Magnetoresistance controls of arborous bead-dendritic growth of magnetic electrodeposits: Experimental and theoretical results

Article abstract of DOI:10.1149/1.1776591

The effect of magnetic fields applied on magnetic metals electrodeposition was examined. Nickel deposits obtained from a Watt solution with coumarin, at cathodic potentials of -1000, -1200, and -1300mV/SCE, without and with, both, perpendicular and parallel oriented to the electrode surface low applied magnetic fields (up to 500 Oe) were examined by scanning electron microscopy (SEM) technique. At a potential of -1300 mV/SCE, a dramatic difference was observed between nickel morphologies obtained with a perpendicular oriented magnetic field (zero MHD effect) and those obtained in the absence of one. The nickel deposit obtained with perpendicular oriented magnetic fields was a very developed 3D arboreous-bead-dendritic structure. On the other hand, the nickel deposit obtained without the presence of magnetic field was very rough, with a clearly visible clustered structure. The obtained nickel morphologies are then compared with copper morphologies. Based on the fact that copper deposits obtained with and without a perpendicular oriented magnetic field were dendritic structures, the observed difference between nickel deposits with and those without a perpendicular oriented field, is essentially ascribed to the magnetoresistance effect on the magnetic deposits, which are nonexistent in nonmagnetic materials. We also have done experiments with iron deposits.

Full text of DOI:10.1149/1.1776591

Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
C577
0013-4651/2004/151͑9͒/C577/8/$7.00 © The Electrochemical Society, Inc.
Magnetoresistance Controls of Arborous Bead-Dendritic
Growth of Magnetic Electrodeposits
Experimental and Theoretical Results
a
N. D. Nikolic, Hai Wang,a Hao Cheng,a C. Guerrero,a E. V. Ponizovskaya,a
´
Genhua Pan,b and N. Garciaa,z
aLaboratorio de Fisica de Sistemas Pequenos y Nanotecnologia, Consejo Superior de Investigaciones
Cientificas (CSIC), E-28 006 Madrid, Spain
bCRIST, Department of Communication and Electronic Engineering, University of Plymouth, Plymouth,
Devon PL4 8AA, United Kingdom
The effect of magnetic fields applied on magnetic metals electrodeposition was examined. Nickel deposits obtained from a Watt
solution with coumarin, at cathodic potentials of Ϫ1000, Ϫ1200, and Ϫ1300 mV/SCE, without and with, both, perpendicular and
parallel oriented to the electrode surface low applied magnetic fields ͑up to 500 Oe͒ were examined by scanning electron
microscopy ͑SEM͒ technique. At a potential of Ϫ1300 mV/SCE, a dramatic difference was observed between nickel morphologies
obtained with a perpendicular oriented magnetic field ͑zero MHD effect͒ and those obtained in the absence of one. The nickel
deposit obtained with perpendicular oriented magnetic fields was a very developed 3D arboreous-bead-dendritic structure. On the
other hand, the nickel deposit obtained without the presence of magnetic field was very rough, with a clearly visible clustered
structure. The obtained nickel morphologies are then compared with copper morphologies. Based on the fact that copper deposits
obtained with and without a perpendicular oriented magnetic field were dendritic structures, the observed difference between
nickel deposits with and those without a perpendicular oriented field, is essentially ascribed to the magnetoresistance effect on the
magnetic deposits, which are nonexistent in nonmagnetic materials. We also have done experiments with iron deposits.
© 2004 The Electrochemical Society. ͓DOI: 10.1149/1.1776591͔ All rights reserved.
Manuscript submitted May 19, 2003; revised manuscript received January 6, 2004. This is in part Paper 642 presented at the Paris,
France, Meeting of the Society, April 27-May 2, 2003. Available electronically August 11, 2004.
The effect of an applied magnetic field on metal electrodeposi-
tion has been a subject of many investigations.1-8 It was shown that
an imposed magnetic field realizes various effects on electrolytic
processes and in particular on the morphology and structure of met-
als or alloys prepared by electrodeposition. Morphologies of elec-
trochemically obtained metal deposits are often strongly changed if
metal electrodeposition was performed in the presence of a magnetic
field. For example, a dense and compact deposit can be obtained in
the presence of a magnetic field instead of dendritic one obtained
without a magnetic field.8
changes on the growth are a priori expected.7 Then, the applied
magnetic field is parallel to the direction of the ion flux, what cor-
responds to J ϫ B ϭ 0.
Meanwhile, there are papers which report possible large effects
of magnetic field with perpendicular orientation to the electrode sur-
face on electrochemical process and morphology of a metal deposit
obtained by electrodeposition.7,9 This effect is ascribed to the
change of electrode size ͑i.e., change from a transition from planar
to radial diffusion as the electrode size is reduced͒.9 According to
Bodea et al.,7 if the deposit gets magnetized as with iron, then mag-
netic dipolar forces are induced, which should influence the growth.
