The concept of a gamma-ray telescope based on a Laue lens offers the possibility to increase the sensitivity by more than an order of magnitude with respect to existing instruments. Laue lenses have been developed by our collaboration for several years : the main achievement of this R&D program was the CLAIRE lens prototype, which has successfully demonstrated the feasibility of the concept in astrophysical conditions. Since then, the endeavour has been oriented towards the development of efficient diffracting elements (crystal slabs) in order to increase both the effective area and the width of the energy bandpass focused, the aim being to step from a technological Laue lens to a scientifically exploitable lens. The latest mission concept featuring a gamma-ray lens is the European Gamma- Ray Imager (GRI) which intends to make use of the Laue lens to cover energies from 200 keV to 1300 keV. Investigations of two promising materials, low mosaicity copper and gradient concentration silicongermanium are presented in this paper. The measurements have been performed during three runs: 6 + 4 days at the European Synchrotron Radiation Facility (Grenoble, France), on beamline ID15A, using a 500 keV monochromatic beam, and 14 days on the GAMS 4 instrument of the Institute Laue Langevin (Grenoble, France) featuring a highly monochromatic beam of 517 keV. Despite it was not perfectly homogeneous, the presented copper crystal has exhibited peak reflectivity of 25 % in accordance with theoretical predictions, and a mosaicity around 26 arcsec, the ideal range for the realization of a Laue lens such as GRI. Silicon-germanium featuring a constant gradient have been measured for the very first time at 500 keV. Two samples showed a quite homogeneous reflectivity reaching 26%, which is far from the 48 % already observed in experimental crystals but a very encouraging beginning. The measured results have been used to estimate the performance of the GRI Laue lens design.