Arrhenius Diffusion Coefficient Calculator
Calculate solid-state diffusion coefficient using the Arrhenius equation.
Enter pre-exponential factor, activation energy, and temperature to find D and diffusion distance.
Diffusion in solids follows an Arrhenius relationship: atoms need enough thermal energy to jump from one lattice site to another. Higher temperature means more jumps per second and faster diffusion.
The Arrhenius diffusion equation:
D = D0 x exp(-Q / (R x T))
where D is the diffusion coefficient in m²/s, D0 is the pre-exponential factor (m²/s), Q is the activation energy (J/mol), R is the gas constant (8.314 J/mol K), and T is temperature in Kelvin.
Diffusion distance. The root-mean-square diffusion distance in time t is:
x = sqrt(2 x D x t)
This tells you how far atoms have spread on average.
Representative values for carbon in iron:
- In austenite (FCC iron): D0 = 2.0×10⁻⁵ m²/s, Q = 142 kJ/mol
- In ferrite (BCC iron): D0 = 1.1×10⁻⁶ m²/s, Q = 80 kJ/mol
Carbon diffuses ~100x faster in ferrite than austenite at the same temperature because the more open BCC structure has larger interstitial sites. This difference is exploited in carburizing heat treatments — austenite is used for carburizing because it dissolves more carbon, even though diffusion is slower.
Why Arrhenius? The probability of a thermal fluctuation providing energy Q follows the Boltzmann factor exp(-Q/kT). This same form appears throughout materials science, chemistry, and biology wherever rate processes must overcome an energy barrier.