BONDS Coord. No Length(A Limiting and Optimal radius Ratios for Specific Coordinations 464666 ot"in touch in touch Notes: alon radii for given element increase with coordination Ion radii for given element decrease with increasing oxidation state/positive charge Anions often bigger thancations Radius ratio rules fr Rationalization for octahedral "rattle inside the octahedral site coordination: R= radius of large alf r/R>0.414, the anions are pushed apart ion. Gradius of small ion Coordination Minimum r/R Linear. 2 R+r-c0s45= Trigonal 3 Tetrahedral, 4 0.225 √ER=R+r Octahedral. 6 0.414 Cubic. 8 0.732 Close packed, 12 1.000 A simple prediction tool, but beware- it doesn't always work us Rati ZnS 4:4 miting Radius Ratios anions in the coordination polyhedron of cation are in contact with the cation d with each other Radius ratio Coordination lary (AB) agenda 2 body diagonal a rA/=1 1>x+h。>0732 073>r/>044 0414>r/E>025 篱 七/·3-1.1 0.414 02255 BONDS Coord. No. Length (Å) C-O 3 1.32 Si-O 4 1.66 Si-O 6 1.80 G e-O 4 1.79 G e-O 6 1.94 SnI V -O 6 2.09 PbI V -O 6 2.18 PbII -O 6 2.59 Notes: Ion radii for given element increase with coordination number (CN) Ion radii for given element decrease with increasing oxidation state/positive charge Radii increase going down a group Anions often bigger thancations not “in touch” in touch Limiting and Optimal Radius Ratios for Specific Coordinations Radius Ratio Rules Rationalization for octahedral coordination: R= radius of large ion, r=radius of small ion 0.414 R r ( 2 1)R r 2R R r 2 1 cos45 R r R Þ = Þ - = Þ = + = = + o If r/R < 0.414, the cation is too small and can “rattle”inside the octahedral site If r/R > 0.414, the anions are pushed apart If r/R £ or ³ 0.414, coordination changes: Coordination Minimum r/R Linear, 2 - Trigonal, 3 0.155 Tetrahedral, 4 0.225 Octahedral, 6 0.414 Cubic, 8 0.732 Close packed, 12 1.000 A simple prediction tool, but beware ¾ it doesn’t always work! Limiting Radius Ratios - anions in the coordination polyhedron of cation are in contact with the cation and with each other Radius Ratio Coordination no. Binary (AB) Structure-type r+/r- = 1 12 none known 1 > r+/r- > 0.732 8 CsCl 0.732 > r+/r- > 0.414 6 NaCl 0.414 > r+/r- > 0.225 4 ZnS