodes for different
magnetic flux densities; B is aligned upward, dE/dt = 20 mV/s, 3rd scan.
B2
F
= ␹
ٌ c
͓4͔
ٌp
2␮
0
was discussed by O’Brien and Santhanam,24,25 Waskaas and
Kharkats,26,27 and Bund et al.28 for different electrochemical sys-
tems and cell geometries. This gradient force has a short range and
thus acts only near the electrode. Besides that, the magnetic field
gradient force, caused by nonhomogeneous magnetic fields or in-
duced by ferromagnetic substrates, can sufficiently influence the
transport of paramagnetic or diamagnetic active species
susceptibility. For paramagnetic systems under unstable conditions
the average current density has been derived to
1/3
1/3
1/3
1
ץ␹
dB
4/3
i = 0.0969nFc D
͉⌬c͉
B
͓6͔
ͯ ͯ
ͩ ͪ ͩ ͪ
ͩ ͪ
ϱ
␮0D␩
ץc
dz
z=0
With increasing radius of the disk electrode the diffusion current is
increasingly determined by MHD convection, inducing a rotating
flow. Therefore, for systems with high gradients of concentration
and magnetic susceptibilities, respectively, and gradients of mag-
netic flux density, both phenomena, the magnetoconvection and the
MHD effect, overlap and have to be taken into account.
B ٌ B
F
= ␹
c
͓5͔
ٌB
␮
0
The parameter ␮0 is the magnetic permeability and ␹ is the magnetic
susceptibility of the elecroactive species. This force can be effective
in the whole volume as well as close to the electrode for ferromag-
netic substrates. White et al.29-32 investigated this magnetic gradient
force generated in nonhomogeneous fields on microelectrodes. The
magnitude of the different magnetically induced forces and the in-
fluence on the fluid motion were estimated by Hinds et al.33 Re-
cently, Sugiyama et al.34,35 have visualized and quantitatively exam-
ined that heterogeneous convection takes place on microdisk
electrodes in nonuniform vertical magnetic fields. It has been con-
cluded that the current density is controlled by magnetoconvection
and is proportional to the power of one third of the magnetic flux
density and its gradient as well as of the gradient of the magnetic
First, results are presented regarding the effect of uniform high
magnetic fields on the electrodeposition of Co in dependence on the
cell and electrode geometry, the orientation, and the strength of the
magnetic flux density. The change of ilim and of the current effi-
ciency as well as the effect of the magnetic field on the morphology
of the deposited Co films are discussed with respect to the different
magnetically induced forces and the thereby-generated macro- and
microconvections.
Experimental
The electrochemical investigations concerning the deposition of
Co were carried out in two different types of cylindrical cells with
different electrode geometries and electrode materials at 20°C. In
one case the working electrode ͑WE͒ was a Cu disk with an area of
1 cm2 embedded in epoxy resin ͑Fig. 1a͒. This electrode was placed
horizontally or vertically in a thermostated cylindrical glass cell
with an electrolyte volume of 200 mL described in detail in Ref. 23.
Before each experiment the electrode was mechanically ground with
emery paper grade 1000. In a second case the cell was a Teflon
cylinder with a volume of 50 mL ͑Fig. 1b͒. The electrodes were
slices cut from a Si wafer sputtered with a 100-nm Cu seedlayer for
the investigation of the deposited film morphology or quartz slices
with a Au layer for the electrochemical measurements. The area of
the electrode was 1.55 cm2. These electrodes were fixed with Viton
O-rings and horizontally placed in the magnet. This construction
leads to a wall around the electrode ͑wall electrode͒, which should
influence the convection close to the surface.
