Nucleation and growth of the electrodeposited iron layers in the presence of an external magnetic field

Electrochimica Acta 53 (2008) 7972–7980

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Nucleation and growth of the electrodeposited iron layers in the presence of an external magnetic field Jakub Adam Koza ∗ , Margitta Uhlemann, Annett Gebert, Ludwig Schultz Leibniz Institute for Solid State and Materials Research IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany

a r t i c l e

i n f o

Article history: Received 7 April 2008 Received in revised form 6 June 2008 Accepted 7 June 2008 Available online 19 June 2008 Keywords: Magnetoelectrodeposition Nucleation and growth Iron Lorentz force Rotating disc electrode (RDE)

a b s t r a c t The effect of an uniform magnetic field with a flux density up to 1 T and different configurations relative to the electrode surface on the electrocrystallization of Fe on polycrystalline Au(1 1 1) from acidic sulphate electrolyte has been investigated. It was found, irrespective of the applied parameters, that the deposition proceeds through successive nucleation and growth steps. The first one related to 2D growth was followed by a second nucleation and 3D diffusion controlled growth. At potential of −1500 and −1550 mVMSE nucleation proceeds via a progressive mode, while at −1650 mVMSE it follows an instantaneous mode. A strong influence of the parallel-to-electrode magnetic field on the nucleation processes was found for the progressive mode, which leads to the increase of the growth rate and as a consequence to retardation of the nucleation rate of the 3D step. Additionally, in this configuration at a sufficiently high magnetic flux density a third nucleation step could be observed (3D), which was found to be also affected by a magnetic field. No effect of a perpendicular-to-electrode magnetic field on the nucleation has been observed. The effects of a magnetic field on the nucleation and growth processes are discussed with respect to the magnetohydrodynamic effect (MHD) and confirmed by rotating disc electrode (RDE) experiments. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction Electrodeposition is an efficient and relatively cheap process suitable for fabrication of a variety of functional metallic films. A huge interest has been focused on the thin layers deposition, which is important for microelectronic applications. When thin films are deposited, the nucleation process will determine the physical properties of the film. Thus, the understanding of the earliest stages of a film growth and the influence of deposition parameters on it is of great importance for the process development and optimisation. It is known that the potential and the electrolyte composition [1–7], but also the hydrodynamic conditions [8,9] affect the nucleation and further growth of the layers. It was found that the increase of the applied potential as well as of the concentration of electroactive species in the electrolyte increases the number of nuclei and the nucleation rate, resulting with in a reduced grain size and more homogenous size distribution over the electrode. The organic additives have a great impact on the nucleation processes, for example even very small addition of thiourea to the Cu electrolyte increases the number of nuclei [2].

∗ Corresponding author. Tel.: +49 351 4659 767; fax: +49 351 4659 541. E-mail address: [email protected] (J.A. Koza). 0013-4686/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2008.06.011

The electrodeposition of the iron group metals and alloys is of interest because of their magnetic properties [10–12]. They have found a wide application in the magnetic storage [11,12] and in the microelectromechanical systems (MEMS) technology [13–15]. It is known that the superimposition of a magnetic field during the electrodeposition process can change the deposits significantly. Mainly the morphology of the deposited layers is affected [16–19]. The most established effect introduced by a magnetic field is the so-called magnetohydrodynamic (MHD) effect. The MHD effect is generated by the Lorentz force (1) acting in the bulk electrolyte, which leads to an additional convection:  FL = j × B

(1)

 is the magnetic flux density. where j is the current density and B There are also other magnetic forces discussed in the literature, mainly the field gradient force (F∇ B ) [20] and the concentration gradient force (F∇ C ) [21], which may introduce additional effects. But the latter one (F∇ C ) is quite controvert [22,23]. The aim of this work is to investigate effects of a homogeneous magnetic field with different strength and orientation, on the nucleation and early stages of the growth of Fe layers on a polycrystalline Au(1 1 1) electrode.

