2.10 Nucleation During Electrochemical Phase Formation
37
islands produced in the nucleation period. It is the Volmer–Weber type growth that
should be kept in mind when the nucleation takes place on a defect of the surface
instead of a perfect crystal plane. In such cases, the large difference in the activation
energy of the nucleation favours the defect sites whose surface density can also be
taken as the upper limit of the number of grains.
For the Stransky–Krastanov type nucleation, the role of the interaction energy is
decisive: E(Su-Me) E(Me-Me), and hence, a monoatomic coverage of the deposit
can form at the substrate, despite the relative misfit is definitely not zero. In other
words, the strong interaction between the substrate and the deposit stabilizes the
first (potentially incomplete) atomic layer of the deposit. Later, this tends to grow
further as if islands were formed on the first atomic layer, and the stress due to the
misfit is relaxed in the upcoming atomic layers, finally leading to the natural relaxed
atomic distances of the deposit crystals. The Stransky–Krastanov-type growth is
an intermediate mode between the island-like Volmer–Weber type growth and the
heteroepitaxial growth. The latter is called the Frank–van der Merwe type nucleation,
where not only the E(Su-Me) > E(Me-Me) relationship holds but the relative misfit
is very close to zero.
The analysis of the aforementioned nucleation and growth modes is essential
for the understanding of electrochemical methods that are used for the study of the
phase formation. When a Volmer–Weber type nucleation takes place, the temporal
evolution of the surface density of the newly formed crystallites is a key parameter.
The density of the grains plays a crucial role in the variation in the deposition current
density until the surface of the substrate is completely covered with the deposit.
When the substrate coverage becomes full at all points, the deposit has a significant
mean thickness, and the surface roughness may also differ considerably from that of
the bare substrate due to the uneven growth.
The number (or surface density) of the newly formed grains always has to be
studied on the time scale of the experiment. If all grains form in a very early phase
of the experiment and the number of nuclei is practically constant for the rest of the
observation period, one can speak about an instantaneous nucleation. In contrast, it
is also possible that the age of the newly formed grains has a wide distribution in the
full time scale of the experiment, which is equivalent to that the grain nucleation has
an even probability throughout the observation. This is the case of the progressive
nucleation. The two extreme cases of the nucleation can be regarded as a result of
the same nuclei formation rate law with different rate constants:
dN
dt
= −A(N − N 0 )
(2.22)
where N 0 is the number (or density) of the surface sites that are suitable for the
nucleation of a new grain, N is the actual number (density) of the grains at the
surface. The parameter A is the nucleation rate constant, which can be taken as
invariant in the first approximation only since it may vary also as a function of the
near-substrate concentration of the reactants that is consumed by the growth of the
already existing grains. The solution of the 2.21 differential equation is:
37
islands produced in the nucleation period. It is the Volmer–Weber type growth that
should be kept in mind when the nucleation takes place on a defect of the surface
instead of a perfect crystal plane. In such cases, the large difference in the activation
energy of the nucleation favours the defect sites whose surface density can also be
taken as the upper limit of the number of grains.
For the Stransky–Krastanov type nucleation, the role of the interaction energy is
decisive: E(Su-Me) E(Me-Me), and hence, a monoatomic coverage of the deposit
can form at the substrate, despite the relative misfit is definitely not zero. In other
words, the strong interaction between the substrate and the deposit stabilizes the
first (potentially incomplete) atomic layer of the deposit. Later, this tends to grow
further as if islands were formed on the first atomic layer, and the stress due to the
misfit is relaxed in the upcoming atomic layers, finally leading to the natural relaxed
atomic distances of the deposit crystals. The Stransky–Krastanov-type growth is
an intermediate mode between the island-like Volmer–Weber type growth and the
heteroepitaxial growth. The latter is called the Frank–van der Merwe type nucleation,
where not only the E(Su-Me) > E(Me-Me) relationship holds but the relative misfit
is very close to zero.
The analysis of the aforementioned nucleation and growth modes is essential
for the understanding of electrochemical methods that are used for the study of the
phase formation. When a Volmer–Weber type nucleation takes place, the temporal
evolution of the surface density of the newly formed crystallites is a key parameter.
The density of the grains plays a crucial role in the variation in the deposition current
density until the surface of the substrate is completely covered with the deposit.
When the substrate coverage becomes full at all points, the deposit has a significant
mean thickness, and the surface roughness may also differ considerably from that of
the bare substrate due to the uneven growth.
The number (or surface density) of the newly formed grains always has to be
studied on the time scale of the experiment. If all grains form in a very early phase
of the experiment and the number of nuclei is practically constant for the rest of the
observation period, one can speak about an instantaneous nucleation. In contrast, it
is also possible that the age of the newly formed grains has a wide distribution in the
full time scale of the experiment, which is equivalent to that the grain nucleation has
an even probability throughout the observation. This is the case of the progressive
nucleation. The two extreme cases of the nucleation can be regarded as a result of
the same nuclei formation rate law with different rate constants:
dN
dt
= −A(N − N 0 )
(2.22)
where N 0 is the number (or density) of the surface sites that are suitable for the
nucleation of a new grain, N is the actual number (density) of the grains at the
surface. The parameter A is the nucleation rate constant, which can be taken as
invariant in the first approximation only since it may vary also as a function of the
near-substrate concentration of the reactants that is consumed by the growth of the
already existing grains. The solution of the 2.21 differential equation is: