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The ratio of packing fraction in fcc, bc...

The ratio of packing fraction in fcc, bcc, and cubic structure is, respectively,

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The packing fraction of a simple cubic structure is pi//6 . Prove.

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The packing fraction of a simple cubic structure is (pi)/(6) . Prove.

The packing fractionin fcc and hcp structure is same. Moreover, this is the highest packing fraction of all the possible unit cells with same atoms. Can you explain this ?

The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell respectively-

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