The influence of Al substrate intermetallic precipitates on zinc electrodeposition

The influence of Al substrate intermetallic precipitates on zinc electrodeposition

hydrometallurgy ELSEVIER Hydrometallurgy37 (1995) 267-281 The influence of Al substrate intermetallic precipitates on zinc electrodeposition Ping Gu...

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hydrometallurgy ELSEVIER

Hydrometallurgy37 (1995) 267-281

The influence of Al substrate intermetallic precipitates on zinc electrodeposition Ping Gu a, R. Pascual a, M. Shirkhanzadeh J.D. Scott b

a, S. Saimoto a,

a Department of Materials and Metallurgical Engineering, Queen’s University, Kingston, Ont. K7L 3N6, Canada h Falconbridge Limited, f&id Creek Division, P.O. Bag 2002, Timmins, Ont., P4N 7KI Canada

Received 13 January 1993;accepted3 August 1994

Abstract

The cathodic reaction during zinc electrodeposition is usually characterized by cyclic voltammetry on the assumption that homogeneous nucleation is taking place on the cathodic substrates. In this present study, this premise was examined for pure Al and its alloys, including Al-Fe, Al-Si, Al-FeSi-Mg and the commercial alloy Al-Fe-Si, by systematic observations of the substrates in the scanning electron microscope, using various modes of detection such as secondary electrons, back scattered electrons, for electron channelling contrast, and X-ray energy dispersive spectrometry. The results clearly show that zinc nuclei form heterogeneously on precipitates rather than on the alumina-coated matrix. Under constant potential, alloys with precipitates had deposition rates a few orders of magnitude larger than in the case of high purity Al. Normalization of the electrochemical data with the volume fraction of precipitates indicates that the deposition rates and morphology of the deposits are affected by the chemistry of the precipitates. The effectiveness of the alumina barrier was demonstrated by the observation that the specific features of the microstructure, such as grain boundaries and plastically deformed substrate, as observed by electron channelling contrast, did not act as locations for zinc nucleation. The high rate of electrodeposition on Al alloys was determined to be due to the presence of intermetallic particles, which significantly improve the electronic conductivity through the alumina film. For the Al-Fe-Si-Mg alloy, two types of intermetallic particles, one rich in Fe and the other in Si, were identified. The voltammetry study indicates that Fe-rich particles provide more favorable sites for zinc electrodeposition. In order to examine the influence of Fe and Si particles, binary alloys of Al-Fe and Al-Si were tested and their deposition characteristics, together with the integratedcharge accumulation, were compared. These studies clearly revealed that a one-to-one correlation exists between the intermetallic particles and Zn nucleation locations.

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1. Introduction The main factors that must be considered in any electrowinning process are: ( 1) the electrochemical properties of the cathodic materials; (2) the effects of ionic impurities in the electrolyte; and (3) the cohesion strength between the deposited metal and its substrate. The study of the influences of various impurities or additives on the deposition of Zn by means of cyclic-voltammetry was pioneered by Lamping and O’Keefe [ l] and a number of papers have pursued this avenue to examine the electrode reactions, especially those by MacKinnon [ 2-61 and his co-workers. Such studies have shown that the presence of even ppm levels of certain ionic impurities in the electrowinning solution can not only lead to a dramatic decline in the current efficiency (CE) but also can alter the deposit morphology. It is quite clear that the decrease in the CE is due to the co-deposition of foreign adatoms; for instance, Fe, Cu and Ni impurities may become the active centres for hydrogen evolution or a cathode in a local micro-galvanic cell, hence inducing zinc re-dissolution [ 71. In order to eliminate these deleterious impurities, the electrolyte is purified by adding Zn powder so that ions with more positive potentials in the electromotive force series than that of Zn will be removed by cementation. Until recently, most of the research has been focused on the electrolyte, for the above reasons, and very few have studied the importance of the electrochemical properties of the cathodic materials, especially the influence of intermetallic precipitates. In the authors’ previous work [ 891 it has been shown that a measurable difference exists in terms of electrochemical properties between pure Al and Al-Fe cathodes during the Zn nucleation stage. This indicates that an important aspect of the initial nucleation on a freshly prepared cathode must be the presence of the intermetallic particles embedded in the Al matrix. In this paper, the presence of intermetallic particles is directly associated with the Zn crystal morphology and the adhesion of Zn to the substrate. In addition, the rapid coverage of the cathode surface with Zn may increase the tolerance of the electrode surface to Fion, which is known to cause the sticking problem by perforating the protective A1203 coating [ 10-l 21.

