How to estimate isotropic distributions and mean values in crystalline solids

The concept of special directions in the Brillouin zone and the applicability of Houston's formula (or its extended versions) to both theoretical and experimental investigations are discussed. We propose some expressions to describe the isotropic component in systems having both cubic and non-cubic symmetry. The results presented have implications for both experimentalists who want to obtain average properties from a small number of measurements on single crystals, and for theoretical calculations which are to be compared with isotropic experimental measurements, for example coming from investigations of polycrystalline or powder samples. As George Orwell might have put it: all directions are equal, but some directions are more equal than others.

Special directions in momentum space. I. Cubic symmetries

Some new sets of special directions (SDs) in the Brillouin zone for cubic structures are presented. They allow for construction in the reciprocal space of anisotropic quantities, having Γ1symmetry, from knowledge of such quantities along a limited number of SDs. These SDs also define which spectra, measured, for example, in Compton scattering experiments, are the most efficient for reconstructing three-dimensional densities from their one-dimensional projections. The new SDs are compared with results obtained by other authors.

Study of colloidal quantum-dot surfaces using an innovative thin-film positron 2D-ACAR method

Nanosized inorganic particles are of great interest because their electronic properties can be easily tailored, providing a tremendous potential for applications in optoelectronic devices, light-emitting diodes, solar cells and hydrogen storage. Confinement of electrons and holes to dimensions comparable to their wavelength leads to quantum-well states with modified wavefunctions and density of states. Surface phenomena are crucial in determining nanoparticle properties in view of their large surface-to-volume ratio. Despite a wealth of information, many fundamental questions about the nature of the surface and its relationship with the electronic structure remain unsolved. Ab initio calculations on CdSe nanocrystals suggest that passivating the ligands does not produce the ideal wurtzite structure and that Se atoms relax outwards irrespective of passivation. Here we show that implanted positrons are trapped at the surface of CdSe nanocrystals. They annihilate mostly with the Se electrons, monitor changes in composition and structure of the surface while hardly sensing the ligand molecules, and we thus unambiguously confirm the predicted strong surface relaxation.