The change of macroscopic morphology of iron electrodeposited
from an aqueous FeSO4 solution from a circular in a zero field to
rectangular in the presence of perpendicular oriented of a magnetic
field is associated with a minimization of the magnetic dipolar en-
ergy of the growing branches.7 Also, in this case, an arboreous-
needle-dendritic structure ͑ANDS͒ was grown. We have tried to re-
peat these experiments but have not been successful. We obtain
arboreous-bead-dendritic structures ͑ABDS͒ which are very differ-
ent of those in Ref. 7. While in this reference, the arboreous
branches were needle-like, in our experiments, the branches are
bead-like, i.e., consisting of aggregations of spherical clusters form-
ing branches like a rosary.
Changes in morphology of metal deposits were ascribed to the
Lorentz force.5 This force, F, exerted by an electromagnetic field B
on the ions of charge q moving at the velocity within an electric
v
field E can be presented by Eq. 11,5
F ϭ q E ϩ ϫ B͒
͓1͔
͑
v
During electrolysis, this force acts on the migration of ions and
induces convective flow of electrolyte close to the electrode surface.
This effect on the electrodeposition process is known as the magne-
tohydrodynamic ͑MHD͒ effect. The magnetohydrodynamic flow in
electrochemical systems is conveniently described by the force per
unit volume acting on the solution, FMHD ͑in N/m3͒, and which is
given by Eq. 2,9 where J ͑in C/m2͒ is the local flux of ions
In this work, the effect of the magnetic field on the electrodepo-
sition of nickel was examined. Nickel was electrodeposited from a
Watt solution in the presence of coumarin as the leveling addition
agent. Nickel deposits obtained without an imposed magnetic field,
as well as with, both, perpendicular and parallel oriented magnetic
fields were examined. Also, iron and copper deposits obtained from
corresponding sulfate solutions were examined. These metal depos-
its were examined by the technique of scanning electron microscopy
͑SEM͒. It is shown that it is possible obtain a large change of the
nickel morphology under an perpendicular-oriented magnetic field,
and the explanation is given in terms of the resistance of the
branched structure. Diffusion-limited aggregation ͑DLA͒ simulation
of dendritic growth is also presented.
F
MHD ϭ J ϫ B
͓2͔
The largest effect of this force, and consequently, the largest
effect on convective mass transport of the electrolyte, can be real-
ized when magnetic field B is applied parallel to the electrode sur-
face ͑i.e., an external magnetic field is oriented perpendicular to the
direction of the ion flux͒.9 This expectation is generally observed in
investigations that have been reported in the literature.10-14
On the other hand, when a magnetic field is applied perpendicu-
lar to the electrode surface, except through the effects associated
with gradients and the gravity-induced convection, no drastic
z E-mail: nicolas.garcia@fsp.csic.es
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

C578
Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
Figure 2. Schematic illustration of the electrochemical cell, the field direc-
tions, the ion velocity, , and the flux ions J.
v
electrode surface. The magnetic system used was model M-50
MMR Technologies, Inc. Nickel, iron and copper deposits were ex-
amined by scanning electron microscopy, SEM, model Philips SEM-
FEG-XL 30.
The electrochemical cell, including the field directions, the ion
Figure 1. ͑a͒ SEM microphotograph of the photolithographically patterned
thin-film microstructures with a micrometer gap that is closed to form a
nanocontact. ͑b͒ Schematic illustration of copper film sample and SEM mi-
crophotograph near-contact area.
velocity, , and the flux of ions, J, is illustrated in Fig. 2.
v
Results and Discussion
Nickel deposits obtained in the presence of coumarin, at a ca-
thodic potential of Ϫ1000 mV/SCE without and with parallel ori-
ented magnetic field are shown in Fig. 3a and b, respectively. It can
be seen from this figure that both surfaces were relatively smooth.
The nickel deposit obtained in the presence of a perpendicular ori-
ented magnetic field was very similar to these mentioned above, and
is not shown here. The fact that nickel surfaces obtained without and
with both perpendicular and parallel oriented magnetic fields were
very smooth and mutually similar can be ascribed to the good lev-
eling characteristics of coumarin as an inhibitor of the deposition
process in the electrocrystallization of nickel, and also to the fact
that the applied fields were moderately weak ͑at most 500 Oe͒. We
notice at this point that most of the effects due to magnetic fields,
observed and existing in the literature, are for fields values of the
order of 1000s of Oe and greater.
Figure 4 shows nickel surfaces obtained in the presence of cou-
marin at a cathodic potential of Ϫ1200 mV/SCE, correspondingly,
without an imposed magnetic field ͑Fig. 4a͒, with a perpendicular
oriented field ͑Fig. 4b͒, and with a parallel oriented ͑Fig. 4c͒ mag-
netic field. It can be observed from this figure that the nickel deposit
obtained in the presence of a perpendicular-oriented magnetic field
͑Fig. 4b͒ was very similar to the nickel deposit obtained without any
magnetic field applied ͑Fig. 4a͒. The latter nickel deposits were
coarser than that obtained under an applied magnetic field with par-
allel orientation ͑Fig. 4c͒.
Experimental
Working conditions.—Nickel was electrodeposited from the fol-
lowing solution: NiSO4•6 H2O, 262.5 g/L; NiCl2•6 H2O, 45 g/L;
H3BO3 , 37.5 g/L; and coumarin, 0.060 g/L, and pH 4.5.