2. Experimental procedure 2.1. Instrumentation The electrochemical measurements were carried out at 23’C using an EG&G Princeton Model 273 potentiostat, coupled with an IBM-compatible computer and a Moseley Autograf, Model 7OOlA recorder. The solution was purged with nitrogen gas for 30 min prior to the measurement and the nitrogen purging was continued throughout the experiment. The specimens were washed rapidly and dried for examination in a JEOL JSM 840 scanning electron microscope. 2.2. Electrolytic

cell

A two-compartment glass cell with a built-in Pt counter electrode and a standard calomel reference electrode (SCE) was used. During the experiment, the stopper between the

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Table 1 The major alloying elements in Al used in the experiments Electrode

Si (wt%)

Fe (wt %)

Mg (wt %)

_

Pure Al” Al-Fe Al-Fe-Si Al-Fe-Si-Mg AI-2%Si AM%Si

0. 04 0. 138 0.48 1 2. 04 5.98

0.7 15 0.2 15 0.2 23 0.0 18 0.0 37

0.0 05 0.0 01 0.5 42 0.0 06 0.0 02

VFh

_ 0.0 19 0.0 07 0.0 08 0.0 2 0.0 6

aVF = estimated volume fraction of intermetallic particles. “Al is 99.99% pure.

working and reference compartments into the working compartment. 2.3. Electrolyte

was always kept closed, to prevent Cl- ion diffusion

composition

Analytical grade ZnS04. 7H,O and H,S04 (from chemical supplier BDH) and deionized distilled water were used to make up 0.3 MZnS04 with 1.O M H2S04 solutions as described in detail elsewhere [ 8,9]. 2.4. Cathodes or working electrodes Six different component cathodes were studied in this work: pure Al; Al-Fe; Al-Fe-Si; Al-Fe-Si-Mg; Al-2%Si; and Al--6%Si alloys. The composition of these cathodes is listed in Table 1. All these specimens were mounted metallographically and polished, leaving a working face with a diameter of 1.O cm. These faces were electropolished in 1:4 perchloric acid/ethanol solution in a dry ice bath for 2-3 min at 20 V, and finally rinsed with distilled water. 2.5. Cyclic voltammetry

studies

Cyclic voltammetry (CV) experiments were conducted in order to determine the polarization characteristics of Zn deposition for all the Al alloy cathodes. The potential was cycled between - 0.750 V and - 1.400 V (SCE) at a rate of 50 mV/s, and the response signals were recorded with an X-Y recorder.

3. Results and discussion 3.1. Cyclic voltammograms

Cyclic voltammograms of Zn electrodeposited on Al alloys, in 0.3 M ZnS04+ 1.0 M H,S04 solution, with various holding times, from 0.1 s to 10 s, at the given potential - 1.400

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-ml -06

, -07

,

,

-0.8

-09

,

-1

-11

Potential/

V

, -1.2

/ -13

-14

-15

-4c/

/

I

-07

-08

-09

,

I

-,

I -12

-1,

-1.3

I

-14

-15

(SEC) Potential/

V

(SEC)

E

-501 -07

, -08

I

-0.9

-1

Potential/

I

1

-11

-12

V

(SEC)

I

-,3

--14

I -151

-25 -07

I -0.8

I -0.9

I -1

I -11

Potential/

I --I.2

v

I

I

-13

-14

-15

(SK)

Fig. 1. Typical cyclic voltammograms for Zn deposition on Al alloys with indicated holding times at - 1.40 V (vs. SCE) at a scan rate of 50 mV/s in 0.3 M ZnSO, + 1.0 M H,S04 solution at 23°C. (a) Al-Fe. (b) Al-Fe-Q. (c) Al-Fe-Si-Mg. (d) Al-2%Si. The numbers correspond to the holding times: 1 = 0.1 s; 2 = 1 s; 3 =5 s; and 4 = 10 s. See text for further information.

