## Packing Voids in Ionic Solids

### Ionic Solids:

• When particles are close packed resulting in either ccp or hcp structure, two types of voids are generated. The number of octahedral voids present in a lattice is equal to the number of close packed particles, the number of tetrahedral voids generated is twice this number.
• Ionic solids are formed fr0m cations and anions. Charge on this ion is balanced by appropriate number of both types of ions so that net charge on solid is zero (neutral).
• 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 tetrahedral voids are occupied, if bigger, then octahedral voids are occupied.
• Not all octahedral or tetrahedral voids are occupied. In a given compound, the fraction of octahedral or tetrahedral voids that are occupied, depends upon the chemical formula of the compound, as can be seen from the following examples.

### Example 1:

A compound is formed by two elements X and Y. Atoms of the element Y (as anions) make ccp and those of the element X (as cations) occupy all the octahedral voids. Obtain the formula of the compound .

• Given that the ccp lattice is formed by the element Y. The number of octahedral voids generated would be equal to the number of atoms of Y present in it.
• Since all the octahedral voids are occupied by the atoms of X, their number would also be equal to that of the element Y. Thus, the atoms of elements X and Y are present in equal numbers or 1:1 ratio. Therefore, the formula of the compound is XY.

### Example 2:

Atoms of element B form hcp lattice and those of the element A occupy 2/3rd of tetrahedral voids. Obtain the formula of the compound formed by the elements A and B,

• The number of tetrahedral voids formed is equal to twice the number of atoms of element B and only 2/3rd of these are occupied by the atoms of element A. Hence the ratio of the number of atoms of A and B is 2 × (2/3):1 or 4:3 and the formula of the compound is A4B3.

### Radius Ratio of Ionic Compound:

• The ratio of radius of cations (r+) to the radius of anion (r-) is known as the radius ratio of the ionic solid.

• It is useful in predicting structure of ionic solid.
• The structure of an ionic compound depends upon stoichiometry and the size of ions.
• In crystals cations tends to get surrounded by the largest possible number of anions around it.
• Greater the radius ratio, greater is the coordination number of cations and anions.
• If cations are extremely small and anions are extremely large, then the radius ratio is very small. In such case packing of anions is very close to each other and due to repulsion among anions, system becomes unstable. Hence the structure changes to some suitable stable arrangement.
• The radius ratio at which anions just touch each other as well as central cation is called critical radius ratio.

### Effect of Radius Ratio on Coordination Number:

• A cation would fit exactly into octahedral void and would have coordination number of six, if the radius ratio were exactly 0.414. Similarly a cation would fit exactly into tetrahedral void and would have coordination number of four, if the radius ratio were exactly 0.225.
• In crystal, cations tend to get surrounded by the largest possible number of anions.
• Let us consider a case in which a cation is fitting exactly into octahedral void of close pack anions and have coordination number of six, in this case the radius ratio is exactly 0.414.

• When the radius ratio is greater than this, then the anions move apart to accommodate larger cation. This situation is relatively unstable. If radius ratio is further increased the anions will move farther and farther apart till to reach a stage at which more anions can be accommodated. Now, the bigger cation moves to bigger void i.e. octahedral void whose coordination number is 8. This happens when radius ratio exceeds 0.732.
• In case of radius ratio becomes less than 0.414, the six anions will not be able to touch the smaller cation. To touch the cation, the anions starts overlapping with each other, which is unstable situation. Hence smaller cation moves to smaller void i.e. tetrahedral void and coordination number decreases from 6 to 4.

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