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Electrochimica Acta 54 (2009) 5813–5817

Contents lists available at ScienceDirect

Electrochimica Acta

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inetics of Cu2O electrocrystallization under magnetic fields

nne-Lise Daltin ∗, Frédéric Bohr, Jean-Paul ChopartACM-DTI, LRC CEA, Université de Reims, Moulin de la Housse, B.P. 1039, 51687 Reims Cedex 02, France

r t i c l e i n f o

rticle history:eceived 2 February 2009eceived in revised form 17 April 2009ccepted 9 May 2009vailable online 19 May 2009

a b s t r a c t

The magnetic field effects on cuprous oxide cathodic electrodeposition from alkaline cupric lactate solu-tion have been investigated at 70 ◦C by electrochemical and physical techniques.

Stationary analyses exhibit a tenuous decrease of the plateau electrolytic current as the magnetic fieldincreases. Due to the limited diffusion process of the hydroxide species which reacts during the electro-

eywords:uprous oxidelectronucleationagnetoelectrochemistryHD

chemical process, a magnetically induced effect can be suspected but deposition of Cu2O that covers theelectrode and “passivates” the surface leads to antagonist effects that explain the current decrease.

For a cathodic applied potential corresponding to the current plateau, X-ray diffraction studies revealthe formation of single phase cubic Cu2O films with or without magnetic field, but a change in elec-trocrystallization kinetics of Cu2O is observed in the presence of the magnetic field. Analyses of thetransient current curves reveal a convective effect of the magnetic field from the very first moments of

.

ransient current the electrocrystallization

. Introduction

Cuprous oxide thin films are non-toxic and suitable for numer-us applications such as photovoltaic tools and are used inonversion of optical, electrical and chemical energy [1–9]. Cu2O islso used as a photocatalyst for overall water splitting under lightrradiation [10].

The grain size of thin cuprous oxide films is a key to improveolar application devices [11] and Cu2O electrical properties dependtrongly on the preparation conditions [12], therefore many exper-mental works have dealt with Cu2O film synthesis by numerous

ethods such as chemical deposition, sol–gel, sputtering, acti-ated reactive evaporation, and thermal oxidation [4–6,9,13 and refherein].

Deposition of cuprous oxide by electrochemical technique fromqueous solutions has attracted much research interest because its an inexpensive and convenient method [12,14–16].

Pure Cu2O films can be obtained in potentiostatic mode byathodic reduction of alkaline cupric lactate solution. Severaluthors have reported electrodeposition of Cu2O on copper and tinxide [17], gold [18] and stainless steel [19] substrates and its char-cterization. Some thin films have been obtained with the same

lectrolytic bath that Mahalingam et al. [17] used. In this last case,t must be noticed that potential oscillations occur in galvanos-atic mode. This effect originates from modulations of the pH inhe vicinity of the working electrode. These oscillations led to elec-

∗ Corresponding author. Tel.: +33 3 26 91 84 77; fax: +33 3 26 91 89 15.E-mail address: al.daltin@univ-reims.fr (A.-L. Daltin).

013-4686/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2009.05.036

© 2009 Elsevier Ltd. All rights reserved.

trodeposition of copper and cuprous oxide multilayers instead ofpure Cu2O film [20].

Due to the importance of the very first electrodepositionmoments on material properties, we have undertaken experimen-tal investigations on the cuprous oxide electronucleation process.

Directly related to the problem of nucleation and crystal growth,electrochemical deposition process and more specially electrocrys-tallization have attracted much interest. The study of nucleation viapotentiostatic current transient modelling is a convenient methodto explore these processes and has been extensively used to ana-lyze metal deposition current transient curves. Large reviews onthis topic have been made by Budevski et al. [21] and more recentlyby Hyde and Compton [22]. In this last paper, multiple nucleationswith diffusion controlled growth have been analyzed and differentmodels were reported for the current-time transients showing amaximum followed by an exponential decay.

A classical treatment of the experimental data that leads tonumerous models [23–26] considers that the nuclei are formedaccording to the equation:

dN

dt= AN0e(−At) or N = N0(1 − e−At) (1)

where t is the time since the overpotential is applied to the elec-trode, N is the number of nuclei, N0 is the saturation nucleus density(i.e. the number of active sites) and A is the nucleation rate con-

stant. To treat the overlap of diffusion zones, authors generally applythe Avrami’s theorem that considers collisions and overlaps of thegrowing centres in a process of multiple nucleations and growth.

