Graduate school of Science and Engineering, Yamaguchi University^* Department of Earth Sciences, Kanazawa University, Japan^** Department of Earth Sciences, Kumamoto University, Japan^***
○Akihiko Nakatsuka^* Noriaki Nakayama^* Hiroki Okudera^** Akira Yoshiasa^*** Kazuake Iishi^*

Garnets can accommodate various cations, which occupy tetrahedral, octahedral and dodecahedral sites. These three types of coordination polyhedra link in a complex manner by sharing edges and corners with each other. We have reported that the repulsions between cations across the shared edges of polyhedra contribute greatly to the structural stability of garnets. In the present study, we investigated the relationship between the cationic thermal vibration behaviors and the cation-cation repulsions. Consequently, we found that the ratios RMSD_X-Z/RMSD_X-O and RMSD_Z-X/RMSD_Z-O have the negative correlations with the repulsions between tetrahedral and dodecahedral cations, where RMSD_X-Z and RMSD_Z-X are the root mean square displacements (RMSD) of dodecahedral and tetrahedral cations in the tetrahedral-dodecahedral directions, respectively; RMSD_X-O and RMSD_Z-O are the RMSD's of dodecahedral and tetrahedral cations in the respective cation-oxygen directions. In most of reported garnets, the RMSD_X-Z and RMSD_Z-X are smaller than RMSD_X-O and RMSD_Z-O, respectively, which indicates that the repulsions between tetrahedral and dodecahedral cations are stronger than the interactions between dodecahedral cation and oxygen and between tetrahedral cation and oxygen. On the other hand, only NaPb₂M₂V₃O₁₂ ( M = Mg, Co, Ni) vanadate garnets among the investigated garnets are in the opposite situation. Moreover, in these vanadate garnets, the repulsions between adjacent dodecahedral cations and between dodecahedral and octahedral cations are remarkably weak, which yields the unusually long dodecahedral-dodecahedral and octahedral-dodecahedral shared edges.