Popov K.I., Djokic S.S., Grgur B.N. Fundamental Aspects of Electrometallurgy
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132
Chapter 4
For the ammonium bath there is a region where deposition is under
activation control because and a slope of
Hence, nucleation occurs over all surface. For deposition from the
ammonium bath, as predicted by Fig. 4.28, a more homogenous distribution
of the deposit is obtained, which is illustrated in Figs. 4.29c and 29d.
In this way the effects of the deposition process parameters, ohmic
resistivity on the current distribution are shown. It is obvious that decrease of
the ohmic resistance and the increase of cathodic Tafel slope improve the
current density distribution and in the case of
the decrease of
to the
value
The effect of cell geometry and deposition conditions was
treated in the previous section.
4. The Current Distribution in Electrochemical Cells
133
4.3 CORNER WEAKNESS PHENOMENA IN
ELECTROFORMING
“Corner weakness” occurs in heavy deposits or electroforms at screened
cathode parts i.e. corners. The deposit is thinner and at these areas,, in extreme
cases, there is no deposition at all along the line of the corner bisector
18
.
The consequence is the emergence of fracture under negligible load along
the line of the corner bisection, instead of fracture at much higher loads across
the narrowest cross-section of an electroform normal to the line of pull.
To the best of our knowledge, a theoretical analysis of this phenomenon
has not been reported so far. The purpose of this work was to undertake one,
using the following assumptions
19
:
the potential difference between each of two points on the anode and
cathode is equal to the cell voltage,
the current lines are normal to the electrode surface,
along each current line a corresponding ohmic resistance exists and the
current lines are independent of and insulated from each other,
current lines in the vicinity of a protrusion divide into components
which are normal to the electrode surface and
the Kirchoff laws are valid for current lines branching.
4.3.1 Ohmic controlled deposition
According to the assumed model of current line division it follows that
there is no deposition along the line of bisection if the division of the current
lines occurs along the line indicated by the dashed line in Fig. 4.31. It can be
134
Chapter 4
seen that this configuration provides the same density of current lines at the
cathode as at the anode.
The ohmic potential drops along the current lines j and are given by
Eqs. 4.47 and 4.48 respectively, asuming E=0.
where U is the cell voltage and is the resistivity of the solution. The ohmic
resistance along the current line is somewhat different. It consists of the
resistance between the anode and the dividing point (DP) and two
resistances, proportional to x and h – x connected in parallel between the DP
and the cathode. Hence, the ohmic potential drop along current line can be
written as:
Elimination of U from Eqs. 4.47 and 4.49 and further rearrangement
gives
4. The Current Distribution in Electrochemical Cells
135
The current densities and are given by
and
Substitution of from Eq. 4.50 into Eq. 4.51 and 4.52 and further
rearrangement with use of Eqn. 4.47 gives
and
which enable the calculation of the deposit profiles at the cathode
represented by Fig. 4.31
The proposed model implies that there is no current component in the
direction of the corner vertex, and that the appearance of a crack along the
corner bisector is to be expected.
A compact deposit cannot be obtained directly, but rather by the build up
of the deposit in the x and y direction. An overlap of the x and y oriented
deposits should occur when the current density virtually does not depend on
the distance from the very corner. However, if the current density decreases
upon approaching the corner vertex, the deposits would not overlap and a
flaw would be created.
Equations 4.53 and 4.54 may be utilized for the calculation of the current
density distribution at the beginning of deposition. The results of this
calculation are shown in Fig. 4.32, as well as for different deposition times.
It is obvious that there should be no overlap of the deposit upon prolonged
deposition. Moreover, it should be noted that the profiles were calculated
assuming a constant current density, which is not the case in a real system
where the space in the vicinity of the corner vertex is increasingly screened as
the deposit grows. This implies that the real distribution of the metal deposit in
the corners is worse than that calculated and shown in Fig. 4.32.
136
Chapter 4
A number of microphotographs of deposit cross-sections illustrating the
"corner weakness" effect can be found in the literature. They are schemati-
cally exemplified by Fig. 4.30. It can be seen that the calculated deposit
profile (Fig. 4.32), with a crack appearing along the corner bisector, looks
very similar to that typically obtained in plating practice (Fig. 4.30).
