The recent progress in photon-counting detector technology using high-Z semiconductor sensors provides new possibilities for spectral x-ray imaging. The benefits of the approach to extract spectral information directly from measurements in the projection domain are very advantageous for material science studies with x-rays as polychromatic artifacts like beam-hardening are handled properly. Since related methods require accurate knowledge of all energy-dependent system parameters, we utilize an adapted semi-empirical model, which relies on a simple calibration procedure. The method enables a projection-based decomposition of photon-counting raw-data into basis material projections. The objective of this paper is to investigate the method's performance applied to x-ray micro-CT with special focus on applications in material science and non-destructive testing. Projection-based dual-energy micro-CT is shown to be of good quantitative accuracy regarding material properties such as electron densities and effective atomic numbers. Furthermore, we show that the proposed approach strongly reduces beam-hardening artifacts and improves image contrast at constant measurement time.