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In a crystal lattice A atoms are at corners,B atoms at edge centres,C atoms at face centres and D atoms at the body centre.If a diagonal plane cuts the lattice then what is the formula of the resulting lattice structure?

In a crystal lattice A atoms are at corners,B atoms at edge centres,C atoms at face centres and D atoms at the body centre.If a diagonal plane cuts the lattice then what is the formula of the resulting lattice structure?

Grade:12th pass

1 Answers

Sakshi
askIITians Faculty 652 Points
6 years ago
There are eight corners and the contribution at each corner is 1/8, therefore total number of A atoms are 1.
In a crystal, there are 12 edges, the contribution of each atom at the edge centre is ¼,
thus the total number of B atoms in the crystal is 12/4=3
The total number of faces are 6 and the contribution of each atom at the face center is ½, thus the total number of C atoms is 3
Since the D atom is at the body centre and the contribution is 1 therefore the number of D atoms is 1
Thus, the formula of a unit cell formed as described above is AB3C3D
IF A DIAGONAL PLANE CUTS THE LATTICE, THE RESULTING FORMULA FOR HALF THE LATTICE WILL BE,
A1/2B3/2C3/2D½ .. The exact formula will actually be same as the above mentioned formula.

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