In both cells the potentials were measured vs a sulfate reference
electrode ͑SE͒ Hg/Hg2SO4/1 M H2SO4͑+674 mV/SHE͒. Pt sheets
were used as counter electrode ͑CE͒. The electrolyte was a 0.01 M
CoSO4 solution with addition of 0.1 M Na2SO4 as a supporting
electrolyte. The pH value was adjusted with H2SO4 to pH 3. Cyclic
voltammograms were recorded in the potential range between E =
Figure 2. Homogeneity of the magnetic flux density in dependence on the
distance z from the center of the magnet ͑Ref. 36͒; the diagonal pattern
shows the size of the Teflon cell ͑Fig. 1b͒.
−500 mV to − 1650 mV/SE with a scan rate of 20 mV s−1
.
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Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
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Figure 4. Cyclic voltammograms recorded in 0.01 M CoSO4
+ 0.1 M Na2SO4, pH 3, on flat embedded horizontal Cu electrodes for dif-
ferent magnetic flux densities; B is aligned ͑a͒ upward and ͑b͒ downward.
dE/dt = 20 mV/s, 3rd scan.
Figure 6. ͑a͒ Charge and ͑b͒ current efficiency in dependence on the mag-
netic flux density calculated from the deposition/dissolution measurements in
Fig. 5.
the Co deposition were calculated from these stripping experiments.
The electrochemical investigations were carried out without and
with superimposition of magnetic fields with a magnetic flux density
up to 13 T. The magnetic field was generated in a resistive bore
magnet of the Grenoble High Magnetic Field Laboratory ͑GHMFL͒
with a bore diameter of 130 mm and a high field homogeneity
shown in Fig. 2.36 The diagonal pattern indicates the distance of the
electrode in the Teflon cell from the center of the magnet and the
deviation in the magnetic flux density. For a magnetic field of 10 T
the gradient B͑dB/dz͒ in the small Teflon cell is Ͻ1.7 T2/m and
therefore, is stated to be uniform across the geometry of the Teflon
cell. The magnetic field gradient for the other cell amounts to maxi-
mum 20 T2/m for a magnetic flux density of 10 T. Besides the
measurements at constant magnetic flux densities, the magnetic field
was linearly increased with a rate of 10 mT/s. Different configura-
tions of the magnetic field to the electrode surface and thus to the
electric field have been investigated, which are always highlighted
in the figures. The morphology and roughness of the deposited Co
layers were analyzed by atomic force microscopy ͑AFM͒ and the
phase formation by X-ray diffraction ͑XRD͒ measurements.
From these scans the potential of E = −1460 mV/SE for deposi-
tion of Co and E = −450 mV/SE for dissolution of Co were selected
for chronoamperometric measurements. The partial charges of Co
deposition and hydrogen evolution as well as current efficiency for
Results
Cyclic voltammograms recorded in 0.01 M CoSO4 on flat em-
bedded horizontally and vertically aligned Cu electrodes with an
upward and downward oriented magnetic field are shown in Fig. 3
and 4.
Figure 5. Limiting current density for the Co deposition in dependence on
the magnetic flux density applied on the vertical flat embedded Cu electrode
at E = −1460 mV/SE.
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C820
Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
Figure 7. Limiting current density for the Co deposition at E = −1460 mV/SE in dependence on the magnetic flux density for two cell geometries and magnetic
field orientations, ͑a, b͒ flat embedded electrodes and ͑c, d͒ wall electrodes.
The figures show clearly the differences in the cyclic voltammo-
grams for the horizontally ͑Fig. 4͒ and vertically ͑Fig. 3͒ placed flat
embedded Cu electrodes. The maximum limiting current density in
dependence on the magnetic flux density is in the same order for
both electrode alignments, but the Co dissolution peak is explicitly
higher in the case of the vertically aligned electrode ͑Fig. 3͒, which
indicates that a higher amount of Co was previously deposited. Os-
cillations in the current density are observed for high magnetic
fields, especially in the case of the horizontally placed electrodes. It
is obvious for the vertical electrode that the cathodic peak maximum
shifts to more negative values with increasing magnetic field,
whereas for the horizontal electrodes this maximum is more or less
unaffected.
