Positron annihilation spectroscopy of the equilibrium vacancy ensemble in aluminium

Abstract
One- and two-dimensional angular correlation of positron-electron annihilation radiation (1D and 2D ACAR) data have been obtained as a function of temperature between 293 and 903K for single crystals of aluminium. The 2D ACAR data are compared with calculated 2D ACAR spectra for positrons annihilating from the Bloch state and from monovacancy- and divacancy-trapped states. The theoretical formalism incorporates many-body enhancement effects into supercell band-structure calculations for the defects; lattice constants appropriate to the experimental temperatures were used. Assuming the consequences of dynamic temperature effects to be small, the experimental 2D ACAR results can be accounted for the fraction of monovacancy-trapped positrons increasing with temperature, along with an additional and continually increasing contribution from divacancy-trapped positrons at high temperatures (above 613K). The analysis indicates that about 44% of the trapped positrons annihilate from a divacancy-trapped state at 903K. Comparison of these results with those from previous measurements concerning the equilibrium vacancy ensemble in aluminium indicates that the ratio of positron trapping rates at divacancies and monovacancies ( mu 2v/ mu 1v) is about two. The present results regarding the contributions from divacancies are found to be consistent with those from the quantitative analysis of the peak-count rate 1D ACAR data using a monovacancy-divacancy analysis, which is presented elsewhere.