V (vs. SCE) are shown in Fig. 1. These diagrams are very similar in terms of their shape. The interpretation of this kind of diagram has been given elsewhere [ 2-6,8,9]. The cycle, starting from point A, goes through a low current region until point B, where Zn deposition commences. The current then gradually increases to point C. After holding at point C for a given time, the sweep is reversed. The current then decreases and reaches zero at point D, past which the anodic dissolution of deposited Zn takes place, and reaches its maximum anodic current at E. Finally, it returns to A after the Zn dissolution is complete. This is a distinctive charge-transfer process in which nucleation of a phase and growth of the nucleated crystal control the overall kinetics. The region BCD is called a nucleation hysteresis loop. For practical purposes, a position B’ (Fig. la) is determined as the value of potential at which some arbitrary small current (0.4 mA cm-‘) [ 131 is reached. The width of DB’ is defined as the ‘Nucleation Overpotential’ (NOP) . However, in the case of a mercury cathode [ 141, there is no hysteresis loop and no NOP is observed, since there is no ratecontrolling nucleation process. The deposition of Zn to form an amalgam is uniform over the mercury surface.

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For the Al-Si alloy, the voltammogram (Fig. Id) exhibits two anodic peaks at the short holding times, which gradually coalesce. Similar multiple peaks were observed in glassy carbon and lead electrodes by Biegler [ 151, who suggested that the distinguishable peaks could be due to the stripping charge of the bulk Zn deposit and the charge for a monolayer of Zn on the basal plane. In addition, there are other possible explanations for this type of phenomenon, such as underpotential deposition, alloy formation, diffusion of Zn into the substrate and the presence of more than one type of deposited Zn (such as epitaxial growth on different faces or non-epitaxial growth). The possibility of alloy formation seems impossible for the case of the Al-Si alloy because the mutual solubilities of Si and Zn in the solid state are negligible [ 161. The multiple peaks cannot be attributed to the presence of impurities in the solution because the same phenomenon is not observed in other Al alloys. 3.2. Anodic

integrated charge

Since the anodic current is only due to the dissolution of the Zn that was previously deposited in the cathodic scan, the Zn dissolution charge is obtained by integrating the

0

4

8 Holding

Fig. 2. Plot of integrated

12

16

Time/S

charges of anodic area against holding time for pure Al and Al alloys.

20 o 0 LI

Al-Fe Al-Fe-Si AI-Fe-Si-Mg

16 --

OJ 0

2

4

6

a

lc1

Time/s

Fig. 3. Plots for Al-Fe and Al-Fe-Si

alloys using the same data as Fig. 2 but corrected for volume fraction.

212

Fig. 4. Comparison zinc dissolution.

P. Gu et al. /Hydrometallurgy

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37 (1995) 267-281

of the pure Al cathode.

(a) SE1 before zinc dissolution.

(b) ECC after

anodic peak area. Fig. 2 presents the plot of the integrated charge against holding time at - 1.40 V (vs. SCE) . A linear relation with a positive intercept on the charge axis is obtained. This implies that the growth of zinc depends on the initial nucleation sites, which were established prior to a holding time of 0.1 s. It should be noted that the lowest curve in Fig. 2 is for pure Al. Its Zn deposition rate is 100 times smaller than those of the alloys (its cyclic voltammogram is not shown in Fig. 1) . The small integrated charge is attributed to the presence of an adherent aluminum oxide film which inhibits zinc nucleation. On the other hand, the much larger anodic integrated charges for the alloys must be due to the existence of the intermetallic particles. Although the charge for Al-Fe alloy is about 2.5 times larger than that for Al-Fe-Si (Fig. 2)) upon normalizing with the volume fraction (Fig. 3), the Al-Fe-Si alloys appear to be more effective charge carriers than Al-Fe. The Al-Fe-Si-Mg alloy indicated can be taken to be

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Fig. 5. Comparison zinc dissolution.

of SEM examination

of the AI-Fe cathode.

(a) SE1 before zinc dissolution.

213

(b) ECC after

the equivalent of the Al-Fe-Si alloy since it is shown subsequently that Mg in solid solution does not promote nucleation on the Al matrix. In the Al-Si case (Fig. 2), the charge is smaller than for the other alloys examined. It should be noted that in all of the above comparisons Fe is always present. Moreover, Si, being a semiconductor, possesses a lower charge-carrying capacity than metals. The NOP for Zn nucleation on Al-Si is larger than that for the other Al alloys investigated (values were determined at current equal to 2.5 mA cm-‘): Al-Si ( 107 mV) > Al-Fe-Si (88 mV) > Al-Fe (70 mV) . The overpotential required to deposit a metal on a semiconductor is generally higher than that for a metal electrode, mainly because of the potential drop inside the material. With a metal electrode, a small negative shift in the Fermi level is usually sufficient to start the deposition process. For a semiconductor, however, a more negative shift of the Fermi level

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Fig. 6. Comparison zinc dissolution.

of SEM examination

of the Al-Fe-Si

cathode. (a) SE1 before zinc dissolution.