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2. Experimental The electrodeposition was carried out in a three electrode Teflon® cell described in details elsewhere [19]. Polycrystalline Au(1 1 1) layers sputtered on quartz crystals were used as working electrode and a Pt sheet as counter electrode. The potentiostate (Jaissle) was coupled with a selfconstructed electrochemical quartz crystal microbalance (EQCM). A membrane (Nafion® ) was used between the working and counter electrode to prevent oxidation of iron(II) ions [19,24]. Depositions were carried out from an electrolyte solution containing 6.5 mM FeSO4 and 0.1 M Na2 SO4 which was used as supporting electrolyte. A pH value of 3 was adjusted with H2 SO4 . The electrolyte was purged prior to the experiment with nitrogen for about 1 h to reduce the oxygen content. All potentials were measured vs. a Hg/Hg2 SO4 /K2 SO4(sat.) reference electrode (MSE, 640 mV vs. SHE). Before each experiment the working electrode was degreased in the acetone for 5 min, rinsed with deionised water, activated in HCl (37%) and then rinsed with the deionised water again. Cycling voltammetry experiments were performed at a sweep rate of 20 mV s−1 . From the cyclic voltammograms, potentials for the chronoamperometric experiments were chosen, i.e. the potential steps were applied from OCP to the desired value in a single step. Homogeneous magnetic fields up to 1 T (HV7, Walker Scientific) have been superimposed during deposition with two different configurations, i.e. parallel and perpendicular to the electrode surface (Fig. 1). For clarification of the hydrodynamic effects observed during the superimposition of a magnetic field, rotating disc electrode (RDE) experiments were performed with a polycrystalline Au working electrode. A Pyrex glass electrolytic cell, a platinum net counter electrode and a MSE reference electrode were used. The rotation speed was varied in the range from 0 to 10 rpm (EG&G Model 616 RDE). All deposition experiments were carried out at room temperature. 3. Results 3.1. Potentiodynamic polarization In Fig. 2a cyclic voltammogram and the corresponding mass change curve obtained in the Fe electrolyte are shown. The current density–potential curves show three characteristic peaks in the cathodic region. The first one (I) at a potential of about −1100 mVMSE is related to the reduction of oxygen [19] which is dissolved in the electrolyte despite N2 -purging. The second peak is observed at a potential of about −1420 mVMSE (II) and is related to the hydrogen reduction reaction (HER). The onset of bulk Fe deposition occurs at about −1460 mVMSE and reaches maximum

Fig. 1. B-field to electrode configurations.

Fig. 2. Cyclic voltammogram and corresponding mass changes obtained in 6.5 mM FeSO4 ; dE/dt = 20 mV s−1 , B = 0.

at −1550 mVMSE (III). Analysing the cathodic branches of the CVs it has to be noticed, that after the reverse potential the currentpotential curve in the back scan crosses the one recorded in the cathodic sweep twice (Va-b). Such a shape of the CV is caused by the iron deposition on its own, which occurs at lower overpotentials than the deposition on the foreign substrate (Au). The double crossing phenomenon indicates that the overpotential deposition of the investigated system occurs via a nucleation process [4]. Mass growth is observed from a potential of ca. −1300 mVMSE —point (IV) (Fig. 2). Up to potential of −1600 mVMSE the metal deposition reaction dominates. More negative than this potential the decomposition of water and the hydrogen reduction is the main reaction, what causes a dramatic increase of the interfacial pH value and a spontaneous formation of the hydroxides [25]. In Fig. 3 the cathodic parts of the CVs obtained in superimposed magnetic fields in the parallel (a) and perpendicular (b) configuration are shown. When a magnetic field is applied in the parallel-to-electrode configuration the current density of the maximum of the bulk Fe deposition peak is increased and shifted to more negative potentials (Fig. 3a). Contrary, in the case of a magnetic field in the perpendicular configuration (Fig. 3b) no significant effect on the current density–potential curves was observed. The increase in the current density of the Fe deposition peak with a magnetic field applied in parallel configuration can be explained by the MHD effect (Fig. 3a). Since this reaction is diffusion-controlled [26,27], the superimposition of a magnetic field induces additional convection due to the Lorentz force generated as a cross product of the electric and the magnetic filed Eq. (1). The induced convection reduces the diffusion layer thickness and as a result an increased current density is observed. This behaviour is also clearly visible in the back scan of the CVs in Fig. 3a, which also show an increase of the limiting current density with an increasing B. The shift of the peak’s maximum potential to more negative values with a magnetic field in this configuration can be also explained by the MHD effect acting in the electrolyte solution. During the cathodic sweep of the CV, at the potential range where the bulk Fe deposition occurs, a pH value at the electrode surface reaches a high extend in comparison to the bulk value [25]. Increase of the interfacial pH value is sufficient for hydroxide species formation. It is generally accepted that the reduction of iron proceeds through a multistep-reaction pathway as follows [37]: Fe2+ + H2 O ↔ FeOH(aq) + + H+

(2)

FeOH(aq) + ↔ FeOH(ads) +

(3)

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Fig. 3. Cyclic voltammograms recorded in 6.5 mM FeSO4 with a superimposed magnetic field in the parallel (a) and perpendicular (b) configuration at different flux densities and on RDE (c) at different rotation rates; dE/dt = 20 mV s−1 .

FeOH(ads) + + e ↔ FeOH +

FeOH + H + e ↔ Fe + H2 O

(4) (5)

When a magnetic field is applied in the parallel-to-electrode configuration the maximal Lorentz force occurs, inducing additional convection, which removes some of the hydroxide species from the electrode surface and therefore the peak’s maximum potential is shifted to a more cathodic value. Hinds et al. [17] studied the influence of a magnetic field on the electrodeposition of Cu and found that the MHD effect could

be compared with the convective phenomena generated by a RDE. Similar dependencies of the limiting current density vs. applied potential were obtained with either parallel-to-electrode magnetic field (B = 0.5 T) or a rotation rate of 10 rpm. They [17] also stressed that the magnitude of these effects is strongly dependent on the electrode and cell geometry. Therefore, for better demonstration of the convective origin of the shift of cathodic peak with the magnetic flux density in the parallel configuration (Fig. 3a) RDE experiments were performed. In Fig. 3c the cathodic parts of the CVs obtained with different rotation rates of the RDE are shown. It is obvious

Fig. 4. Chronoamperometric response (a, c) and corresponding mass changes (b, d) of Fe deposition obtained at a potential of −1500 and −1550 mVMSE , respectively; parallel-to-electrode configuration.

