Positron Lifetime Calculations of Hexagonal Metals with the True Geometry

The approaches to get lifetimes of the hexagonal metals have been performed making use of the face centred cubic (f.c.c.) structure, instead of the real hexagonal one. Although some structural reasons allow this approximation, it is expected to fail when free volume is created in the solid. In this work, we have used the real hexagonal geometry to study these metals. For the cases of bulk, mono-, diand trivacancies no appreciable differences have been observed in the calculated lifetimes. However, when studying clusters of vacancies in the real hexagonal structure and in the f.c.c. one, differences between 3.2% and 7.4% appear in lifetimes between these structures. This fact shows that the approximation of using the f.c.c. structure is not good for studies of extended defects. Positron lifetimes in these metals have also been obtained by means of the local density and general gradient approximations, using for enhancement factors Arponen-Pajanne and Boro  nskiNieminen approximations. In alkaline earth and early transition metals the calculations performed with the general gradient approximation do not improve the results obtained using Bor onski-Nieminen's formula for the enhancement factor.