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1. The problem statement, all variables and given/known data

This is part of a series of short questions (i.e. prove everything in Kittel Ch. 1, Table 2):

Prove that the packing fraction of a BCC (body-centered) cubic lattice is:

1/8 * pi * \sqrt{3}

2. Relevant equations

packing fraction = volume of a sphere / volume of primitive cell

3. The attempt at a solution

each lattice point (there are two total for BCC) can hold a sphere (or at least part of one) with radius a\sqrt{3} / 2. subbing in:

2 * 4/3 * pi * (a\sqrt{3} / 2) ^{3} / (a^{3}/2)

the \sqrt{3} becomes a 9. how does the \sqrt{3} possibly remain?

my question: how the heck did kittel get 1/8 * pi * \sqrt{3}?

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# Packing fraction of body-centered cubic lattice - solid state physics

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