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Fig. 5. SEM micrographs of layers (∼100 nm) deposited without superimposed magnetic field (a), B = 1 T in parallel-to-electrode configuration (b) and perpendicular-toelectrode configuration (c, f, i); −1550 mVMSE .

that the peak maximum current density is increased and the potential is shifted to more negative values with increasing rotation rate (Fig. 3c). That is a direct proof that the shift of the bulk Fe deposition peak in the parallel-to-electrode magnetic field (Fig. 3a) is due to the MHD effect acting in the electrolyte. Based on the above results (Fig. 2) the deposition potentials for the following potentiostatic experiments were chosen at the onset, in the maximum and at the end of the metal deposition peak, i.e. at −1500, −1550 and −1650 mVMSE . 3.2. Chronoamperometry Fig. 4a and b shows the i(t) and corresponding m(t) transients for the deposition of Fe at a potential of −1500 mVMSE , and Fig. 4c, d at −1550 mVMSE at different magnetic flux densities in parallel-to-electrode configuration. As it was expected, a magnetic field applied in the parallel-to-electrode configuration increases the limiting current density and deposition rate in the stationary regime. This result is linked to the MHD effect acting in the electrolyte [19]. Neither a significant effect on the current density nor on the deposited mass was observed in perpendicular-to-electrode configuration, but morphology of the deposited layers is strongly affected in this configuration, what is shown in Fig. 5, more details regarding this phenomenon can be found in Ref. [19]. Because no influence of the perpendicular magnetic field on the electrochemical behaviour was observed, further analysis is going to be reduced only to the parallel configuration. When analysing the early stages of the potentiostatic polarization, it can be seen that after applying the potential step the current density increases sharply and then a current decay is observed (Fig. 4a, c). Such a initial shape of the i(t) transient is often explained by the double layer (DL) charging [2,28]. However, in the present studies, experiments were supported by in situ EQCM mass measurements and based on the results shown in Fig. 4b, d (insertions) it is obvious, that a mass growth occurs even at those very short deposition times. Similar behaviour, of Fe deposition onto Au/EQCM was also observed by Lachenwitzer and Magnussen [29]. This suggests, that this part of the i(t) transient is not only related to DL charging phenomenon but also to the nucleation and growth of the phase (Fe) on the foreign substrate (Au). This deposition step seems to be unaffected by superimposed magnetic field and applied potential (Fig. 4I). It has to be noticed that the amounts of mass deposited at very short times are not of high accuracy because of the time delay of the EQCM device itself, which is in the range of tens ms. When compared with the acquisition rate of the potentiostate (50 ms), it might be more than 50% of a time delay for the first two points (insertion of Fig. 4b, d).

The current decay observed in Fig. 4a, c is then followed by the current density peak (II), which indicates another nucleation and growth phenomenon. This peak is affected by a magnetic field applied parallel-to-electrode (insertion of Fig. 4a, c), i.e. the magnetic field reduces the current density of the peak maximum and shifts it to shorter times. This effect is also visible in the m(t) curves (Fig. 4b, d), i.e. a magnetic field decreases the deposited mass in the early beginning of the deposition step (up to ca. 27 s). It is also possible to observe a second current maximum (III) on the i(t) transients obtained with B ≥ 0.4 T at −1500 mVMSE and B ≥ 0.8 T at −1550 mVMSE . In general it can be said, that the current density–time transients obtained without and with a superimposed magnetic field show a typical response of the multiple nucleation and growth processes with a layer-by-layer growth [30]. For a clarification of the origin of a magnetic field influence on the nucleation and growth processes, chronoamperometric experiments with an Au-RDE were performed. In Fig. 6 i(t) transients for the deposition of Fe at a potential of CV’s peak maximum (−1550 mVMSE ) with different rotation rates of RDE are shown. As it was expected, the limiting current density is increased with the rotation rate. The shape of the chronoamperograms obtained with the RDE is very similar to those obtained with a superimposed magnetic field, i.e. after a sharp increase of the current density, a decay occurs followed by the current density–time peak. The current density–time peak’s maximum is decreased with the increase

Fig. 6. Chronoamperometric response of Fe deposition on Au-RDE obtained at different rotation rates; −1550 mVMSE .

