Precipitation Kinetics of the GP Zones in Al4,65at.% Ag(15%Wt.)

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Figures 1. X-ray diffractograms of Al(a) and Al-Ag (b) as quenched solid solution

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3.2. Electrical Resistivity Curve

During the GP zones formation, the electrical resistivity of the alloy decreases and reaches a constant value at the metastable equilibrium state (Figure 2 ) during which the volume fraction of the GP zones is maximum ^{[8, 9, 10]}.

Figure 2. Electrical resistivity variation during the GP zones precipitation at 125°C

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3.3. Precipitation Kinetics

During the precipitation of the GP zones, the transformed fraction, F, which represents the ratio between the volume occupied by the GP zones at a time t and their volume at the metastable equilibrium state, is given by the relation:

where ρ(0) is the as quenched electrical resistivity, ρ(t), the electrical resistivity of the alloy at the time t during the precipitation of the GP zones, and ρ_{(metastable equilibrium)}, the electrical resistivity of the alloy at the metastable equilibrium state of the GP zones precipitation.

The transformed fraction curves show a short incubation time determined by extrapolation of the curves, due to the high supersaturation of the vacancies obtained at the quenching (Figure 3). The curves show also the steps of the growth and the coarsening of the GP zones.

3.3.1. Growth Regime

The variation curve of LogLog(1/1-F) against Log t suggests that GP zones precipitation kinetics obeys to the JMAK law of the growth controlled by the diffusion of solute atoms: F = 1 – exp – (kt)ⁿ, where n and k are the growth parameters (Figure 4). The slope of the LogLog(1/1-F) curve, gives, for n and k, the respective values 0,91 and 11.10^-4s^-1.

Figure 3. Transformed fraction during isothermal aging at 125°C

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Figure 4. Determination of the growth parameters

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3.3.2. Coarsening Regime

According to the LSW theory ^{[11, 12]}, in a highly diluted alloy and closely to the metastable equilibrium state of the GP zones precipitation, the matrix supersaturation is given by the relation x_m – x_e = (kt)^-1/3 where x_mis the solute matrix concentration at a time t, x_e, the solute matrix concentration at the metastable equilibrium state and k = D(RT)²/9σ²x_e²V_m, where D is the diffusion coefficient, T, the temperature, σ,the interfacial energy between the GP zones and the matrix and V_m, the molar fraction of the GP zones.

The solute atom concentration of the matrix during the precipitation of the GP zones is determined from the transformed fraction using the relation F=(x₀-x_m)/(x₀-x_e) where x₀ is the alloy solute atom concentration and x_e, the solute atom concentration of the matrix at the metastable equilibrium state (Figure 5). At 125°C, the value of x_e, determined from the metastable equilibrium diagram ^[13] is equal to 0,53 at.%.

Figure 5. Matrix solute atom concentration during the GP zones precipitation at 125°C

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The curve of the Figure 6 shows that the supersaturation in solute atoms vary linearly against t ^-1/3 and is in accordance with the LSW theory of the coarsening (Figure 6). Using the value of k obtained from the slope of this curve, and taking σ = 0,3 J/m² ^[14] and V_m = 10^-5 m³/mol, we determine a diffusion coefficient of the solute atoms, during the GP zones formation at 125°C, in the order of (8,69 ± 2,17).10^-21m²/s.

Figure 6. Variation of the solute atom matrix concentration during the coarsening stage

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4. Contributions of the Matrix and of the GP Zones to the Electrical Resistivity

According to the Matthiessen rule, the electrical resistivity results from the contribution of the phonons and that of all defects in the alloy such the dislocations, the grain boundaries, the solute atoms and the precipitate particles. During an isothermal aging treatment, the contribution of phonons remains constant and, in a non deformed alloy, the contributions of defects such the dislocations and the grain boundaries remain constant while that of the solute atoms and the precipitate particles vary. The electrical resistivity contribution of the matrix is determined from the variation curve of the electrical resistivity of homogenized alloys containing different concentrations of solute atoms (Figure 7) and the matrix solute atom concentration (Figure 4).

Figure 7. Electrical resistivity of homogenized Alxat.%Ag alloys

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The electrical resistivity contribution of the GP zones is obtained from the difference between the electrical resistivity of the alloy and the electrical resistivity contribution of the matrix (Figure 8).

Figure 8. Contributions to the alloy electrical resistivity of the matrix, R_m, and of the GP zones, R_GP, during the GP zones precipitation at 125°C

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The preponderant contribution to the electrical resistivity of the alloy is that of the matrix. This is due to the weak GP zones volume fraction which is given by the relation

where x₀ is the alloy concentration in solute atoms, x_m, that of the matrix and x_p that of the precipitate particles at the equilibrium metastable state, and represented in Figure 9 taking a value of 55% for x_p ^[13]. The maximum value of the GP zones volume fraction obtained at the metastable equilibrium state is in the order of 7,49 %.

Figure 9. GP zones volume fraction during isothermal aging at 125°C

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