The effect of the magnetic field on the deposition behavior
is established by the results of the chronoamperometric experi-
ments shown in Fig. 5-7. The Co deposition potential of
E = −1460 mV/SE was chosen from the cyclic voltammograms.
From stripping experiments the total and partial charges as well
as the current efficiency with respect to the Co deposition were
calculated. The limiting current density ͑Fig. 5͒ and the charge and
current efficiency ͑Fig. 6a and b͒, respectively, reveal a strong in-
crease with increasing magnetic flux density up to 13 T for the
vertically aligned electrode and an upward oriented magnetic field.
As seen in Fig. 6a, both reactions—the Co deposition and the H-ion
reduction—increase in the same ratio. These results are in agree-
ment with the results derived from the dynamic measurements ͑Fig.
3͒.
or downward ͑b, d͒. For both geometries and field orientations the
current density increases with increasing magnetic flux density. The
change of the limiting current density is negligible for magnetic flux
densities up to 2 T and it is small up to 6 T for the wall electrode. At
high magnetic-flux densities a more pronounced increase occurs and
the current density shows fluctuations. In contrast to that are the
results obtained for flat embedded electrodes ͑a, b͒. The limiting
current density increases by about a factor 2.5 already at magnetic
flux densities of 2 T.
At high magnetic flux densities ͑Ͼ6 T͒ oscillations and no fur-
ther increase of the limiting current density are observed. The cur-
rent density oscillates with an amplitude of about 0.5 mA/cm2. This
behavior suggests that different magnetically induced driving forces
overlap and determine the convection.
The partial charges and current efficiencies calculated on the
basis of results shown in Fig. 7 are summarized in Fig. 8 and 9.
They reveal very clearly the effect of the geometry of the cell. Al-
together, the total charges ͑Co + H͒ as well as the partial charges for
Co and for hydrogen-ion reduction increase with increasing mag-
netic field, but for the flat embedded electrodes it is obvious that the
charge fraction of Co is always higher than the fraction of hydrogen.
The increase of the slope of the total charges as well as of the partial
charges is the highest for magnetic flux densities up to 4 T ͑Fig. 8a
and b͒ and reaches a plateau at higher magnetic flux densities. Es-
pecially for the case of the downward oriented magnetic field ͑Fig.
8b͒, the charges and the limiting current densities keep constant at
high magnetic flux densities. Besides that, the total charge and the
partial charges of Co and hydrogen are higher in the upward ori-
ented magnetic field than in the downward oriented magnetic field.
This is in agreement with the cyclic voltammograms illustrated in
Figure 7a-d summarizes the change of the limiting current den-
sity for the Co deposition for two cell geometries of a horizontal
placed electrode, i.e., the flat embedded electrode ͑a, b͒ and the
electrode with a wall ͑c, d͒. The magnetic field is oriented up ͑a, c͒
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Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
C821
Figure 8. Total charge and partial charges of the reduction of Co and hydrogen ions in dependence on the magnetic flux densities and the cell geometry: ͑a, b͒
flat electrodes; ͑c, d͒ wall electrodes ͑c-the electrode was not 100% horizontal͒.
Fig. 3a and b and Fig. 4. For this flat cell geometry a strong rise in
the current efficiency is observed from 0 to 2 T, but at high mag-
netic flux densities the current efficiency declines slightly ͑Fig. 8a
and b͒. At high magnetic flux densities the Co deposition seems to
be diminished at the expense of the hydrogen-ion reduction. This is
also more pronounced for the case of the downward oriented mag-
netic field. The field-dependent behavior of the charges and current
efficiencies is completely different for the wall electrodes shown in
Fig. 8c and d, and Fig. 9c and d. A remarkable increase of the
charges has not been observed below 2 T, but it strongly increases at
magnetic flux densities above 4 T. For this cell geometry the
hydrogen-ion reduction dominates the total reduction process, espe-
cially at high fields. The current efficiencies of Co decrease strongly
for the wall electrodes at high fields ͑Fig. 9a and b͒.