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of the rotation rate (insertion of Fig. 6), what is in good correlation with results obtained with a magnetic field (Fig. 4a). This is again a direct proof that the magnetically induced changes in the nucleation and growth of Fe are due to the MHD effect acting in the electrolyte. It was observed that the HER partial current superimposes the chronoamperometric response of the system. The analysis of the i(t) transients with a protonic reaction contribution might lead to the misinterpretation of results. To prevent it, further analysis will be performed only for the Fe partial current densities. A detailed procedure for the separation of the partial current densities is given elsewhere [19]. The nucleation and growth studies are mainly based on the raising part of the peak as well as its maximum position analysis [1,31,32]. In the presented studies both of them were affected by the HER (Fig. 8—Ref. [19]). That is why the subtraction of the HER contribution is so crucial for a more accurate description of the early stages of electrocrystallization. It was also observed that the shape of the i(t) transients at the very beginning of the deposition, obtained with the same parameters may significantly vary from one to another experiment [3]. Because of that, analysis of a single, independent transient may lead to a misinterpretation in the nucleation and growth mechanism. For this purpose it was proposed [3] to use transients which are an average value of many measurements. This procedure was adopted for the presented studies and all transients were averaged on at least three independent measurements. Nevertheless, the reproducibility of the experiments was very good, what is clearly visible in Fig. 7, where the exemplary m(t) transients measured with one set of parameters are shown. 3.3. Nucleation and growth—i(t) transients analysis The investigations of the early stages of electrocrystallization were based on the analysis of the partial Fe current–time response as an answer on the applied potential step. In Fig. 8a–c i(t) transients obtained with different magnetic flux densities in the parallel-toelectrode configuration and potentials are shown. It is obvious that the limiting current density is increased with the magnetic flux density irrespective of the applied potential. At a very beginning of the deposition the current density increases rapidly and then decreases gradually due to a diffusionlimited growth until the i(t) peak is observed (I—Fig. 8a–c). This part

of the transient, irrespective of the applied potential, may be related to the first monolayer (ML) formation or successive layer-by-layer growth with a 2D mode [30]. This step seems to be independent of a magnetic field. It was observed by Gündel et al. [33], with the in situ STM investigations, that the overpotential (OVP) deposition of iron could proceed via a layer-by-layer growth up to the thickness of 4–5 ML onto the Au(1 1 1) electrode. In the case of the first two applied potentials, i.e. −1500 and −1550 mVMSE (Fig. 8a, b), the current density of first peak’s maximum (I) is affected by a magnetic field, i.e. the peak’s current density is decreased and shifted to a shorter time with a magnetic field. Moreover, when the magnetic flux density is sufficiently high a second i(t) peak (II) is observed at longer times. The position of the second peak’s maximum is also dependent on the magnetic flux density (II—Fig. 8a, b). This is more pronounced with the lowest applied potential, i.e. the increased maximum current density and the peak position shifted to a longer time (Fig. 8a). In the case of the highest applied potential no significant influence on the i(t)—peak’s maximum position was observed (Fig. 8c). It has to be stressed that after about 50 s of the deposition at −1650 mVMSE without the superimposition of a magnetic field no further current flow is observed. This effect can be explained by the increase of the interfacial pH value due to the parallel HER, which reaches a very high extend in comparison to the bulk electrolyte and is sufficient for the spontaneous hydroxides formation [25]. The precipitated hydroxides successively block the electrode surface and finally, deposition is prevented. When a magnetic field is applied during the deposition, the Lorentz force occurs resulting in an additional convection (MHD effect). The additional convection removes a part of the hydroxides from the electrode surface and further deposition is possible (Fig. 8c) [25]. As it was mentioned before (Fig. 4), a magnetic field affects the position of the current density peak’s maxima during the deposition at the first two potentials (Fig. 8a, b). This influence on the first maximum (I—Fig. 8a, b), is clearly illustrated in Fig. 9, where the maximum current density (a) and the time of maximum (b) in dependence of the magnetic flux density are shown. It is obvious that a parallel-to-electrode magnetic field reduces the current density of the peak maximum and shifts it to a shorter time. The analytical expression, mostly used for the description of the current time transients with the 3D multiple nucleation and diffusion-controlled growth process was developed by Scharifker and Mostany (6) [34]: I(t) =

zFD0.5 c ∗ (1 − exp[−kN0 Dt]) 0.5 t 0.5

(6)

where I is the current, z is the number of electrons, D and c* are the diffusion coefficient and the bulk concentration of the electroactive 0.5 species, respectively, k = (8Mc ∗ /) , M is the molar mass,  is the density of a solid material, N0 is the number density of active sites (saturation nucleus density) on the substrate and  is given by: =1−

Fig. 7. m(t) transients obtained at −1550 mVMSE potential and B = 0.2 T (//).

