Mass-transport effects on texture formation of nickel electrodeposits

Mass-transport effects on texture formation of nickel electrodeposits

Materials Chemistry and Physics 66 (2000) 278–285 Mass-transport effects on texture formation of nickel electrodeposits Benedetto Bozzini∗ INFM — Dip...

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Materials Chemistry and Physics 66 (2000) 278–285

Mass-transport effects on texture formation of nickel electrodeposits Benedetto Bozzini∗ INFM — Dipartimento di Ingegneria dell’Innovazione, Università di Lecce, via Arnesano, I-73100 Lecce, Italy

Abstract Mass-transport effects on the degree of perfection of the preferred orientation of electrodeposited Ni are taken into account in this research. Laminar and turbulent flow conditions were considered in rotating disk electrode and natural convection systems. A clear correlation emerges between the amount of [1 1 1] preferred orientation and the cathodic current efficiency, the latter being determined by a combination of hydrodynamic conditions and total electrodeposition current density. Once the limiting current density for the concomitant hydrogen evolution reaction is known experimentally, the cathodic current efficiency can be related in a straightforward way to the product of the hydrodynamic boundary layer thickness and the total electrodeposition current density. This product is negatively correlated with the degree of preferred orientation perfection. A simple semi-empirical correlation follows between operating conditions and crystallographic properties of Ni deposits. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Mass-transport effect; Texture formation; Electrodeposition; Nickel

1. Introduction Comprehensive and detailed investigations [1–7] provide evidence and explanations for the formation of fibre texture in nickel electrodeposits as a function current density (c.d.), bulk bath pH, Ni2+ concentration and nature of additivation; the topic has been recently reviewed in [7]. Ni electroforming with defined texture is raising industrial interest for applications as a material for microactuators, based on electromagnetic principles [8–11]; control of texture over possibly large surfaces is therefore becoming an important technological topic. Little attention was given in the literature to mass-transport conditions as a factor explicitly affecting texture. The only data known to the author, dealing with the subject is a small section of Ref. [3] where the dispersion of the [2 1 0] texture was measured as a function of rotating disk electrode (RDE) rotation speed. In some of the papers listed previously, mention is made of the use of an RDE ([2,3], ω=2000 rpm; [8], ω=1000 rpm), the main concern being reproducibility of the experimental results (for an accurate discussion see [2], p. 211); in many papers [1,4–6,9,10] hydrodynamic conditions are simply not mentioned. Previous experience with industrial-scale electrodeposition [12–14] suggests that mass transport can be a critical parameter for the achievement of the desired structural and functional properties. In this paper, we report on mass-transport effects on Ni elec∗ Tel.: +39-02-2399-3116; fax: +39-02-2399-3180. E-mail address: [email protected] (B. Bozzini).

trocrystallisation of deposits with [2 1 1] texture strongly perturbed by [1 1 1] texture under forced (RDE) and natural (vertical plane-parallel electrodes) convection conditions. 2. Experimental 2.1. Materials The electrolyte composition and operating conditions were: NiSO4 ·6H2 O 1.07 M, NiCl2 ·6H2 O 0.08 M, pH 4.50, T=25◦ C, c.d. 5, 10, 25 mA cm−2 . The anode was a spectroscopically pure Ni foil, the dissolution efficiency is very close to 100%. No H3 BO3 was added, since on one side this will very effectively hinder cathodic pH increase and hydroxide/basic salt precipitation, on the other side it introduces different reaction intermediates and probably Ni-complexes [15], which make things fuzzier than working with simple salts and aquocomplexes. The bulk pH is the quantity which is generally considered as an operating variable in the above-mentioned works; this did not vary to a measurable extent within one deposition run by using a cell containing 5 l of electrolyte. Composition (in order to compensate for Ni2+ concentration increases due to higher anodic than cathodic efficiency) and (preventive) pH correction was performed after each electrodeposition run by adding calculated amounts of an aqueous solution of H2 SO4 and HCl in the same ratio as the respective Ni2+ salts. Layers of thicknesses in the range 150–200 ␮m were plated onto polycrystalline two-phase brass substrates with a mirror finish obtained by mechanical polishing.

