Advanced semiconductor heterostructures are at the very heart of many modern technologies, including aggressively scaled complementary metal oxide semiconductor transistors for high performance computing and laser diodes for low power solid state lighting applications. The control of structural and compositional homogeneity of these semiconductor heterostructures is the key to success to further develop these state-of-the-art technologies. In this article, we report on the lateral distribution of tilt, composition, and strain across step-graded SiGe strain relaxed buffer layers on 300 mm Si(001) wafers treated with and without chemical-mechanical polishing. By using the advanced synchrotron based scanning X-ray diffraction microscopy technique K-Map together with micro-Raman spectroscopy and Atomic Force Microscopy, we are able to establish a partial correlation between real space morphology and structural properties of the sample resolved at the micrometer scale. In particular, we demonstrate that the lattice plane bending of the commonly observed cross-hatch pattern is caused by dislocations. Our results show a strong local correlation between the strain field and composition distribution, indicating that the adatom surface diffusion during growth is driven by strain field fluctuations induced by the underlying dislocation network. Finally, it is revealed that a superficial chemical-mechanical polishing of cross-hatched surfaces does not lead to any significant change of tilt, composition, and strain variation compared to that of as-grown samples.