Nickel was deposited potentiostatically, at room temperature, at
the following cathodic potentials: Ϫ1000 mV/SCE ͑with respect to a
saturated calomel reference electrode͒, Ϫ1200 and Ϫ1300 mV/SCE,
respectively. The counter electrode was pure nickel.
Iron was electrodeposited from 225 g/L FeSO4•7 H2O in 120 g/L
Na2SO4•10 H2O; pH 3; at cathodic potentials between Ϫ1 and Ϫ5
V/SCE, and at room temperature. The anode was pure platinum.
Copper was electrodeposited from 0.2 M CuSO4 in 0.5 M
H2SO4 , ͑pH 1.5͒, at room temperature, at the cathodic potential of
Ϫ500 mV/SCE. The counter electrode was pure copper.
The electrodepositions were performed in photolithographically
patterned thin-film microstructures with a micrometer gap that is
closed to form a nanocontact ͑Fig. 1a͒, in the T configuration of
wires that has been used previously to form nanocontacts to measure
15
ballistic magnetoresistance ͑BMR͒ or at special fabricated copper
films ͑Fig. 1b͒. The procedure for preparation of these copper films
was one of the traditional methods used to get printed circuit boards.
It consists of drawing on the virgin board ͑20 ␮m of copper depos-
ited in an epoxy resin͒ with a waterproof pen. Then, the board was
put in a solution of chloridic acid and sodic perborate. This solution
attacks the exposed parts ͑and does not attack the painted ones͒.
After all the copper has been removed from the exposed parts, we
take out the sample and wash it in water. The process is completed
by taking off the paint with alcohol. No matter what substrate or
electrode is used, in all cases the same structures are observed which
are reported below.
The obtained nickel morphologies can be explained through the
influence of magnetic fields on the nickel electrodeposition process
in the following way:
As mentioned earlier, the perpendicular orientation of a magnetic
field should have an insignificant effect on metal electrodeposition
processes, which is shown in our case as well. Nickel deposits ob-
tained without and with perpendicular oriented magnetic field were
very similar to each other ͑Fig. 4a and b, respectively͒. This result
was in accordance with Eq. 2, that when the applied magnetic field
is perpendicular to the electrode surface, then J ϫ B ϭ 0, and a
change in the structure of a metal deposit is not expected. On the
other hand, it is known that parallel orientations of a magnetic field
exhibit the largest effect on metal electrodeposition processes,
Equipment.—The deposition of nickel, iron, and copper was per-
formed using a bipotentiostat, model AFCBP 1, Pine Instruments
Company. The electrochemical cell was plunged into a uniform
magnetic field of 500 Oe, which was perpendicular or parallel to the
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
C579
2-butyne-1,4-diol.5 These structural characteristics can be ascribed
to the enhancement of the transport of the inhibitor toward the cath-
ode by MHD convection.5
We should mention that for Ϫ1000 and Ϫ1200 mV/SCE the
depicted current were 20 and 25 mA, respectively. When Ϫ1300
mV/SCE was applied, however, a large enhancement of the current
was observed, up to 40 mA without applied field, and up to 80 mA
with a 500 Oe perpendicular applied magnetic field. In all cases the
electrodeposition surface area was same. This is very important
since it already shows the strong influence of the magnetic field as
well as a strong nonlinearity in the I-U/SCE characteristics as indi-
cated in Fig. 6 for nickel electrodeposition. It is necessary to em-
phasize here that these I-U/SCE characteristics are not polarization
curves for the electrodeposition of nickel. We take for every applied
cathodic potential the current value at the end of electrodeposition,
i.e., at the moment when a nanocontact is formed, and then, we plot
the dependence of I-U/SCE. Based on this observation, we decided
to perform a more detailed study of the structure of the deposits at
the last cathodic potential.
Nickel deposits obtained at a cathodic potential of Ϫ1300 mV/
SCE are shown in Fig. 7a and b ͑without a magnetic field͒, and Fig.
7c and d ͑perpendicular orientation of the magnetic field͒, respec-
tively. The nickel deposit obtained in the absence of a magnetic field
was very rough, with a clearly visible clustered nickel structure ͑Fig.
7a͒. In addition, every nickel cluster consisted of very small clusters
of nanosized dimensions ͑Fig. 7b͒. On the other hand, the nickel
deposit obtained in the presence of a magnetic field showed a very
developed 3D arboreous-bead-dendritic structure ͑ABDS͒ ͑Fig. 7c͒.
