Abstract
A mechanism for copper powder formation in potentiostatic deposition is proposed, and the critical overpotential of copper powder formation is determined. A good agreement between theoretical and experimental results has been obtained.
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Abbreviations
- C 0 :
-
bulk concentration (mol cm−3)
- D :
-
diffusion coefficient (cm2 s−1)
- F :
-
Faraday's constant (C mol−1)
- h :
-
height of protrusion (cm)
- h c :
-
height at which dendrites crack (cm)
- h i :
-
height (cm)
- h 0 :
-
initial height of protrusion (cm)
- h j,t :
-
elevation at pointj and timet (cm)
- h j,0 :
-
initial elevation at pointj (cm)
- I :
-
limiting diffusion current (A)
- I 0 :
-
initial limiting diffusion current (A)
- i :
-
limiting current density (A cm−2)
- i d :
-
current density on the tip of dendrite of height h (A cm−2)
- i t :
-
total current (A cm−2)
- j :
-
number
- k :
-
proportionality factor [cm (mol cm−3)m]
- k′ :
-
constant
- M :
-
number of dendrites
- m :
-
number
- N :
-
number of elevated points
- n :
-
number of electrons
- p :
-
concentration exponent
- Q c :
-
quantity of electricity (C)
- R :
-
gas constant (J mol−1 K−1)
- S :
-
electrode surface area (cm2)
- T :
-
temperature (K)
- t :
-
time (s)
- t a :
-
longest time in which approximation δ≫h is valid (s)
- t i :
-
induction time (s)
- V :
-
molar volume (cm3 mol−1)
- γ :
-
surface tension (J cm−2)
- δ:
-
thickness of diffusion layer (cm)
- η :
-
overpotential (V)
- η c,p :
-
critical overpotential of powder formation (V)
- θ :
-
fraction of flat surface
- τ :
-
apparent induction time (s)
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Popov, K.I., Maksimović, M.D., Lukić, D.T. et al. The mechanism of copper powder formation in potentiostatic deposition. J Appl Electrochem 10, 299–308 (1980). https://doi.org/10.1007/BF00617204
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DOI: https://doi.org/10.1007/BF00617204