Question

I a crystal, oxide ions are arranged at fcc and A2+ions occupy 1/8th of the tetrahedral voids and ions B3+ occupy 1/2 of the octahedral voids. Calculate the packing fraction of the crystal if oxide ions of the crystals are removed from alternate corners and A2+ions are placed at 2 of the corners.

Answer 1

Answer:

Oxide ions O  

−2

 arranged in FCC⟶O  ^−2

 

B^  3+ occupied  1/2  of the octahedral voids ⟶1/2 ×1=1/2  

A  ^2+  occupied  1/8th  of the tetrahedral voids.

∵ Number of Tetrahedral voids= 2× Number of octahedral voids

                                                   ⇒2×1=2

∴ 1/8th  of 2 Tetrahedral voids=  1/8×2=1/4

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A     B        O Convert into integer ⟶ A        B          O

1/4    1/2      1                                           1         2           4  

Therefore, formula of the oxide is AB  

AB2O4