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Close Packed Structures: Packing In Three Dimensions

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Close Packed Structures: Packing In Three Dimensions - Lesson Summary

Three-dimensional close packing from two-dimensional square close packing: To build a three-dimensional structure, it is easier to stack two-dimensional square close packed planes one above the other. The spheres are aligned horizontally as well as vertically.

If the arrangement of spheres in the first layer is considered to be of A type, then the arrangement of spheres in the subsequent layers is also of A type. This three-dimensional arrangement is referred to as AAA type packing.
 
       
 
This arrangement has resulted in the formation of a simple cubic lattice. The unit cell of this lattice is a primitive cubic unit cell. Another way to build a three-dimensional close packing is from a two-dimensional hexagonal close packing. As the spheres of the two layers are aligned differently, let the arrangement of spheres in the first layer be referred to as “A’ type and in the second layer as ‘B’ type.



This arrangement indicates the formation of two different kinds of voids, marked as ‘O’ and ‘T.’



The void formed when a sphere in the second layer is placed over a void in the first layer is tetrahedral or of “T’ type. It is known as a tetrahedral void. Another type of void is formed when a void in the second layer lies on a void in the first layer. Such a void is called an octahedral void or an ‘O’ type void. The third layer can be stacked in two different ways. If the third layer is placed over the second layer in such a way that the tetrahedral voids of the second layer get covered, then a close packing is obtained. This type of an arrangement is called ABAB type packing or hexagonal close packing.
EX: magnesium and zinc crystallise in hexagonal close packing structures



If we continue to add the layers, then we get the arrangement the spheres of the third layer called C layer are not aligned with those of either the first or the second layer. This type of packing is referred to as ABCABC type of packing.



It is also called cubic close packing (ccp) or face-centred close packing (fcc).
EX: Metals like iron, copper and silver crystallise in ccp structures.

In hexagonal close packing and cubic close packing, a sphere has the coordination number 12. In hexagonal close packing and cubic close packing 74% of the space in the crystal is filled up. In a close packed structure, whether ccp or hcp if there are N spheres in the packing per unit cell, then The number of octahedral voids= N. The number of the tetrahedral voids =2N.

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