The structure of this deposit consisted of thin nickel branches which
terminated in flower-like aggregates of nickel. The flower-like ag-
gregates of nickel consisted of thin nickel branches ͑or filaments͒
made of small nanosized nickel clusters ͑Fig. 7d͒, like a rosary. It is
noteworthy that these clusters of beads constituting the branches of
the structure were connected by nanocontact-size junctions ͑as illus-
trated in Fig. 7e͒, which may exhibit very strong magnetoresistance,
such as has been observed already in electrodeposited magnetic
nanocontacts.15-18
The large change in the morphology of nickel deposits, however,
is obtained for an orientation of the magnetic field for which the
expected MHD effect is zero (J ϫ B ϭ 0). At this cathodic poten-
tial, a magnetic field with a parallel orientation to the electrode
surface showed an effect on the nickel electrodeposition process that
was consistent with the predictions of MHD theory. The nickel de-
posit obtained in the presence of coumarin with a parallel-oriented
magnetic field is shown in Fig. 8, where we observe that this deposit
exhibited a more uniform structure than the nickel surface obtained
without the presence of magnetic field ͑Fig. 7a and b͒. In order to
establish whether having coumarin in the nickel plating bath con-
tributed to unexpected changes in nickel morphologies under a
perpendicular-oriented magnetic field, nickel deposits obtained from
a pure Watt solution were also examined. The obtained nickel de-
posits were very similar to ones obtained in the presence of cou-
marin. Hence, at this cathodic potential, the presence of coumarin in
the plating solution had no effect on the morphology of the nickel
deposits. The big change of the nickel morphology under a
perpendicular-oriented magnetic field is, therefore, unexpected; the
reason being that the energy introduced by the field in the medium is
only a paramagnetic term on the ions, SB, where S is the magnetic
moment of the ion. At room temperature, however, this effect is
completely negligible, as well as the possible gradient effect that has
been observed for applied fields much larger than 500 Oe.
Figure 3. Nickel deposits obtained at a cathodic potential of Ϫ1000 mV/
SCE from a Watt plating solution (NiSO4•6 H2O, 262.5 g/L; NiCl2•6 H2O,
45 g/L; H3BO3 , 37.5 g/L͒ with the addition of 0.060 g/L coumarin, ͑a͒
without and ͑b͒ with imposed magnetic field ͑parallel orientation to the elec-
trode surface͒ of 500 Oe.
shown also in this case. The nickel deposit obtained in the presence
of this magnetic field orientation had a more uniform structure than
nickel deposits obtained without and with a perpendicular oriented
magnetic field. This result was also in accordance with Eq. 2, so that
when the applied magnetic field is parallel to the electrode surface,
the product J ϫ B is at its maximum, and then the effect of the
magnetic field on the growth process is the largest. However, the
change of the orientation of the magnetic field from perpendicular to
parallel led to an expected change in nickel morphologies, i.e., it led
to a change that was consistent with the predictions of MHD
theory.5
At this cathodic potential, the hydrogen evolution was more vis-
ible than at a cathodic potential of Ϫ1000 mV/SCE. The effect of
hydrogen evolution on the morphology of a nickel deposit can be
clearly observed from Fig. 5, which shows a part of the nickel de-
posit obtained at a potential of Ϫ1200 mV/SCE with a parallel ori-
ented magnetic field. This part of the deposit consists of elliptical
rings, formed by the attachment of bubbles resulting from hydrogen
evolution and the effect of a parallel oriented magnetic field. Figure
5 also shows that the bubbles of hydrogen are deformed shapes, and
that this part of the nickel surface represents a depression on the
whole of that surface. A similar phenomenon is observed as well
Our explanation for the perpendicular field effects are based on
the ferromagnetic characteristics of nickel. At variance with nickel is
the case of a nonmagnetic material such as copper, where changes of
morphology with the application of perpendicular oriented magnetic
fields are not observed, as can be seen from the analysis of Fig. 9.
This figure shows copper deposits obtained without ͑Fig. 9a͒ and
with a perpendicular oriented magnetic field ͑Fig. 9b͒. It can be
observed that both Cu deposits showed a developed ABDS structure,
during
nickel
electrodeposition
in
the
presence
of
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

C580
Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
Figure 4. Nickel deposits obtained at a cathodic potential of Ϫ1200 mV/
SCE from a Watt plating solution (NiSO4•6 H2O, 262.5 g/L; NiCl2•6 H2O,
45 g/L; H3BO3 , 37.5 g/L͒ with addition of coumarin, 0.060 g/L: ͑a͒ without
magnetic field, and with an imposed magnetic field of 500 Oe; ͑b͒ perpen-
dicular, and ͑c͒ parallel orientation to the electrode surface.
and were very similar to each other. As expected in this case, the
magnetic field with a perpendicular orientation exhibited an insig-
nificant influence on the morphology of the Cu deposit.
Therefore, when the perpendicular field is applied, the resistance
of the filamentary deposits should change due to the magnetoresis-
tance of the nanocontacts that make up the filaments ͑Fig. 7d and e͒,
due to removal of domain walls. This resistance changes with ap-
Figure 5. The nickel deposit obtained at a cathodic potential of Ϫ1200
mV/SCE from
a
Watt plating solution (NiSO4•6 H2O, 262.5 g/L;
Figure 6. I-U/SCE characteristics for electrodeposition of nickel in the
presence of coumarin, and iron. For every cathodic potential we take the
value of the current at the end of electrodeposition, i.e., at the moment when
a nanocontact is formed.
NiCl2•6 H2O, 45 g/L; H3BO3 , 37.5 g/L͒ with the addition of coumarin,
0.060 g/L, with the imposed magnetic field ͑parallel orientation to the elec-
trode surface͒ of 500 Oe.
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
C581
Figure 9. Copper deposits obtained at a cathodic potential of Ϫ500 mV/
SCE from the sulfate solution ͑0.2 M CuSO4 in 0.5 M H2SO4): ͑a͒ without
and ͑b͒ with a perpendicular-oriented magnetic field of 500 Oe.
netic domain walls that exist at zero or low-field values. At 500 Oe
field the domain walls will be removed, and the resistance lowered
up to a factor of 10.
