Packing and Packing efficiency in Solids-Class 12 Chemistry

We know that there are 7 crystal systems and 14 types of unit cells that occur in nature. The solid states of the majority of metallic elements, some covalent compounds, and many ionic compounds occur as cubic lattices. There are three types of cubic unit cells within the cubic system.

Let’s pack the three cubic unit cells and the hexagonal unit cell and also determine their packing efficiency. The packing efficiency is the percentage of the total volume occupied by the spheres themselves. We already know that unit cells result from the way the atoms pack together in a crystal lattice.

The simple cubic unit cell: When we arrange the first layer of spheres (imagine particles of the crystals to be identical spheres) in vertical and horizontal rows, then large diamond-shaped spaces are formed. If we place the second layer of spheres directly above the first layer, we obtain the arrangement based on the simple cubic unit cell. The spheres occupy only 52% of the unit cell volume, so 48% of the empty space is left. Hence it is a very inefficient way of packing of particles.
The body-centered cubic unit cell (bcc): If we place the second layer of spheres over the diamond-shaped spaces created, rather than directly above the first layer, than the packing will be more efficient. The third layer is placed on to the diamond-shaped space formed in the second layer. Thus the first and the third layer line up vertically. This arrangement gives body-centered cubic unit cells. This gives the packing efficiency of 68%, which is higher than the simple cubic unit cell arrangement. Several metallic elements, including chromium, iron, and all the elements of Group 1A of Periodic Table, have this arrangement.

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Face-centered unit cells and Hexagonal unit cells: The spheres are arranged most efficiently in these cells. The spheres in the first layer are arranged such that triangular shaped spaces are formed, which are smaller than the diamond-shaped Then we place the second layer over these spaces. In the second layer, some spaces lie above the spheres in the first layer, whereas some spaces lie above the spaces in the first layer. The third layer can be arranged in either of the two ways-

Hexagonal unit cells: If the third layer of spheres is placed on to the spaces of the second layer that lies just above the spheres of the first layer, then the spheres of the third layer are exactly over the spheres in the first layer. The third layer has the same arrangement of spheres as the first layer. Since the structure repeats itself after every two layers, the stacking is described as (abab…) layering pattern, and we get Hexagonal closed packing(hcp) which is based on the hexagonal unit cell. In this, the atoms occupy 74% of space.

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