(b) ECC after

is required in order to obtain a sufficient electron density at the surface. This is because of the Schottky barrier [ 181 (i.e., the hybridization according to the band theory of semiconductors) . Therefore, it is not surprising that a higher NOP is observed for Al--%. Because of the differences in NOP, these constant voltage tests are not the best way to compare the growth rate as a function of precipitate chemistry: a constant current test, such as that used to measure current efficiency, is required. A new computer program to assess current efficiency has been developed and it supports the present indication that the Al-Si alloy is detectably more efficient than Al-Fe [ 171. 3.3. SEM examinations

of zinc nucleation sites

In order to confirm that Zn nucleation corresponds to the precipitate sites, the Electron Channelling Contrast (ECC) technique was used. Since the ECC technique is sensitive to

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Fig. 7. Comparison of SEM examination after zinc dissolution.

of the Al-Fe-Si-Mg

cathode. (a) SE1 before zinc dissolution.

275

(b) ECC

crystal structure, it has the capability of identifying grain boundaries, subboundaries and precipitates. The optimum procedure was to deposit Zn on the electropolished surface for 30 s (except in the case of pure Al, for which the deposition time was 2 min) and then quickly wash and dry the specimen for topographical observation using Secondary Electron Imaging (SEI) . The regions of observations were located by microhardness indentation markers. The same specimen was then re-introduced into the cell for potential scanning between - 0.7 and - 0.9 V (vs. SCE), to induce anodic dissolution and complete removal of the deposit, as indicated by zero current change with potential. The same area was once again examined in the SEM and the observations compared: ( 1) Pure Al (Fig. 4) : Only a few Zn crystals at isolated spots were observed. The Zn nucleation is not necessarily on the boundaries and no particles were detected, which implies that an impervious A&O? film covered the entire surface.

216

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Fig. 8. Comparison of SEM examination of the AI-2%Si cathode. (a) SE1 before zinc dissoh Ition. (b) ECC after zinc di solution. (2)

(3)

(4)

Al-Fe (Fig. 5) : Many small Zn nuclei appear on the electrode surface and they are correlated to the sites of intermetallic particles, which are identified as white particles in the ECC micrograph. The black spots are holes where the Fe particles were removed during electropolishing. Grain boundaries are easily seen but there is no indication that they are preferential sites for Zn electrodeposition. Al-Fe-Si (Fig. 6) : The one-to-one relation between the deposited Zn and intermetallic precipitates is clearly seen. The white particles in this alloy have also been identified as Fe- rich with a small amount of Si present. The microstructure is typical of that observed for hot-rolled products, depicting many subgrains within large grains. It did not affect the zinc nucleation, due to the protective oxide film. Al-Fe-Si-Mg (Fig. 7): Again, a very clear one-to-one relation between deposit and precipitate was observed. The EDS examination showed that the white particles are Fe-rich and the black are Si-rich.

Fig. 9. High magnification ( X 7000) of the zinc deposit on AL2%Si shown in Fig. 8a.

(5)