In order to grow branched structures, it is necessary for the ef-
fective potential at the end of these branches to be the same as the
applied one. However, if the branches are very resistive, this poten-
tial will be reduced to one smaller than that needed for electrodepo-
sition of Ni. In the case of magnetic deposits, with or without an
applied field, the effective potential at the end of the wires or fila-
ments will be
Ueff ϭ U Ϫ IR B ϭ 0,l͒
͓3͔
͑
c
for zero field, and
Figure 7. Nickel deposits obtained at a cathodic potential of Ϫ1300 mV/
SCE from Watt plating solution (NiSO4•6 H2O, 262.5 g/L; NiCl2•6 H2O, 45
g/L; H3BO3 , 37.5 g/L͒ with addition of coumarin, 0.060 g/L: ͑a͒ and ͑b͒
without, ͑c͒ and ͑d͒ with imposed magnetic field ͑perpendicular orientation
to the electrode surface͒ of 500 Oe, ͑e͒ schematic illustration of the part of a
surface from Fig. 7d with clearly denoted place of nanocontact.
Ueff ϭ U Ϫ IR B ϭ B ,l͒
͓4͔
͑
c
0
for a field B ϭ B0 , where Ueff and Uc are the effective and the
applied cathodic potentials, respectively, I is the current of deposi-
tion, and R the resistance of the filament l under a field or field-free,
and is field-dependent in the case of magnetic materials. In other
words, these materials are magnetoresistive. This resistance for
magnetic materials may be very different without or with applied
plied fields in magnetic nanocontacts, and it has been observed with
values up to ten times less than those without field.15-17
Figure 10 shows a schematic illustration of nickel deposits ob-
tained at a cathodic potential of Ϫ1300 mV/SCE, without ͑Fig. 10a͒
and with a perpendicular-oriented magnetic field of 500 Oe ͑Fig.
10b͒. The deposit consists of microwires or filaments of length l.
The short lines within the branches ͑Fig. 10b͒ are indicative of mag-
Figure 8. The nickel deposit obtained at a cathodic potential of Ϫ1300
mV/SCE from
a
Watt plating solution (NiSO4•6 H2O, 262.5 g/L;
NiCl2•6 H2O, 45 g/L; H3BO3 , 37.5 g/L͒ with the addition of coumarin,
0.060 g/L, with the imposed magnetic field ͑parallel orientation to the elec-
trode surface͒ of 500 Oe.
Figure 10. Schematic illustration of different nickel deposits obtained at
Ϫ1300 mV/SCE; ͑a͒ without and ͑b͒ with a perpendicular-oriented magnetic
field.
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

C582
Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
magnetic fields. In fact, it was shown that when nanocontacts are
formed, the differences due to domain wall scattering when no field
is applied, can be up to factors of 10.15-17
In the absence of a magnetic field, the resistance of nickel fila-
ments is too large and the effective potential on their ends is much
smaller than that needed for their further growth and branches, i.e.,
for the electrodeposition of a very developed ABDS structure. That
is why a rough nickel structure is formed, with very large nickel
clusters, consisting of small nanosized nickel clusters. In the pres-
ence of a sufficiently large magnetic field ͑500 Oe, fields smaller
than 300 Oe have a much smaller effect͒, the resistance of these
filaments is much smaller, because the domain walls are erased and
the effective potential at the end of the branches is large enough for
the electrodeposition of an ABDS structure.
The effect of the resistance creating a potential drop is enhanced
by the nonlinear behavior of the current, which increases abruptly
when the potential is Ϫ1300 mV/SCE ͑Fig. 6͒. This causes the
potential drop at the filaments (Ud ϭ IR) to be much larger due to
the increase of current. As mentioned earlier, during nickel elec-
trodeposition in the absence of a magnetic field the current response
was up to 40.0 mA, while during nickel electrodeposition in the
presence of a magnetic field the current response was up to 80.0
mA. On the other hand, current responses during nickel electrodepo-
sition at cathodic potentials of Ϫ1000 and Ϫ1200 mV/SCE ͑20.0
and 25.0 mA, respectively͒, without and with a perpendicular-
oriented magnetic field were the same, as expected. This is because
compact electrodeposits are formed at these potentials, and not ones
with a filament formation.
The case of Ni is specially interesting because of the following:
͑i͒ the minimum potential for deposition of Ni is Um Ϸ Ϫ700 mV/
SCE, (ii) the critical potential for the drastic increase of the current
is Ucrit Ϸ Ϫ1300 mV/SCE, therefore, (iii) a 600 mV drop in po-
tential due to resistance of the filaments is enough to stop the fila-
mentary growth of Ni, while the application of the magnetic field
can change this potential due to magnetoresistance.
As a possible cause for this unexpected change in the nickel
morphology, it is also necessary to take into account the fact that at
this potential the evolution of hydrogen was very intense. However,
it can be assumed that the electrodeposition of a very developed 3D
ABDS structure of nickel is a consequence of a complex phenom-
enon caused by the effect of magnetic field and the hydrogen evo-
lution. Having to view the values of currents during nickel elec-
trodepositions at the examened cathodic potentials, as well as the
obtained nickel morphologies, it can also be said that the growth of
this structure is controlled by convective phenomenon caused by the
magnetic field and diffusion one.
