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Home / Chemistry / Close Packing In Solids In Three Dimensions - Explained | Testbook.com

Close Packing In Solids In Three Dimensions - Explained | Testbook.com

Last Updated on Mar 12, 2025
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Crystalline solids are fascinating as they showcase a systematic and recurring arrangement of their constituent particles. This arrangement, known as a crystal lattice, is represented diagrammatically where each particle is illustrated as a point in space. The unique aspect of a crystal lattice is the close packing of atoms, leaving minimal space between them. Let's delve deeper into the concept of close packing in solids in three dimensions.

  • Three-dimensional close packing from two-dimensional square close-packed layers:

In this type of close packing, the second layer is positioned over the first layer in a manner that the spheres of the top layer align perfectly with the spheres of the first layer. As a result, we observe a simple cubic lattice with an AAA…. type pattern, where spheres of all layers are aligned both horizontally and vertically.

  • Three-dimensional close packing from two-dimensional hexagonal close-packed layers :

This three-dimensional close-packed structure is created by stacking layers over each other.

Placing the second layer over the first layer:

In this type of close packing, the second layer is placed such that its spheres fit into the depressions of the first layer. This results in a different alignment of spheres in the two layers, creating two types of voids - tetrahedral and octahedral. The number of these voids can be calculated as follows - if there are N close packed spheres, then the number of octahedral voids = N and the number of tetrahedral voids = 2N.

Placing the third layer over the second layer:

The third layer can be placed over the second layer in two main ways:

Covering Tetrahedral Voids

In this arrangement, the spheres of the third layer align exactly with those of the first layer, creating an ABAB ……. pattern. This structure is called a hexagonal close-packed (hcp) structure.

Covering Octahedral Voids

In this arrangement, the spheres of the third layer do not align with those of either the first or the second layer, resulting in an ABCABC……….. pattern. This crystal structure is called cubic close-packed (ccp) or face-centered cubic (fcc) structure.

Both these structures have a coordination number of 12, meaning each sphere is in contact with twelve other spheres. These types of close packing fill 74% of the space in the crystal.

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Frequently Asked Questions

Near crystal packing refers to the effective arrangement of constituent particles in a crystal lattice in vacuum. We have to assume that all particles (atoms , molecules and ions) are of the same spherical solid form to grasp this set more precisely. So a cubic structure is the unit cell of a lattice.

Inside a unit cell, the most powerful conformation atomic spheres can take is known as the nearest packing configuration. In two modes, there are closely packed atomic spheres: hexagonal closest packing (HCP) and cubic closest packing (CCP).

The tight packing of the hexagon is denoted as HCP. In one repeated unit, this arrangement has two layers of spheres. The main distinction between hexagonal close packing and cubic close packing is that there are 6 spheres in a unit cell of hexagonal close packing, whereas there are 4 spheres in a unit cell of cubic close packing.

Hexagonal tightly packed (hcp) refers to layers of packed spheres such that spheres overlay each other in alternating layers. A slip framework, which is a close-packed structure, is hexagonal near packed. For elemental metals, the hcp structure is very general, including: beryllium.

The packing quality is the proportion of the atoms directly occupied by the crystal (or unit cell). It must often be less than 100 percent, since spheres (atoms are usually spherical) can not be filled without any empty space between them.
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