Name: Relation Between Edge Length and Radius Ratios
Uploaded: 2019-07-19
Duration: 14 min 49 s
Description: The ratio of the radius of cation to anion is called radius ratio. Watch the video to learn the tricks to remember the relation between edge length and radiu...

Question

Briefly explain the packing of the constituent particles in a crystal.

Accepted Answer

Packaging of the constituent particles: The constituent particles in a crystal are hard spheres of identical size (e.g., those of a metal). The packing of these spheres takes place in such a way that they occupy the maximum available space resulting in the maximum energy. Also, there is minimum empty space and hence the crystal has maximum density. This type of packing is called close packing in crystal lattice. These particles may be of different sizes and shapes, but we will consider them as identical hard spheres as described below:

(a) Close-Packing in One Dimension. In this close packing, the spheres are arranged in $1 - D$ closed packed structure. In this arrangement, each sphere is touching two neighbouring spheres. Hence, in one dimension arrangement, the coordination number is $2$ .

(b) Close-Packing in Two Dimensions. When the rows are stacked over each other, a $2 - D$ close-packed structure which is called a crystal plane is produced. This stacking can be done in two different ways as follows :

(i) $AAA$ Type: The spheres in the second row may be placed in such a way that they are touching the spheres of the first row and are exactly above the spheres of the first row, i.e., there is horizontal as well as vertical alignment of the spheres in the two rows. If the first row is called $' A'$ type row, the second row, being exactly the same, will also be $' A'$ type. Further rows may also be built up exactly in the same way. Hence, we call this arrangement as $AAA$ type of arrangement and also referred to as square closed packing. In this packing of spheres, the coordination number is $4$ .

(ii) $ABA$ Type: In this type the spheres of the second row to be placed on the first row in a staggered manner, i.e. in the depressions of the first layer. The stacking is not uniform as in the $AAA$ type. Here, the spheres are in contact with six other spheres, so the coordination number is $6$ . Also, when you join these contact points it will form a hexagonal shape.

(c) Close-Packing in Three Dimensions: Three-dimensional close packing is obtained by stacking two-dimensional square close-packed layers. Starting from the square close-packed layer, the second layer and all further layers will be built up such that they are horizontally as well as vertically aligned with each other. It can also happen in two ways:

(i) Hexagonal Closest Packing: Here the alternating layers cover each other's gap. Spheres in one layer align to fit in the gaps of the previous layer. The first and the third rows have the same alignment. So we call this $ABA$ type.

(ii) Cubic Closest Packing: Here the layers are placed exactly above each other in symmetry. This shape takes the form of a cube and hence the name. The coordination of such a structure is $12$ .

Briefly explain the packing of the constituent particles in a crystal.

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