Figure 11. ͑a͒, ͑b͒ The iron deposit obtained at cathodic potential of Ϫ4
V/SCE from 225 g/L FeSO4•7 H2O in 120 g/L Na2SO4•10 H2O, with
perpendicular-orientated magnetic field of 500 Oe.
branches are more needle-like, the direction of the branches does not
depend on the direction of the applied magnetic field. In our case,
however, the branches grow in all directions. Perhaps the differences
are due to the shape and configuration of the electrolytic cell. In any
case, we do not understand why the dipolar interaction should result
in a preferential orientation of the growth with respect to the direc-
tion of the field. Our experiments shown in Fig. 7 and 11, further-
more indicate that Ni and Fe branches grow in all directions.
To simulate our experiments, we argue that the obtained ABDS
structure represents a phenomenon known as laplacian growth in the
far from equilibrium limit, such as the case when nickel is electrode-
posited at Ϫ1300 mV/SCE ͑Fig. 7͒. In this scenario, the diffusion-
limited aggregation ͑DLA͒ model19 can be applied ͑see Ref. 20,
Chap. 10, for illustrative exposition͒, and it is a characteristic of
many phenomena, not just in electrochemistry,21 but also regarding
crystallization and viscous fingering,22 cracks,23 etc.
Shannon et al.4 also showed that for a small applied magnetic
field value, a change of nickel morphology is possible with both
parallel and perpendicular oriented magnetic fields. This change is
ascribed to the existence of a metastable hydrodynamic condition in
the plating solution. This metastable condition is subjected to local
disturbances via the applied magnetic fields and gas evolution. The
magnetic field, in addition to acting on the paramagnetic Ni ions,
influences the flow dynamics and stability of the evolved gas
bubbles.4
This behavior of Ni is at variance with that of the Fe electrode-
posits because, in the case of Fe, there is no drastic increase of the
current ͑Fig. 6͒ at investigated cathodic potentials between Ϫ1000
and Ϫ5000 mV/SCE. At all investigated potentials, an ABDS struc-
ture appeared. Figure 11 shows the iron deposit obtained in the
presence of a perpendicular-oriented magnetic field. From this figure
we can easily observe the very developed ABDS structure of iron.
However, the removal of the magnetic field does not change the
structure. The reason is that, in the case of iron, there is no drastic
increase of the electrodeposition current, that is to say, the ohmic
drop is not enough to stop the electrodeposition of the ABDS struc-
ture of iron. At this point, we should say that we have tried to
reproduce the data of Ref. 7 without success, even when the pH of
our solution is practically the same as in Ref. 7 ͑pH 3͒. Although the
DLA Simulations with Resistive Ferromagnetic Wires
We use the two-dimensional diffusion-limited aggregation model
19,21
͑DLA͒
in our simulation. The growth rule in the model is as
follows. We start with an immobile seed at a certain point or on the
surface. A particle ͑walker͒ is then launched from a random position
far away and is allowed to diffuse. If it touches the seed, it is im-
mobilized instantly and becomes part of the aggregate. We launch
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
C583
Figure 13. The result of the simulation of a cluster growth on the point
seed with k1 ϭ 1 ͑a͒ and k1 ϭ 5 ͑b͒, k3 ϭ 0, with potential reducing in
the vicinity of long branches; the same on the surface for k1 ϭ 1 ͑c͒ and
k1 ϭ 5 ͑d͒.
When we take ⌬V into account, the direction with the greatest
probability will shift clockwise from the direction toward the aggre-
gation center. Finally, we simulated the resistive ferromagnetic
wires. In this case, the potential will not be uniform, but will be
reduced in the vicinity of the long branches of the growing structure.
We assume that the probability of the particle to maintain a velocity
toward the long branch is reduced by k3l/r, where l is the length of
the branch, r is the radius of launching, and k3 is a coefficient that
represents the material properties. The longer the branch the higher
is the reduction of the potential. Therefore, it is the potential-
reducing effect that results in the more compact clusters. In the Fig.
13a and b, the cluster structures for k1 ϭ 1 and 5 are shown then the
effect is taken into account. We attain the same result for growth on
the surface ͑Fig. 13c and d͒, where the structures are more compact
and the clusters have a smoother surface compared to the structures
in Fig. 12 with the same parameter k1 .
The calculations of the magnetic field parallel to the surface and
perpendicular to the plane of growth are shown in Fig. 14. The
resulting structures for the parameter k2 ϭ 0.83 are shown for
growth at the center point. The branches of the structure are curved
clockwise, and the structures are rougher and less dense. Figure 14a
shows the result for k1 ϭ 1 and Fig. 14b for k1 ϭ 5, while the
potential reducing effect was also taken into account. The same
calculation was performed for the plane surface. The branches de-
cline to the left, and the cluster structures become rougher and less
Figure 12. The result of simulation of a cluster growth on the point center of
aggregation ͑a͒ and on the surface ͑b͒ with k1 ϭ 0, k3 ϭ 0, without potential
reducing in the vicinity of long branches; the same for k1 ϭ 1 on the point
seed ͑c͒ and on the surface ͑d͒; the same for k1 ϭ 5 on the point seed ͑e͒ and
on the surface ͑f͒.
similar particle-walkers one-by-one and each of them stops upon
hitting the cluster or walks away and disappears if it goes beyond a
certain distance. After launching a few hundred particles, a cluster
with intricate branch structures results as shown, correspondingly, in
Fig. 12a and b, for the growth on a surface.
