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Electrochemical nucleation and growth of three-dimensional clusters: the case of multi-step ions discharge–I

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Abstract

Electrochemical nucleation and growth of three-dimensional spherical clusters on a foreign substrate are considered in case of multi- and single-step ions discharge reaction. Theoretical expressions are derived for the stationary nucleation rate and for the current-time and the radius-time relationships of single clusters growing at a constant electrochemical supersaturation. The error that would be made if the important physical quantities critical nucleus size and exchange current density are determined not using correct theoretical formulas accounting for the actual multi- or single-step reaction mechanism is evaluated.

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Fig. 1
Fig. 2
Fig. 3
Fig. 4

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Notes

  1. In this paper, the cathodic overpotential η = E ∞  − E is considered as a positive quantity.

  2. Note that Eq. (13) does not take into account the line tension effects at the clusters periphery which become significant at sufficiently low values of R. Readers who are interested in this subject can find additional information in refs. [34, 35] as well as in the references cited therein.

  3. Note that the numerical evaluations that follow are performed for α = 0.5 and i 0 = 7 × 10−3 Acm−2 both in case of multi-step and in case of single-step electrochemical reactions, so that Figs. 2 and 3 illustrate only qualitatively the shape of the R(t) and the I(t) relationships.

  4. Remember that the absolute error is defined as the modulus of the difference between the measured and the real value of a given quantity, whereas, the relative error is given by the ratio of the absolute error and the measured value of the same quantity.

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Authors and Affiliations

  1. Evgeni Budevski Institute of Electrochemistry and Energy Systems, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 10, 1113, Sofia, Bulgaria

    Emilia Mladenova & Alexander Milchev

Authors
  1. Emilia Mladenova
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  2. Alexander Milchev
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Correspondence to Emilia Mladenova.

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Mladenova, E., Milchev, A. Electrochemical nucleation and growth of three-dimensional clusters: the case of multi-step ions discharge–I. J Solid State Electrochem 21, 1599–1604 (2017). https://doi.org/10.1007/s10008-017-3511-9

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  • DOI: https://doi.org/10.1007/s10008-017-3511-9

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