Electroplating Faraday Thickness Calculator
Electrochemical Surface Finishing: Determine metal coating thickness, plating duration, mass deposited, and electrical energy via Faraday's law of electrolysis.
Plating Bath & Metal Chemistry
Deposition & Electrical Outputs
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Engineering Fundamentals of Electroplating Kinetics
Electrodeposition is an electrochemical reduction process where dissolved metallic cations ($M^{z+}$) in an aqueous or non-aqueous electrolyte are reduced to metallic atoms on the cathode workpiece surface upon gaining electrons from an external direct-current power supply.
1. Governing Faraday Equation
The total mass of metal reduced and deposited is governed by:
m = (I · t · M · η) / (z · F)
- m = mass deposited (grams)
- I = electrical current (Amperes)
- t = duration (seconds)
- M = molar mass of depositing element (g/mol)
- z = valence state / electron count per ion (e.g., $z=2$ for $\text{Cu}^{2+}$, $z=1$ for $\text{Au}^+$)
- F = Faraday's constant ($96,485.33\text{ C/mol}$)
- η = cathode current efficiency (fraction, $0 < \eta \le 1.0$)
2. Coating Thickness & Deposition Rate
The volumetric deposit is $V = m / \rho$. Substituting into uniform surface area $A$ yields coating thickness $d$:
d = (J · t · M · η) / (100 · z · F · ρ) × 10,000 [in micrometers, μm]
where $J$ is current density in $\text{A/dm}^2$, and $\rho$ is density in $\text{g/cm}^3$.
Frequently Asked Questions
How does Faraday's Law calculate electroplating thickness?
Faraday's law states that the mass of metal deposited ($m$) is directly proportional to the total electrical charge passed ($Q = I \cdot t$) and the chemical equivalent weight ($M / z$), divided by Faraday's constant ($F \approx 96,485\text{ C/mol}$), multiplied by the cathode current efficiency ($\eta$). Thickness is then derived by dividing the deposited mass by metal density and active surface area: $d = m / (\rho \cdot A)$.
Why is cathode current efficiency less than 100% in chromium baths?
In decorative or hard chromium electroplating, hexavalent chromium baths typically operate at only 12% to 18% cathode efficiency. The remaining 80% to 88% of electrical current is consumed by parasitic hydrogen evolution ($2\text{H}^+ + 2e^- \to \text{H}_2$), requiring high current densities and robust exhaust ventilation.
What is the conversion between A/dm² and ASF (A/ft²)?
One square foot equals approximately $9.2903\text{ dm}^2$. Therefore, $1.0\text{ A/dm}^2 \approx 9.29\text{ A/ft}^2$ (Amperes per Square Foot, or ASF). Conversely, $10\text{ ASF} \approx 1.076\text{ A/dm}^2$.