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 E (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 E from chemical potentials of interstitial atoms which are, for instance, available in the form of CALPHAD-type thermodynamic databases.Exemplarily, the values of E 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.

Mg–Si couples formed from atomic Mg and Si represent the first step in Mg–Si cluster formation in a dilute Al–Mg–Si system. Based on the thermodynamic extremal principle, a kinetic model for Mg–Si couple formation is developed. The model utilizes the trapping concept for the calculation of Gibbs energy of the non-equilibrium system and provides a generalized (multiplicative) form of the Oriani equation for description of the equilibrium state. The dissipation in the system accounts for diffusion of both Mg and Si atoms in the lattice. The model is compared with the classical Lidiard and Howard equilibrium theory. Some demonstrative examples are presented. Finally the model is applied to an experimentally studied system. Good quantitative agreement with quenching experiments is obtained, if, simultaneously, the impact of excess quenched-in vacancies and their gradual annihilation in the system, which has been already treated in a previous paper, are accounted for. The model is generally applicable for any couple (and pair) formation.

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Kinetics of formation of couples (B–C) and pairs (B–B, C–C) is studied in an alloy with B-atoms and C-atoms as dilute solutes and A-atoms as solvent. The trapping concept, allowing division of the system into subsystems, the Bragg–Williams approximation used for the configurational entropy of each subsystem, and the thermodynamic extremal principle are applied in the model. The derived equilibrium conditions provide an extended Oriani-type equation. The kinetics of couples and pairs formation is given by explicit ordinary differential equations for the concentrations of couples and pairs allowing calculation of all relevant state variables. The concept is applied to an Al–Mg–Si system with the bonding energy terms E BB, E CC, E BC taken from ab-initio calculations. The presence of excess vacancies that are eventually frozen in by instant quenching as well as their subsequent annihilation influence the formation kinetics in a decisive way.