Couples and pairs formation—thermodynamic and kinetic modelling applied to Al–Mg–Si

Abstract

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.

High-precision isothermal dilatometry as tool for quantitative analysis of precipitation kinetics: case study of dilute Al alloy

“…Although it is evident that detailed insight into precipitation processes in Al alloys on an atomistic scale ultimately requires more advanced models (see, e.g., Refs. [10][11][12][13]), the application of simple models, like JMAK, allows a direct and analytical fit to experimental data.…”

Modelling the Spatial Evolution of Excess Vacancies and its Influence on Age Hardening Behaviors in Multicomponent Aluminium Alloys

“…Among different atom clusters, only Mg-Si pairs in the first nearest neighbor inherited from the solid solution treatment at temperature T SS , are regarded as trapping sites for vacancies, while the other clusters are neglected since their site fractions are several orders of magnitude lower than that of individual solute atoms. In thermodynamic equilibrium at T SS , the concentration of Mg-Si pairs can be calculated by [28,49] x MgSi = Zx Mg x Si exp where ΔE B Mg− Si is the binding energy between Mg and Si atoms in the Al matrix. Moreover, the cluster-related parameters for Mg-Si pairs are assumed to be Z Mg− Si =12 and N Mg− Si =2, which are the same as the approximations in [20].…”

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

“…The kinetics of the system is determined by means of the thermodynamic extremal principle (TEP) [39]. Kinetics of both Cs and Ps in the ternary Al-Mg-Si system has been modelled in the follow-up paper [40]. In the current paper, however, we present a general model for formation of Cs and Ps of all alloying elements in a multicomponent system.…”

“…The i-atoms, diffusing with the tracer diffusion coefficient D i , mutate from an isolated status to a trapped one in the nearest neighbourhood of fixed j-atoms yielding,ċ i i1 = −ċ i ij , whereċ i ij denotes their contribution toċ ij . The according to dissipation function Q i ij is given with J(r), see Equation (22) and the according to derivations in [38,40] as…”