Question

calculate packing efficiency of unit cell in which atoms are present at corner and at edge centre​

Answer 1

Answer:

Packing efficiency in face-centered cubic (with the assumptions that atoms are touching each other)

Let us calculate the efficiency in ccp or fcc structure

Let the unit cell edge length be 'a' and face diagonal AC=b

In ΔABC

AC2=b2=BC2+AB2

b2=a2+a2=2a2

b=2–√a

If r is the radius of the sphere

We find b=4r

4r=2–√a

a=4r2–√=22–√r

We know that in fcc structure has effectively 4 spheres

Total volume of the four spheres is equal to 4×43πr3 and the volume of the cube a3=(22–√r)3

Therefore packing efficiency =Volume occupied by four spheres in unit cellTotal volume of the unit cell×100%

⇒4×43πr3×100(22–√r)3%

⇒163πr3×100162–√r3%=74%

Explanation:

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