1 − exp(−At) At

(7)

where A is a nucleation rate constant. This model considers two limiting situations: progressive and instantaneous. Progressive nucleation corresponds to a growth of the nuclei on the nucleation sites, which are activated during the whole course of the process with a constant nucleation rate (A). Contrary, the instantaneous nucleation refers to a growth of the nuclei on a relatively small number of active sites. In this case the nuclei are formed at the same time with a very high nucleation rate at the beginning of the potential step (t → 0 s) and grow with the same rate, i.e. all nuclei are at the same age. Irrespective of the nucleation mode, the Sharifker and Mostany model predicts a

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Fig. 8. Fe partial current density vs. time transients and corresponding reduced current–reduced time dependences obtained without and with magnetic field in parallelto-electrode configuration at a potential of −1500 mVMSE (a, d), −1550 mVMSE (b, e) and −1650 mVMSE (c, f).

maximum in the i(t) transient followed by a decay, which obey the Cottrell behaviour, i.e. at the peak maximum nuclei diffusion zones overlap and the further diffusion occurs normal to the electrode surface. In order to distinguish between these two limiting cases, it was proposed [1] to plot chronoamperometric data in the reduced current–reduced time coordinates and compare them with the theoretical expressions for the progressive (8) and instantaneous (9) nucleation and growth:

 I(t) 2 Imax

 I(t) 2 Imax





=

1.2254 t/tmax

=

1.9542 1 − exp −1.2564 t/tmax

 t 2 2

1 − exp −2.3367





tmax

 t  2 tmax

(8)

(9)

where Imax and tmax are the current and time of the peak maximum, respectively. It has to be pointed out that the first i(t) transient maximum (I—Fig. 8a–c) occurs at relatively long times, especially for the lowest applied potential (Fig. 8a). To minimize the contribution of the previous layer growth current (2D) on the first i(t) peak (I), the onset of a nucleation time (t0 ) was estimated. The estimation of the t0 was performed by means of the m(t) curves analysis. A linear fit to a steady state deposition rate of the previous layer has been made. A nucleation of another layer was assumed to start from a point where a deviation from the linearity is observed. According to the Scharifker and Mostany model [34], irrespective of the growth

mode, at a very beginning of the potential step, the i(t) transient can be described with a simple power function of time (t). Based on this a power function was fitted to the part of a m(t) where the deviation from the linearity was observed and t0 was found at the crossover of the linear and the power fits. A determination procedure of the onset of nucleation time is shown in Fig. 10. In Fig. 8d–f the reduced current density–reduced time dependences calculated at the first peak (I) from the i(t) transients obtained with different magnetic flux densities and applied potentials are shown. Deposition at the potential of −1500 and −1550 mVMSE could be assigned as a progressive one (Fig. 8d, e). When a magnetic field is applied during the deposition at the −1550 mVMSE potential it seems that the nucleation and growth mechanism is slightly shifted in the direction of the instantaneous mode (Fig. 8d). Floate et al. [9] studied the influence of ultrasounds on the nucleation and growth of Co onto a glassy carbon electrode. They [9] found that the application of ultrasounds favours the instantaneous nucleation. An effect of ultrasounds cannot be compared with a MHD effect directly, because it is of orders of magnitude larger [8]. But nevertheless, both of these effects are related to the increase of the mass transport of the electroactive species towards the electrode surface and seem to be responsible of the change in the nucleation and growth mechanism. As it was already observed in the i(t) transients at first two potentials (II—Fig. 8a, b), in the reduced coordinates plots at high enough magnetic flux densities another nucleation step could be observed (Fig. 8d, e—indicated by arrows). Another observation in the dimensionless plots cal-

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culated at low magnetic flux densities, is that after reaching the maximum, the experimental transients lie below the theoretical ones (Fig. 8d, e). This situation was commonly observed in nucleation studies [5–7,28]. In many cases this behaviour was related to the HER [5–7], but this is not the case since the Fe partial currents were calculated from the m(t) transients. No influence of the applied magnetic field on the nucleation and growth mechanism was found at the highest applied potential, i.e. −1650 mVMSE . At this potential it fits best to the instantaneous mode (Fig. 8f). But deviation from the theoretical behaviour is observed at the times before the maximum. This is due to the contribution of the previous layer current which is still significant and experimental points are above the theoretical lines. 4. Discussion

Fig. 9. CA’s (I—Fig. 7a, b) first peak maximum current density (a) and its position (b) in dependence of magnetic flux density, parallel-to-electrode configuration.

As it was mentioned before, the nucleation and growth of Fe is affected not only by the applied potential but also by a magnetic field in parallel-to-electrode configuration. In order to determine the influence of these parameters on the nucleation and growth, the non-dimensional plots proposed by Scharifker and Hills [1] were used. It has to be pointed out that the model proposed by Scharifker and Hills predicts current densities which cannot reach higher values then those calculated with the Cottrell equation. It is a quite common situation, that the maximum current density in the i(t) transient is higher than the one predicted by the theoretical Cottrell behaviour [3,35]. When the non-dimensional plots are used to distinguish between the nucleation and growth modes, this problem is hidden. Heerman and Tarallo [35] suggested, contrary to the Scharifker and Mostany model, that the expansion of the diffusion layer has to be a function not only of time but also of the nucleation rate constant (A). This excepts the instantaneous mode, where all the nuclei are formed at the beginning of the potential step with a very high nucleation rate constant. They [35] proposed a correction (10) to the Scharifker and Mostany model. Eq. (10) predicts current densities which, at times close to the i(t) peak maximum, might be higher than the ones predicted by the Cottrell behaviour. At the progressive limit the i(t) values calculated with Eq. (10) are of factor 4/3 higher than those calculated with Eq. (6). For the instantaneous limiting case (A 1) both of the models reduce to the same equation: I(t) =

