The Solid State

Close Packing in Crystals

Most of the solids we find around ourselves are crystal solids. These crystalline shapes form due to the arrangement of constituent particles in a specific arrangement known as crystal lattices. These structures form due to close packing of their atoms. Let us study this in detail.

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Close Packing in Crystal

Close packing in crystals refers to space efficient arrangement of constituent particles in a crystal lattice. To understand this packing more clearly we have to assume all particles (atoms, molecules and ions) are of the same spherical solid shape.

So the unit cell of a lattice is a cubic shape. Now when we stack spheres in the cell, there will always be some empty spaces. To minimize these empty spaces, the arrangement of these spheres must be very efficient. The spheres should be arranged as close together as possible to eliminate empty spaces.

Another related concept is that of Coordination Number. The coordination number is the number of atoms that surround a central atom in a crystal lattice arrangement. It is also known as Ligancy. So this close packaging of the constituent particles happens in three ways. Let us take a look at each of them.

Close Packing in Crystals

One Dimensional Close Packing

Close Packing in Crystal Solids

In this arrangement, the spheres (i.e. the atoms) are arranged in a row. All the spheres are closely packed and are in contact with each other. So one sphere is in contact with the sphere to both its sides. So there are two spheres or particles near any one particular sphere. This makes the coordination number of the one-dimensional structure 2.

Two Dimensional Close Packing

Close Packing in Crystal Solids

Two-dimensional arrangement is when stacking the rows (from the above one-dimensional structure) one after another. This stacking of the rows can be done in two ways.

  • AAA Type: In this type of packing arrangement the two rows are stacked right above each other. One row is packed directly above or below the other one. So whether you consider the stacking horizontally or vertically it will be the same structure. Here the spheres are directly touching the two spheres above and below them, and also to two spheres to the right and the left. So the coordination number of this will be 4.
  • ABA Type: In this type the spheres of the second row to be seated on the first row in a staggered manner, that is, 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.

Three Dimensional Close Packing

This is the real structure of the space lattice. It happens due to the three-dimensional arrangement of the unit cells. Now, this structure forms by the continuous and repetitive stacking of the two-dimensional structures above each other. It can also happen in two ways

  • Hexagonal Closest Packing: Here the alternating layers cover each others 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
  • 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.

Solved Questions for You

Q: The cubic close-packed structure is based on an fcc unit cell. True or False?

Sol: The statement is True. Cubic closed packed (ccp) structure has 3-fold axes of symmetry which pass through the diagonal of the cube since in this system, there is a sphere at the center of each face of the unit cell and hence, this structure is also known as face-centered cubic (fcc) structure.

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