Figure 10 establishes the findings for the horizontally and verti-
cally placed flat electrodes during a continuous change of the mag-
netic flux density. For the vertically oriented electrode the limiting
current density increases continuously with the magnetic field,
whereas for the horizontal electrode the limiting current density ini-
tially decreases followed by a strong rise and some fluctuations oc-
cur.
͑Fig. 6a, 6b, 8c, and 9a͒. Magnetic fields oriented parallel to the
electrode surface yield layers with randomly distributed spherical
shaped grains ͑Fig. 11a-c͒. The shape of the grains and the rough-
ness of the layer is similar for magnetic flux densities of 2 and 6 T.
The morphology of the horizontal electrodes with the magnetic field
oriented perpendicular to the surface is different. The surface is
more rough with oval-formed grains ͑Fig. 11d-f͒. Figure 11e refers
to microconvection on the surface.
Interestingly, the XRD patterns in Fig. 12 taken from the depos-
ited Co layers of flat electrodes as well as the wall electrodes reveal
that the structure is not changed in high magnetic fields oriented
parallel or perpendicular to the surface as compared to low magnetic
fields discussed in Ref. 37 and 38. All Co layers show reflexes at the
same angle between the face-centered cubic ͑fcc͒ and hexagonal
close-packed ͑hcp͒ lattice structures of Co.
Discussion
The Co deposition from the 0.01 CoSO4 electrolyte at pH 3 is
always accompanied by the reduction of hydrogen ions. For the
chosen experimental conditions both reactions are mass controlled
in the potential range of −1200 to − 1500 mV/SE, as it has been
shown in earlier investigations.21-23 Therefore, in order to discuss
the results both reactions have to be considered.
The morphology of 50-nm-thick Co layers deposited by
potentiostatic polarization at E = −1450 mV/SE on Si sheets with a
100-nm Cu seedlayer was investigated by AFM ͑Fig. 11͒ for vertical
and horizontal wall electrodes and an upward-oriented magnetic
field with flux densities up to 6 T. The deposition time was calcu-
lated from the Co charge in consideration of the current efficiency
B parallel to the surface.— For the classical configuration, with
a magnetic field applied parallel to the electrode surface it is ex-
pected that both partial reactions should be affected by the field. As
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Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
in agreement with the result for the Cu deposition obtained in earlier
experiments under the same conditions.23 The threshold of about
2 N/m3 has to be exceeded to overcome the natural convection,
which induces a weak upward flow of the electrolyte to compensate
the depletion of ions. The vertical laminar natural convection is
overlapped by a horizontal tangential flow in the vicinity of the
surface. This flow is directed clockwise or counterclockwise de-
pending on the orientation of the magnetic field, i.e., if it is aligned
upward or downward. Figure 6a shows that both reactions, the Co2+
and the hydrogen-ion reduction, increase but the latter to a less
extent, and Fig. 6b reveals that the Co efficiency increases too. An
increasing hydrogen-ion reduction was also proved for magnetic
field of 1 T.37 It has been shown in Ref. 21 and 22 that in an
external field of 1 T the layers are more homogeneous and without
defects caused by hydrogen bubbles that are removed faster by the
forced convection. An additional convection might be expected due
to the take-off of hydrogen bubbles, which are formed during polar-
ization. However, this contribution should be negligible because the
partial charge after 60 s polarization is only between 20 and
50 mC/cm2. This corresponds to a hydrogen volume of 2–5 mm3,
which is formed on a area of 1 cm2 during a period of 60 s. A
significant convective contribution is improbable. Besides that the
threshold of the magnetic field for generating convection is the same
for the Co deposition and for the Cu deposition, during which no
hydrogen ions are reduced.23 As generally known, convection di-
minishes the diffusion layer thickness. Taking into account that the
diffusion coefficient is unaffected by an external magnetic field,1 the
diffusion layer thickness ␦ can be calculated by the relation ilim
= nFDcϱ/␦. The diffusion coefficient was determined to 8.8
ϫ 10−6 cm2/s by the Cottrell equation from the current–time tran-
sient recorded without magnetic field. The current efficiency is only
about 60% at B = 0 T and 70% at B = 13 T. Therefore, the calcu-
lated diffusion coefficient has to be regarded as a guiding value.