zFD0.5 c ∗ ˚ (1 − exp[−kN0 Dt]) 0.5 t 0.5 

(10)

where ˚=1−

Fig. 10. Illustration of the onset of nucleation time (t0 ) determination; −1550 mVMSE , 0 T.

exp(−At) (At)0.5



(At)0.5

exp(2 ) d

(11)

0

The Levenberg–Marquart algorithm was used to fit Eq. (10) to the experimental results, with the A, N0 and D as fitting parameters. Because the maximum (I) in the i(t) transients occurs at relatively long times a modification to Eq. (10) was introduced, the onset of the nucleation time (t0 ) correction, i.e. the time was expressed as t − t0 . In Fig. 11 the comparison between the experimental and best fits of Eq. (10) for transients obtained without the superimposition of a magnetic field are shown. Additionally a perfect Cottrell behaviour is illustrated (also corrected with the t0 ). It is known that the i(t) peak current density is affected by the applied potential as well as by the concentration of the electroactive species. With the increased potential the number of active sites (N0 ) is higher, which explains the higher maximum current density. Another consequence of higher N0 is a shift of the maximum to shorter times, which means that the overlap of the diffusion zones occurs faster. As it is visible in Fig. 11 and already explained before,

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Table 1 Nucleation parameters; B = 0 T A (s−1 )

N0 (10−6 cm−2 )

Heerman and Tarallo Eq. (10) −1500 150 −1550 200 −1650 300

0.11 0.16 6.84

2.31 4.12 5.86

Instantaneous Eq. (12) −1650

–

6.36

E (mVMSE )

Fig. 11. Comparison of the experimental transients (full lines) with the theoretical (symbols) calculated according to Eq. (10) and the Cottrell behaviour (dashed lines); 0 T.

at the −1650 mVMSE potential, above 50 s of deposition the electrode surface is blocked by the precipitated hydroxides and further deposition is prevented. Because of that the fitting procedure was performed with a time range below 6 s and the diffusion coefficient was adopted from the fittings obtained with lower potentials (D = 4.7 × 10−6 cm2 s−1 ). From Fig. 8f it was concluded that the deposition at −1650 mVMSE proceeds through the instantaneous mode. To test this observation a fitting procedure was performed with Eq. (10) reduced to the limiting instantaneous case Eq. (12). The best fit results obtained with Eqs. (10) and (12) are compared in Fig. 12: I(t) =

zFD0.5 c ∗ (1 − exp[−kN0 Dt]) 0.5 t 0.5

(12)

It is visible that a fit obtained with Eq. (10) gives a better quantitative description of the experiment than the one obtained with Eq. (12), but both of them lie close to the experimental data. The nucleation parameters obtained from the fittings are listed in Table 1.

Fig. 12. Comparison of fitting procedures; −1650 mVMSE , 0 T.

 (mV)

300

Considering the values collected in Table 1 it is clear that the nucleation rate constant (A) and the number of active sites (N0 ) are increased with the applied potential. Comparing the values of N0 obtained with Eqs. (10) and (12) at −1650 mVMSE , they are quite similar, which suggest that deposition at this potential proceed with a mode which is close to the instantaneous limiting case. It has to be stressed that a good qualitative description of the experiment by a model does not mean that the absolute values are correct and those should be confronted with a direct measurement [3]. But in the most cases more important than the absolute values is the general trend of changes with the investigated parameters. The second and the most interesting investigated parameter is the magnetic flux density, which clearly affects the i(t) transients (Fig. 8a–c). It is obvious that the nucleation, at potential of −1500 and −1550 mVMSE , is affected by a magnetic field (Fig. 8a, b). At long deposition times it is apparent that the growth process is affected by B, irrespective of the applied potential (MHD effect). If one has a closer look at the i(t) transients obtained in a magnetic field, their wavy structure can be observed. The fitting procedure employed previously to the deposition without magnetic field is not really applicable to the curves obtained in a magnetic field. The reason is that the first (I) i(t) maximum position (I in Fig. 8a, b) is clearly affected by the following layer growth (another nucleation step—II in Fig. 8a, b) and a deconvolution is not straightforward anymore. But nevertheless, it can be said that two processes occur simultaneously, i.e. the nucleation and growth. Both of them are competitive, so when the growth rate is increased the nucleation rate has to be retarded. This could explain the decreased i(t) peak’s current density with a magnetic field. The deposition without a magnetic field is progressive and nuclei appear at the electrode surface with a constant rate, what means that they are at different age and size. The total current density over the whole geometric electrode area is high due to the large number of nuclei per unit surface (N(t) = N0 At), i.e. the area of the electrode active for deposition is large. When a magnetic field is applied the number of initially formed nuclei (t → 0 s) seems to be unaffected but the growth rate of nucleus is increased, as a consequence A is retarded. Another consequence of a reduced A value is a lower number of nuclei at saturation N0 . The electrode area active for deposition is lower than without a magnetic field. As a consequence the current density related to the whole geometric electrode area is reduced. The retardation of A and the increase of growth rate is proportional to the magnetic flux density and is related to the increased mass transport to the nuclei due to the MHD effect acting in the electrolyte [19]. This is the reason of a slight shift in the nucleation mechanism towards the instantaneous mode with a magnetic field observed in the reduced coordinates plots (Fig. 8e). The above interpretation is consistent with the results obtained at highest applied potential, i.e. −1650 mVMSE . At this potential nucleation proceeds via an almost instantaneous mode and no influence of a magnetic field is observed. All the nuclei are formed at the very beginning of the i(t) peak’s raising part (At → 0 s 1) and then grow with a constant rate. A magnetic field increases the growth rate but it cannot affect A because all the nuclei are formed initially and after that no further