However, to simulate the process of electrodeposition we had
to modify the DLA model. In electrodeposition the particles have
a velocity towards the aggregation surface or center due to
the cathodic potential applied. We introduced the parameter
k1 ϭ ͉Vp͉/͉Vd͉ that represents the ratio between the modulus of ve-
locity towards the aggregation center Vp and the modulus of the
random diffusion velocity Vd . For each step we assumed that the
velocity of the particle was the sum of the two velocities Vp and Vd ,
which increased the probability of the particle maintaining a veloc-
ity towards the center of the aggregation. The arrows in Fig. 12a and
b show the direction of Vp . The calculations have been done for
k1 ϭ 1 and 5, Fig. 12c and d, respectively, for the growth around a
center and Fig. 12e and f for the growth on the surface.
In addition, we simulated the influence of the magnetic field
applied in the direction perpendicular the plane of growth and par-
allel to the surface of aggregation. In this case, the particles have
an acceleration proportional to a product of the velocity vector of
V the particle and the vector of the magnetic field B, directed per-
pendicular to the vectors V and B. Thus, in each step of the simu-
lation, we have the additional increment of the velocity ⌬V whose
dense with the increasing of the product modulus
͉
VÃB
͉
or k1•k3 in
the simulations. For big enough values of k1•k3 we have the sepa-
rate long branches.
Figure 15 shows the different kinds of structures resulting with
different values of k1 and k3 , without taking into account the
potential-reducing effect in the vicinity of the long branches. Our
calculations show that if the potential-reducing effect is less due to
the magnetic field toward the aggregation surface, the structure is
less compact and has long branches as it shown in Fig. 12f. At this
point it should be mentioned that simulations made taking into ac-
count the drop of potential due to the resistance of the wires may be
comparable to another proposal24 based on the idea of screening. If
there is a perfect screening of the potential, one should have a com-
pact structure since that implies that the cathodic potential drops at
the surface of the deposits. If, however, screening is not complete
and the electric field penetrates and drops inside the deposits, then
this points to an Ueff that is reduced from the Uc due to de potential
drop in the deposits. One then obtains similar results to those ex-
pressed in Eq. 3 and shown in our simulations. There is a problem in
this treatment, and this is that the effect should be independent of the
modulus is proportional to
lation represents the value of the magnetic field B. We assumed
⌬V ϭ k2 , where k2 is proportional to the magnetic field, and V
͉VÃB͉. The other parameter of the simu-
͉
͉
͉V͉
is the modulus of the velocity of the particle, as well as being the
sum of the vectors Vp and Vd .
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).

C584
Journal of The Electrochemical Society, 151 ͑9͒ C577-C584 ͑2004͒
At a cathodic potential of Ϫ1000 mV/SCE, there was no differ-
ence between nickel deposits obtained without and with a parallel-
oriented magnetic field. Both surfaces were relatively smooth, which
is ascribed to the good leveling characteristics of coumarin.
At a cathodic potential of Ϫ1200 mV/SCE, the nickel deposit
obtained with a parallel-oriented magnetic field had a more uniform
structure than that obtained without and with a perpendicular-
oriented magnetic field. The obtained result was in accordance with
predictions of MHD theory.
At a cathodic potential of Ϫ1300 mV/SCE, a great change in the
morphology of the nickel deposit is obtained for an orientation of
the magnetic field for which the expected MHD effect is zero. Fur-
thermore, at this potential a large enhancement of the deposition
current takes places that plays an important role in the developed
structure. The nickel deposit obtained in the presence of a
perpendicular-oriented magnetic field was a very developed 3D
ABDS structure, with thin branches made of beads or clusters as in
a rosary. On the other hand, the nickel deposit obtained without the
presence of a magnetic field was a very rough and clustered struc-
ture. Based on the fact that copper ͑paramagnetic͒ deposits always
exhibited a dendritic structure, we essentially ascribed the difference
in morphologies of these nickel deposits to the influence of the
magnetic field on magnetic properties of nickel. The explanation is
given in terms of the resistance of the branched structure ͑i.e., fila-
ments of deposits͒ due to magnetic domain wall scattering. Finally,
for Fe at Ϫ4000 mV/SCE, we have obtained ABDS structures, but
the branches of this deposit are oriented in all directions and are not
much affected by the direction of the applied field.
Figure 14. The result of the simulation of a cluster growth on the point
seed with k1 ϭ 1 ͑a͒ and k1 ϭ 5 ͑b͒, k3 ϭ 0.83, with potential reducing in
the vicinity of long branches; the same on the surface for k1 ϭ 1 ͑c͒ and
k1 ϭ 5 ͑d͒.
Acknowledgments
applied magnetic field. The reason is that the screening is due just to
the metallic character or not of the deposits. In our experiments the
applied magnetic field clearly plays a role.
