Question

a mineral having the formula AB2 , crystallises in ccp , with A atoms occupying lattice points . the coordination number of A atoms is x and that of B atoms is y find x-y

Answer 1

4

Answer 2

1. Identify the crystal structure and atom positions:

The mineral has the formula AB2 and crystallizes in ccp (cubic close packing) with A atoms occupying lattice points.

In a ccp structure, the atoms form an FCC (Face-Centered Cubic) lattice.

• Number of atoms per unit cell (Z) in FCC = 4.
• Since A atoms occupy lattice points, there are 4 A atoms per unit cell.

2. Determine the number of B atoms and their locations:

The formula is AB2, meaning for every 1 A atom, there are 2 B atoms.

Since there are 4 A atoms per unit cell, the number of B atoms per unit cell will be 4 * 2 = 8.

In an FCC unit cell:

• Number of octahedral voids = Z = 4.
• Number of tetrahedral voids = 2Z = 2 * 4 = 8.

Since we have 8 B atoms and there are exactly 8 tetrahedral voids, all the tetrahedral voids must be occupied by B atoms.

3. Determine the coordination number of A (x):

A atoms are at the FCC lattice points. B atoms occupy all tetrahedral voids.

This arrangement is characteristic of the fluorite (CaF2) structure type, where Ca2+ forms the FCC lattice and F- occupies all tetrahedral voids.

In the fluorite structure, the cation (A) is surrounded by 8 anions (B).

Therefore, the coordination number of A (x) = 8.

4. Determine the coordination number of B (y):

B atoms occupy the tetrahedral voids. Each tetrahedral void is surrounded by 4 atoms that form the tetrahedron. These 4 atoms are A atoms (since A atoms form the lattice).

Therefore, the coordination number of B (y) = 4.

5. Calculate x - y:

x = 8

y = 4

x - y = 8 - 4 = 4

The final answer is $\boxed{4}$