Measurement of Equilibrium Vacancy Concentrations in Dilute Aluminum-Magnesium Alloys

Precise measurements were made of the differential length expansion (ΔL^'L^'-ΔL⁰L⁰) and differential x-ray lattice-parameter expansions (Δa^'a^'-Δa⁰a⁰), between specimens of pure aluminum and aluminum-base alloys containing 0.56 and 1.11 at.% magnesium, during slow reversible heating and cooling between the solidus and 185^∘{}C. The differential-expansion data are used to determine absolute differences between the equilibrium vacancy concentrations Cᵥ in the dilute alloys and the pure metal from the relation ${Δ}{C}ᵥ={{C}ᵥ}^{{'}}{-}{{C}ᵥ}⁰=3({{Δ}{L}^{{'}}}{{L}^{{'}}}{-}{{Δ}{L}⁰}{{L}⁰}){-}3({{Δ}{a}^{{'}}}{{a}^{{'}}}{-}{{Δ}{a}⁰}{{a}⁰}).$ Here ${{Δ}L}{L}$ and ${{Δ}a}{a}$ are length and lattice-parameter expansions, and the prime and zero superscripts refer to the alloy and pure aluminum, respectively. Since ${{C}ᵥ}⁰$ is known from previous measurements, the vacancy concentrations in each alloy ${{C}ᵥ}^{{'}}$ are then determined. The differential length and lattice-parameter measurements were carried out using the same technique previously employed in the determination of equilibrium vacancy concentrations in dilute aluminum-silver alloys. The technique allows the measurement of concentration differences as small as ±{}4×{}10^-5. The addition of magnesium caused only exceedingly small changes in the equilibrium vacancy concentrations. The changes did not exceed a few percent of the concentrations in pure aluminum. The results are compared at 650^∘{}C to the simple first-order vacancy-solute-atom-binding model of Lidiard and others. It is concluded that the vacancy-magnesium-atom binding free energy was Gv,Mgᵇ(650^∘C)⋜0.01 eV. Possible values of binding energies and entropies consistent with these results are discussed. The results are compared to the previous measurements for dilute aluminum-silver alloys where larger (but still small) solute-induced vacancy increments were found, and where Gv,Agᵇ(650^∘C)≈0.08 eV.