C.N. rra Geometry Coordination Number The critical ratio 2 Geometrical Shapes determined by geometrical 0.155-0225 Cubie hole C.N.=3 0.225-0.414 60.414-0.732 C.N.=4 80.732-1.0 ①O Cuboctahedral and Anti-cuboctahedral Common Coordination Polyhedra Structure 份 Cuboctahedron Cubic close packing Hexagonal close packing CN aB CNaB Ceramic Crystal Structures of ionic radii Greation/ranion )dictates the coordination number of anions around each cation Crystal Structure of AB I As the ratio gets larger ( i.e. as rcation/ranion 1, the coordination number gets larger and on Ratio (r+/r)6 The critical ratio determined by geometrical analysis 2 <0.155 3 0.155-0225 4 0.225 - 0.414 6 0.414 - 0.732 8 0.732 - 1.0 C.N. rC/rA Geometry Coordination Number vs Geometrical Shapes C.N. = 3 C.N. = 4 C.N. = 6 Cubic hole Cuboctahedral hole Cuboctahedral and Anti-cuboctahedral Structure Cuboctahedron ¾¾ Cubic close packing Anti-cuboctahedron ¾¾ Hexagonal close packing Common Coordination Polyhedra Ceramic Crystal Structures The ratio of ionic radii (rcation/ranion ) dictates the coordination number of anions around each cation. As the ratio gets larger (i.e. as rcation/ranion®1), the coordination number gets larger and larger. Crystal Structure of AB vs Ion Ratio (r+/r-)