This work has been supported by the Spanish DGICyT.
References
1. J. A. Shercliff, A Textbook of Magnetohydrodynamics, Pergamon Press, Oxford
͑1965͒.
Conclusions
2. R. Aogaki, J. Electrochem. Soc., 142, 2954 ͑1995͒; K. Shinohara and R. Aogaki,
Electrochemistry (Tokyo, Jpn.), 67, 126 ͑1999͒; R. Aogaki, A. Tadano, and K.
Shinohara, Transfer Phenomena in Magnetohydrodynamic and Electroconducting
Flows, A. Alemany, Ph. Marty, and J. P. Thibault, Editors, p. 169, Kluwer, Neth-
erlands ͑1999͒; R. Aogaki and M. Asanuma, Paper presented at 1st International
Symposium on New Magneto-Science, Omiya, Japan ͑1999͒.
3. I. Mogy, M. Kamiko, S. Okubo, and G. Kido, Physica B, 201, 606 ͑1994͒.
4. J. C. Shannon, Z. H. Gu, and T. Z. Fahidy, J. Electrochem. Soc., 144, L314 ͑1997͒.
5. O. Devos, A. Olivier, J. P. Chopart, O. Aaboubi, and G. Maurin, J. Electrochem.
Soc., 145, 401 ͑1998͒.
The effect of a magnetic field, with both perpendicular and par-
allel orientation, on the morphology of nickel deposits from a Watt
solution in the presence of coumarin was examined.
6. O. Devos, O. Aaboubi, J. P. Chopart, E. Merienne, A. Olivier, and J. Amblard, J.
Electrochem. Soc., 145, 4135 ͑1998͒.
7. S. Bodea, L. Vignon, R. Ballou, and P. Molho, Phys. Rev. Lett., 83, 2612 ͑1999͒.
8. I. Mogy, M. Kamiko, and S. Okubo, Physica B, 211, 319 ͑1995͒.
9. K. M. Grant, J. W. Hemmert, and H. S. White, J. Electroanal. Chem., 500, 95
͑2001͒.
10. N. Leventis, M. Chen, X. Gao, M. Canalas, and P. Zhang, J. Phys. Chem. B, 102,
3512 ͑1998͒.
11. M. Waskaas and I. K. Yurij, J. Phys. Chem. B, 103, 4876 ͑1999͒.
12. A. Oliver, J. P. Chopart, and J. Douglade, J. Electroanal. Chem., 217, 443 ͑1987͒.
13. O. Aaboubi, J. P. Chopart, J. Douglade, A. Oliver, C. Gabrielli, and B. Tribollet, J.
Electrochem. Soc., 137, 1796 ͑1990͒.
14. T. Z. Fahidy, Chem. Eng. J., 7, 21 ͑1974͒.
´
˜
15. N. Garcıa, M. Munoz, G. G. Qian, H. Rohrer, I. G. Saveliev, and Y.-W. Zhao, Appl.
Phys. Lett., 79, 4550 ͑2001͒.
16. G. G. Cabrera and L. M. Falicov, Phys. Status Solidi B, 61, 539 ͑1974͒; G. Tatara,
˜
´
Y.-W. Zhao, M. Munoz, and N. Garcıa, Phys. Rev. Lett., 83, 2030 ͑1999͒.
˜
17. N. Garcia, M. Munoz, and Y.-W. Zhao, Phys. Rev. Lett., 82, 2923 ͑1999͒; S. H.
˜
´
Chung, M. Munoz, N. Garcıa, W. F. Egelhoff, and R. D. Gomez, Phys. Rev. Lett.,
89, 287203 ͑2002͒.
18. H. D. Chopra and S. Z. Hua, Phys. Rev. B, 66, 020403 ͑2002͒.
19. T. A. Witten and L. M. Sander, Phys. Rev. Lett., 47, 1400 ͑1981͒.
20. T. Vicsek, Fractal Growth Phenomena, Chap. 10, 2nd, ed., World Scientific, River
Edge, NJ ͑1992͒.
21. D. Grier, E. Ben-Jacob, R. Clarke, and L. M. Sander, Phys. Rev. Lett., 56, 1264
͑1986͒.
22. E. Ben-Jacob, R. Godbey, N. Goldenfeld, J. Koplik, H. Levine, T. Mueller, and L.
M. Sander, Phys. Rev. Lett., 55, 1315 ͑1985͒; E. Ben-Jacob, G. Deutscher, P. Garik,
N. D. Goldenfeld, and Y. Lareah, Phys. Rev. Lett., 57, 1903 ͑1986͒.
23. E. Louis and F. Guinea, Europhys. Lett., 3, 871 ͑1987͒.
24. E. Louis, F. Guinea, and L. M. Sander, Phys. Rev. Lett., 68, 209 ͑1992͒.
Figure 15. The result of the simulation of a cluster growth on the surface
without potential reducing in the vicinity of long branches with k1 ϭ 5 and
k3 ϭ 1.1 ͑a͒, 1.5 ͑b͒, 2.0 ͑c͒, and k1 ϭ 1 and k3 ϭ 2.0 ͑d͒, 10 ͑e͒, 20 ͑f͒.
Downloaded on 2015-06-20 to IP 134.117.10.200 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).