Nucleation ofAl3ZrandAl3

Abstract

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of Al3Zr and Al3Sc. These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test different mean-field approximations (Bragg-Williams approximation as well as Cluster Variation Method) for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small L12 clusters.

Using cluster dynamics to model electrical resistivity measurements in precipitating AlSc alloys

“…2, in the case where the precipitates present a ragged interface. This is not the case in Al-Sc alloys as the Al 3 Sc precipitate interfaces are rather sharp as shown by our atomic simulations [15,16]. Therefore, one expects Eq.…”

“…3 Looking at the cluster size distribution, one should notice the abnormally high concentration of clusters containing 8 solute atoms. This is due to the low interface free energy associated with this size because of the existence of a compact cluster corresponding to a cube for this size [15]. the kinetics, (t = 10 2 or 10 4 s), only small clusters (n Sc ≤ 10) are present.…”

“…The time evolution of the cluster size distribution is governed by a master equation which input parameters are the solute diffusion coefficient and the precipitate interface free energy. For Al-Sc alloys, these needed parameters were directly deduced from an atomic diffusion model [15,16,18] previously built for Al-Zr-Sc alloys. It should be stressed that, although none of these input parameters were intentionally fitted, cluster dynamics managed to reproduce reasonably experimental data on the time evolution of the precipitate size distribution.…”

“…if one can obtain reliable information concerning the precipitates as well as the solid solution in the whole time range of precipitation kinetics and not only in the asymptotic limit of the coarsening stage like LSW theory does. Confronting cluster dynamics predictions with resistivity measurements will validate too the multiscale approach developed for precipitation in Al-Zr-Sc alloys [11,[15][16][17][18]. The use of resistivity experiments to validate a multiscale kinetic modeling has already proved its efficiency for irradiated iron [19].…”

Modeling Microstructure and Irradiation Effects

“…Pareige and co-workers investigated ordering and phase separation in NiCrAl alloys, which are model systems of Ni-based superalloys used in the aerospace industry. [30] In Al alloys, the introduction of transition elements such as Mn, Zr, or Sc leads to the formation of ordered precipitates, which increase the tensile strength and inhibit recrystallization, and Clouet et al investigated the formation of L12 precipitates in Al-Zr-Sc alloys [36,256,257] by means of a pair bond AKMC model. The behavior of He in Fe has also been investigated using this technique: the nucleation of He bubbles in bcc Fe was modeled by Deo et al, [258] and He-bubble migration in bcc Fe by Morishita et al [259] Figure 5 represents the microstructure of an Fe alloy containing 1.12 pct at.…”