Literature data for metal ions are in the same order of magnitude,
i.e., about 10−5 cm2/s. The decrease of the diffusion layer thickness
in dependence on the magnetic field is shown in a double-log plot in
Fig. 13. The circles represent the data calculated from the potentio-
static measurements ͑Fig. 5͒, whereas the line is calculated from the
curve in Fig. 10 recorded with dB/dt = 10 mT/s. Both results are
consistent. At 2 T the diffusion layer is reduced to one half of the
original value at 0 T and is only about one quarter at 13 T.
Figure 9. Current efficiency for the Co deposition in dependence on the
magnetic flux densities and the cell geometry: ͑a͒ upward oriented magnetic
field and ͑b͒ downward oriented magnetic field.
The slope of the double-log plot ilim ͑Fig. 10͒ and ␦ ͑Fig. 13͒,
respectively, vs B is a useful tool to compare the results with pub-
lished data and especially to evaluate the generated convection. The
curves of the flat embedded vertical electrode are nearly linear after
exceeding the threshold of B. Therefore, they fit to the expected and
proved progression. The exponents for B and the diffusion layer are
1/3 and −1/3, respectively.7-11
has been shown in Fig. 3, 5, 6, and 10, the limiting current density
increases with the magnetic flux density, which is only due to the
Lorentz force and thus convection generated, but a significant rise
does not start before the magnetic flux density exceeds 250 mT ͑Fig.
10͒. This corresponds to a Lorentz force of nearly 2 N/m3, which is
Different considerations were made to describe the magnetic-
field-induced convection under hydrodynamic conditions.7,8,13,14
The mathematical analysis of the convective diffusion equation and
Navier–Stokes equation yielded the semiquantitative relations to de-
scribe the laminar or rotating flow of planar hydrodynamic elec-
trodes in general6 ͑see Eq. 1 and 2͒, but only some numerical simu-
lations are published to describe the concentration and velocity
gradient in the vicinity of the electrode superimposed with parallel
magnetic fields. These calculations are not transferable to other ex-
perimental setups. In order to estimate the laminar flow, the simpli-
fied approach of Eq. 1 was applied for the flat embedded disk elec-
trode. A Lorentz force of about 2 N/m2 is required to induce a
convection and to counteract the natural convection, as was dis-
cussed above and also in Ref. 23. From this threshold the velocity
increases continuously with increasing magnetic flux density and the
slope of the double-log plot corresponds to Bb with b = 0.74 ͑Fig.
14͒. Therefore, the slope is higher than the expected b = 2/3 and the
laminar flow is overestimated by this simple approach. One reason
is that for the estimation of the laminar flow the overall current
density was used. It has to be considered that the electrochemical
process consists of two reactions, the Co deposition and hydrogen-
Figure 10. Limiting current density for different cell and magnetic field
orientation recorded during continuous change of the magnetic flux density,
dB/dt = 10 mT/s.
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Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
C823
Figure 11. AFM images showing the morphology and roughness of 50-nm-thick Co layers deposited on Cu: ͑a–c͒ vertical electrode and ͑d–f͒ horizontal wall
electrode.
ion reduction, which contribute differently to the convection due to
the different diffusion coefficients, different concentrations, and dif-
ferent thicknesses of the diffusion layer. Therefore, overlapping con-
vective effects have to be taken into account, whereby the flux of the
Co ions should determine the resulting convection. Besides the lami-
nar convection, a rotating flow at the edge of the electrode due to the
electric field lines that are not parallel should have a small, but
additional influence. In summary, it has to be concluded that the
investigated system obeys the known and well-established theory of
MHD in magnetic fields with high magnetic flux densities up to
13 T aligned parallel to the electrode surface of flat embedded mac-
roscopic disk electrodes.
