Chapter 9 Structural chemistry of ionic compounds9.1 lonic radius ratio & coordination polyhedra of ionsIn ionic crystals the positions in the crystal lattice areoccupiedbycationsandanions·In most cases, anions have much larger radii than cations,andformaclose-packedstructure·Consequently cations occupy the interstices of the close-packedstructureformedbyanionsLocal motifaround a cation:coordination polyhedronformed by cation and its surroundinganions
Chapter 9 Structural chemistry of ionic compounds 9.1 Ionic radius ratio & coordination polyhedra of ions • In most cases, anions have much larger radii than cations, and form a close-packed structure. • Consequently cations occupy the interstices of the closepacked structure formed by anions. Local motif around a cation: coordination polyhedron formed by cation and its surrounding anions. In ionic crystals the positions in the crystal lattice are occupied by cations and anions
Interstices in fcc close-packed structure(Ifformed by anions with a radius ofR)octahedralholestetrahedralholes4Ra=V2=2V2Ra/3aR=0.414RR(hole)R= 0.225RR(hole)24Hole size is 0.414R: CN = 6Holesizeis0.225R:CN=4
octahedral holes • Hole size is 0.414R; CN = 6 tetrahedral holes • Hole size is 0.225R; CN=4 Interstices in fcc close-packed structure (If formed by anions with a radius of R) R R a 2 2 2 4 R R a R hole 0.414 2 ( ) R R a R hole 0.225 4 3 ( )
C.N.Thole /RInterstice type30.155Triangular0.2254Tetrahedral60.414Octahedral80.732CubicRadiusof anion121.000Cuboctahedral(rnole: the radius of interstice formed by close-packing of anions)triangularCubicCuboctahedral
Triangular 3 0.155 Tetrahedral 4 0.225 Octahedral 6 0.414 Cubic 8 0.732 Cuboctahedral 12 1.000 Interstice type C.N. rhole /R Cubic Cuboctahedral triangular (rhole: the radius of interstice formed by close-packing of anions) Radius of anion
The rule for the packing of ionsAnions directlyAnions directlyAnions directlycontact with eachcontact with cationcontact with eachwithout anion-anionother with no cationother as well as thecentral cation!anion contact.contact.(R <rhole)(R, ≥> rhole)(R, = rhole)Strong C-A attraction!SStrong C-A attraction!weak C-Aattraction!Weak A-Arepulsion!Strong A-A repulsion!Strong A-A repulsion!Condition of coordination polyhedron: R, ≥ rhole
The rule for the packing of ions Anions directly contact with cation without anion-anion contact. Anions directly contact with each other as well as the central cation! Anions directly contact with each other with no cationanion contact. Strong C-A attraction! Weak A-A repulsion! Strong C-A attraction! Strong A-A repulsion! weak C-A attraction! Strong A-A repulsion! Condition of coordination polyhedron: R+ rhole (R+ > rhole) (R+ = rhole) (R+ < rhole)
Table 1.The limiting R./R_ratio ofsome coordination polyhedraC.N.Coordination polyhedronminimumR/R≥ 0.1553Triangular≥ 0.225Tetrahedral6≥ 0.414Octahedral8Cubic≥ 0.73212≥1.000Cuboctahedral
Coordination polyhedron C.N. minimum R+ /R Triangular 3 0.155 Tetrahedral 4 0.225 Octahedral 6 0.414 Cubic 8 0.732 Cuboctahedral 12 1.000 Table 1. The limiting R+ /R ratio of some coordination polyhedra