In a face centred lattice with all the positions occupied by A atoms the body centred octahedral hole in it is occupied by an atom B of an appropriate size for such a crystal, calculate the void space per unit volume of

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Quantrex Academy · Accepted Answer

Correct answer: 0.75

Let a be the edge of the cube so that aligned & 4 r_A= 2 a & a=2 2 a_A aligned Now since the atoms B has occupied the body centre octaheedral void aligned & 2 r_A+2 r_B=a & 2 r_A+2 r_B=2 2 r_A aligned 2 rB=(2 2 -2) r_ A ; r_ B r_ A = 2 -1=1.414-1=0.414 Volume of the cube a^3=16 2 r_A^3 Volume occupied by A and B= [4 × (4)/(3) π r_A^3]+[(4)/(3) π r_B^3]=(4)/(3) π(4 r_A^3+r_B^3) Volume occupied per unit volume of unit cell φ= 4 / 3 π(4 r_A^3+r_B^3) 16 2 r_A^3 = π 12 2 [4+((r_B)/(r_A))^3] =(3.14)/(1.2 × 1.414)(4+(0.414)^3)=(3.14 × 4.071)/(12 × 1.414)=0.75

In a face centred lattice with all the positions occupied by A...

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