The purpose of this paper is to provide an example of a real-world application in which Tanabe-Sugano diagrams can be used to relate the optical properties and performance of a material to its physical and chemical properties. Tanabe-Sugano diagrams illustrate the effect of the strength of the octahedral ligand field on the relative positions of the various energy level components that arise as a result of the splitting of the degenerate free-ion states. The application of these diagrams can also be extended to the spectra of transition metal ions found in solid state matrices where the predominant external force is the crystal field. In insulating materials, transition metal ions occupy sites with six anions as nearest-neighbors, forming a coordination sphere characterized as a distorted octahedron. Although the actual site symmetry is lower than Oh in most cases, an octahedral approximation is qualitatively sufficient for the present application involving an analysis and interpretation of the emission spectra of chromium-doped garnets.
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