Popov K.I., Djokic S.S., Grgur B.N. Fundamental Aspects of Electrometallurgy
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72
Chapter 3
3.2.3.4 Conclusions
Finally, it can be concluded that increasing the overpotential at one and
the same current density leads to less coarse deposits with prolonged
deposition, because of lower grains formed during the formation of the
surface metal film. This conclusion is valid if In the opposite case, a
rough deposit is often not formed because of disperse or granular deposit
formation. Hence, the first condition that must be satisfied in thick metal
film deposition is that the exchange current density must be considerably
lower than the limiting diffusion current density in the system under
consideration. The second conditions is that the deposition current density
must be a little larger than the one corresponding to the end of the Tafel
linearity. In this way, the formation of large and well-defined crystal grains
due to deposition under activation control will be prevented. At the same
time, the increase of the surface coarseness due to the deposition in mixed
activation-diffusion control will be minimal and the formation of carrot-like
protrusion will be avoided.
On the other hand smooth and bright deposits can be obtained in the
presence of organic additives only in the presence of additives which are
incorporated into the deposits or undergo electrochemical reaction, or, in the
presence of additives which are adsorbed on the flat part of the surfaces,
permitting the deposition at the steps. In fact, bright deposits are obtained by
the synergetic effect of the above two type of additives.
3.3
DISPERSE DEPOSITS
It was shown in the previous sections how compact electrodeposits are
obtained during electrodeposition at low degrees of diffusion control. In
condition close to complete diffusion control, disperse deposits are formed
by the mechanisms discussed below.
3.3.1
Spongy deposits
3.3.1.1
Mathematical Model
It follows from Eq. 2.28
that deposition in systems with low exchange current densities comes under
full diffusion control at sufficiently large overpotentials. On the other hand, if:
3. Surface Morphology of Metal Electrodeposits
73
deposition will be under complete diffusion control at all overpotentials if
some other kind of control does not take place (e.g., for silver deposition on
a well defined silver crystal grains at a silver electrode at low overpotentials
two-dimensional nucleation is the rate-determining step
61
).
At low overpotentials a small number of nuclei are formed, and they can
grow independently. The limiting diffusion current density to the growing
nucleus is given by
or
where is the tip radius of the nucleus. Hence, if
the condition given
by Eq. 3.48 is not satisfied and deposition is under activation or mixed
control. Pure activation-controlled deposition is, thus, possible even at
on very small electrodes such as nuclei on an inert substrate.
An increase in leads to a decrease of and, at sufficiently large
the deposition comes under mixed activation-diffusion control, i.e. when:
where is the radius of a growing nucleus where the process comes under
mixed control
9,32
.
Under mixed control of the deposition, amplification of the surface
irregularities on the growing nucleus occurs, leading to the formation of a
spherical agglomerate of filaments. Thereby a spongy deposit is formed. The
above reasoning is valid if spherical diffusion control can occur around
growing grains, as in the case of cauliflower deposit growth. Assuming that
around each grain with radius growing under spherical diffusion control,
a diffusion layer of the same thickness is formed, then the initiation of
spongy growth is possible if the number of nuclei per square centimetre, N,
satisfies the condition
74
Chapter 3
On the basis of all the above facts, it can be concluded that the formation of a
spongy deposit on an inert substrate may be caused by mass-transport limita-
tions when the nucleation rate is low. Hence, suitable conditions for the for-
mation of spongy deposits arise at low overpotentials in systems where
The validity of the condition, given by Eq. 3.48 can be easily tested using
solutions of widely varying concentrations. The values for
cadmium deposition from sulfate solutions are estimated as for
(solution 1) and for
(solution 2). The corresponding limiting diffusion currents can be assumed
to be and respectively. Hence, and,
where the subscripts 1 and 2 correspond to solutions 1 and 2.
The cadmium deposit obtained from solution 1 is spongy as can be seen in
Fig. 3.34a, meaning that the conditions given by Eq. 3.48 and Eqs. 3.51 and
3.52 are all satisfied. In the case of solution 2, Eq. 3.48 is not satisfied and so
suitable conditions for the formation of a spongy deposit are not given.
