Contribution of the GP Zones to the Hardening and to the Electrical Resistivity in Al10at.%Ag Alloy

View current table in a new window

Tables index

Veiw figure View Table

The as quenched solid solution, Al10at.%Ag is characterized by X-ray diffraction. It is well known that an as quenched substitutional solid solution is in a disordered state. In the case of aluminum based solid solutions, the X-ray powder diffraction spectra gives peaks diffraction at the analogous positions of those given by the aluminum. The Al and Al-Ag powder diffraction spectra show that the successive peaks are at analogous positions (Figure 1a,b) and their integrated intensities vary in the same ratio (Table 1). The lattice parameters of Al and Al-Ag, determined using the Nelson-Riley ^[8] extrapolation function, are respectively 4,0462 Å and 4,0478 Å.

Figure 1. X-ray powder diffraction spectra of Al(a) and Al-Ag (b) as quenched solid solution

Download as

Veiw figure View Figure

3.2. Hardening Contributions

The hardness isotherm curve, established at 125°C (Figure 2) shows a first step of hardening due to the GP zones precipitation and a second step due to the precipitation of the metastable γ’ phase. The intermediate bearing corresponds to the metastable equilibrium state of the GP zones precipitation during which their volume fraction is maximum. The softening is due to the coarsening of the particles of the metastable γ’phase and to the precipitation of the particles of the equilibrium γ phase.

Figure 2. Isotherm hardness curve at 125°C

Download as

Veiw figure View Figure

During the GP zones formation, the hardness, H_v, results from the matrix contribution, H_vm, and the GP zones contribution, H_vGP :

(1)

The matrix contribution to the hardening, H_vm, depends on its solute atom concentration, x_m. The matrix solute atom concentration during the GP zones formation is determined from the transformed fraction, F. The transformed fraction (Figure 3), is established from the Merle relation ^[9]:

(2)

where H_v(0) is the as quenched hardness, H_v(t), the hardness of the alloy at the time t during the GP zones precipitation, and H_{v(metastable equilibrium)}, the hardness of the alloy at the metastable equilibrium state of the GP zones precipitation. The matrix solute atom concentration is obtained using the relation ^[10]:

(3)

where x₀ is the solute atom concentration of the alloy and x_e, the solute atom concentration of the matrix at the metastable equilibrium state. At 125°C, the value of x_e, determined from the metastable equilibrium diagram ^[11] is 0,53 at.%.

The matrix contribution to the hardening, H_vm, is deduced from the hardness variation curve of homogenized alloys containing different solute atom concentrations (Figure 4) and the variation curve of the matrix solute atom concentration during the GP zones formation (Figure 5).

Figure 3. Transformed fraction during the GP zones precipitation at 125°C

Download as

Veiw figure View Figure

Figure 4. Hardness curve variation of homogenized Alxat.%Ag alloys

Download as

Veiw figure View Figure

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

Download as

Veiw figure View Figure

Thus, the GP zones contribution to the hardness, H_vGP, is given by the difference H_v - H_vm (Figure 6).

Figure 6. Contribution to the alloy hardening of the matrix, H_Vm, and that of the GP zones, H_VGP, during the GP zones precipitation at 125°C.

Download as

Veiw figure View Figure

3.3. Electrical Resistivity Contributions

During the GP zones formation, the electrical resistivity of the alloy decreases and reaches a constant value at the metastable equilibrium state (Figure 7) during which the volume fraction of the GP zones is maximum.

Figure 7. Electrical resistivity variation of the alloy during the GP zones precipitation at 125°C

Download as

Veiw figure View Figure

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 the phonons remains constant. Also, in a non deformed alloy, during an isothermal aging treatment, the contributions of the defects such the dislocations and the grain boundaries remain constant while those of the solute atoms and the precipitate particles vary.

In an as quenched and non deformed solid solution, during an isothermal aging treatment, the electrical resistivity, ρ, results from the contributions of the matrix, ρ_m, and that of the GP zones, ρ_GP:

(4)

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 8) and the variation curve of the matrix solute atom concentration during the GP zones formation (Figure 5). The variation curve of electrical resistivity of homogenized alloys shows an increase of the electrical resistivity with the solute atom concentration ^[12],

Figure 8. Electrical resistivity of homogenized Alxat.%Ag alloys.

Download as

Veiw figure View Figure

The GP zones contribution to the electrical resistivity, ρ_GP,is given by the difference ρ - ρ_m (Figure 9).

Figure 9. Contributions to the alloy electrical resistivity of the matrix, ρ_m, and of the GP zones, ρ_GP, during the GP zones precipitation at 125°C

Download as

Veiw figure View Figure

4. Correlation between Hardness and Electrical Resistivity

A linear relationship is observed between the hardness and the electrical resistivity of the as quenched alloys (Figure 10). In the as quenched alloys, the hardness and the electrical resistivity variations are due only to the presence of the solute atoms. In the isothermal aged alloy, there is, also, a linear relationship between the contributions of the matrix to the hardness and to the electrical resistivity of the alloy (Figure 11). However, no linear relation exists between the hardness and the electrical resistivity of the isothermal aged alloy (Figure 12). In the as quenched alloys, the hardness and the electrical resistivity variations are due only to the presence of solute atoms while in the isothermal aged alloy, there are due to the presence of the solute atoms and the GP zones. In such a case, the solute atom concentration of the matrix and the volume fraction of the GP zones vary simultaneously and no linear relation is observed in accordance with the results reported by Koch and Colijn ^[13].

Figure 10. Variation of the hardness versus the electrical resistivity of the as quenched alloys

Download as

Veiw figure View Figure

Figure 11. Variation of the hardness contribution versus the electrical resistivity contribution of the matrix during the GP zones precipitation

Download as

Veiw figure View Figure

Figure 12. Variation of the hardness versus the electrical resistivity of the isothermal aged alloy

Download as

Veiw figure View Figure