ing magnetic flux density. The maximum current density at 13 T is
comparable for both types of horizontal electrode and is only
slightly lower in comparison with that of the vertical electrode. Os-
cillations are observed for high flux densities, especially for the flat
electrodes. The main difference between the electrode types has
been detected in the current efficiency of the Co2+ reduction. It
increases for vertical flat electrodes ͑see above͒, remains constant or
increases only slightly for horizontal flat electrodes, and decreases
for the horizontal wall electrodes with increasing magnetic flux den-
sity, in upward as well as downward aligned magnetic fields ͑Fig. 9͒.
The same conclusions are drawn from the cyclic voltammograms.
The scans in Fig. 4 reveal that the onset potential of the decrease of
cathodic current density and the peak maximum are equal for all
magnetic flux densities for the horizontal flat electrode, whereas a
shift to more negative values is observed for the vertical electrode.
These findings are attributed to a preferred reduction of hydrogen
ions, which is confirmed by the smaller dissolution peak of Co.
Therefore, the results cannot be discussed only by MHD effects.
Other magnetically induced forces have to be taken into account to
understand the changed deposition behavior. In contrary to the in-
vestigations in Ref. 18-20 and 29-34, the magnetic field of the re-
sistive magnet in the GHMFL is very homogeneous. The field gra-
dient of the magnet itself in the small cell with the wall electrode is
negligible, as can be seen from Fig. 2. The same constant magnetic
field can be assumed for the large cell in front of the electrode.
Therefore, an effect of the magnetic field gradient force induced by
the magnet is improbable and is not discussed. During the deposi-
tion the formed Co layer is ferromagnetic and could contribute to an
additional field gradient in the close vicinity of the surface, but in
B perpendicular to the surface.— In general, convective effects
have been controversially discussed for the case of magnetic fields
oriented perpendicular to the electrode surface. Investigations on
microdisk electrodes have shown that the field gradient force can act
in the volume electrolyte as well as in the vicinity of the electrode
inside the electrochemical diffusion layer and induces microfluctua-
tions on the surface, thus moving paramagnetic/diamagnetic ions
toward or away from the surface.18-20,24,25,29-35 Recently, it has been
shown by us that different magnetically induced forces can induce a
convection also on macroscopic electrodes and influence deposition
behavior.21-23 The results of the cyclic voltammograms ͑Fig. 4͒, the
chronoamperometric measurements ͑Fig. 7͒, the calculated partial
charges for the two reactions ͑Fig. 8͒, and the current efficiency for
the Co deposition ͑Fig. 9͒ reveal that the magnetic field affects the
deposition behavior significantly and that the cell/electrode geom-
etry is an important factor. For both electrode geometries, i.e., the
flat disk electrode and the wall electrode, ilim increases with increas-
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Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
Figure 14. Lorentz force ͑FL͒ and estimated velocity of the induced laminar
flow ͑u͒ in dependence on the magnetic field of the vertical flat Cu disk
electrode, upward aligned B, dB/dt = 10 mT/s.
deposition of nonmagnetic Cu, as reported in Ref. 22. For a hori-
zontal electrode with the magnetic field perpendicular to the surface,
a rotating flow can be expected due to the nonparallel field lines at
the edge. The estimated rotating flow from Eq. 2 is shown in Fig. 15.
To simplify, it was assumed that the total current density and there-
fore the sum of the moved electroactive species contribute to the
rotational flow. The rotation for the flat electrode is fast at low fields
and merges in an apparently stable state with increasing magnetic
field. Because of the wall of the other electrode type and the more
parallel electric field lines, the rotational flow is negligible for low
fields but increases with increasing magnetic field and attains the
same value at 13 T as for the flat electrode. The assumption of a
stable rotation is not really true, as can be seen from the oscillating
behavior of ilim in Fig. 7. The mean circumferential velocity at the
edge of the electrodes is therefore lower than the laminar flow in
front of the vertical electrode. These results and the fact that the
current efficiency for the Co deposition decreases with increasing
magnetic flux density allow the prediction to be made that other
forces superimpose the behavior and act opposite.
