D. Vasilakopoulos et al. / Electrochimica Acta 54 (2009) 2509–2514
2513
where |Á| (V) is the overpotential, ꢂ (J cm−2) the interfacial energy,
and the other symbols as described previously.
The nucleation rate constant presents an exponential depen-
2
dence on (1/|Á|) according to Eq. (7):
8
ꢀM ꢂ3
2
1
ln A = ln BJ −
·
(7)
2 2 2
ꢁ n F kBT |Á|2
3
where BJ (s 1) is a frequency factor, kB the Boltzmann constant,
−
and T (K) is the temperature. Therefore, the interfacial energy could
−
2
be calculated from the slope of ln A vs. |Á| plots using the val-
ues estimated for the nucleation rate constant A. The slopes were
2
found to be −0.11 and −0.35 V for pH 2.5 and 4.0, respectively
(
2
Fig. 10), giving an interfacial energy for Zn nuclei in the range
.96 × 10 –4.37 × 10 J cm . Substituting these values to Eq. (6),
−
5
−5
−2
the radius of the circular base of the critical nucleus was found to
lie between 26 and 142 pm. However, the atomic radius of a Zn
atom is known to be 133 pm, while the classical theory is strictly
valid when the nucleus contains an appreciable number of atoms
Fig. 9. Simplified diagram of dominant nucleation and growth modes in the range
of conditions used to electrodeposit zinc from typical sulphate bath on low-carbon
steel, under DC conditions. The cathodic potentials correspond to the respective
current densities of the texture diagram (Fig. 6).
(at least a hundred) [21]. Consequently, the estimated radius of
the critical nucleus is too small to be consistent with this sim-
ple theory. More sophisticated approaches, e.g. those based on the
atomistic theory of nucleation [21,22], should have a more realistic
outcome.
parameters determine also the type of nucleation. Hence it would
be useful to establish a correlation involving the type of charge-
transfer controlled nucleation on the steel electrode and the XRD
texture of the final deposit. Fig. 9 shows the nucleation and growth
modes as estimated from the present analysis of experimental CTTs
for various conditions. By inspection of the corresponding texture
domains in Fig. 6 one can see that a well-defined texture, i.e. ori-
ented growth, is connected to 3D nucleation, while the absence of
a plain orientation is connected to the assumed mixed dimension-
ality mechanism. The latter occurs for deposition potentials near
the equilibrium value which actually promote a 2D layer-by-layer
growth, restrained though for the most part as a result of the non-
uniform distribution of active nucleation sites and defects on the
steel substrate. Under these circumstances, the initially disturbed
growth leads to the formation of slightly misoriented crystallites
which give rise finally to a deposit without any dominant tex-
ture, because the low-supersaturation conditions are not capable
of restoring a directional growth.
4. Conclusions
A systematic study of zinc electrocrystallisation on low-carbon
steel from an acidic sulphate medium, under charge transfer con-
trol, was performed. Depending on applied potential and bath pH,
different nucleation and growth modes were identified.
At cathodic overpotentials less than 0.30 V, a 2D-nucleated layer-
by-layer growth strained by the substrate effect is established,
rapidly degenerating to a 3D type of growth. At overpotentials
higher than 0.30 V, instantaneous 3D nucleation and growth was
found to be predominant, while progressive 3D nucleation was
seen to prevail at overpotentials greater than 0.55 V and highly
acidic baths. Progressive nucleation was generally dominant at low
pH values, as the intense hydrogen adsorption in these conditions,
inhibits the active nucleation sites. The electrocrystallisation pro-
cess was controlled by the incorporation of Zn ad-atoms in the solid
lattice.
The radius of the critical nucleus for zinc nucleation, as
estimated by means of the classical theory of heterogeneous nucle-
ation, was found to be in the range 26–142 pm corresponding to
maximum one zinc atom. Since the classical theory is strictly valid
when the nucleus contains an appreciable number of atoms, alter-
native approaches should be employed in order to get satisfactory
results in this connection.
Finally, as an illustration of the complexities involved in deter-
mining reasonable parameters of the nucleation process, the
classical theory of heterogeneous nucleation will be used to esti-
mate analytically the critical size of the three-dimensional nuclei
assumed to initiate the construction of the deposit grains for over-
potentials greater than 0.30 V. In this theory, the radius rcrit (cm) of
the circular base of a critical nucleus is given by Eq. (6) [20]:
2
nF|Á|
Mꢂ
rcrit = ꢁ
(6)
References
[1] X. Ye, J.P. Celis, M. De Bonte, J.R. Roos, J. Electrochem. Soc. 141 (1994) 2698.
[2] D. Vasilakopoulos, M. Bouroushian, N. Spyrellis, J. Mater. Sci. 41 (2006) 2869.
[3] D. Vasilakopoulos, M. Bouroushian, N. Spyrellis, Trans. IMF 79 (2001) 107.
[4] K. Raeissi, A. Saatchi, M.A. Golozar, J. Appl. Electrochem. 33 (2003) 635.
[5] K. Raeissi, A. Saatchi, M.A. Golozar, J.A. Szpunar, J. Appl. Electrochem. 34 (2004)
1249.
[6] A. Gomes, M.I. da Silva Pereira, Electrochim. Acta 51 (2006) 1342.
[
7] V. Velinov, E. Bełtowska-Lehman, A. Riesenkampf, Surf. Coat. Technol. 29 (1986)
77.
[
[
8] A.E. Alvarez, D.R. Salinas, J. Electroanal. Chem. 566 (2004) 393.
9] J. Torrent-Burgués, E. Guaus, J. Appl. Electrochem. 37 (2007) 643.
[
10] A. Gomes, A.S. Viana, M.I. da Silva Pereira, J. Electrochem. Soc. 154 (2007)
D452.
[11] P.J. Sonneveld, W. Visscher, E. Barendrecht, Elecrochim. Acta 37 (1992)
1
199.
[12] R. Greef, R. Peat, L.M. Peter, D. Pletcher, J. Robinson, Instrumental Methods in
Electrochemistry, Ellis Horwood, London, 1993 (Chapter 9).
[13] R.D. Armstrong, M. Fleischmann, H.R. Thirsk, J. Electroanal. Chem. 11 (1966)
208.
Fig. 10. Plot of ln A vs. |Á|−2 according to data obtained from the non-linear regression
analysis of the experimental CTTs recorded at pH 2.5 (i) and pH 4.0 (ii).