According to this school, the Scharifker and Hills’ model [27]in which two limiting nucleation mechanisms instantaneous

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shape of a nucleation process. After a rapid decay correspond-ing to the double-layer charging, the current increased due to thenucleation and growth of copper oxide nuclei. This rising currentreached quickly a maximum value (Im) as the discrete diffusionzones for each growing crystallites began to overlap at time tm.

814 A.-L. Daltin et al. / Electroch

nd progressive are described is commonly used to discriminateucleation kinetics:

An instantaneous nucleation corresponds to a slow growth ofnuclei with a quite small number of active sites appearing at thesame moment. In this case, nuclei are born before being affectedby the spreading of nucleation exclusion zones.During a progressive nucleation, corresponding to a fast growthof nuclei on many active sites which are progressively born, thebreak in nucleation process is dominated by spreading of nucle-ation exclusion zones.

For these two limiting cases, it is possible to express the ratio ofhe total current I per the maximum current Im versus the ratio ofhe time t per the time tm corresponding to Im.

For an instantaneous nucleation, the theoretical reduced curvebeys the relationship:

I2

I2m

= 1.9542t/tm

{1 − exp

[−1.2564

(t

tm

)]}2(2)

For a progressive nucleation, the expression turns to:

I2

I2m

= 1.2254t/tm

{1 − exp

[−2.3367

(t

tm

)2]}2

(3)

By developing the former situation, Scharifker and Mostany [23]btained a more general equation for the transient current–timeurve in the case of a three-dimensional nucleation of hemispheri-al nuclei, followed by diffusion controlled growth. In this case, theyxpressed the current density I onto the electrode as a function ofhe time t:

=(

zFD1/2 C

�1/2t1/2

)(1 − exp{−N0�kD[t − (1 − e−At)/A]}) (4)

here z is the electron number involved in the reaction, D and C areespectively the diffusion coefficient and the bulk concentration ofhe electroactive species that are under diffusion control.

k is equal to (8�CM/�)1/2 where M and � are respectively theolar weight and mass density of the deposit.While numerous papers deal with diffusion limited three-

imensional growth of metals, only few investigations have beeneported on mechanism and kinetics of electrochemical nucleationnd growth of oxide materials [28–32].

When a magnetic field is applied onto an electrochemical cell indirection parallel to the electrode surface, the MHD Lorentz force

reates liquid motion in the vicinity of the electrode that reducesiffusion layer thickness and enhances limiting currents. Therefore,rowth processes and deposit morphologies are changed for met-ls, alloys and oxide [33–40] but not as much as forced mechanicalonvection case (e.g. rotating electrode) that deeply modifies theucleation process [22,41].

In this paper we analyze some experiments on the mechanismf Cu2O nucleation on stainless steel electrode with or without aurimposed magnetic field on the electrochemical cell.

. Experimental

The copper(I) oxide has been obtained by cathodic reduction ofopper(II) lactate species. The electrochemical experiments werearried out in a conventional three-electrode cell. The referencelectrode was a saturated mercury sulphate electrode (SSE), the

ounter-electrode was made of platinum wire. The working elec-rode was a 1-cm2 stainless steel substrate; it was polished beforeach experiment with different grades of SiC papers, up to 4000.he 100-cm3 cell was plunged into the gap of an electromagnetDrusch EAM 20G) that delivers a uniform horizontal magnetic field

Acta 54 (2009) 5813–5817

B (up to 1 T) parallel to the upward electrode surface. The elec-trolytic solution was a Cu(II) lactate solution (CuSO4 0.45 mol L−1,lactic acid 3.25 mol L−1). The bath pH was adjusted to 8–9 by addi-tion of sodium hydroxide pellets. The solution was stirred 8 h, andthe pH was adjusted to its final value 9.5 with further addition ofNaOH. The potential of the working electrode was controlled bymeans of a potentiostat–galvanostat (PGZ 100, Radiometer Analyt-ical), interfaced with a personal computer.

Cu2O deposits have been analyzed by X-ray diffraction by meansof a Bruker D8 diffractometer using Cu K� radiation. The surfacemorphology has been studied by means of a Jeol JSM-6460 LA scan-ning electron microscope (SEM).

