If the unit cell of a mineral has cubic close packed (ccp) 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

Engineering

Chemistry

Voids or Interstitial Site and Radius Ratio

HCP and CCP Parameters

Question

If the unit cell of a mineral has cubic close packed (ccp) 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

$1, \frac{1}{4}$

$\frac{1}{2}, \frac{1}{8}$

$\frac{1}{2}, \frac{1}{2}$

$\frac{1}{4}, \frac{1}{8}$

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In ccp lattice:

Number of O atoms → 4

Number of Octahedral voids → 4

Number of tetrahedral voids → 8

Number of Al³⁺ = 4 × m

Number of Mg²⁺ = 8 × n

Due to charge neutrality = 0

4(-2) + 4m (+3) + 8n (+2) = 0

$∴ m = \frac{1}{2} and n = \frac{1}{8}$