Question

In an ionic compund AxBy, A occupies all the corners of the cube and at each center of the face, and B occupies 50% of the tetrahedral holes in the crystal. What is the emperical formula of the compund?

** I got A=3 but I get stuck trying to determine B because I still don't fully quite understand what exactly a tetrahedral hole is.

Answer 1

A single atom is in contact with the three atoms in the layers directly below it, the void space is known as a tetrahedral hole.

Tetrahedron is just an imaginary construction whose four corners point to the centers of the four atoms that are in contact.

A = 8 corners * (1/8) + 6 faces * (1/2) = 3

We know that, there is 8 corners in cube. From each corner and three nearest below atom made one tetrahedral hole. Hence in cube there is 8 tetrahedral hole.

50 % tetrahedral hole = only 4 tetrahedral hole occupy. Each tetrahedral hole contribution is 1.

B = (1/2 * 8 tetrahedral hole ) * 1 = 4

Emperical Formula = A₃B₄