3. Results and discussion

Linear sweep voltammograms of Cu2O deposition on stainlesssteel from lactate solution at pH = 9.5 are shown in Fig. 1 for variousmagnetic field amplitudes. The potential sweep started at an opencircuit potential and was scanned cathodically at 700 mV/s scanrate. In these experimental conditions the coverage of the electrodeby Cu2O is not efficient for total passivation but effect of B is intricatebecause several processes as diffusion, fluid motion and nucleationoccur during the transient phenomena due to the high scan rate. Acurve change is observed for potential values between −0.8 V/SSE,and −0.9 V/SSE, corresponding to the deposition of Cu2O [18].

As reported by Mahalingam et al. [17], for low cathodic overpo-tential, a very weak current can be attributed to the reaction:

Cu2+ + e− → Cu+. (5)

When the cathodic potential is increased (−0.8 V/SSE) Fig. 1, a wavedepending on the magnetic field is due to the formation of:

2Cu+ + 2OH− → Cu2O + H2O (6)

To be sure that only Cu2O deposition took place and no cop-per was included in the reduction product, we have achievedcuprous oxide electrodeposition at a fixed potential value equal to−0.8 V/SSE. For this potential value and all magnetic field ampli-tudes, only Cu2O peaks have been identified on X-ray diffractionpatterns in accordance to the JCPDS (05-0667) data (Fig. 2). The(1 0 0) preferential orientation that has been obtained is similar tothe results that Switzer et al. [18] have reported.

Chronamperometry experiments were carried out in order toinvestigate the copper oxide nucleation growth kinetics. Typi-cal current–time transients obtained at a cathodic potential of−0.8 V/SSE are shown in Fig. 3. These transients exhibit the classic

Fig. 1. Current density–potential curves for Cu(II) lactate reduction and differentmagnetic fields; scanning rate = 700 mV/s.

A.-L. Daltin et al. / Electrochimica Acta 54 (2009) 5813–5817 5815

Fig. 2. X-ray diffraction pattern of cuprous oxide electrodeposited at cathodic poten-tial (−0.8 V/SSE) during 1200 s with a superimposed 1 T magnetic field.

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AlBts1Ctfi

mcaw(1

nop(

FpF

ig. 3. Cathodic transient current density during copper oxide electrodeposition atcathodic potential (−0.8 V/SSE) on a stainless steel substrate for different magneticelds.

fter this maximum value, the current decayed as the diffusionayer increased, to reach a stationary value. When magnetic fieldup to 1 T was superimposed, tm decreased, while im increased up

o a maximum value for B = 1 T. For all experiments realized withoutuperimposed magnetic induction, the tm value is always more than00 s when it is less than 50 s with 1 T magnetic field. Morphology ofu2O layers obtained with and without B has been observed by SEMechnique and the microphotographies showed that the magneticeld does not alter the deposit.

We have analyzed the experimental curves by means of theodel proposed by Scharifker and Hills [27] and data have been

ompared to the behavior for three-dimensional (3D) nucleationnd have been plotted in reduced variable form (I/Im)2 versus (t/tm)hen no magnetic field was applied onto the electrochemical cell

Fig. 4) and with magnetic fields superimposed with values up toT (Fig. 5).

For the very first moments, during the formation of criticaluclei and before the curve maximum, the experimental databtained without magnetic field (B = 0 T) are in agreement with arogressive 3D nucleation mechanism (Fig. 4). After the maximumI/Im)2 value, deviation from progressive model curve and lower

ig. 4. Normalized potentiostatic transient curves I(t). (a) Instantaneous mode, (b)rogressive mode, (c) and (d) experimental B = 0 T. Same electrolytic conditions asig. 3.

Fig. 5. Normalized potentiostatic transient curves I(t). (a) Instantaneous mode, (b)progressive mode, (e) and (f) experimental B = 1 T. Same electrolytic conditions asFig. 3.

current values indicate that the electrode is partly passivated by theCu2O deposit. When a magnetic field is superimposed onto the elec-trochemical cell in a direction parallel to the electrode surface, theexperimental data are in a good accordance with the instantaneousnucleation process (Fig. 5). Once more after the current maximumtime (I/Im)2 value decreases as it is without magnetic field, indi-cating a passivation of the electrode with oxide growth. For someexperiments realized with the highest B value (1 T), the whole curveis in accordance with the model. In fact, the mean electrical chargeinvolved in the deposition process that can be calculated up to themaximum current is decreasing when the magnetic field is applied,so for an equivalent reduced time value (t/tm), higher is the mag-netic field amplitude thinner is the deposited Cu2O thickness. Themean thickness is 0.27 �m with no magnetic field and 0.14 �m with1 T-magnetic field; therefore the passivation phenomenon is lesseffective.

