The crystal CaCO3 doped with the transition-metal ion Mn2+ has caused considerable interest of people in the recent decades. However, how to determine the local lattice structure of CaCO3:Mn2+ systems still a problem needing to be solved. Therefore, the research on the local lattice structure becomes a very important scientific issue. In the present paper, we first introduce the method of building complete energy matrix of d5 configuration ion with a trigonal symmetry as well as EPR theory. By diagonalizing the complete energy matrix, we calculate the ground-state zero-field splitting of CaCO3:Mn2+ system in the single crystal and the ostracum layer of operculum of fresh water snail P. globosa simultaneity. The result shows that the distortion is compressed distortion in above both cases. From this, we get an important conclusion: when Mn2+ ion doped in the CaCO3 crystal, it will substitute the location of Ca2+ ion, thus there will be a compressed distortion along the C3 axis in the local lattice structure.
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