Hence, the grains grow under pure activation control until a complete
surface film is formed, as illustrated in Fig. 3.34b, c
9,32
.
3.3.1.2 Physical Model
As was mentioned before, at a fixed value of the overpotential, the
growth of a spongy deposit is possible if:
The situation in which spongy deposits can start to grow can easily be
demonstrated
62
. Grains of the desired size and distribution can be grown at low
overpotentials under conditions of activation-controlled deposition. This
3. Surface Morphology of Metal Electrodeposits
75
corresponds to growth of grains when The situation in which can be
simulated by increasing the overpotential to a sufficiently high value to result in
diffusion control around the growing grains and the amplification of surface
irregularities. With increasing overpotential decreases. This permits the
simulation of the initial stage of spongy growth, as is illustrated in Fig. 3.35.
The growth of protrusions in all directions is a good proof that the
deposition on the grain is under spherical diffusion control. At longer
deposition times, the protrusions branch and interweave, as is shown in Fig.
3.36, causing the macroelectrode to have a spongy appearance.
76
Chapter 3
3.3.1.3 Real Systems
Typical spongy electrodeposits are formed during zinc and cadmium
electrodeposition at low overpotentials
9,32
. Scanning electron microscopy
images of zinc deposited at an overpotental of 20 mV onto a copper
electrode from an alkaline zincate solution are shown in Fig. 3.37.
The increase in the number of nuclei formed with increasing deposition
time can be seen in Fig. 3.37a and b, and a spongy deposit is formed as can
be seen in Fig. 3.37b. The spongy growth takes place on a relatively small
number of nuclei, as is shown in Fig. 3.37b and c.
3. Surface Morphology of Metal Electrodeposits
77
The initiation of spongy growth at a fixed overpotential is possible if the
condition (Eq. 3.51) is satisfied, which is the case after some time.
On the other hand, increasing the deposition time leads to the formation of a
larger number of nuclei, and so the condition given by Eq. 3.52 is not
satisfied over a large part of the electrode surface. Regardless of this, the
coverage of the electrode surface by spongy deposits increases with
increasing deposition time up to full coverage, as can be seen in Fig. 3.37d,
in the same way as was illustrated earlier by Fig. 3.36.
Spongy growth can start on the growing nucleus if the conditions given by
Eqs. 3.51 and 3.52 are both satisfied simultaneously.
In the first stage of deposition, the formation of nuclei having a regular
crystal shape can be expected because the deposition is activation-controlled.
After is reached, the system comes under mixed control, producing
polycrystalline grains like those shown in Fig. 3.38a, just as in the case of
mixed control of copper deposition
39
, Fig. 3.21c. In this situation,
amplification of the surface irregularities on the growing grains occurs, and
spongy growth is initiated.
An ideal spongy nucleus obtained in a real system is shown in Fig. 3.38b
which illustrates the above discussion and physical simulation well
63
. The
agglomerate of filaments in Fig. 3.37b is obviously formed by further growth
of nuclei like that in Fig. 3.38b.
Hence, it can be concluded that at low overpotentials the initiation of
spongy growth is due to the amplification of surface protrusions directly
inside the spherical diffusion layer formed around each independently
78
Chapter 3
growing grain, as in the case of the formation of cauliflower deposits. The
growth of protrusions in all directions is good proof that the initial stage of
deposition on the grain is under spherical diffusion control, while further
growth takes place in the diffusion layer of the macroelectrode. In less ideal
situations, non-ideal spongy nuclei are formed, which, however, after further
deposition result in a macroelectrode with the same appearance.
It should be noted that some other possible mechanisms of spongy
deposit formation have been considered in a qualitative way, as reviewed in
Refs. 64 and 65, but the mechanism presented above seems to be the most
probable
65
. However, the mechanism of formation of a spongy deposit over
an initial coating, which is not seen in the case of cadmium but occurs in
zinc deposition
9,63
requires clarification. For instance, the mechanism of
spongy growth initiation in this case has not been elucidated.
