Method for the identification of crystalline phases in a polycrystalline sample, comprising the method steps: a) for crystal structures which are assumed to be in the sample, determining a normalized vector p(i) for the chemical composition of the crystal structure in each case, wherein the basis of the vector represents elements and/or compounds and the coordinates of the vector comprise details relating to the concentration of the elements and/or compounds within the crystal structure; b) at each measuring point of the sample: (i) acquiring a spectrum by means of energy-dispersive X-ray spectroscopy and determining the chemical composition and (ii) acquiring an electron diffraction pattern and determining the diffraction bands; c) determining a normalized vector v for the chemical composition at the measuring point whereof the coordinates comprise details relating to the concentration of the elements and/or compounds at the measuring point; d) comparing the normalized vector v for the chemical composition at the measuring point to each of the normalized vectors p(i) of the assumed crystal structures while outputting an evaluation factor s(i) for the respective correspondence of the vectors; e) for the assumed crystal structures, comparing the diffraction bands determined at the measuring point to the diffraction bands of the assumed crystal structure and outputting an evaluation factor n(i) for the correspondence of the diffraction bands; and f) for the assumed crystal structures, determining an overall quality from the two evaluation factors s(i) and n(i) and assigning the crystal structure with the highest overall quality to the measuring point. a) for crystal structures which are assumed to be in the sample, determining a normalized vector p(i) for the chemical composition of the crystal structure in each case, wherein the basis of the vector represents elements and/or compounds and the coordinates of the vector comprise details relating to the concentration of the elements and/or compounds within the crystal structure; b) at each measuring point of the sample: (i) acquiring a spectrum by means of energy-dispersive X-ray spectroscopy and determining the chemical composition and (ii) acquiring an electron diffraction pattern and determining the diffraction bands; (i) acquiring a spectrum by means of energy-dispersive X-ray spectroscopy and determining the chemical composition and (ii) acquiring an electron diffraction pattern and determining the diffraction bands; c) determining a normalized vector v for the chemical composition at the measuring point whereof the coordinates comprise details relating to the concentration of the elements and/or compounds at the measuring point; d) comparing the normalized vector v for the chemical composition at the measuring point to each of the normalized vectors p(i) of the assumed crystal structures while outputting an evaluation factor s(i) for the respective correspondence of the vectors; e) for the assumed crystal structures, comparing the diffraction bands determined at the measuring point to the diffraction bands of the assumed crystal structure and outputting an evaluation factor n(i) for the correspondence of the diffraction bands; and f) for the assumed crystal structures, determining an overall quality from the two evaluation factors s(i) and n(i) and assigning the crystal structure with the highest overall quality to the measuring point.