Interdiffusion experiments have been performed in austenitic and ferritic steels.34 The determination of the intrinsic diffusion coefficients requires the mea­surement of the interdiffusion coefficient and of the Kirkendall speed for each composition.68 In general, an interdiffusion experiment provides the Kirkendall speed for one composition only, leading to a pair of intrinsic diffusion coefficients in a binary alloy. Therefore, few values of intrinsic diffusion coeffi­cients have been recorded at high temperatures and on a limited range of the alloy composition. More­over, experiments such as those by Anthony happened to be feasible in some Al, Cu, and Ag dilute alloys. As a result, a complete characterization of the L-coefficients of a specific concentrated alloy (even limited to the vacancy mechanism) has, to our knowledge, never been achieved. In the case of the interstitial diffusion mechanism, the tracer diffusion measurements under irradiation were not very con­vincing and did not lead to interstitial diffusion data. The interstitial data, which could be used in RIS models,12 were the effective migration energies deduced from resistivity recovery experiments.

1.18.3.2 Determination of the Fluxes from Atomic Models

First-principles methods are now able to provide us with accurate values of jump frequencies in alloys,
not only for the vacancy, but also for the interstitial in the split configuration (dumbbell). Therefore, an appropriate solution to estimate the L-coefficients is to start from an atomic jump frequency model for which the parameters are fitted to first-principles calculations.

1.18.3.4.1 Jump frequencies

In the framework of thermally activated rate theory, the exchange frequency between a vacancy V and a neighboring atom A is given by:

G ( D EAVg

kB T

if the activation energy (or migration barrier) AeAV is significantly greater than thermal fluctuations kB T (a similar expression holds for interstitial jumps). aeAV? is the increase in the system energy when the A atom goes from its initial site on the crystal lattice to the saddle point between its initial and final posi­tions. One of the key points in the kinetic studies is the description of these jump frequencies and of their dependence on the local atomic configuration, a description that encompasses all the information on the thermodynamic and kinetic properties of the system.