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

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162

Chapter 5

where and

Hence, for the same current density:

as illustrated in Fig. 5.10.

On the other hand the increased amplitude on the current density leads to

an increase of the ohmic potential drop during the pulses in EPCR relative to

constant regimes and Eq. 3.5

can be rewritten in the form:

It follows from Eq. 3.5 and Eq. 5.58 that:

because with increasing p

Hence, the increasing nucleation density is also due to the decreasing

zero nucleation zone radii. This effect leads to an increased coverage of the

foreign substrate by the same quantity of deposited metal and to decreased

porosity, surface resistance and increased density of deposit. Also, it can be

expected that increase in compactness is associated with a decrease in

internal stresses and increased ductility and hardness of metal deposits

. Electrodeposition at a Periodically Changing Rate

163

5.4.2 Electrode surface coarsening

The general equation of the polarization curve is given by:

for the flat part of an electrode and by

for the tip of a protrusion around which the lateral diffusion flux can

be neglected.

Using Eq. 5.19 in the form

it is easy to show that

164

Chapter 5

and

where and are the surface concentration of depositing ions on the flat

electrode surface and on the tip of a protrusion respectively.

The rate of increase at the tip of a protrusion relative to the flat surface is

given by

after substitution of and from Eqs.5.62 and 5.63 into Eq.

5.65a and further rearranging, assuming

It was shown earlier that at sufficiently high frequencies, the average

current density in electrodeposition at a periodically changing rate produces

the same concentration distribution inside the diffusion layer as a constant

current density of the same intensity. Hence, Eq. 5.65b is valid for all cases

of electrodeposition at a constant and periodically changing rate at

sufficiently high frequencies.

However, an increase in surface coarseness in deposition using a

rectangular pulsating overpotential or pulsating current is only possible

during the pulses of current or overpotential

and the integral form of Eq.

5.65 can be written as

. Electrodeposition at a Periodically Changing Rate

165

Equation 5.66 is valid for a pulsating current, square wave pulsating

overpotential and reversing current in the millisecond range under the

assumption that the entire surface dissolves uniformly during the pauses. The

deposits obtained by constant and pulsating overpotential in the mixed

control under other conditions are the same are shown in Fig 5.11. The

deposit obtained by pulsating overpotential is considerably less rough.

The copper deposits obtained under activation and mixed control as those

from Fig. 3.21 are shown in Fig 5.12. A considerable decrease in the grain

size of deposit obtained at low current densities (in the activation controlled

region Fig. 3.21a and Fig. 5.12a) due to the increase of the amplitude of the

overpotential relative to the corresponding value in constant overpotential

deposition, can be seen. There is no qualitative change, however, in the

structure of the deposit.

A qualitative change in the structure of the deposit appears in mixed

controlled deposition (Fig 3.21c and Fig. 5.12b). It is seen that the

protrusions caused by mass transport limitations are strongly reduced

relative to the deposits shown in Fig. 3.21c, but the grain size in enlarged. It

is obvious that the grains obtained by pulsating overpotential with current

densities belonging to the region of mixed control, Fig. 5.12b, are almost as

regular as those deposited under activation control (Fig. 5.12a). This is

obviously due to the increased degree of activation control during the

overpotential pulses and the increased grain size relative to those in Fig.

3.21b and c is due to the selective dissolution during the "off” periods. The

smaller nuclei formed during the overpotential pulse will be completely or

partially dissolved during the overpotential pause and the current density and

the current density on the partially dissolved ones during the next

overpotential pulse will be considerably lower than on larger ones because of

their more negative reversible potentials, and the growth of larger grains will

be favorized.

In this way the appearance of the deposit shown in Fig. 3.21c changes

and becomes that shown in Fig. 5.12b which was formed using PO

deposition of the same quantity of deposited metal and average current

density. It can be also seen from Fig. 5.12 that a good deposit can be

obtained by PO deposition over a wide range of current densities. This

means that in EPCR deposition current density can be considerably

increased relative to DC case.

166

Chapter 5

On the other hand, it is known that the orientation of nuclei strongly

depends on the depositing overpotential and that the electrode reaction

parameters can be different for different crystal planes. It is therefore not

surprising that the effect of structure on EPCR has been reported for many

cases. In some cases, deposits which behave as monocrystals

and deposits

with improved crystal perfection can be obtained.