4.3.2 Mixed activation - diffusion - ohmic controlled deposition
In this case, it is not possible to perform an analysis of the current density
distribution in the same manner as in the case of ohmic controlled deposi-
tion. Only a numerical solution can be obtained, regardless of the fact that
the current line distribution is the same as shown in Fig. 4.31.
It is to be noted that in the model used anode and cathode are not
isopotentional. Because of this the overpotentials in different points are
calculated by direct using of Eqs.2.39 and 2.44 and corresponding current
densities. It is assumed that cathode deposition is under mixed activation
diffusion control and that anode dissolution is under activation control.
In this case, the first step is the calculation of the voltage current curves,
for interelectrode distances l and l + h, using Eqs 4.55 and 4.56.
4. The Current Distribution in Electrochemical Cells
137
where U is the cell voltage, and and are the anodic and cathodic Tafel
slopes and exchange current density respectively and is the limiting diffusion
current density for the cathodic process, assuming the zero value of the
reversible potential difference. The corresponding cell voltage-current curves
shown in Fig. 4.33 enable the determination of the current densities on the
frontal parts of the cathode (j and ) for any cell voltage.
The overall current density along the current line from the anode to the
DP is obviously the sum of the partial ones branching at the DP, i.e.
Hence, Eqs. 4.57 and 4.58 are valid
Elimination of U from Eqs. 4.57 and 4.58 gives
138
Chapter 4
Obviously, both sides of Eq. 4.59 represent the potential drop between
the DP and the cathode, which can be plotted as a function of either
or as shown in Fig. 4.34a and 4.34b, respectively.
From the dependencies shown in Fig. 4.34, the corresponding values of
and can be extracted by interpolation, for any and x. These are
required for the calculation of the potential drop between the anode and the
DP, according to Eq. 4.60 and the overall cell voltage, U, according to
Eq.
4.61.
Now, U, and can be tabulated or plotted as functions of the overall
current density, as exemplified in Fig. 4.35, for one value of x.
The situation is similar in the case of mixed diffusion-activation control.
The profiles of the deposit at different times (Fig. 4.36) were calculated
according to the procedures given above and the corresponding parameters:
and
h=10
cm and
l=5
cm.
4. The Current Distribution in Electrochemical Cells
139
Comparing the calculated deposit profiles for pure ohmic control (Fig.
4.32) with those pertaining to diffusion-activation control (Fig. 4.36), a
significant difference in the cross section can be noticed. In the latter case,
despite a much poorer system geometry
(
cf. h to l ratio) from the viewpoint
of current distribution, no failure in the deposit appears. Even so, a flaw in
the deposit along the corner bisector may be expected in both cases.
140
Chapter 4
4.3.3 Activation - diffusion controlled deposition
In this case, the current line between the DP and the cathode splits into
two equal parts. Hence, for one can write:
and simultaneously:
Elimination of U from Eqs. 4.62 and 4.63 permits the correlation between
j and in the form of Eq. 4.64, which cannot be solved explicitly if
If and Eq. 4.64 can be rewritten in the form:
or
which holds for pure activation control.
Evenly distributed deposits, without "comer weakness", may be obtained
only by deposition under complete activation control at high Tafel slopes
(Fig. 4.37). In practice, this is usually achieved by employing appropriate
surface-active additives, as seen in Fig. 4.38.
In this way not only is the “corner weakness” effect fully explained, but
also a new method of current density distribution evaluation in
electrochemical cells is promoted.
4. The Current Distribution in Electrochemical Cells
141
4.4 CONCLUSIONS
The current density distribution in electrochemical cell was considered in
a new manner on the basis of equation of the electrode kinetics. In this way
it was possible to illustrate the effect of deposition conditions, geometry of
the system and kinetic parameters of deposition processes. Besides, three
main problems of current density distribution in electrometallurgy were
treated semiquantitatively. The edge effect in metal electrorefinning and
electrowinning processes was discussed in details and it was shown that the