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 ______.

विकल्प

• `1/2, 1/8`

• `1, 1/4`

• `1/2, 1/2`

• `1/4, 1/8`

Answer 1

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 `bbunderline(1/2, 1/8)`.

Explanation:

In a cubic close-packed (ccp) or face-centred cubic (fcc) arrangement:

Number of atoms per unit cell = 4 (for oxygen in this case)

Number of octahedral voids = equal to the number of atoms = 4

Number of tetrahedral voids = 2 × number of atoms = 8

In mineral like Spinel (MgAl₂O₄):

Al³⁺ ions occupy half of the octahedral voids ⇒ m = `1/2`

Mg²⁺ ions occupy one-eighth of the tetrahedral voids ⇒ n = `1/8`