Why is the number of tetrahedral holes double that of the octahedral holes?
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If we regard a fixed sphere, we find four tetrahedral and three octahedral voids next to it and between and . Since each tetrahedral void is adjacent to four spheres, while each octahedral void is adjacent to six spheres, we get 4 ⋅ 1 4 = 1 tetrahedral and 3 ⋅ 1 6 = 1 2 octahedreal void per sphere..
If we regard a fixed sphere, we find four tetrahedral and three octahedral voids next to it and between and . Since each tetrahedral void is adjacent to four spheres, while each octahedral void is adjacent to six spheres, we get 4 ⋅ 1 4 = 1 tetrahedral and 3 ⋅ 1 6 = 1 2 octahedreal void per sphere..
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