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how much fraction of area of one face is covered by carbon atoms in diamond

how much fraction of area of one face is covered by carbon  atoms in diamond

Grade:12

1 Answers

Gaurav
askIITians Faculty 164 Points
8 years ago
Diamond has FCC structure
For FCC crystal



Let ‘r’ be the radius of sphere and ‘a’ be the edge length of the cube

As there are 4 sphere in fcc unit cell

∴Volume of four spheres = 4 (4/3πr3)

In fcc, the corner spheres are in touch with the face centred sphere. Therefore, face diagonal AD is equal to four times the radius of sphere

AC= 4r
But from the right angled triangle ACDAC = √AD2+ DC2=√a2+a2=√2a

4r = √2a

or a = 4/√2 r
Packng Fraction = 75%

∴volume of cube = (2/√2 r)3

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