3.3.2
Dendritic deposits
3.3.2.1 Mathematical Model
Two phenomena seem to distinguish dendritic from carrot-like
growth
31,32
:
1. a certain well-defined critical overpotential value appears to exist
below which dendrites do not grow,
2. dendrites exhibit a highly ordered structure and grow and branch in
well-defined directions. According to Wranglen
66
, a dendrite is a skeleton of
a monocrystal and consists of a stalk and branches, thereby resembling a
tree.
It is known that dendritic growth occurs selectively at three types of
growth sites
31
:
1. dendritic growth occurs at screw dislocations. Sword-like dendrites
with pyramidal tips are formed by this process
31,36
.
2. many investigations of the crystallographic properties of dendrites
have reported the existence of twin structures
67-69
. In the twinning process, a
so-called indestructible re-entrant groove is formed. Repeated one-
dimensional nucleation in the groove is sufficient to provide for growth
extending in the direction defined by the bisector of the angle between the
twin plants
31,32
.
3. it is a particular feature of a hexagonal close-packed lattice that growth
along a high-index axis does not lead to the formation of low index planes.
Grooves containing planes are perpetuated, and so is the chance for extended
growth by the one-dimensional nucleation mechanism
70
.
In all the above cases, the adatoms are incorporated into the lattice by
repeated one-dimensional nucleation. On the other hand deposition to the tip
of screw dislocations can be theoretically considered as deposition to a point;
in the other two cases, the deposition is to a line.
3. Surface Morphology of Metal Electrodeposits
79
From the electrochemical point of view, a dendrite can be defined as an
electrode surface protrusion that grows under activation control, while
deposition to the macroelectrode is predominantly under diffusion
control
31,32,36
. The polarisation curve for a flat macroelectrode is given by Eq.
2.28
and that for the tip of a protrusion growing inside the macroelectrode
diffusion layer is given by Eq. 3.25
It follows from Eq. 2.28 that if and On the other
hand, if h >> r and activation-controlled deposition to the tip of
the protrusion takes place, and Eq. 3.25 can be rewritten in the form:
where is the corrected value of the exchange current density. This is so
because if r/h << 1,
Eq. 3.22
can be rewritten in the form
where is the concentration at the tip of a protrusion growing under
activation control inside the diffusion layer of the macroelectrode if the
deposition to it is under full diffusion control
36
. A similar situation can arise
if cylindrical diffusion around the tip of a growing protrusion occurrs
71
.
The exchange current density at the tip of such a protrusion is given
by
72
:
80
C
hapter 3
or, taking into account Eq. 3.54,
where is a function of the symmetry factor and is the exchange current
density corresponding to the bulk concentration of the depositing ion.
Assuming for the sake of simplicity that is approximately 1, Eq. 3.53 can
then be rewritten in the form:
Dendrites grow faster than the flat electrode surface, and the condition
for the initiation of dendritic growth is:
where corresponds to the critical overpotential at which initiation of
dendritic growth from the tip of a growing protrusion, whose height is h, is
instantaneously possible after the steady-state concentration distribution
inside the diffusion layer of the macroelectrode has been reached. Taking
into account the relationship:
Eq. 3.58 can be rewritten in the form:
The minimum overpotential at which dendritic growth can be initiated,
corresponds to and Eq. 3.59 becomes:
3. Surface Morphology of Metal Electrodeposits
81
A different situation arises if and but
The current density to the tip of the protrusion is then given by:
for while the diffusion current density to the macroelectrode is
given by
Assuming that can be used instead of and following the same
reasoning as in the derivation of Eqs. 3.58 and 3.60, one obtains:
It should be noted that all the above derivations are valid, if the
protrusion tip radius is sufficiently large to make the effect of the surface
energy term negligible
37
, and if Eqn. 2.32 is also valid.
It follows from Eq. 3.63 that for systems with dendritic growth is
possible at all overpotentials. Experimentally, some critical overpotential of
dendritic growth initiation exists in all cases, being of the order of 10
mV
37,73,74
. Assuming that under complete diffusion and surface energy
control the current density to the macroelectrode is given by
37
:
and, assuming that Eq. 3.54 is valid, the current density on the tip of a
dendrite growing inside the diffusion layer of a macroelectrode is given by:
then, it is possible to derive the relationships: