In a crystals A atom are present at the each corners and B atoms at the center of each face of the cube. Calculate the number of A atom and B atom in one unit cell and write the formula of the compound?
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Atoms are present at the corners. and one of these is missing. so there are 7 corners at which A atoms are present in a cell. Thus the total number of A atoms per unit cell = 7/8
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There are 6 face centers and each is occupied by B atoms. However, every B atom is shared by 2 unit cells. thus total number of B atoms = 1/2 x 6 = 3.
Since it is a FCC arrangement there are 8 tetrahedral voids and each is occupied by C atoms. so total number of C atoms = 8
thus the ratio of atoms of A:B:C is
8/7 :3:8 ...
multiplying by 8 on all sides, the ratio becomes 7: 24: 64
thus the formula is A 7 B 24 C 64
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