# Close Packing in Crystals

Last Updated : 06 Jun, 2023

In the formation of crystals, the constituent particles (atoms, ions, or molecules) are closely intertwined. A tightly packed arrangement is one in which maximum available space is occupied by leaving minimum free space. This corresponds to the condition of the maximum possible density. The closer the packing, the higher the stability of the packed system.

The majority of solids we come across are crystal solids. The arrangement of constituent particles in a precise configuration known as crystal lattices causes these crystalline structures to develop. The close packing of their atoms causes these formations to form. Let’s take a closer look at this.

### Close Packing in Crystal

The constituent particles of a crystal can be of different sizes and therefore the method of closest packing of the particles will vary according to their size and shape. However, to understand why we can use uniform rigid spheres of equal size to represent atoms in metal as the closest packing of similar spheres.

In crystals, close packing refers to the efficient arrangement of constituent particles in the lattice. To further comprehend this packing, we must suppose that all particles (atoms, molecules, and ions) have the same spherical solid shape. As a result, the cubic shape of a lattice’s unit cell. There will always be some vacant spots in the cell when we stack the spheres. The arrangement of these spheres must be exceedingly effective in order to minimise these empty areas. To avoid empty spaces, the spheres should be positioned as near together as feasible.

The concept of Coordination Number is also connected. In a crystal lattice arrangement, the coordination number is the number of atoms that surround a centre atom. Ligancy is another name for it. As a result, there are three ways in which the constituent particles are tightly packed.

Close Packing in one Dimension:

There is an exclusive thoroughfare to arrange spheres in a one-dimensional densely packed structure in which the spheres are placed in a horizontal row touching each other. As shown in figure-

Close Packing of particles in one Dimension

As can be perceived, in this arrangement each sphere is in contact with its two neighbours. The number of proximate neighbours of a particle is called its coordination number. Hereby, in a one-dimensional densely packed arrangement, the coordination number is 2.

Close Packing in two Dimension:

Close-packed structures can be generated by placing rows of close-packed spheres. The rows can be joined in the following two ways concerning the first row to form a crystal plane.

• Square close packing or AAA… type arrangement in two dimensions- Linear arrangement of spheres in one direction is repeated in two dimensions i.e. more number of rows can be generated similar to a one-dimensional arrangement such that all spheres of different rows are aligned vertically as well as horizontally. If the first row is represented as an A-type arrangement, the packing described above is said to be AAA… type, since all rows are the same as the first row.

Close Packing of particles in two Dimension

A sphere is in contact with four spheres in a square closed packing. This type of packing is also called AAA… type arrangement in two dimensions.

Note: The space enclosed by four spheres is called a tetrahedral void.

• Hexagonal close-packing or ABABA… type arrangement in two dimensions- In this type of arrangement, the spheres of the second row are arranged in such a way that they fit into the depression of the first row. The second row is indicated as type B. The third row is arranged like the first row A, and the fourth row is arranged like the second row. i.e., the arrangement is depicted as ABAB… On comparing these two arrangements (AAAA…type and ABAB…type) we find that the closest arrangement is ABAB…type.

A sphere is in contact with six spheres in a hexagonal closed packing. This type of packing is also called ABABA… type arrangement in two dimensions.

Note: The space enclosed by six spheres is called an octahedral void.

Close Packing in three Dimension:

Three-dimensional packaging can be done by building up layers on a square pack and a hexagonal close-pack arrangement of the first layer.

• Three-dimensional close packing from two-dimensional square close-packed layers- This type of three-dimensional packing arrangement can be the AAAA type of two-dimensional arrangement is procured by restating it in three dimensions. Only polonium of all the metals in the periodic table crystallizes in a simple cubic pattern.
• Three-dimensional close packing from two-dimensional hexagonal close-packed layers- In this arrangement, the spheres in the first layer (type A) are separated slightly and the second layer is constituted by arranging the spheres in the depressions between the spheres in layer A. The third layer is a reiteration of the first. This arrangement ABABAB is go over again ubiquitously the crystal.

### Difference between Hexagonal Close Packing and Cubic Close Packing

The key difference between Hexagonal Close Packing and Cubic Close Packing is listed below:

### Sample Questions

Question 1. What is meant by “Coordination number”?

The coordination number describes the number of nearest neighbours with which a given atom is in contact. In the case of ionic crystals, the coordination number of an ion in the crystal is the number of oppositely charged ions around that ion.

• The coordination number of the atom in the cubic closed pack structure is 12.
• In a body-centred cubic structure, the atom has 8 coordination numbers.

Question 2. What are interstitial compounds?

The presence of interstitial vacancies or interstitial sites plays an important role in the chemistry of transition metals. Transition metals can easily accommodate smaller non-metal atoms such as hydrogen, boron, carbon, and nitrogen due to the spaces between metal atoms. These compounds are called interstitial compounds.

Question 3. Define primitive Unit cells.

Those unit cells whose constituent particles are present only at the corners are called primitive unit cells.

Question 4. What are crystalline solids anisotropic?

Crystalline solids are anisotropic because the particles have different arrangements in different directions, some of their physical properties such as electrical resistance or refractive index show different values when measured in different directions in the same crystal.

Question 5. What is a distinguishing feature of metallic solids?

Metallic solids are malleable, ductile, and good conductors of electricity in the solid-state as well as in the molten state.

Question 6. What is the coordination number of types of ions in a rock salt type crystal structure?

The crystal structure of the rock salt type has a 6:6 coordination number for each type of ion. This means that in a NaCl crystal, each Na+ is surrounded by 6Cl ions and each CI ion is surrounded by 6 Na+ ions.

Question 7. How many effective atoms are located at the edge centre of a unit cell in a sodium chloride crystal?

1 atom at the edge is shared by 4 unit cells. Thus, the contribution of each atom at the edge = 1/4

The number of sodium ions present in the centre of the edge =12 Ã— 1/4 = 3 atoms.

Question 8. Why is glass considered a supercooled liquid?