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nucleation occurs (A = 0). Matsushima et al. [36] have found a similar influence of magnetic field with the studies on the initial stages of Cu deposition. After a maximum in the current density–time plot, the nuclei’s spherical diffusion zones overlap and the Cottrell behaviour is expected, which corresponds to a planar diffusion to the electrode surface. This situation is evident at the −1650 mVMSE potential and at low magnetic flux densities at lower potentials. At high enough magnetic flux densities the Cottrell behaviour is disrupted and another maximum is observed (II—Fig. 8a, b). The analysis of the second maximum (II) is extremely difficult, if not impossible. The reason is that, the nucleation and growth of this layer appear at a point were the growth of the previous layer has a significant contribution to the current. As a result the determination of the onset time of the nucleation as well as the exact maximum position is not straightforward. Nevertheless, the position of the second (II) i(t) peak maximum (Fig. 8a) is affected by a magnetic field and it could be concluded that the nucleation of this layer is affected as well. 5. Conclusions The influence of an external magnetic field with different flux density (up to 1 T) and orientation relative to the electrode surface on the electrocrystallization of Fe was investigated. When the deposition is carried out without the superimposition of a magnetic field two nucleation steps could be observed. The first one is most probably related to the successive layer-by-layer growth with a 2D mode [30] and leads to a formation of approximately 4–5 monolayers. Then this step is followed by a second nucleation and growth process, which was classified as a nucleation and 3D diffusion controlled growth. It was found that at two applied potentials, i.e. −1500 and −1550 mVMSE , the nucleation is progressive and the nucleation rate constant (A) and the number of active sites (N0 ) is increased with the applied potential. At the highest potential, −1650 mVMSE , the nucleation proceeds via an instantaneous mode. Irrespective of its strength and orientation the magnetic field seems to have no influence on the first nucleation step at all investigated potentials. Also no effect of the perpendicular-to-electrode magnetic field on the current–time transients, in the whole investigated time range, was observed. Thus, it is concluded that the nucleation is unaffected by the field in this configuration. When a parallel-to-electrode magnetic field is applied during the deposition at the two potentials, i.e. −1500 and 1550 mVMSE , it has a strong influence on the nucleation and growth processes. The current density of the first nucleation peak maximum is decreased and its position is shifted to a shorter times. This effect is attributed to the MHD effect acting in the bulk electrolyte, which retards the nucleation rate and favours the growth of nuclei. At a potential of −1650 mVMSE , where the nucleation was classified as instantaneous no effect of a parallel magnetic field was noticed. Additionally, with a parallel magnetic field a third nucleation step could be observed, which was also classified as a nucleation and 3D diffusion controlled growth. This step is also affected by a magnetic field. The hydrodynamic origin of the observed effects was confirmed by independent experiments with a RDE.

