Hexagonal Close Packing Formula

Crystalline solids exhibit a regular and repeating pattern of constituent particles. The diagrammatic representation of three-dimensional arrangements of constituent particles in a crystal, in which each particle is depicted as a point in space is known as a crystal lattice. In a crystal lattice, the atoms are very closely packed, leaving very little space between them. This arrangement of elements in solids also helps us in the determination of the formula of a compound. We have learned three-dimensional solid packing can be packed in two ways viz., cubical close packing (CCP) and hexagonal close packing (HCP).

Hexagonal Close Packing

In hexagonal close packing (HCP) too, there are two basic kinds of voids are involved, namely, octahedral voids and tetrahedral voids. We know that the number of tetrahedral voids present in a lattice is twice the number of close-packed particles. While the number of octahedral voids generated is equal to the number of close-packed particles. The arrangement of particles in these voids depends on other factors too. For example, in ionic solids, the bigger ions from the close-packed structure and the smaller ions occupy the voids. Tetrahedral voids are occupied if the latter ions are small. Whereas if the latter ions are bigger, octahedral voids are occupied. The fraction of octahedral or tetrahedral voids occupied by the molecules helps us in the determination of the formula of the compound.

Problems on hexagonal close packing Formula

Question: Atoms of element Y form hexagonal close packing lattice and those of the element X occupy 1/4^th of tetrahedral voids. What is the formula of the compound formed by the elements X and Y?

Solution: The number of tetrahedral voids formed = 2 × (number of atoms of element Y)

Since only 1/4^th of these voids are occupied by X, the ratio of elements of X to Y can be given by:

2 × (1/4):1 or 1:2

Thus, the formula of the compound is XY₂.

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