From the experimental data, the diffusive species which areinvolved in the electrochemical reaction can be determined.

The I2mtm products that result from Scharifker and Hills [27]

model are:for an instantaneous nucleation

I2mtm = 0.1629(zFc)2D (7)

and for a progressive nucleation

I2mtm = 0.2598(zFc)2D (8)

where D, zF and c are respectively the diffusion coefficient, themolar charge and the bulk concentration of the reactive species.The species that are involved in the Cu2O electrodeposition are cop-per(II) and hydroxide ions. The copper(II) and OH− concentrationsthat are respectively equal to 0.45 mol L−1 and 3.2 × 10−5 mol L−1

(pH = 9.5), the current efficiency that is equal to 1 and the exper-imental values for Im and tm allow to calculate the diffusioncoefficient of the diffusive species.

- Considering hydroxide ions as diffusive species, calculations leadto an average diffusion coefficient equal to 0.2 m2 s−1, that is anabsurd value.

- Considering the Cu(II) ions as diffusive species, a diffusion coef-ficient value included between 1.3 × 10−10 and 2.6 × 10−10 m2 s−1

is obtained for B = 0 T and progressive nucleation relation.- Considering the Cu(II) ions as diffusive species, a diffusion coeffi-

cient value included between 1.7 × 10−10 and 1.9 × 10−10 m2 s−1 isobtained for B = 1 T and instantaneous nucleation relation. For thislast case, the value is very accurate because there is no scatteringfor experimental data when a 1T-magnetic field is applied.

For time larger than tm, in spite of the passivation process, aCottrell’s law is roughly valid (Fig. 6) and the apparent diffusioncoefficient value that can be obtained is in accordance with theprevious ones.

5816 A.-L. Daltin et al. / Electrochimica Acta 54 (2009) 5813–5817

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trr

atnlthm

L(f

toapattm

ne[1fw[

t

TSi

B

00001

ig. 6. Transient current versus 1/t1/2 for Cu2O electrocrystallization for differentagnetic fields. Same electrolytic conditions as Fig. 3.

Therefore, it can be obviously conclude that Cu(II) ions controlhe limited diffusion current. These results confirm that the limitingate step is the first one of the process which corresponds to theeduction of the copper ion: Cu2+ + e− → Cu+

ads.All these results give the evidence that magnetic field induction

lters electrodeposition kinetics in the same way that overpoten-ial can act. Such modification can be induced by a change of theumber of active sites N0, but this change needs an actual energy

evel that cannot be obtained by the involved magnetic field ampli-ude. To get a better understanding of this magnetic field effect, weave undertaken numerical fits of current transient curves for manyagnetic field amplitudes.Numerical fits have been carried out using the LSM program [42].

SM program carries computation with the Least Square Methodnon-linear regression), i.e., fit parameters given in analytic wayunction (Eq. (4)) for given points. Examples are given in Fig. 7.

These numerical fits reveal that the number of active sites N0 andhe nucleation rate constant A have values with a constant orderf magnitude and which are not depending on the magnetic fieldmplitude (Table 1). In fact N0 is imposed by the substrate surfaceretreatment which is kept as similar as possible and the nucle-tion rate constant mainly depends on the applied overpotentialhat is always the same for all our experiments. It is obvious thathe scattering of these values obtained for B = 0 T is larger than for

agnetic field up to 1 T.Therefore, only a mass transport effect induced by the mag-

etic field can be considered as the effective cause that acts on thelectrodeposition kinetics. As it has been proved in previous paper43], magnetic fields are efficient on ultramicroelectrodes down to0 �m diameter. If we consider the equivalent surface as the dif-usion zone around a nucleus, we obtain the age t of the nucleus

hen magnetic field begins to be effective; this t value is given by

23]:

= r2

kD(9)

able 1aturation nucleus density (N0) and nucleation rate constant (A) deduced by numer-cal fit (Eq. (4)) for various magnetic fields B.

