Question

Which one of the following crystal structures is a loosely packed one? *


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Answer 1

Explanation:

Two Types of Atom Packing in a Crystal

The three dimensional structure of a solid crystalline material is established through the periodic patterning of the atoms that make up the crystal. The most efficient conformation of atomic spheres within a unit cell is known as the closest packing formation. In a three dimensional representation of this hypothetical unit cell—with the spheres packed as efficiently as possible—there are two methods to densely pack the cell.

Imagine a single layer of spheres packed into the bottom of a unit cell.

In the first method, each successive layer of spheres covers gaps in the previous layer. Three neighboring spheres in the first layer will form a hollow space where they meet. Spheres in one layer align to fit in the hollows formed in the previous layer. The third layer aligns directly above the first layer. Because the third layer is aligned the same way as the first, this configuration is referred to as “ABA” and results in hexagonal closest packing (HCP).

Alternatively, the gaps in the first layer are covered by the second layer. But the third layer is offset relative to the intersphere gaps of the first layer. The third layer of spheres does not align with the first layer. This configuration is referred to as “ABC” and results in cubic closest packing (CCP).

Two ways to stack closest packed spheresTwo methods of packing spheres into a unit cell yield the most common closest packing conformations: CCP and HCP.

A CCP arrangement has a total of 4 spheres per unit cell and an HCP arrangement has 8 spheres per unit cell. However, both configurations have a coordination number of 12.

The packing efficiency is the fraction of volume in a crystal structure that is occupied by constituent particles, rather than empty space. In order to find this, the volume of the spheres needs to be divided by the total volume (including empty spaces) occupied by the packed spheres. For both HCP and CCP, the packing efficiency is 74.05 %.

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