It has been discussed that for the investigated electrochemical
system and the used experimental facility the field gradient force is
negligible. Suiyama et al.35 predict a convective diffusion layer with
a self-organizing process for adjusting the diffusion layer thickness
wherein magnetoconvection drives the electroactive species. Numer-
ous minute convection cells are formed due to the magnetic field
gradient and the gradient of concentration. Because the magnetic
field gradient is negligible in our case, only a driving force caused
by the gradient of the magnetic susceptibility can determine the
Figure 12. XRD pattern of 50-nm Co layers deposited on vertically placed
flat Cu electrodes, ͑a͒ Co ͑K␣͒ and horizontally placed wall electrodes, ͑b͒
Cu ͑K␣͒.
the high external magnetic fields the formed layer is in a single
domain state and a field gradient should be marginal. Besides that a
potential magnetic field gradient due to the magnetization of the
formed thin Co layer should lead to an increased Co deposition,
because the paramagnetic Co2+ ions should move in the direction of
the field gradient, which is always oriented in the direction of the
highest flux density ͑Eq. 4͒. The contribution of a magnetic field
gradient to the general electrochemical behavior seems to be negli-
gible, because the oscillation at high fields ͑Fig. 7a and b͒ and the
decrease of the current density as well as the decrease of the depos-
ited metal already at low fields ͑Fig. 10͒ were also observed for the
magnetoconvection. This paramagnetic gradient force F ͑Eq. 5͒ is
ٌp
aligned perpendicular to the surface due to the same direction of the
concentration gradient. The volume magnetic susceptibility ␹ of the
paramagnetic Co ion is 10−8 m3/mol, whereas the hydrogen ions are
nonmagnetic and anions and molecular hydrogen are diamagnetic
with a weak magnetic susceptibility. These species will not contrib-
ute to a remarkable weakening of the flow of electrolyte close to the
surface. Because the volume magnetic susceptibility of the Co ions
has a positive algebraic sign, the ions were moved away from the
electrode in the direction of the concentration gradient, that means
opposite to the driving force of the diffusion. Therefore, caused by
the magnetic properties of the Co ions, a paramagnetic gradient
force drives a convection inside the diffusion layer. The orientation
of the magnetic field should be irrelevant because the magnetic flux
density is B2 in the formula ͑Eq. 5͒.
Figure 13. Evolution of the diffusion layer thickness at the surface of a
vertical flat Cu disk electrode with an increasing upward aligned magnetic
field.
Derived from the relations discussed in Ref. 35, the convective
diffusion layer in uniform magnetic fields can calculated by
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Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
C825
Figure 17. Partial current densities of the Co ion reduction in dependence on
the magnetic field for various electrode geometries and orientations.
Figure 15. Estimated rotating flow ͑␻͒ in dependence on the magnetic field
of the horizontal flat electrodes and wall electrodes ͑Eq. 2͒. The dashed lines
are guides for the eyes.
