What is unit cell ? Calculate the packing efficiency of metal crystal that has simple cubic structure
Answers
the smallest group of atoms which has the overall symmetry of a crystal, and from which the entire lattice can be built up by repetition in three dimensions.
Answer:
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(i) The efficiency of packing in case of simple cubic unit cell is given below:
A simple cubic unit cell contains one atom per unit cell.
Also, a=2r, where a is the edge length and r is the radius of atom.
Total volume of unit cell =a
3
.
Packing efficiency =
Total volume of unit cell
Volume of one sphere
×100
Packing efficiency =
8r 3 34 πr 3
×100=52.4%
(ii) The efficiency of packing in case of body-centred cubic unit cell is given below:
A body-centred cubic unit cell contains two atoms per unit cell.
Also,
3
a=4r, where a is the edge length and r is the radius of atom.
Total volume of unit cell =a
3
.
Packing efficiency =
Total volume of unit cell
Volume of two spheres ×100
Packing efficiency =
3 3 64 ×r 3
38 πr 3 ×100=68%
(iii) The efficiency of packing in case of face-centered cubic unit cell (with the assumptions that atoms are touching each other) is given below:
A face-centered cubic unit cell contains four atoms per unit cell.
Also, a=2
2
r, where a is the edge length and r is the radius of atom.
Total volume of unit cell =a
3
Packing efficiency =
Total volume of unit cell
Volume of four spheres ×100
Packing efficiency =
16 2 r 3316
πr 3 ×100=74%
Explanation:
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