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Calculate the number of particles in Bod...

Calculate the number of particles in Body Centered Cubic (BCC) lattice.

Text Solution

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In `/_\ABG`
`b^2=a^2+a^2" ":.b^2=2a^2`
In `/_\AGD`
`C^2=a^2+b^2=a^2+2a^2" ":.C=sqrt(3a)`
Radius of the atom=r

Length of the body diagonal C=4r
`sqrt(3a)=4r," "a=(4r)/(sqrt3)`
Edge length of the cube`=a=(4r)/(sqrt3)`
Volume of the cubic unit cell `=a^3=((4r)/(sqrt3))^3`
Volume of one particle (Sphere)`=4/3pir^3`
The number of particles per unit cell of a BCC=2
Total volume occupied by two spheres `=2xx4/3pir^3`
Packing efficiency `=(4/3pir^3xx2)/((4/(sqrt3)^3)xx100)=(8/3pir^3)/((64)/(3sqrt3)r^3)xx100=68%`
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