20. LECT20 - Radius ratio rules PDF

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Radius ratio rules

NaCl structure  

A ccp array of Cl- w/ Na+ in all octahedral holes Each ion has CN 6 o 6:6 coordination

**why radius ratio rule doesn’t work for some compounds CsCl structure   

CN 8 Primitive cubic array of [Cl- w/ Cs+ or Cs+ w/ Cl-] at centre (non-close pack structure) 8:8 coordination

ZnS structures   

CN 4 4:4 coordination 2 structures: o Zinc Blende  Ccp of S2- w/ Zn2+ in half of the tetrahedral holes  Half bc tetrahedral holes are double the amount of circles thus would have a ratio 2:1, whereas we want 1:1  +notebook o Zinc Wurtzite  Hcp of S2- w/ Zn2+ in half of the tetrahedral holes

Radius ratio rules assume the compound is 100% ionic and ions are hard spheres w/ fixed radii A molecule may not follow the radius ratio rules when the assumption is not valid (i.e. the introduction of covalency means that the bonds are directional – there is a preferred orientation)

Fluorite (CaF2) structure 

 

Ccp of Ca2+ w/ F- occupying all tetrahedral holes o Problem w/ this description is Ca2+ is smaller than F- and so F- would not fit into the tetrahedral holes of close packed array of Ca2+ o But it leads to correct 3D Primitive cubic array of F- ions w/ Ca2+ occupying half of the body centres o Ca is coordinated to 8F and each F is coordinated to 4 Ca so 8:4 coordination Drawing a unit cell: (“Alternating” unit cell)

Rutile Structure (TiO2)  

Distorted hcp array of O2- w/ Ti4+ in half octahedral holes 6:3 coordination

The CdI2 structure  

CdI2 consists of hcp of I- w/ Cd2+ filling the octahedral holes in alternate layers 6:3 coordination

ReO3 structure (ionic compound)   

Ccp of oxide ions w/ ¼ of the oxide ions missing. The Re cations occupy a ¼ of the octahedral holes 6(Re):2(O) coordination Re is blue...