Question

What is the formula of the compound in which the element Y forms CCP lattice and atoms of X occupy two third of tetrahedral voids?

Answer 1

Hint: Y is the effective number of atoms in the CCP lattice and X is the number of tetrahedral voids which is twice the effective number of atoms in the unit cell.

Step by step answer: CCP is called Cubic close packed which is also called Face centred cubic. This system has lattice points on the faces of the cue, that each gives exactly one half contribution, in addition to the corner lattice points which gives a total of 4 lattice points per unit cell. Each sphere in a CCP lattice has coordination number 12. Coordination number is the number of nearest neighbours of a central atom in the structure. The plane of a face-centred cubic system is a hexagonal grid.
Voids are gaps in between the constituent particles. Voids in solid states mean the vacant space between the constituent particles in a closed packed structure. Close packing in solids can be generally done in three ways which are 1D, 2D and 3D close packing. The empty spaces between the atoms are called voids and in case of hexagonal packing, these voids are in triangular shapes and they are called triangular voids. In 2D closed packed structure, when spheres of the second layer lie above the triangular voids of the first layer, each sphere touches the three spheres of the first layer. By joining the centre of these four spheres, a tetrahedron is formed. This forms a tetrahedral void.
According to the question, we need to find a formula for X and Y where Y forms CCP lattice and X occupy 2/3rd of tetrahedral voids.
As effective number of atoms in CCP is 4, therefore $Y = 4$
Now, we know that tetrahedral voids generated in a unit cell are 2 , which is twice the effective number of atoms in the unit cell. So,
$ \Rightarrow 2 \times 4 = 8$
Since, X occupies 2/3rd of tetrahedral voids, so effective number of $X = \dfrac{2}{3} \times 8 = \dfrac{{16}}{3}$
So, $X = \dfrac{{16}}{3}$ and $Y = 4$
Hence, the simplest formula is ${X_4}{Y_3}$ .

Note: Tetrahedral voids are voids generated in 2D closed structure. When second layer spheres lie above the first layer a tetrahedron is formed because each sphere touches three spheres of the first layer. Due to the formation of tetrahedron, the void is called tetrahedral void.