The crystalline structures in thin films of polystyrene-b-poly(ethylene oxide) (PS-b-PEO) diblock copolymers were studied in dependence on the degree of supercooling. Atomic force microscopy showed that the crystalline domains (lamellae) consist of grains, which are macroscopic at low and intermediate degrees of supercooling, but of submicrometer size for strong supercooling. Using grazing-incidence wide-angle x-ray scattering, we could determine the grain orientation distribution function which shows that the chain stems are perpendicular to the lamellae at low supercooling, but tilted at intermediate and strong supercooling. These results suggest that, at intermediate and strong supercooling, the crystalline PEO lamellae do not grow homogeneously, but by the formation of small crystallites at the growth front.