0254-0584/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 0 ) 0 0 3 1 3 - 8

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The kinematic viscosity ν was measured for the working electrolyte by measuring the viscosity µ by an efflux technique and the density ρ by gravimetry: ν=1.3×10−2 cm2 s−1 . For Ni2+ we assume a diffusion coefficient D∼ =10−5 cm2 −1 s , which is a reasonable value for metal electrodeposition case [16] with similar systems. No literature data are available for the densification coefficient α of Ni2+ solutions (see Section 2.2.3.2), for a reasonable estimate we referred to a published value ([17], p. 215) for CuSO4 solutions of similar concentrations: α=1.5×102 cm3 mol−1 . 2.2. Deposition cells 2.2.1. Geometry 2.2.1.1. RDE cell. An RDE system was used comprising a threaded two-phase brass rod of diameter 1.75 cm as the cathode and an outer coaxial coating of polytetrafluoroethylene (0.25 cm thick), the overall RDE diameter being 2.0 cm. The RDE was dipped in a 5 l beaker, the bottom of the beaker was gently stirred with a magnetic stirrer, in order to ensure compositional homogeneity of the bath without affecting the electrolyte flow at the cathode. The anode was a 5 cm×5 cm Ni slab hanging along a wall of the beaker from a Pt wire (of quantitatively insignificant anodic surface area), located 8 cm from the centre of the RDE with the upper side of the square anode at the level of the RDE plane. 2.2.1.2. Natural convection cell. A prismatic “box” cell with a square basis of 4 cm×10 cm (4 cm broad electrodes and 10 cm interelectrode distance) and a height of 35 cm was built with plane-parallel electrodes and PVC side, bottom and upper walls for c.d. distribution control reasons (see Section 2.2.2.2); the upper wall was bored in order to avoid the trapping of gas bubbles. In order to contain the electrolyte, the cell was plunged in a glass cylinder. The 35 cm×4 cm electrodes were: cathode, brass slab; anode, a platinised Ti expanded mesh. 2.2.2. Current density distribution The c.d. distribution can be confidently judged secondary for the following two reasons: (i) as proved in Section 4, the electrodeposition experiments performed in this study were carried out far from the limiting c.d. for Ni and (ii) the cathodic polarisation is high. 2.2.2.1. RDE cell. The degree of uniformity of the secondary c.d. distribution over the RDE was evaluated according to the method proposed in ([18], p. 386), where the secondary c.d. distribution can be parametrised with the quantity J: J =

hiir BT k

(1)

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where hii is the average c.d., r the radial position on the disk, BT the Tafel slope (measured by LSV: BT ∼ =450 mV dec−1 ) and k the electrolyte specific conductivity (measured: k=0.15 −1 cm). The c.d. distribution homogeneity is high for low values of J. In the case at hand J varies in the range 0.0741–0.3704 for c.d.s in the range 5–25 mA cm−2 ; this implies maximum deviations from the average c.d. value of −5.0 and +7.1% in the worst case (25 mA cm−2 ). 2.2.2.2. Natural convection cell. Owing to the geometry of the cell (the electrodes are embedded into insulating walls on all sides), the primary c.d. distribution — and hence also the secondary one — are perfectly flat. 2.2.3. Mass transport The hydrodynamic conditions of the deposition cells were characterised by a single parameter: the concentration boundary layer thickness for Ni2+ : δ C . In the general case of flows with surface reaction, the ratio of δ C to the velocity boundary layer thickness δ v is a function of Sc=ν/D, reaction rate and kind of flow prevailing in the relevant system [19]. In the systems and operating conditions of interest, the reaction corrections are immaterial (amounting to a few ppm) and the non-reacting flow ratio δ C /δ v =Sc−1/3 can be applied. 2.2.3.1. RDE. δ C can be expressed as follows in laminar (Eq. (2), see [18], p.86) and turbulent (Eq. (3), [16]) conditions: r r ν D 3 (2) δC = 3.6 ω ν r r ν D (3) δC = 0.525 2 3 ν r ω where ν is the kinematic viscosity (cm2 s−1 ), ω the RDE rotation rate (s−1 ), D the diffusion coefficient of Ni2+ (cm2 s−1 ), and r the (external, i.e. electrode and insulating outer cylinder, see above) RDE radius. The critical Re for an RDE is: Re =

r 2ω ν

Recrit ∼ = 105

(4a) (4b)

