Popov K.I., Djokic S.S., Grgur B.N. Fundamental Aspects of Electrometallurgy

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152

Chapter 5

It is obvious from Eqs. 5.2, 5.4, and 5.7 and Eqs. 5.21 and 5.26 that, in

both cases,

taking into account also Eq. 2.29

For j(t) given by Eq. 5.15, the surface concentration under periodic

conditions is approximately given by

Hence, at sufficiently small value of T and not extremely high values of

in AC will also be given by Eq. 5.27, implying that at sufficiently high

frequencies, surface concentration is determined by the average current

density regardless of the shape of the current wave.

In the case of a rectangular pulsating overpotential, as a function of

time, is given by

Assuming that the surface concentration is determined by the average

current density, Eq. 5.16 can be rewritten in the form

For a sufficiently high value of Eq. 5.30 reduces during the on

periods to:

and during the off periods to:

5. Electrodeposition at a Periodically Changing Rate

153

The average current in PO deposition can easily be determined by

The overpotential amplitude is then given by

and

where

and

Polarization curves for the average values for the copper deposition

have been successfully calculated from the stationary polarization curve

using Eq. 5.35

for This is a good evidence that in PO deposition,

the average current density also determines the surface concentration of the

depositing ion.

The overpotential amplitude is larger than in the DC regime for one and

the same average current density. At the same time, the diffusion overpo-

tential remains constant, depending on the average current density only.

Hence, the part of activation control in the overall amplitude overpotential

increases with increasing pause to pulse ratio.

The situation is similar in pulsating or reversing current electrode-

position.

154

Chapter 5

5.2.2

Capacitance effects

From the above discussion, it can be concluded that the useful range of

frequencies is limited by mass-transfer effects at low frequencies. At high

frequencies, the useful range is limited by the effect of the capacitance of

the electrical double layer

. This is shown here for PC deposition. The

time dependencies of the overpotential during the current pulses are shown

Fig. 5.4.

Mass-transfer limitations cause an increase of the overpotential at

deposition times longer than the transition time as shown in Fig. 5.4a; the

system enters full diffusion control at low frequencies if This is

followed by an increase in the average overpotential

10,15

. At high

frequencies, the PC is used both for double-layer charging and discharging,

and for the deposition process, as illustrated by Fig. 5.5. The capacitance

current during periodic charging and discharging of the double layer, at

5. Electrodeposition at a Periodically Changing Rate

155

frequencies at which the effect of the double layer cannot be neglected,

produces a smearing effect on the Faradic current wave, as illustrated by

Fig. 5.4b.

Hence, as the frequency increases, the faradic current wave flattens,

approaching a DC shape, and gives the same quality of deposit as DC even

though the overall current appears to be pulsating. This is also followed by

an increase in the average overpotential. Hence, the minimum average

overpotential is a good indicator of the optimum frequency range of

pulsation

3,10,15

in PC deposition. This range depends on the average current

density and p, but, in general, the frequency lies in the range between 10 and

100 Hz, as illustrated in Figs. 5.4c and 5.4d.

In PO deposition, the effect of the double layer capacitance becomes less

pronounced at higher frequencies compared to the other cases

. Also, at

very high frequencies, the shape of the PO wave changes; for example, a

square-wave PO becomes similar to a triangular one

10,17

156

Chapter 5

5.2.3 Reversing current in the second range

For T close to the behaviour of the system under RC conditions has to

be analyzed using Eq. 5.18

. In this case, the concentration distribution

inside the diffusion layer at the end of the anodic pulse is close to that given

by Eq. 5.10. It follows from Eq. 5.18 that this will occur at:

It is known

that for the series in Eq. 5.39 can be

approximated using only the first term

(

k = 0). Hence, for

It is easy to show that for T = 3 r = 0.7 and for T = 16 r = 0.2 by

assuming that Eq. 5.40 is valid for T > 3 and that for T > 16 the system

behaves as under DC conditions. The optimum ratio is given by

for periods T such that

5. Electrodeposition at a Periodically Changing Rate

157

if for cm and A good agreement between

the shape and the frequency of the RC calculated in this way and literature

data is obtained, because in practically all cases, according to Bakhvalov

On the other hand, the solution of Eqs. 5.9 to 5.12 for

is given by

It follows from Eq. 5.46 that the surface concentration of depositing ions

for can be given by:

The maximum amplitude of the current density variation,

corresponding to after a deposition time is given by

It is obvious that using Eqs. 5.1 and 5.4 and r =f(T) given by Eq. 5.41,

Eq. 5.48 can be rewritten in the form

In this way the complete RC wave can be estimated, or precisely

calculated without approximations using a computer.

