EQUILIBRIUM VACANCY CONCENTRATIONS IN COPPER INVESTIGATED WITH THE ABSOLUTE TECHNIQUE

The molar fraction of thermally generated vacant lattice sites N(upsilon) 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 DELTA-a(T)/a0 is determined by the Debye-Scherrer technique. The macroscopic expansion DELTA-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 N(upsilon)(T) = 3[DELTA-L(T)/L0 - DELTA-a(T)/a0]. The lattice expansion DELTA-a(T)/a0 can be determined with a relative accuracy of 2 x 10(-5). At high temperatures the error of the laser interferometer is 2 x 10(-6) for each point, respectively, equivalent to an absolute length variation of 0.04-mu-m. An extrapolation of N(upsilon) up to the melting point T(m) leads to N(upsilon)(T(m)) = (0.76 +/- 0.03) x 10(-3). The usual Arrhenius evaluation gives a formation enthalpy H(upsilon)f = (1.19 +/- 0.03) eV and a formation entropy S(upsilon)f = (3.0 +/- 0.3)k.