Difference Between Hexagonal Close Packing and Cubic Close Packing

Key Difference – Hexagonal Close Packing vs Cubic Close Packing
 

The terms Hexagonal closed packing (HCP) and cubic close packing (CCP) are used to name two forms of arrangements in chemical geometry. These terms explain the arrangement of atoms, molecules or ions in lattices (regular arrangements). When describing these arrangements, the constituents from which the lattice is made are known as spheres (atoms, molecules or ions). In order to maximize the efficiency of packing and to minimize the empty spaces in the lattice, the spheres are tightly packed. These arrangements are known as closest-packed structures or close packing of equal spheres. The empty spaces between these spheres are known as holes. There are three types of holes; trigonal hole, tetrahedral hole and octahedral hole. A trigonal hole is formed between three spheres. The shape of this hole resembles a triangle. A tetrahedral hole is formed when the second layer of spheres are placed on the layer of spheres in such a way that the trigonal hole is covered by a sphere. The octahedral hole is formed when the second layer of spheres is placed on a layer of spheres in such a way that the trigonal hole is uncovered. The hexagonal close packing is denoted as HCP. This arrangement has two layers of spheres in one repeating unit.  The cubic close packing is denoted as CCP. It has three layers of spheres in one repeating unit. The key difference between hexagonal close packing and cubic close packing is that, a unit cell of hexagonal close packing has 6 spheres whereas a unit cell of cubic close packing has 4 spheres.

CONTENTS

1. Overview and Key Difference
2. What is Hexagonal Close Packing (HCP)
3. What is Cubic Close Packing (CCP)
4. Similarities Between Hexagonal Close Packing and Cubic Close Packing
5. Side by Side Comparison – Hexagonal Close Packing vs Cubic Close Packing in Tabular Form
6. Summary

What is Hexagonal Close Packing?

Hexagonal close packing (HCP) is an arrangement of spheres in a lattice; there are two layers of spheres placed one on the other, forming tetrahedral and octahedral holes. This means the second layer of spheres are placed in such a way that the trigonal holes of the first layer are covered by the spheres of the second layer. The third layer of spheres resembles the first layer, and the fourth layer resembles the second layer, hence, the structure repeats. Therefore, the repeating unit of a hexagonal close packing arrangement is composed of two layers of spheres.

Since the same structure repeats after every two layers of spheres, the spheres efficiently fill up 74% of the volume of the lattice. The empty spaces are around 26%. Each sphere in this arrangement is surrounded by 12 neighbouring spheres. When the centres of these 13 spheres (one sphere + 12 neighbouring spheres) were considered, it gives a six-sided pyramid with a hexagonal base. This leads to name this structure as hexagonal close packing arrangement. The hexagonal close packing arrangement has one large octahedral hole per sphere that is surrounded by six spheres, and also, for each sphere, there are two tetrahedral holes surrounded by four spheres.

What is Cubic Close Packing?

Cubic close packing (CCP) is an arrangement of spheres in a lattice; there are three layers of spheres placed one on the other, covering all the octahedral holes by a third layer of spheres. The repeating unit of a cubic close packing contains three layers of spheres. The arrangement of the first layer and the second layer is similar to that of the hexagonal close packing. But the third layer is placed in a completely different way. It is stacked in the voids of the second layer of spheres. This results in covering all the octahedral spheres. Therefore, the cubic close packing arrangement has only tetrahedral holes.

The cubic close packing efficiently fills up 74% of the lattice volume with spheres and 26% is empty space. Since the repeating unit of a cubic close packing has three layers of spheres, the fourth layer of spheres resembles the first layer and the same structure repeats. Each sphere in this arrangement is surrounded by 12 neighbouring spheres. There are three types of cubic lattices, based on the arrangement of spheres and holes;

1. Simple cubic (SC)
2. Face-centred cubic (FCC)
3. Body-centred cubic (BCC)

The cubic close pacing arrangement can be seen in FCC (face-centred cubic) arrangement. The unit cell of a cubic close packing arrangement has 4 spheres.

What are the Similarities Between Hexagonal Close Packing and Cubic Close Packing?

• Both Hexagonal Close Packing and Cubic Close Packing terms describe arraignments of spheres and holes (empty spaces) in lattices.
• Both Hexagonal Close Packing and Cubic Close Packing arrangements have spheres having 12 neighbouring spheres.
• Both Hexagonal Close Packing and Cubic Close Packing arrangements have 74% of lattice volume filled with spheres and 26% filled with empty spaces.

What is the Difference Between Hexagonal Close Packing and Cubic Close Packing?

Summary – Hexagonal Close Packing vs Cubic Close Packing

The hexagonal and cubic close packing arrangement are used to describe the arrangement of spheres and holes in lattices. The difference between hexagonal close packing and cubic close packing is that a unit cell of hexagonal close packing has 6 spheres whereas a unit cell of cubic close packing has 4 spheres.

Reference:

1.“Closest Packed Structures.” Chemistry LibreTexts, Libretexts, 21 Feb. 2018. Available here 
2.“Close-Packing of equal spheres.” Wikipedia, Wikimedia Foundation, 8 Mar. 2018. Available here

Image Courtesy:

1.’Hexagonal close-packed unit cel’By User:Greg L – English Wikipedia, (CC BY-SA 3.0) via Commons Wikimedia 
2.’Empilement compact’By Christophe Dang Ngoc Chan (cdang) – Own work, (CC BY-SA 3.0) via Commons Wikimedia