(T) N0 (×10−7 m−2) A (×103 s−1)

13.0 ± 0.2 5.0 ± 0.61.94 ± 0.02 88 ± 4

.25 5.1 ± 0.6 65 ± 3

.5 12.6 ± 0.3 14.5 ± 0.53.47 ± 0.04 67 ± 3

Fig. 7. Comparison between experimental current transients (thin) (a) 0 T; (b) 0.5 T;and (c) 1 T with theorical (Eq. (4)) transients (bold).

with r = 5 × 10−6 m, D = 1.8 × 10−10 m2 s−1 and k = 0.52, the age t isfound to be equal to 0.3 s, that is about one-hundredth of tm when amagnetic field is applied. This value highlights that magnetic fieldis efficient at the very first moments of the electronucleation pro-cess. In this case, the growth of the nuclei is highly enhanced andoverlapping happens more rapidly therefore progressive nucleationturns to instantaneous process. The magnetic field phenomenonthat leads to mass transport enhancement is not a classical MHDconvective effect. The current density in the bulk of the solution isvery weak and therefore the Lorentz force in the solution cannot beefficient. In return, the 3D nucleation creates a hemispherical dif-fusion zone around the nuclei in which a microMHD effect can beexpected as mentioned by Aogaki and coworkers [44–46]. A MHDflow is created in the diffusion layer that decreases its thickness.

4. Conclusion

The initial stages of the electrochemical Cu2O deposition havebeen analyzed by means of transient current–time curves. With

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[43] O. Aaboubi, P. Los, J. Amblard, J.-P. Chopart, A. Olivier, J. Electrochem. Soc. 150

A.-L. Daltin et al. / Electroch

n applied overpotential that induces a pure Cu2O with (1 0 0)referential orientation, a magnetic field applied in a parallel direc-ion to the electrode, modifies the electrocrystallization kinetics.he apparent progressive mode which was highlighted when noagnetic field was applied on the electrochemical cell turns to an

nstantaneous regime with a 1 T-magnetic field. By means of numer-cal fits of the transient curves, the saturation nucleus density andhe nucleation rate constant are proved to be not depending onhe magnetic field amplitude. The effects that are brought out arenly due to the magnetically induced effect that is effective on theass transport process from the very beginning of the nucleation

rocess and that favours a more rapid overlapping of the diffusionones around the nuclei.

cknowledgement

Authors thank the “Conseil Régional de Champagne-Ardenne”or financial support. This study has been done in the frame of GDREAMAS.

eferences

[1] G.P. Pollack, D. Trivich, J. Appl. Phys. 46 (1975) 163.[2] K. Akimoto, S. Ishizuka, M. Yanagita, Y. Nawa, G.K. Paul, T. Sakurai, Solar Energy

80 (2006) 715.[3] J. Katayama, K. Ito, M. Matsuoka, J. Tamaki, J. Appl. Electrochem. 34 (2004) 687.[4] S.C. Ray, Solar Energy Mater. Solar Cells 68 (2001) 307.[5] Y.M. Lua, C.Y. Chena, M.H. Lin, Thin Solid Films 480–481 (2005) 482.[6] B. Balamurugan, B.R. Mehta, Thin Solid Films 396 (2001) 90.[7] Y.S. Chaudhary, A. Agrawal, R. Shivastav, V.R. Satsangi, S. Dass, J. Hydrogen

Energy 29 (2004) 131.[8] J. Ramirez-Ortiz, T. Ogura, J. Medina-Valtierra, S.E. Acosta-Ortiz, P. Bosch, J.A. de

los Reyes, V.H. Lara, 174, Appl. Surf. Sci. (2001) 177.[9] S.T. Shishiyanu, T.S. Shishiyanu, O.I. Lupan, Sens. Actuators B 113 (2006) 468.10] M. Hara, T. Kondo, M. Komoda, S. Ikeda, J.N. Kondo, K. Domen, K. Shinohara, A.

Tanaka, Chem. Commun. 3 (1998) 357.

11] Y. Tang, Z. Chen, Z. Jia, L. Zhang, J. Li, Mater. Lett. 59 (2005) 434.12] P.E. Jongh, D. Vanmaekelbergh, J.J. Kelly, Chem. Mater. 11 (1999) 3512.13] V. Figueiredo, E. Elangovan, G. Goncalves, P. Barquinha, L. Pereira, N. Franco, E.