158

Chapter 5

5.3 PREVENTION OF THE FORMATION OF

SPONGY DEPOSITS AND THE EFFECT ON

DENDRITIC PARTICLES

EPCR is used in the charging of silver-zinc storage batteries, to prevent, or to

delay, the formation of spongy and dendritic deposits of zinc

19,20

. It is impossible

to obtain smooth deposits of zinc from alkaline zincate solutions during

prolonged deposition at a constant rate

20,21

, because at lower overpotentials,

spongy deposits arise while at higher overpotentials, dendritic zinc is formed.

It is well known that the reversible potential of a surface with radius of

curvature would depart from that of a planar surface by the quantity

where is the interfacial energy. The filaments which form spongy deposits

have extremely small tip radii. This makes the equilibrium potential of the

spongy deposit 7 to 10 mV more cathodic than that of zinc foil

23,24

Spongy deposit formation can, however, be completely prevented by PO

deposition

, as illustrated in Fig. 5.6.

Obviously, the more negative filaments dissolve faster during the off

period than the flat surface, resulting in a smooth deposit. This is also valid

for deposition using all current or overpotential waveforms that are

characterized by some anodic current flow

3,7

If spongy deposit formation is prevented or delayed the charging of the

silver -zinc batteries is considerably improved

5. Electrodeposition at a Periodically Changing Rate

159

The quantitative treatment of the selective dissolution during pauses can

be performed as follows

. Equation 5.30 is valid for a flat electrode surface

or protrusions with sufficiently large tip radii, where the surface energy term

can be neglected. If it can not be neglected in zinc deposition, Eq. 5.30. can

be rewritten for the tip of a protrusion inside the diffusion layer (h – height

of protrusion and tip radius) in the form:

where is the tip current density and is the average current density to the

macroelectrode.

This is because:

if or ( and are the concentration of the depositing ions on

the electrode surface and on the tip of a protrusion, respectively), if

The output current during pauses become

It is easy to show that the difference between the current density on the

tip of a dendrite and the flat surface during the "off ” period can be given by

This means that the dissolution of the a protrusion with tip radius is faster

relative to the flat surface or a protrusion with a sufficiently large value of

It is obvious that spongy filaments can be completely (Fig. 5.6), and

dendrites with low tip radii partially or completely dissolved during the

pause, (Fig 5.7.). This means that both branching of dendrites and the

formation of agglomerates can be prevented in square-wave pulsating

overpotential deposition. In this way, even powder particle like that in Figs.

5.8 and 5.9 can be obtained.

160

Chapter 5

. Electrodeposition at a Periodically Changing Rate

161

The monocrystal surfaces of silver powder particles can be explained by

the assumption that during the off period of PO the adatoms in nonstable

positions will dissolve faster than atoms in stable position in lattice. The

similar effect on the morphology of powder particles can be seen in RC

deposition

28,29

, which leads to the strong effect on the apparent density of

copper powders

5.4

COMPACT DEPOSITS

5.4.1

Surface film

The first stage of metal film formation is nucleation on a foreign

substrate. The nucleation rate, J, is given by Eq. 3.10 and depends strongly

on the deposition overpotential. The nucleation overpotential is larger than

the stationary one in galvanostatic deposition, and stationary values of the

overpotential can be used in discussions of the effect of EPCR in

galvanostatic as well as in potentiostatic deposition. It is obvious that in all

cases of EPCR, the overpotential amplitude, is larger than in constant-

current or constant overpotential deposition, for the same average current

density.

Nucleation rate, J, in DC regime is given by:

Therefore,