from the electrode. For the wall electrode the partial current of Co
decreases slightly up to 1 T, as was discussed in Ref. 22, and in-
creases at higher magnetic flux densities with a slope of b = 0.78,
whereby the maximum partial current of the flat electrode is not
achieved. This slope is consistent with the deviation of Eq. 8,34
which claims a B2/3 dependency for magnetic and concentration
gradient forces
1/3
␦c = 10.32͑2␮0D␩/B2␹ ٌ c͒
͓7͔
Figure 16 shows the theoretical change of ␦c vs the magnetic field
without consideration of the rotational flow and the resultant para-
magnetic gradient force. Comparable to the parallel magnetic field
configuration, the thickness of the diffusion layer decreases and
reaches a similar value of about 50 ␮m ͑compare Fig. 13͒ at a
1/3
1/3
magnetic flux density of 13 T. Hence, the resulting force F is
ٌp
1
ץ␹
͉⌬c͉4/3B2/3
͓8͔
1.4 ϫ 106 N/m3. The curves of the current density for Co in Fig. 17
as well as the total and partial charges in Fig. 6 and 8 indicate no
difference between the partial current density of Co-ion reduction
for flat embedded vertical and horizontal electrodes. The result of
this might be that the convection is determined in principle by the
same origin, the MHD effect, caused by the laminar flow or the
rotating flow. This conclusion is supported by the slope of the
double-log plot in which b is 0.37 for the flat embedded electrodes
up to 6 T ͑Fig. 10 and 17͒. This laminar or rotating flow is driven by
a Lorentz force of maximum 150 N/m3. The expected convection in
dependence on the magnetic flux density is schematically drawn for
the two types of horizontal electrodes in Fig. 18. For low magnetic
flux densities, after exceeding a threshold the deposition is domi-
nated by the rotating convection due to the Lorentz force for the flat
electrodes. At higher magnetic fields, the Co deposition is sup-
pressed for this electrode type caused by the paramagnetic gradient
force that repulses the Co ions and the molecular hydrogen away
ͩ ͪ ͩ ͪ
i = 0.0969nFc D
ϱ
2␮0D␩
ץc
The current efficiency ͑Fig. 9͒ reveals a pronounced reduction of
hydrogen ions favored by the fast removal of the reduced hydrogen
molecules from the electrode surface. The rotation induced by the
total flow of the electroactive species dominates the electrochemical
behavior on the flat embedded electrode for magnetic flux densities
up to 6 T caused by the predominantly higher amount of nonparallel
electric field lines at the edge of the disk electrode, in comparison to
the alignment at the wall electrode. At high fields the Co deposition
is suppressed by the strong paramagnetic gradient force of about
106 N/m3. With decreasing diffusion layer thickness and increasing
concentration gradient, the probability for the influence of the para-
magnetic gradient force should be more dominant and more deter-
mined for the deposition behavior. The oscillations in the current
density reveal the effect of overlapping forces ͑Fig. 5͒. For the wall
electrodes the rotation is low at low magnetic flux densities. There-
fore this paramagnetic gradient force has a predominant effect al-
ready at low magnetic flux densities. Higher fields induce also at the
wall a rotational flow which counteracts the paramagnetic force. It is
discussed in Ref. 18-20, 34, and 35 that gradients of the magnetic
flux density and susceptibility together with charge fluctuations lead
to microconvections and vortexes directly at the surface. The AFM
investigations show clearly differences between the Co layers de-
posited on vertically and horizontally arranged electrodes. Whereas
for the vertical electrode the spherical shaped grains are randomly
distributed, the morphology of the deposits on the horizontal elec-
trode shows an inhomogeneous structure. An evolution of this mor-
phology can be due to the proposed magnetoconvection, but this is
only caused by the gradient of the concentration and volume mag-
netic susceptibility and not by the gradient of the magnetic flux
density. Differences in the morphology in the cross section of the
deposits were observed but not systematically investigated.
Conclusion
The effect of vertically oriented, uniform high magnetic fields on
the electrodeposition of Co has been investigated in dependence on
the cell and electrode geometry as well as the orientation and
Figure 16. Calculated change of the convective diffusion layer thickness ␦c
͑Ref. 35͒ and the paramagnetic gradient force Fp, respectively, vs the mag-
netic flux density.
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C826
Journal of The Electrochemical Society, 152 ͑12͒ C817-C826 ͑2005͒
shown that micro-magnetoconvection is not only bounded to mag-
netic field gradients but also to gradients of concentration and mag-
netic susceptibility, respectively.
Acknowledgment
The measurements were carried out in the Grenoble High Mag-
netic Field Laboratory. The German Research Council ͑DFG͒ is
gratefully acknowledged for support within the framework of the
SFB 609.
The Leibniz-Institute for Solid State and Materials Research assisted in
meeting the publication costs of this article.
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