RIGID UNIT MODES IN CRYSTAL-STRUCTURES WITH OCTAHEDRALLY COORDINATED ATOMS

The rigid unit mode analysis was initially developed to understand the phase transitions in aluminosilicate minerals containing corner-linke d tetrahedra. Here the model is applied to a range of minerals with cr ystal structures that can be described as frameworks of linked octahed ral and tetrahedral units, including garnet, sillimanite, titanite, an d ellenbergerite. Consistent with a constraint analysis, there are no rigid unit modes in these minerals. Generalizing these results suggest s that there will not be any easy ways to distort structures that have frameworks containing octahedral units. This result explains why poly hedral-tilting displacive phase transitions are not common in such min erals, whereas they occur in most aluminosilicate minerals containing only tetrahedral units. It also explains that it will be necessary for the tetrahedra and octahedra to distort when solid solutions are form ed.