. Electrodeposition at a Periodically Changing Rate

167

It is obvious that the same reasoning is valid for RC in the millisecond

range and PC. Some different situations appear in the case of RC in the

second range

The surface concentration changes during the cathodic pulse in RC

deposition in the second range according to Eq.

5.46.

where

In this case

is also valid and substitution of from Eq. 5.67 in Eq. 5.69 gives

for the tip of a protrusion and

for a position a flat surface. If all the surface is isopotential, elimination of

from Eqs. 5.70 and 5.71 and further rearranging produces

168

Chapter 5

The difference in the current densities at the tip of a protrusion and the

flat portion of the electrode is then given by:

for

Now, according to Eqs. 5.72 and 5.73 it can be written

or in the integral form:

where

for the first phase.

Assuming that the surface will dissolute uniformly during the anodic

is satisfied. The above reasoning is valid if a polycrystalline deposit is

obtained and the same derivation as in case of CO deposition can be used.

It can be seen from Fig. 5.13 that the structure of the deposit obtained by

RC in the second range is more similar to that obtained in the DC than in the

PC regime, but the surface coarseness of this deposit is considerably lower

than in DC case, being close to this in PC deposition.

This is because in RC deposition there is a considerable concentration

polarisation, producing polycrystalline deposit.

period, it is obvious that because f

(0)

= 0 and the increase in the

surface coarseness in the RC regime will be lower than in the DC regime

until the condition

. Electrodeposition at a Periodically Changing Rate

169

5.5 Current density and morphology distribution on a

macroprofile

The current density distribution on a macroprofile in EPCR has been

treated in several papers

. It seems that this distribution improves the

deposition by current waves with anodic flow but that without this flow it is

worse than in DC deposition. This behaviour can be successfully

explained

Assuming that Eq. 4.43 is valid for the flat electrode in a cell with low

anode polarization also, the current densities in the middle, j, and at the edge,

of a flat electrode in a cell with low anode polarization can be related by

if the deposition in both cases is under activation control in the Tafel region

and that the limiting diffusion current density is the same in the middle and

at the edge of the electrode, I is the cell current corresponding to j. During

the current pulses the amplitude values of current densities and current

should be substituted in Eq. 4.43 producing

where and are the amplitude values of current densities in the middle

and at the edge of electrode and is the amplitude of the current in the cell.

On the other hand, the amplitude in pulsating current deposition and average

current density are related by Eq. 5.7

170

Chapter 5

so Eq. 5.78 can be rewritten in the form

then meaning worse current density distribution in PC than in DC

conditions

The effect of reversing current on the current distribution at the

macroprofile level can easily be discussed for the case of activation-

controlled deposition if the Tafel slopes of the anodic and cathodic processes

are different, as they are for copper deposition and dissolution in sulphate

solutions. With the assumption that the current density in RC deposition is

sufficiently high so that the effect of the opposing processes can be

neglected, the limiting diffusion current density is the same over all

electrode surface. The difference between the current density at the edge and

that at the middle of the electrode in cathodic deposition is

and for anodic case

since for copper deposition, where and are the cell currents

assuming that if

corresponding to and It is obvious that for

. Electrodeposition at a Periodically Changing Rate

171

which occurs when

The best current distribution is expected in the case of PO if all the

electrode surface can be taken as an isopotential. Under the assumption that

the limiting diffusion current density does not vary over the electrode surface

area, the same current density can be expected over all points of the

electrode. A good approximation of PO deposition can be the RC deposition

by the current wave optimized relative both current density distribution on

micro and macro profile as recently shown

. Hence, it seams that RC should

be the optimum regime of EPCR. Besides, the crack-free chromium deposits

with improved current density distribution on both micro and macroprofile

and with practically no reduced hardness were obtained recently

36,37

, by RC

deposition. This means that the formation of unstable chromium hydride can

also be prevented by RC, but this phenomenon has been not treated

semiquantitatively so far.

(if and

deposits of equal thickness can be obtained at the

edge and at the middle of the electrode. In this way, a completely uniform

average current density distribution at the macroprofile level can be obtained

in RC deposition. The diffusion limitations of the cathodic processes will

improve the distribution in RC, but this approach is sufficient to explain the

essence of the effect, as illustrated in Fig. 5.14