Benchmark solidification experiments were successfully performed under microgravity conditions on-board the International Space Station (ISS) within the ESAprogramme CETSOL (Columnar-to-Equiaxed Transition in SOLidification Processing). Cylindrical samples of grain-refined Al-4wt.%Cu, Al-10wt.%Cu and Al-20wt.%Cu alloys were directionally solidified in a gradient furnace to investigate columnar and equiaxed dendritic growth structures as well as the columnar to equiaxed transition under diffusive conditions. The determination of temperature gradients; interface velocities; and cooling rates at liquidus, solidus, and eutectic front positions provides well-defined thermal experimental characterization. The evaluation of the flight samples demonstrates that no significant macrosegregation along the sample axis occurred and no radial effects were observed. Therefore, purely diffusive solidification behaviour without any residual melt convection can be assumed for these microgravity experiments. The analyses of the microstructure in longitudinal cross-sections show dendritic structures without any pore formation and the averaged eutectic fraction is largely constant along the sample. The samples of refined Al-4wt.%Cu alloy show a sharp CET from columnar dendrites to a fine equiaxed steady-state grain structure whereas in the samples of refined Al-10wt.%Cu and Al-20wt.%Cu alloy, only equiaxed dendritic grain growth is observed. A quantitative analysis of the equiaxed grain morphology shows, that the shapes of the equiaxed dendrites depend on the applied temperature gradient, but the grain sizes in radial and longitudinal directions are identical. Therefore, a fully equiaxed dendritic growth structure without dendrite elongation was obtained. Compared to experiments in microgravity with non-refined Al-Cu alloys the average equiaxed grain size is about three times smaller.