Concentration- and temperature-dependent diffusion coefficient of carbon in FCC iron mathematically derived from literature data

Especially in heat treatment and hot forming of high-strength low-alloyed steels or cast iron, e.g. case and through hardening, carbonitriding, soft annealing, forging, upsetting, and decarburization, reliable data on the concentration and temperature dependence of the carbon diffusivity in the face-centered cubic Fe-C austenite lattice is of great technical importance. Since the precise numerical calculation and analysis of depth profiles for process control or failure inspection represent the main objective, the mathematical formulae applied in these simulations should be as simply structured as possible in order to effectively reduce computation time. The temperatures and carbon contents most relevant to steel heat treatment technologies range from 1073 to 1373 K and from 0 to 1.4 m. % C, respectively. In the present paper, eleven appropri-ate linear diffusivity-concentration relationships are derived from three independent literature sources. These representations are fitted with respect to the mentioned tem-perature range. An extensive summary of published references is given for compari-son. Two equivalent defining equations express the dependence of the carbon dif-fusivity on both concentration and temperature: a mathematically handy polynomial and a physically founded Arrhenius type. The comparison of predicted carbon profiles for an isothermal boost-diffuse gas carburizing treatment ranks the derived linearized expression and underlines the serious problem of inconsistent data for process control