Vacancy assisted solute transport mechanisms responsible for the solute atom agglomeration during the early stages of aging in Al-Cu-based alloys

An approach using combined results, obtained by different experimental variants of positron annihilation spectroscopy and from kinetic Monte Carlo simulations, made it possible to determine the fundamental mechanisms by which vacancies assist solute atoms to form clusters during the earliest stages of precipitation kinetics in age-hardenable Al-Cu and Al-Cu-Mg alloys. The investigations were performed on the conventional precipitation-hardening system Al-1.74Cu (at. %) alloy aged at 293 and 342 K; these temperatures were chosen since they are low enough to avoid the formation of more stable nanostructures. To understand the influence of a minor alloying element on the solute clustering, the ternary Al-1.74Cu-0.35Mg (at. %) alloy was also studied. Interpreted in terms of the so-called vacancy pump model of solute aggregation, the results obtained made it possible to give a detailed and precise description concerning the role of the solute-vacancy exchanges in the solute clustering dynamics and the energetic stabilization of the formed clusters. It deserves to be pointed out that the results of our simulations for the ternary alloy indicate that, when aging proceeds, the solute atoms transported by vacancies progressively form Cu-Mg coclusters containing different amounts of nonmixed Cu or Mg solute atoms.

Figure 1

Positron lifetime evolutions in the binary (B) and ternary (T) alloys as a function of the aging time and temperature after Somoza et al. [8, 17, 21]. Dashed lines are the best-fit curves calculated on the basis of the positron trapping model (see Refs. [17, 21]). Labels ${\mathrm{B}}_{\mathrm{AQ}}$, ${\mathrm{B}}_{\mathrm{RT}}$, ${\mathrm{B}}_{\mathrm{HT}}$, ${\mathrm{T}}_{\mathrm{AQ}}$, ${\mathrm{T}}_{\mathrm{RT}}$, and ${\mathrm{T}}_{\mathrm{HT}}$ represent the specific aging stages where coincidence Doppler broadening spectroscopy (CDBS) measurements were carried out (see Table 1 and Ref. [8]).

Figure 2

Fraction of solute atoms forming clusters in the binary and ternary alloys as a function of the physical time and the simulation temperatures. For all the simulated data, the filled areas of the different curves include their associated dispersions (see text). For the sake of clarity, only the average simulated data obtained for the B alloy at 293 K are presented using a solid line. Labels #1, #2, and #3 represent kMC specific stages of the clustering process; that is, #1 is the random starting point, #2 is an intermediate state in which 35% of the solute atoms form clusters, and #3 is the steady state.

Figure 3

Three-dimensional (3D) images of the simulated box $(15\times 15\times 15\mathrm{n}{\mathrm{m}}^3)$ of the fraction of solute atoms forming clusters obtained for the binary alloy at different simulation temperatures. For the sake of clarity, only the Cu atoms forming solute clusters are shown. The labels #1, #2 and #3 were defined in Fig. 2.

Figure 4

Three-dimensional (3D) images of the simulation box $(15\times 15\times 15\mathrm{n}{\mathrm{m}}^3)$ obtained for the ternary alloy at different simulation temperatures. For the sake of clarity, only those Cu and Mg atoms forming solute clusters are shown in full red and full blue circles, respectively. The labels #1, #2 and #3 were defined in Fig. 2.

Figure 5

Density of Cu cluster size distributions as a function of the number of solute atoms (i.e., cluster size) forming Cu clusters for the binary alloy referred to the solute cluster distribution at the initial random state and for simulations at 293 K (top panel) and 342 K (bottom panel). The labels #2 and #3 were defined in Fig. 2. The dispersion associated with the density number of solute clusters is ±5%.

Figure 6

Density of Cu and Cu-Mg cluster size distributions, referred to the solute cluster distribution as a function of the number of solute atoms (i.e., cluster size) at the initial random state, for the ternary alloy and for simulations at 293 K (top panel) and 342 K (bottom panel). In the plots labeled (a) and (c), only the density of Cu clusters distributions are shown. In the plots labeled (b) and (d), only the density of Cu-Mg cocluster distributions are presented. The labels #2 and #3 were defined in Fig. 2. The uncertainty associated with the density number of solute clusters is ±5%.

Figure 7

Three-dimensional (3D) image corresponding to the ternary alloy simulated at 342 K and for stage #3 (see Fig. 4). In the solute clusters, Cu and Mg atoms are shown in full red and full blue circles, respectively. In the right panel, zoomed images of two different representative coclusters for three different viewpoints are shown (more details are given in the text).

Figure 8

Fraction of the physical time $f^{at}(\%)$ that the Al atoms and Cu solute atoms remain in contact with a vacancy in a given interval of time $\tau$ for the binary alloy and for simulations at 293 K (top panel) and 342 K (bottom panel).

Figure 9

Fraction of the physical time $f^{at}(\%)$ that the Al atoms and Cu and/or Mg solute atoms remains in contact with a vacancy in a given interval of time $\tau$ for the ternary alloy and for simulations at 293 K (top panel) and 342 K (bottom panel).