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Heusler compounds exhibit a wide range of different electronic ground states and are hence expected to be applicable as functional materials in novel electronic and spintronic devices. Since the growth of large and defect-free Heusler crystals is still challenging, single crystals of FeTiSn and CuMnAl were grown by the optical floating zone technique. Two positron annihilation techniques-angular correlation of annihilation radiation and Doppler broadening spectroscopy (DBS)-were applied in order to study both the electronic structure and lattice defects. Recently, we succeeded to observe clearly the anisotropy of the Fermi surface of CuMnAl, whereas the spectra of FeTiSn were disturbed by foreign phases. In order to estimate the defect concentration in different samples of Heusler compounds, the positron diffusion length was determined by DBS using a monoenergetic positron beam. [ABSTRACT FROM AUTHOR]