Equilibrium vacancy concentrations in copper investigated with the absolute technique

The molar fraction of thermally generated vacant lattice sites Nᵥ has been measured during thermal equilibrium up to temperatures near the melting point in 99.9998%-grade copper with an absolute technique. A high-resolution differential dilatometric experiment is performed. The thermal expansion of the lattice {Δ}a(T)/a₀ is determined by the Debye-Scherrer technique. The macroscopic expansion {Δ}L(T)/L₀ is measured with a special laser interferometer simultaneously as a function of temperature in the same specimen. The absolute concentration of equilibrium vacancies is obtained from Nᵥ(T)=3[{Δ}L(T)/L₀-{Δ}a(T)/a₀]. The lattice expansion {Δ}a(T)/a₀ can be determined with a relative accuracy of 2×{}10^-5. At high temperatures the error of the Laser interferometer is 2×{}10^-6 for each point, respectively, equilvalent to an absolute length variation of 0.04 {μ}m. An extrapolation of Nᵥ up to the melting point Tᵐ leads to Nᵥ(Tᵐ)=(0.76±{}0.03)×{}10^-3. The usual Arrhenius evaluation gives a formation enthalpy Hᵥᶠ=(1.19±{}0.03) eV and a formation entropy Sᵥᶠ=(3.0±{}0.3)k.