12th chemistry solid state-Formula of a Compound and Number of Voids Filled

Formula of a Compound and Number of Voids Filled

• Number of octahedral voids = Number of close-packed particles

Number of tetrahedral voids = 2 × Number of close-packed particles

• In ionic solids, the bigger ions (usually anions) form the close-packed structure and the smaller ions (usually cations) occupy the voids.

• If the latter ion is small enough, then it occupies the tetrahedral void, and if bigger, then it occupies the octahedral void.

• Not all the voids are occupied. Only a fraction of the octahedral or tetrahedral voids are occupied.
• The fraction of the octahedral or tetrahedral voids that are occupied depends on the chemical formula of the compound.

Example A compound is formed by two elements X and Y. The atoms of element X form hcp lattice and those of element Y occupy thof the tetrahedral voids. What is the formula of the compound formed? Solution: It is known that the number of tetrahedral voids formed is equal to twice the number of atoms of element X. It is given that only of the tetrahedral voids are occupied by the atoms of element Y. Therefore, ratio of the number of atoms of X and Y = = 2: 1 Hence, the formula of the compound formed is X2Y.

Locating Tetrahedral Voids

• A unit cell of ccp or fcc lattice is divided into eight small cubes. Then, each small cube has 4 atoms at alternate corners. When these are joined to each other, a regular tetrahedron is formed.

• This implies that one tetrahedral void is present in each small cube. Therefore, a total of eight tetrahedral voids are present in one unit cell.
• Since each unit cell of ccp structure has 4 atoms, the number of tetrahedral voids is twice the number of atoms.

Locating Octahedral Voids

• When the six atoms of the face centres are joined, an octahedron is generated. This implies that the unit cell has one octahedral void at the body centre.

• Besides the body centre, there is one octahedral void at the centre of each of the 12 edges. But only of each of these voids belongs to the unit cell.

• Now, the total number of octahedral voids in a cubic loose-packed structure

This means that in ccp structure, the number of octahedral voids is equal to the number of atoms in each unit cell.