In the experiments which were carried out in this research ω≤2000 rpm, hence Re≤10 256Recrit , the flow conditions are therefore always laminar, and Eq. (2) can be used to estimate δ C :ω=20 rpm, δ C =655 ␮m; ω=200 rpm, δ C =206 ␮m; ω=1100 rpm, δ C =88 ␮m; ω=2000 rpm, δ C = 53 ␮m. It can be observed that the limiting c.d.s which can be estimated from these values of δ C from the assumption of a linear concentration profile within the concentration bound-

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ary layer [20] are well above the c.d.s adopted for electrodeposition experiments. 2.2.3.2. Natural convection. Mass transport at vertical electrodes under natural convection conditions can be described by the local Sherwood number Sh(x) ([17], p. 169), defined as follows for laminar (Eq. (5)) and turbulent conditions (Eq. (6)) (the critical parameter for onset of turbulence being Gr(x)·Sc∼1013 ): Sh(x) = 0.66[Gr(x) · Sc]1/4

(5)

Sh(x) = 0.31[Gr(x) · Sc]0.28

(6)

with gαCB x 3 Gr(x) · Sc = νD

From Fig. 1, it can be observed that, in the turbulent regime, the proportionality relationship between velocity and concentration boundary layer thicknesses (see Section 2.2.3) breaks down, since mass transport is enhanced by turbulent conditions. The limiting c.d.s which can be predicted for this system are well above the c.d.s adopted for electrodeposition experiments. 2.2.3.3. Effect of hydrogen gas evolution. Gas-evolution induced electrolyte stirring can be evaluated considering the penetration model [21], by RG d Aν r ν (1 − 0.5Re0.18 ) Sh = Re · DH Re =

(7)

where g is the gravity acceleration, x the vertical ordinate along the electrode, α the densification coefficient for the electroactive species and CB the bulk concentration of the same species. Since the local limiting c.d. can be written as [17] h gα i1/4 5/4 CB (8) iL (x) = 0.67zF Dνx The local concentration boundary layer thickness δ C (x) can be evaluated from the local limiting c.d. [20] which, itself, can be defined in terms of Sh(x), hence r x D 3 (9) δC (x) = Sh(x) ν In the natural convection cell, for xC =20 cm, Gr(xC )· Sc=1013 , hence the portion of the cathode with x<20 cm is expected to display a laminar flow, while the one above is expected to show a turbulent flow. The estimated concentration boundary layer thickness — computed according to Eq. (9) — is shown in Fig. 1.

Fig. 1. Estimated concentration boundary layer thickness δ C as a function of vertical coordinate x in the natural convection cell.

(10)

(11)

where RG is the rate of production of gas volume, A the electrode surface area, DH the diffusion coefficient of protons (D∼10−4 cm2 s−1 ) and d the diameter of a sphere having the same volume as the gas bubbles (assumed to be monodispersed); for the case of hydrogen bubbles, d can be expected to lie in the range 0.08–0.10 mm [22]. To make a conservative estimate of gas-evolution related Sh, we assume that the cathodic efficiency is 80%, and we set ν=0.01 cm2 s−1 ; from simple algebra it follows that for c.d. of 5, 10 and 25 mA cm−2 , Sh values of 0.10, 0.13, 0.21 are obtained. These values are orders of magnitude lower than Sh typical for the laminar RDE and both laminar and turbulent natural convection systems considered in this work, the contribution of gas-evolution stirring to mass transport can therefore be considered to be quantitatively irrelevant. 2.3. Structural and morphological observations Current efficiencies were evaluated by gravimetry. The surfaces of the deposits were observed by SEM. The textures were measured by XRD with a powder Bragg–Brentano goniometer (repeated scans with different orientations of the sample were used to ensure that the true vertical texture is observed) and Cu K␣ radiation operated with the following parameters: step size 0.02◦ 2θ , time per step 1 s, 40 kV, 30 mA, fixed divergence, divergence slit angle 1◦ . Detailed analysis of the diffractograms leading to quantitative evaluation of texture type and perfection (as, e.g., reported in [2]) were not performed in this work, where comparative work is of interest. The texture type is [2 1 1] strongly perturbed by [1 1 1]; the (2 0 0) to (1 1 1) peak intensity ratio RI =I(2 0 0)/I(1 1 1) was used to quantify the degree of perfection of the texture (the lower the value of RI , the higher the degree of [1 1 1] preferred orientation).

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Fig. 2. X-ray diffractograms at deposition times t=7, 10, 16, 80 ks, c.d.=5 mA cm−2 and RDE ω=20 rpm.

