Positron localization effects on the Doppler broadening of the annihilation line: Aluminum as a case study

The coincidence Doppler broadening (CDB) technique is widely used to measure one-dimensional momentum distributions of annihilation photons, with the aim of obtaining information on the chemical environment of open-volume defects. However, the quantitative analysis of CDB spectra needs to include also purely geometrical effects. A demonstration is given here, on the basis of CDB spectra measured in quenched and in deformed pure aluminum. The comparison of the experimental results with ab initio computations shows that the observed differences come from the difference in free volume seen by positrons trapped in quenched-in vacancies or in vacancylike defects associated to dislocations. The computation reproduces accurately all details of CDB spectra, including the peak near the Fermi break, which is due to the zero-point motion of the confined positron.

Figure 1

CDB spectra for defected Al (relative differences to annealed Al). The solid line is the result of the ab initio LDA calculation (see text).

Figure 2

CDB spectra for defected Al (relative differences to annealed Al), after scaling to 100% trapping.

Figure 3

Computed momentum densities (relative differences to bulk Al) for positron trapping at an empty site; labels on the curves show the isotropic inward relaxation of the nearest-neighbor positions (here, and in the following figures, negative values are conventionally attributed to outward relaxations). The Fermi momentum $p_F$ is denoted by the upward arrow.

Figure 4

Contribution of valence electrons to the $e^{+}\text{−}{e}^{-}$ one-dimensional momentum density in bulk aluminum and in vacancylike defects with different inward linear relaxations (see labels). The Fermi momentum is denoted by the upward arrow.

Figure 5

Core annihilation rate (solid line, left vertical scale) and lifetime (dashed line, right vertical scale) for trapped positrons (relative to free positrons in bulk Al) vs the inward displacement of the nearest neighbors of the empty atomic site.

Figure 6

One-dimensional momentum density for positrons trapped in vacancylike defects. The labels on the curves indicate the inward displacement of the nearest neighbors of the empty atomic site. The horizontal bar shows the expected momentum width for quantum confinement within $2.0\mathrm{\AA }$.

Figure 7

Width of the positron momentum distribution vs inward linear relaxation. See text for the different definitions of the width parameters.

Figure 8

Simulated effect of positron confinement in an unrelaxed vacancy on the relative difference of momentum densities. Solid line: resolution $2\times {10}^{-3}{m}_{0}c$; dashed line: resolution $4\times {10}^{-3}{m}_{0}c$. Fermi momentum: downward arrow.