Alves, R. Martins, E. Fortunato, Appl. Surf. Sci. 254 (2008) 3949.14] T. Mahalingam, J.S.P. Chitra, S. Rajendran, M. Jayachandran, M.J. Chockalingam,

J. Cryst. Growth 216 (2000) 304.

[[[

Acta 54 (2009) 5813–5817 5817

15] T. Mahalingam, J.S.P. Chitra, J.P. Chu, S. Velumani, P.J. Sebastian, Solar EnergySolar Cells 88 (2005) 209.

16] R. Liu, E.A. Kulp, F. Oba, E.W. Bohannan, F. Ernst, J.A. Switzer, Chem. Mater. 17(2005) 725.

[17] T. Mahalingam, J.S.P. Chitra, S. Rajendran, P.J. Sebastian, Semicond. Sci. Technol.17 (2002) 565.

18] J.A. Switzer, H.M. Kothari, E.W. Bohannan, J. Phys. Chem. B 106 (2002)4027.

19] A.L. Daltin, A. Addad, J.P. Chopart, J. Cryst. Growth 282 (2005) 414.20] E.W. Bohannan, L.Y. Huang, F.S. Miller, M.G. Shumsky, J.A. Switzer, Langmuir 15

(1999) 813.21] E. Budevski, G. Staikov, W.J. Lorenz, Electrochim. Acta 45 (2000) 2559.22] M.E. Hyde, R.G. Compton, J. Electroanal. Chem. 581 (2005) 224.23] B.R. Scharifker, J. Mostany, J. Electroanal. Chem. 177 (1984) 13.24] M. Sluyters-Rehbach, J.H.O.J. Wijenberg, E. Bosco, J.H. Sluyters, J. Electroanal.

Chem. 236 (1987) 1.25] M.V. Mirkin, A.P. Nilov, J. Electroanal. Chem. 283 (1990) 35.26] L. Heerman, A. Tarallo, J. Electroanal. Chem. 470 (1999) 70.27] B.R. Scharifker, G.J. Hills, Electrochim. Acta 28 (1983) 879.28] S. Omanovic, M. Metikos-Hukovic, Thin Solid Films 458 (2004) 52.29] Z. Grubac, M. Metikos-Hukovi, Electrochim. Acta 43 (1998) 3175.30] J. Gonzalez-Garcia, F. Gallud, J. Iniesta, V. Montiel, A. Aldaz, A. Lasia, J. Elec-

trochem. Soc. 147 (2000) 2969.31] G.A. Tsirlina, O.A. Petrii, S.Yu. Vassiliev, J. Electroanal. Chem. 414 (1996) 41.32] J.A. Garrido, F. Centellas, P.Ll. Cabot, R.M. Rodríguez, E. Pérez, J. Appl. Elec-

trochem. 17 (1987) 1093.33] I. Mogi, M. Kamiko, S. Okubo, Physica B 211 (1995) 319.34] S. Bodea, L. Vignon, R. Ballou, P. Molho, Phys. Rev. Lett. 83 (1999) 2612.35] K. Msellak, J.P. Chopart, O. Jbara, O. Aaboubi, J. Amblard, J. Magn. Magn. Mater.

281 (2004) 295.36] H. Matsushima, T. Nohira, I. Mogi, Y. Ito, Surf. Coat. Technol. 179 (2004) 245.37] M. Motoyama, Y. Fukunaka, S. Kikuchi, Electrochim. Acta 51 (2005) 897.38] M. Morisue, M. Nambu, H. Osaki, Y. Fukunaka, J. Solid State Electrochem. 11

(2007) 719.39] A. Krause, M. Uhlemann, A. Gebert, L. Schultz, J. Solid State Electrochem. 11

(2007) 679.40] S. Chouchane, A. Levesque, J. Douglade, R. Rehamnia, J.-P. Chopart, Surf. Coat.

Technol. 201 (2007) 6212.41] M.E. Hyde, O.V. Klymenko, R.G. Compton, J. Electroanal. Chem. 534 (2002)

13.42] LSM Program, J.A. Mamczur, Rzeszow University of Technology, Poland,

http://www.prz.rzeszow.pl/∼janand/.

(2003) E125.44] R. Aogaki, Magnetohydrodynamics 37 (1–2) (2001) 143.45] R. Aogaki, Magnetohydrodynamics 39 (2003) 453, No. 4.46] A. Sugiyama, M. Hashiride, R. Morimoto, Y. Nagai, R. Aogaki, Electrochim. Acta

49 (2004) 5115.