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Fig. 4. X-ray diffractograms for deposits obtained at c.d.=5, 10, 25 mA cm−2 and RDE ω=200 rpm.

3.2. RDE experiments — laminar flow 3. Results

As discussed elsewhere (e.g. [6]), a transition exists from substrate-induced texture to the texture typical for the electrodeposition conditions. This phenomenon was measured quantitatively at the three deposition c.d.s used in this research at ω=20 rpm. X-ray diffractograms measured at different deposition times for a c.d. of 5 mA cm−2 are shown in Fig. 2, the texture evolution as a function of deposition time and c.d. is reported in Fig. 3. From Fig. 2 it can be observed that the intensity ratio for thinner deposits matches that of the substrate, while the one imposed by the bath and operating conditions sets in gradually; the intensity ratio inversion occurs at a deposit thickness of a few tens of ␮m, much higher than the values required for loss of epitaxy (typically of the order of 100 nm [6]). The same kind of behaviour is typical for all the three c.d.s considered (Fig. 3).

In this section results of the effects of RDE rotation rate (within the laminar range) and total imposed c.d. are studied. In the range of investigated conditions, the bath always imposes the [2 1 1] texture perturbed by [1 1 1], as mentioned in Section 1, but the amount of [1 1 1] preferred orientation is markedly affected by the above-mentioned deposition parameters. In Fig. 4, X-ray diffractograms for deposits obtained at c.d.s 5, 10 and 25 mA cm−2 for an RDE rotation rate ω=200 rpm are shown, all the RI data obtained with RDE in this research are displayed in Fig. 5. In Fig. 6, typical SEM micrographs are reported for some deposits obtained under different c.d. and rotation rate conditions; from these micrographs and from other ones relating to all the investigated samples that are not reported here, it can be concluded that the surface morphology of growth is not markedly affected by rotation rate and c.d. From Fig. 5, it can be observed that RI tends to decrease by increasing the RDE rotation rate ω and by lowering the deposition c.d. iT .

Fig. 3. Texture RI =I(2 0 0)/I(1 1 1) evolution as a function of deposition time and c.d. (RDE ω=20 rpm).

Fig. 5. RI =I(2 0 0)/I(1 1 1) vs. RDE rotation rate ω for c.d.=5, 10 and 25 mA cm−2 .

3.1. Achievement of an asymptotic texture

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Fig. 6. Typical SEM micrographs for deposits obtained under different c.d. and RDE rotation rate conditions: (A) 5 mA cm−2 , 20 rpm; (B) 5 mA cm−2 , 200 rpm; (C) 5 mA cm−2 , 1100 rpm; (D) 10 mA cm−2 , 200 rpm; (E) 25 mA cm−2 , 200 rpm.

The cathodic current efficiencies ηC corresponding to the structural results shown in Fig. 5 are reported in Fig. 7, where it can be noticed that ηC tends to decrease as the RDE rotation rate ω and the deposition c.d. iT are increased and lowered, respectively. From the above-mentioned data, it can be concluded that an approximately linear relation (ρ 2 =0.79) exists between the preferred orientation RI and the cathodic current efficiency ηC , as shown in Fig. 8, in this figure

the least-squares line is displayed with 99% confidence bands. 3.2.1. Limiting c.d.s for hydrogen evolution The limiting c.d. for HER as a function of RDE rotation rate was evaluated by gravimetric measurement of the current efficiency in short deposition runs (∼20 ␮m, except for the cases reported in Fig. 7, which were used in this evalua-

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Fig. 7. Cathodic current efficiencies ηC vs. RDE rotation rate ω for c.d.=5, 10 and 25 mA cm−2 .

283

of the hydrodynamic boundary layer thickness δ H (cm) imposing that stagnant conditions correspond to a vanishing, limiting √ c.d. for HER (an implicit way of stating the Levich iL vs. ω equation for the RDE) obtaining a proportionality constant 1.525±0.064 mA cm−1 (ρ 2 =0.9945). Elaborating on the Levich equation in this case, and solving it for the hydrogen ion diffusion coefficient and using the value of bulk activity of H+ ions deduced from the measured pH, one obtains DH ∼ =1.1 cm2 s−1 , which seems to be an unphysical value. In fact, to the best of the author’s knowledge, no experimental data are available for DH in NiSO4 solutions, some data are nevertheless known for H2 SO4 /H2 O systems and CuSO4 solutions at 25◦ C of ionic strengths similar to that of the Ni plating bath of interest in this research: DH ∼ =2×10−5 cm2 s−1 [17] and DH ∼ =9.37×10−5 cm2 s−1 [23], respectively. The measured limiting c.d. values seem therefore to be related to species electroactive for HER which are different from the hydronium ions and have a concentration close to the cathode surface of the order of 1 M (hydrogen released from metal oxy-hydroxo complexes present at high concentrations at the reacting interface?). 3.3. Natural convection experiments — laminar and turbulent flows

