38
2 Electrochemistry and Electrodeposition
N = N 0
1 − exp(−At)
(2.23)
If we accept Eq. 2.21 as the nucleation rate law, then two extreme cases can be
distinguished. If A (t)
−1 , we get that N = N 0 . Here, t is the period between
two consecutive observation events during the experiment (or, in other words, 1/t
is the sampling frequency). The result means that the sites that are appropriate for
nucleation are saturated with nuclei from the very beginning of the process, which is
the definition of the instantaneous nucleation. However, if A (t)
−1 , N = N 0 At is
obtained, indicating an even nucleation probability throughout the entire observation
period, as defined for the progressive nucleation.
The study of the Volmer–Weber type nucleation in electrochemical systems
usually requires electrolyte solutions that exhibit much lower concentrations than
baths used in the galvanic industry (at most a few tens of mmol dm
−3 versus about
1 mmol dm
−3 , respectively). This is because the instantaneous or progressive nature
of the nucleation is already hidden once the newly-formed grains coalesce. Also, the
substrate used in the nucleation study has to be structurally rather incompatible with
the deposit in order to fulfil the conditions at which this type of nucleation can take
place at all.
The deposit formation usually does not start at a small overvoltage (as referred
to the equilibrium potential of the Me
z+ /Me electrode) because of the energy barrier
of the nucleation. The typical experimental conditions include the potentiostatic
polarization with a potential step to a value so that the deposition becomes diffusionlimited. Under such conditions, a spherical diffusion field develops around all grains,
as shown in various representations in Fig. 2.16.
Although Fig. 2.16 indicates well the overlap of the diffusion field of the grains
as time passes, the limits of the schematic image should also be kept in mind (e.g.,
perfect hemispherical growth in spite of the laterally uneven supply of the precursor,
disregarding the crystalline nature of the deposit and the possible directional preference of the crystal growth etc.). As the grains grow and the solution becomes
depleted with respect of the precursor ions, the diffusion field is planarized, and the
same transport conditions are obtained as during the Cottrell experiment.
The chronoamperometric transient in the early phase of the process bears information on the nature of the nucleation. Here a few works of Sharifker are referred to [14,
15] without the deep mathematical details. The treatment of the chronoamperometric
data includes a normalization of the current density with respect to the peak current
density (j* = {j/j MAX }
2 ). The time also has to be dealt with in a dimensionless form,
using the time belonging to the current density maximum as a normalization parameter (t* = t/t MAX ). Typical results for the major nucleation modes are presented in
Fig. 2.17. The concave or the convex nature of the j*(t*) function near t* = 0 is usually
regarded as a diagnostic criterion for the instantaneous and progressive nucleation,
respectively. Chronoamperometric transients for more complex nucleation cases are
also available in the literature (see Chap. 5 or Ref. [3]).
In contrast to the Volmer–Weber type growth, the initial stage of the phase formation can be completely different if the substrate–deposit interaction is strong enough
to stabilize an at most monoatomic layer of the deposit atoms on the substrate. In
2 Electrochemistry and Electrodeposition
N = N 0
1 − exp(−At)
(2.23)
If we accept Eq. 2.21 as the nucleation rate law, then two extreme cases can be
distinguished. If A (t)
−1 , we get that N = N 0 . Here, t is the period between
two consecutive observation events during the experiment (or, in other words, 1/t
is the sampling frequency). The result means that the sites that are appropriate for
nucleation are saturated with nuclei from the very beginning of the process, which is
the definition of the instantaneous nucleation. However, if A (t)
−1 , N = N 0 At is
obtained, indicating an even nucleation probability throughout the entire observation
period, as defined for the progressive nucleation.
The study of the Volmer–Weber type nucleation in electrochemical systems
usually requires electrolyte solutions that exhibit much lower concentrations than
baths used in the galvanic industry (at most a few tens of mmol dm
−3 versus about
1 mmol dm
−3 , respectively). This is because the instantaneous or progressive nature
of the nucleation is already hidden once the newly-formed grains coalesce. Also, the
substrate used in the nucleation study has to be structurally rather incompatible with
the deposit in order to fulfil the conditions at which this type of nucleation can take
place at all.
The deposit formation usually does not start at a small overvoltage (as referred
to the equilibrium potential of the Me
z+ /Me electrode) because of the energy barrier
of the nucleation. The typical experimental conditions include the potentiostatic
polarization with a potential step to a value so that the deposition becomes diffusionlimited. Under such conditions, a spherical diffusion field develops around all grains,
as shown in various representations in Fig. 2.16.
Although Fig. 2.16 indicates well the overlap of the diffusion field of the grains
as time passes, the limits of the schematic image should also be kept in mind (e.g.,
perfect hemispherical growth in spite of the laterally uneven supply of the precursor,
disregarding the crystalline nature of the deposit and the possible directional preference of the crystal growth etc.). As the grains grow and the solution becomes
depleted with respect of the precursor ions, the diffusion field is planarized, and the
same transport conditions are obtained as during the Cottrell experiment.
The chronoamperometric transient in the early phase of the process bears information on the nature of the nucleation. Here a few works of Sharifker are referred to [14,
15] without the deep mathematical details. The treatment of the chronoamperometric
data includes a normalization of the current density with respect to the peak current
density (j* = {j/j MAX }
2 ). The time also has to be dealt with in a dimensionless form,
using the time belonging to the current density maximum as a normalization parameter (t* = t/t MAX ). Typical results for the major nucleation modes are presented in
Fig. 2.17. The concave or the convex nature of the j*(t*) function near t* = 0 is usually
regarded as a diagnostic criterion for the instantaneous and progressive nucleation,
respectively. Chronoamperometric transients for more complex nucleation cases are
also available in the literature (see Chap. 5 or Ref. [3]).
In contrast to the Volmer–Weber type growth, the initial stage of the phase formation can be completely different if the substrate–deposit interaction is strong enough
to stabilize an at most monoatomic layer of the deposit atoms on the substrate. In