AL2%Si (Fig. 8): Since the volume fraction of precipitates is large, the Zn nuclei are also numerous. The above results indicate that Zn nucleation sites directly correlate to the intermetallic particles. Zn nucleates preferentially on Fe, Si or Fe-Si precipitates in an Al matrix. This result matches with the electrochemical data, which show that the Al-Fe has a larger anodic integrated charge than others, since it has a large volume fraction of intermetallic particles which leads to more Zn nuclei. For the Al4 alloy, the SEM observations are consistent with that obtained by cyclic voltammetry. Fig. 9 reveals that not all Si particles have Zn crystals on them. In fact, the Zn nucleation only occurs on a fraction of the total Si particles, as indicated by the arrows. Detailed studies are required to ascertain whether this is a doping effect of the semiconducting element mentioned earlier or due to crystallographic epitaxial effects. These experimental observations show that the electrochemical properties of Al alloys are determined by the surface topology and composition of the alloy, which, in turn, determine the types of precipitates. It is well known that high purity Al has a uniform oxide film which is electrochemically inactive. However, it is still likely for the Al to have defects in the protective oxide film due to heterogeneities in the microstructure, which explains why the number of Zn nuclei is limited and crystal growth is isolated. The presence of Fe in the commercial Al alloy is one of the major causes for the deterioration of the high resistance of the oxide film. Because of its low solubility in Al, most of the Fe present will precipitate in the Al matrix to form Fe-rich intermetallic phases. These phases are electrochemically more noble than the surrounding matrix so that they are the active sites. Silicon has been regarded as almost equally deleterious as Fe to the protective A&O3 [ 191. The influence of the Fe-rich and various AlFe-Si phases on the pitting of the Al alloy has also been investigated [ 19-211. Such studies reinforce the rationale that Zn nucleation is preferred on the intermetallic particles, since these spots have lower resistance and better electrochemical properties for cathodic reactions. Because Zn does not stick to Al,O, [ 221, the sticking phenomenon then becomes

278

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dependant on the amount and type of the precipitates and their adhesion properties as regards to Zn. 3.4. Zinc crystal morphology and initial deposit characteristics The influence of the grain size of the Al substrates on the Zn crystal morphology has been studied [ 231 but without any attention being given to the intermetallics. In order to obtain more information, a direct inspection of the electrode surface by SEM (Fig. lo), after 5 min zinc deposition at - 1.25 V (vs. SCE), shows the influence of intermetallics present in the Al substrate on the crystallographic orientation of Zn nuclei. In the cases of Al-Si and Al-Fe-Si (Fig. lOc,d) , the Zn nuclei show a preferential, quasi-two-dimensional growth, which indicates that the lateral growth of hexagonal planes is competing with nucleation of new platelets on its surface. On the other hand, Zn nucleation prefers a tbreedimensional growth pattern on Al-Fe and Al-Fe-Si-Mg alloys (Fig. lOa,b) , resulting in small grains with large platelet angles. Many factors could affect the zinc crystallographic orientation [ 241. If only equilibrium considerations are taken into account [ 251, the relative magnitude of the interfacial energy between the deposit and the substrate is an essential factor in determining the nucleation morphology. In other words, the surface energy of intermetallics-Zn and Zn-Zn interfaces could be an influential factor in the crystallographic orientation. More precise information can be obtained through the X-ray or electron diffraction investigations. However, the effect of hydrogen evolution should not be neglected, since hydrogen bubbles evolved from Fe particles might prevent the two-dimensional growth. Fig. 11 shows Zn, with 10 min deposition at - 1.25 V (vs. SCE), examined optically by interference Nomarski microscopy on the four Al alloy substrates. Only the A1-6%Si alloy (Fig. 1la) has a full coverage of zinc in the given deposition time. The initial electropolished surface can be detected as the bright white areas. Thus, Al-6%Si manifests the most homogeneous deposit with the least porosity. The Al-Fe (Fig. 1Id) showed a patchy effect, which may relate to the uneven distribution of Fe-rich particles. The Al-Fe-Si (Fig. 1lc) deposit was not macroscopically planar or flat, unlike Al-Si (Fig. 1 la,b) , but better than the deposit on Al-Fe. Consequently, under this condition of deposition it is expected that the high particle density with uniform distribution will lead to a rapid full coverage of the cathode surface during the initial electrowinning process. This is obvious since more particles will give rise to more nucleation sites and the growth of Zn will easily bridge the deposit within a short time. The electrolyte capture at the Zn-Al substrate interface would be small. Therefore, controlling the density of the particles could lead to an even deposit and fast growth of the first entire Zn layer. These factors are important because uniform growth could reduce the extent of nodule formation and fast coverage could increase the tolerance to the deleterious F- ions, which are known to cause the sticking problem [ lO121.