Fig. 8. RI =I(2 0 0)/I(1 1 1) vs. cathodic current efficiencies ηC : the plot refers to all the RDE data of this paper ω=20, 200, 1100, 2000 rpm and c.d.=5, 10, 25 mA cm−2 .

tion and refer to the thick deposits used in this research for XRD analyses), the results are shown in Fig. 9. Assuming that the HER-related c.d.s iH shown in Fig. 9 are asymptotic and equal to the HER limiting c.d. iHL , these values (mA cm−2 ) can be linearly regressed against the reciprocal

Fig. 9. HER c.d.s vs. total c.d. for RDE rotation rates ω=20, 200, 1100 and 2000 rpm.

One deposition experiment was performed at 5 mA cm−2 with the natural convection cell described in Section 2.2; according to the discussion in Section 2.2.3.2 turbulent flow is likely to be achieved in the upper portions of this cell. The interest in achieving turbulent conditions (which is not practically feasible with the RDE equipment at hand) lies in the endeavour to achieve a general correlation between fluid flow and structure for the electrodeposition bath of interest, in addition a contribution is made to the yet unclear topic regarding the effects of turbulent flow conditions on the quality of metal deposits. As far as the characterisation of flow conditions is concerned, the absolute values of the estimates of concentration boundary layer thicknesses reported in Fig. 1 — based on elaborations of literature correlation (the development of new correlations for the case of interest would be definitely interesting, but is out of the scope of the present paper) — are doubtful, and just the trend ought to be considered in the following discussion. We performed XRD experiments on several sections of the cathode and some results are shown in Fig. 10, corresponding to x=3 cm (laminar, RI =11.4, estimated δ C (3 cm)/δ C (30 cm)=0.66), x=15 cm (laminar, RI =24.14, estimated δ C (15 cm)/δ C (30 cm)=1.01) and x=30 cm (laminar, RI =24.16). In Fig. 10 some traces of diffraction peaks from the substrate can be seen, but they are so low that we judge that the asymptotic texture has been achieved; in any case — as far as the evaluation of a trend is concerned — we are on the safe side, since the relevant RI values are very low and errors due to substrate effects lead to an enhance-

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iLN denote the limiting c.d.s for the reduction of hydrogen and nickel, respectively. By application of the Levich equation, it can be shown that, under the less favourable mass-transport conditions: iLN >62 mA cm−2 . In addition, since nickel deposition occurs mainly with hydrogen being deposited at its limiting c.d., Eq. (13) can be approximated with iT = iAN + iLH

(14)

By definition, the cathodic current efficiency can be written as ηC = Fig. 10. X-ray diffractograms for deposits obtained in the natural convection cell x=3 (laminar), 15 (laminar), 30 (turbulent) cm and c.d. 5 mA cm−2 .

ment of these quantity (see Section 3.1). From Fig. 10, it can be concluded that the trends relating hydrodynamic conditions and preferred orientation observed with laminar RDE, are observed also in this case. The direct correlation between concentration boundary layer thickness and preferred orientation is preserved and does not seem to be affected by the laminar to turbulent transition.

