The areas located near the cooling bores of single-crystalline cored turbine blades made of nickel-based CMSX-4 superalloy were studied. The blades were solidified by the vertical Bridgman technique in the industrial ALD furnace. Longitudinal sections of the blades were studied by Scanning Electron Microscopy, X-ray diffraction topography, X-ray diffraction measurements of the γ′-phase lattice parameter a, and the α angle of the primary crystal orientation. The local changes in α were analyzed in relation to the changes of the dendrite’s growth direction near the cooling bores. It was found that in the area approximately 3 ÷ 4 mm wide around the cooling bores, changes of α and a, both in the blade root and in the airfoil occurred. The local temperature distribution near the cooling bores formed a curved macroscopic solidification front, which caused changes in the chemical composition and, consequently, changes in the a value in a range of 0.002 Å to 0.014 Å. The mechanism of alloying elements segregation by tips of the dendrites on the bent solidification front was proposed. The multi-scale analysis that allows determining a relation between processes proceed both on a millimeter-scale and a micrometric and nanometric scale, was applied in the studies.