1.7.2 Antifluorite (A₂X) and Fluorite (AX₂) Structures

       1.7.2.1 Antifluorite

• FCC packing of anions

• All tetrahedral sites filled by cations

• Coordination : Anions: 8, Cations: 4

• Chemical formula: M₂X

• Example: Li₂O, Na₂O, K₂O

• Radius ratio (r_c/r_a): 0.225-0.414

• Examples: r(Li⁺) : 0.059 nm, r(Na⁺) : 0.099 nm, r(O^-) : 0.14 nm

• Lattice type: FCC

• Motif – X: 0 0 0, M -

• Four formula units per unit cell

• In this structure in many cases, although r_c/r_a ratio predict an octahedral co-ordination, tetrahedral coordination is preferred to fulfill the stoichiometry requirements. In turn, anions are cubic coordinated by cations (CN: 8)

• The structure shows corner sharing of tetrahedra.

       1.7.2.2 Fluorite Structure (CaF₂ Structure)

• Slightly bigger cations in comparison to other structures

• Example:UO₂, ZrO₂, CaF₂, CeO₂

• Typical representation of the structure appears as if cations make a FCC lattice and anions occupy the tetrahedral sites.

• While more appropriate Fluorite structure representation is shown below where eight primitive cubic unit cells made by anions are joined together to make a big cube and cations occupy the centers of four of these small cubes in an ordered fashion.




Figure 1.27 A more appropriate representation of fluorite structure

• Co-ordination number: Cations - 8 ;  Anions - 4

• Lattice: FCC

• Motif: M – 0 0 0; X – ¼ ¼ ¼; ¾ ¾ ¾  

• Examples of ionic radii of a few ions:

• U⁴⁺ : 0.1 nm, Zr⁴⁺: 0.084 nm, Ce⁴⁺: 0.097 nm, O^2- : 0.14 nm (observe that cations are quite large as compared to oxygen ions)

• The structure as you can also see has a large void in the center of unit cell made by cations.

• These empty spaces make such oxides, good ionic conductors which is useful in applications such as energy storage e.g. batteries.

• For having some fun with the structure, we can also draw as projection of this material on (110) plane. Here you can see the row of empty octahedral sites along [110]-direction.