4. Discussion Several phenomenological correlations between hydrodynamic conditions and preferred orientation are reported and discussed in Section 3; in this section we mean to propose a correlation which summarises all of them and might give some suggestions concerning the mechanisms which are likely to bring about the observed phenomenology. The single most important correlation disclosed in this work is the linear relationship between the perfection parameter RI and the cathodic current efficiency ηC ; this correlation holds in all the experiments which were performed in this research, irrespective of total deposition c.d. iT and flow conditions (see Fig. 8). We should like to lay this phenomenological correlation on a simple rational basis. First of all, it is evident that the total deposition c.d. iT is given by the sum of hydrogen iH and nickel iN reduction c.d.s iT = iH + iN

1 1 ∼ = 1 + iH /iN 1 + iLH /iAN

(15)

where the adopted approximations are the same as for Eq. (14). From simple algebra and using Eq. (12) and the phenomenological correlation between hydrogen limiting c.d. and either the hydrodynamic or the concentration boundary layer thickness D∗ iLH =1− ηC ∼ =1− iT δiT

(16)

where D∗ is an empirical effective diffusion coefficient. It follows that the preferred orientation parameter RI can be expressed as a function of the operating parameters of interest boundary layer thickness δ C (or δ H ) and imposed (total) c.d. iT RI = A +

B δC iT

(17)

where A and B are empirical parameters. Fig. 11 shows an acceptable consistency of the simple correlation expressed by Eq. (17) with experimental data. The fact that the most important entity affecting the preferential orientation is the cathodic current efficiency, seems

(12)

Since, in principle, the deposition rates are under mixed activation and mass-transport control, Eq. (12) can be written approximately [24] as iT =

1 1 + 1/ iAH + 1/iLH 1/iAN + 1/iLN

(13)

where iAH and iAN denote the fraction of the hydrogen and nickel c.d.s which are under activation control, while iLH and

Fig. 11. RI =I(2 0 0)/I(1 1 1) vs. a suitable combination of the operating parameters: total c.d. iT and concentration boundary layer thickness for Ni2+ δ C . The plot refers to all the RDE data of this paper ω=20, 200, 1100, 2000 rpm and c.d.=5, 10, 25 mA cm−2 .

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to suggest that the temporary ratio of hydrogen to nickel reduction is the physical quantity affecting electrocrystallisation in the investigated system. A very simple explanation for this phenomenon could be that, as the (1 1 1) face is the most catalytic one for HER (see, e.g. [6,25]), if the ratio of hydrogen reduction to nickel reduction increases, it is expected to grow at the slowest rate and thus to give the most prominent features. Interestingly — as far as the relevant literature correlations hold, and the nominal cathodic surface area is representative of the actual one (Fig. 6 hints at the fact that the latter assumption is correct) — this effect should not be related to surface coverage by hydrogen bubbles. Surface coverage by bubbles evolved cathodically can be correlated to deposition conditions by the following relationship (obtained elaborating on [21]):   iH δH 0.18 (18) ϑ = 0.84 AFν

processes leading to texture formation in electrocrystallisation and (ii) for the industry interested in achieving possibly large Ni electroforms with controlled crystallographic properties. The approach adopted in this work — tough semi-empirical in nature — captures a sizeable amount of the physics of the problem and has predictive value as far as the effects of the process variables are concerned.

In this case igas =iLH (mA cm−2 ) and since iLH ∝1/δ H (see Section 3.2.1), the surface coverage by hydrogen bubbles should be a constant, irrespective of hydrodynamic conditions; in the case of this research, as far as RDE experiments are concerned ␽∼ =21%.

References

5. Conclusions This paper is meant to be a contribution to the field of electrocrystallisation engineering and in particular to the topic of multiscale problems, where the establishment of correlations between macroscopic operating conditions and microscopic structural (and therefore functional) properties of the electrodeposits is vital for both fundamental understanding and industrial applications. Mass-transport effects on the texture development of electrodeposited Ni are explicitly addressed for the first time — to the best of the author’s knowledge. The main part of the research was carried out on thick Ni layers — typical for electroforming processes — deposited on an RDE system under laminar flow conditions. An experiment with a natural convection cell provided data for comparisons in the laminar flow region and extension of the research in the turbulent regime section of the cell. A correlation between the amount of (1 1 1) preferred orientation and the cathodic current efficiency was disclosed. The limiting hydrogen c.d. was measured in this system and correlated to hydrodynamic conditions. The cathodic current efficiency was related by an approximate analytical approach to the product of the hydrodynamic boundary layer thickness and the total electrodeposition c.d. The product of these quantities correlated reasonably with the degree of [1 1 1] preferred orientation yielding a simple semi-empirical correlation between operating conditions and structural properties of interest: (i) for the elucidation of the

Acknowledgements Prof. Pietro Luigi Cavallotti’s (Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Italy) personal and financial support for the start-up of the experimental research in metal electrochemistry at the University of Lecce, Italy — of which the present paper is the first report — is gratefully acknowledged.

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