Determination of depths of traps for interstitials from thermodynamic data: a new view on carbon trapping and diffusion

Abstract

Traps, such as dislocation cores, foreign atoms, surfaces of nano-precipitates, etc, can significantly influence the kinetics of diffusion of interstitial atoms in a crystal lattice. Trapping is reflected in the chemical diffusion coefficient, whose value can be up to several orders of magnitude lower than the corresponding diffusion coefficient in a trap-free system. If we consider trapping only at dilute foreign atoms, we may assume only one sort of traps in the system, the depth of which is characterized by ΔE (trapping enthalpy) given by the decrease in energy due to trapping of one mole of interstitials. In this paper, a rigorous thermodynamically based concept is offered to extract the value of trapping enthalpy ΔE from chemical potentials of interstitial atoms which are, for instance, available in the form of CALPHAD-type thermodynamic databases. Exemplarily, the values of ΔE for C-trapping at Cr impurities are evaluated. For comparison, trapping enthalpies of C at various typical alloying elements in steel are also extracted and compared with literature values. The chemical diffusion coefficient of C in an Fe–Cr–C system at 500 °C is calculated for different mole fractions of C and Cr atoms. The influence of traps on diffusion becomes evident from this analysis.