Abstract The growth of single crystals from melts may be accompanied by creating a sequence of structural imperfections in the solid phase which is given by the conditions of crystallization and the crystal chemical composition. A periodical variation of the crystallization rate happens under certain conditions of the heat and mass transfer, which leads to a variation of the character of distribution of admixtures in the volume of the growing single crystal and its substructure. An accumulation of admixtures in front of the crystallization front and increasing of the crystallization undercooling may cause a considerable rise of the speed of movement of the crystallization front and changes of the admixture occupation in the growing crystal on the phase boundary surface. The variation of the microscopic crystallization rate causes a creation of a band structure observed on longitudinal cross sections of single crystals. The segregation phenomena and the formation of growth bands and cores during the crystallization were theoretically and experimentally studied. Low-alloyed single crystals of W and Mo doped with Ir or Re were prepared by the electron beam zone melting (floating zone method) applying three different zone pass rates. The electron wave dispersive analysis and the instrumental neutron activation analysis were used for the determination of admixtures concentration in specimens. The detected sinusoidal character of concentration profiles of Ir and Re is related to the growth band occurrence in the Mo single crystals. The effective segregation coefficients of admixtures in molybdenum and tungsten were determined by means of INAA with the freeze zone.