How to use this calculator
Pick the diffusing atom and host metal to fill in D0 and Qd, enter the temperature and the starting and surface concentrations, then choose what to solve for. For carburizing, the starting concentration is the steel’s carbon content and the surface concentration is set by the furnace atmosphere.
Formulas
Worked example
Carburizing a 0.25 wt% C steel to 0.80 wt% at 0.5 mm depth, surface at 1.20 wt%, 950 °C (the default)
- D = 2.3 × 10⁻⁵ exp(−148,000/(8.314 × 1223)) = 1.10 × 10⁻¹¹ m²/s.
- erf(z) = (1.20 − 0.80)/(1.20 − 0.25) = 0.4211, so z = 0.3924.
- t = x²/(4z²D) = (5 × 10⁻⁴)²/(4 × 0.3924² × 1.10 × 10⁻¹¹) = 36,900 s = 10.2 hours.
The rule of thumb
Depth scales with √(Dt): to diffuse twice as deep takes four times as long at the same temperature. Temperature is the bigger lever. Raising carburizing from 900 °C to 1000 °C roughly triples D, because D grows exponentially with temperature. Diffusion also sets doping depths in silicon chips, the speed of hardening heat treatments and the life of high-temperature coatings.
Assumptions and limits
- The part is much thicker than the diffusion depth, so the far side never sees the change.
- The surface concentration is held constant and D does not depend on concentration.
- The listed D0 and Qd are typical textbook values; published values vary by several percent, which changes the time noticeably because of the exponential.
Frequently asked questions
How do I find the inverse error function without this calculator?
Use an error-function table: find erf(z) in the body of the table and read z from the margin, interpolating between rows.
Why is carbon in ferrite faster than in austenite at the same temperature?
BCC ferrite is more open, so carbon hops between sites with a lower activation energy. Carburizing is still done in austenite because it can dissolve far more carbon.
What is Qd in electron-volts?
Divide J/mol by 96,485. Carbon in austenite, 148 kJ/mol, is about 1.53 eV per atom. The unit menu converts for you.