4. Conclusions The kinetics of Zn nucleation and growth are greatly affected by the amount and type of second-phase precipitates embedded in the Al solid solution matrix. The electrochemical

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properties of Fe and Si binary experimental alloys were compared to commercial Al sheet. From the SEM examinations of electropolished surfaces, a one-to-one correlation between intermetallic particles and Zn deposit locations has been revealed. This result provides useful information for understanding the intrinsic cause of the sticking which is encountered during the electrowinning of Zn. Acknowledgements

The authors would like to express their thanks to Technology Ontario, through the University Incentive Fund, and Falconbridge Limited for financial support. They also thank Prof. W.C. Cooper for his continued advice and guidance. References [l] Lamping,B.A.andO’Keefe,T.J.,Met.Trans,7B (1976):551-558.

[2] MacKinnon, D.J. and Brannen, J.M., J. Appl. Electrochem., 7 (1977): 451-459. [3] MacKinnon, D.J., Brannen, J.M. and Fenn, P.L., J. Appl. Electrochem., 17 (1987): 1129-l 143. [4] MacKinnon, D.J. and Fenn, P.L., J. Appl. Electrochem., 14 (1984): 701-707. [5] MacKinnon, D.J., Morrison, R.M. and Brannen, J.M., J. Appl. Electrochem., 14 (1986): 53-61. [6] MacKinnon, D.J. and Fenn, P.L., J. Appl. Electrochem., 14 (1984): 467-474. [ 71 Kerby, R.C. and Ingraham, T.R., Effect of impurities on the current efficiency of zinc electrodeposition. Res. Rep. Dept. of Energy, Mines and Resources Branch, Ottawa ( 1971) . [ 8 ] Xue, T., Cooper, WC., Pascual, R. and Saimoto, S., J. Appl. Electrochem., 21 ( 1991): 231-237. [9] Xue, T., Cooper, W.C., Pascual, R. and Saimoto, S., J. Appl. Electrochem., 21 (1991): 238-246. [ 101 Kelly, F.H.C., J. Electrochem. Sot., 101 (1954): 239-243. [ 111 Kammel, R. Gijktepe, M. and Oelmann, H., Zinc electrowinning from flue dusts at a secondary copper smelter and connected adhesion problems of the metal deposits. HydrometalIurgy, 19 ( 1987) : 1l-24. [ 121 Andrianne, P., Scoyer, J. and Winand, R., Zinc electrowinning - a comparison of adherence-reducing pretreatments for aluminium cathode blanks. Hydrometallurgy, 6 ( 1980): 159-169. [ 131 Kerby, R.C. and Krauss, C.J., In: J.M. Cigan, T.S. Mackey and T.J. O’Keefe (Editors), Lead-Zinc-Tin ‘80. Met. Sot. AIME, Warrendale, Pa. (1979), p. 187-203. [ 141 Bond, A.P., Bolling, G.F., Don&n, H.A. and Biloni, H., J. Electrochem. Sot., 113 (1966): 773-778. [ 151 Biegler, T., In: I.H. Warren (Editor), Application of Polarization Measurements in the Control of Metal Deposition. Elsevier, Amsterdam ( 1984), p. 32. [ 161 Massalski, T.B. (Editor), Binary Alloy Phase Diagrams. American Society for Metals, Metals Park, Oh. (1986). 1171 Ping Gu, Orhard, C., Saimoto, S. and Scott, J.D., Investigation of current efficiency in zinc nucleation on freshly prepared Al-alloy cathodes by cyclic voltammetry. In prep. [ 181 Morrison, S.R., Electrochemistry at Semiconductor and Oxidized Metal Electrodes. Plenum Press, New York ( 1980). [ 191 Nisancioglu, K. and Lunder, 0.. In: E.A. Starke Jr. and T.H. Sanders Jr. (Editors), Aluminum Alloys: Their Physical and Mechanical Properties. EMAS, Warley, UK (1986), Vol. 2, p. 1125. [20] Zamin, M., Corrosion, 37 (1981): 627-632. [ 211 Nisancioglu, K., J. Electrochem. Sot., 137 ( 1990): 69-77. 1221 Kerby, R.C., In: I.H. Warren (Editor), Application of Polarization Measurements in the Control of Metal Deposition. Elsevier, Amsterdam (1984), p. 84. [23] MacKinnon, D.J. and Brannen, J.M., J. Appl. Electrochem., 16 (1986): 127-133. [24) Winand, R., In: I.H. Warren (Editor), Application of Polarization Measurements in the Control of Metal Deposition. Elsevier, Amsterdam (1984). p. 42. [ 25 1Markov, I., Electrochim. Acta, 28 ( 1983): 959-966.