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Eutectics are the materials with foreseen application in the field of photonic crystals and metamaterials. In this paper, the dependence on chemical composition of the microstructures of terbium-scandium-aluminium gamet and terbium-scandium perovskite (Tb3Sc2Al3O12-TbScO3) eutectics has been studied. The growth of the eutectic rods by the micro-pulling down method is presented, using compositions with several different volume fractions of the garnet and the perovskite phases, VTSAG:VTSP = 4, 3, 2, 1, 1/2. The phases have been characterized by powder X-ray diffraction and energy dispersive spectrometry. The relationship between the lattice constant of individual phases and the chemical composition is presented. The unidirectional growth of microrods has been also investigated by electron backscattering diffraction. [ABSTRACT FROM AUTHOR]