Annihilation of a positron in a vacancy in aluminum

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Abstract
Results of an augmented-plane-wave calculation of the positron lifetime and the angular-correlation curves for aluminum, both in the vacancy-free crystal and in the crystal with a vacancy, are presented. The environment of the vacancy was simulated by a face-centered-cubic supercell with a volume 27 times that of the standard primitive unit cell of the A1 lattice. The calculated positron-vacancy binding energy is 3.36 eV at room temperature. The temperature dependences of the trapping potential, the positron-vacancy binding energy, and the positron lifetime both in the Bloch state and in the vacancy-trapped state, associated only with the static thermal expansion of the lattice, have been calculated. It is found that the fractional increase in positron lifetime in the Bloch state is only ∼80% of the fractional increase in the volume of the lattice. The lifetime in the vacancy-trapped state is also found to vary with temperature, showing a fractional increase of ∼50% of the fractional increase in the volume of the lattice. These results are consistent with the available experimental results. It is further shown that the core contribution to the angular-correlation curve for the vacancy-trapped state of the positron is anisotropic owing to the highly anisotropic nature of the positron wave function inside the atomic muffin-tin spheres surrounding the vacancy. This is in contrast to the Bloch state of the positron for which the positron wave function may be assumed to be isotropic in the region of the core electron-positron overlap. Modified expressions for the spherically averaged core angular-correlation curves are given. The calculated total angular-correlation curves (including valence-electron contribution) in the Bloch and the vacancy-trapped states of the positron are in good agreement with experiment.