Acknowledgements The German Research Foundation (DFG) is gratefully acknowledged for the support of this work in the framework of the Collaborative Research Centre 609 “Electromagnetic Flow Control in Metallurgy, Crystal-Growth and Electrochemistry”. The authors are indebted to Dr. Thomas George Woodcock from the IFW for the fruitful discussions. References [1] B. Scharifker, G. Hills, Electrochim. Acta 28 (1983) 879. [2] M.H. Hölzle, C.W. Apsel, T. Will, D.M. Kolb, J. Electrochem. Soc. 142 (1995) 3741. [3] A. Milchev, L. Heerman, Electrochim. Acta 48 (2003) 2903. [4] M. Palomar-Padave, B.R. Scharifker, E.M. Arce, M. Romero-Romo, Electrochim. Acta 50 (2005) 4736. [5] D. Grujicic, B. Pesic, Electrochim. Acta 49 (2004) 4719. [6] D. Grujicic, B. Pesic, Electrochim. Acta 50 (2005) 4405. [7] D. Grujicic, B. Pesic, Electrochim. Acta 51 (2006) 2678. [8] M.E. Hyde, O.V. Klymenko, R.G. Compton, J. Electroanal. Chem. 534 (2002) 13. [9] S. Floate, M. Hyde, R.G. Compton, J. Electroanal. Chem. 523 (2002) 49. [10] P.C. Andricacos, C. Arana, J. Tabib, J. Dukovic, L.T. Romankiw, J. Electrochem. Soc. 136 (1989) 1336. [11] E.I. Cooper, C. Bonhote, J. Heidmann, Y. Hsu, P. Kern, J.W. Lam, M. Ramasubramanian, N. Robertson, L.T. Romankiw, H. Xu, IBM J. Res. Dev. 49 (2005) 103. [12] T. Osaka, T. Asahi, J. Kawaji, T. Yokoshima, Electrochim. Acta 50 (2005) 4756. [13] J. O’Sullivan, E.I. Cooper, L.T. Romankiw, K.T. Kwietniak, P.L. Trouilloud, J. Horkans, C.V. Jahnes, I.V. Babich, S. Krongelb, S.G. Hegde, J.A. Tornello, N.C. LaBianca, J.M. Cotte, T.J. Chainer, IBM J. Res. Dev. 42 (1998) 681. [14] C. Liu, T. Tsao, G.B. Lee, J.T.S. Leu, Y.W. Yi, Y.C. Tai, C.M. Ho, Sens. Actuators A 78 (1999) 190. [15] D.J. Sadler, T.M. Liakopoulos, C.H. Ahn, IEEE J. MEMS 9 (2000) 460. [16] K. Msellak, J.-P. Chopart, O. Jbara, O. Aaoubabi, J. Amblard, J. Magn. Magn. Mater. 281 (2004) 295. [17] G. Hinds, F.E. Spada, J.M.D. Coey, T.R. Ní Mhíocháin, M.E.G. Lyons, J. Phys. Chem. B 105 (2001) 9487. [18] A. Krause, C. Hamann, M. Uhlemann, A. Gebert, L. Schultz, J. Magn. Magn. Mater. 290–291 (2005) 261. [19] J. Koza, M. Uhlemann, A. Gebert, L. Schultz, JOSSEC 12 (2008) 181. [20] K.M. Grant, J.W. Hemmert, H.S. White, Electrochem. Commun. 1 (1999) 319. [21] N. Leventis, A. Dass, J. Am. Chem. Soc. 127 (2005) 4988. [22] J.M.D. Coey, F.M.F. Rhen, P. Dunne, S. McMurry, JOSSEC 11 (2007) 711. [23] T. Weier, K. Eckert, S. Mühlenhoff, C. Cierpka, A. Bund, M. Uhlemann, Electrochem. Commun. 9 (2007) 2479. [24] T. Osaka, T. Yokoshima, D. Shiga, K. Imai, K. Takashima, Electrochem. Solid-State Lett. 6 (2003) C53. [25] J.A. Koza, M. Uhlemann, A. Gebert, L. Schultz, J. Electroanal. Chem. 617 (2008) 194. [26] A. Krause, Elektrokristallisation von Kobalt und Kupfer unter Einwirkung homogener Magnetfelder, Ph.D. Thesis, TU Dresden, 2005. [27] J.A. Koza, M. Uhlemann, A. Gebert, L. Schultz, Electrochim. Acta 53 (2008) 5344. [28] J.C. Ziegler, A. Reitzle, O. Bunk, J. Zegenhagen, D.M. Kolb, Electrochim. Acta 45 (2000) 4599. [29] A. Lachenwitzer, O.M. Magnussen, J. Phys. Chem. B 104 (2000) 7424. [30] R.D. Armstrong, J.A. Harrison, J. Electrochem. Soc. 116 (1969) 328. [31] H.R. Thirsk, J.A. Harrison, A Guide to Study of Electrode Kinetic, Academic Press, London, New York, 1972. [32] M. Sluyters-Rehbach, J.H.O.J. Wijenberg, E. Bosco, J.H. Sluyters, J. Electroanal. Chem. 236 (1987) 1. [33] A. Gündel, T. Devolder, C. Chappert, J.E. Schmidt, R. Cortes, P. Allongue, Physica B 354 (2004) 282. [34] B.R. Scharifker, J. Mostany, J. Electroanal. Chem. 177 (1984) 13. [35] L. Heerman, A. Tarallo, J. Electroanal. Chem. 470 (1999) 70. [36] H. Matsushima, A. Ispas, A. Bund, B. Bozzini, J. Electroanal. Chem. 615 (2008) 191. [37] J.O’M. Bockris, D. Drazic, A.R. Despic, Electrochim. Acta 4 (1961) 325.