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Question:

If the unit cell of a mineral has cubic packed (c.c.p.) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n respectively are:

12,18

1,14

12,12

14,18

Solution:

A ccp structure has 4 atoms/ions per unit cell, 4 octahedral voids and 8 tetrahedral voids. Thus, in the unit cell of the mineral, there are 4 oxide ions, 4m Al³⁺ ions and 8n Mg²⁺ ions respectively. For charge balance, 4(-2) + 4m(3+) + 8n(2+) = 0. The above equation will be balanced when m = 12 and n = 18. Hence, m and n, respectively, are 12, 18.