Question

The unit-cell of the compound K_xMg_yF_z is cubic, with Mg²⁺​ at the corners of the cube, F^- ​ions in the 12 edge sites, and the K^​+ in the center of the cube.

(a) Determine the number of magnesium ions per unit cell

(b) Determine the number of fluoride ions per unit cell

(c) Determine the number of potassium ions per unit cell

(d) Determine the coordination number for the magnesium and the potassium ions

(e) Determine the formula for K_xMg_yF_z

Answer 1

(a) Determine the number of magnesium ions per unit cell

   TOTAL 8 corners in a cube,each corner of cube is shared by 8 other cubes(unitcells)

so that, no of atoms of Mg^2+ = 8*1/8 = 1 ion per unit cell

(b) Determine the number of fluoride ions per unit cell

   total 8 edges in a cube,each edge is shared by 4 other cubes(unit cells)

so that, no of F- ions = 12*1/4 = 3 ions per unit cell

(c) Determine the number of potassium ions per unit cell

    K+ ion is present at center of the cube

so that,

   no of K+ ion is present in unit cell = 1

(d) Determine the coordination number for the magnesium and the potassium ions

    coordination number for the magnesium = 8

    coordination number for the potassium = 8

(e) Determine the formula for KxMgyFz

     formula = K1Mg1F3   = KMgF3