Close Packed Structures — Core Principles

Core Principles

Close packed structures describe the most efficient arrangements of identical spheres (atoms) in a crystal lattice, minimizing empty space. This concept is built from 1D (coordination number 2), to 2D (square close packing with CN 4, hexagonal close packing with CN 6), and finally to 3D.

In 3D, two main types emerge from stacking 2D hexagonal layers: Hexagonal Close Packing (HCP) with an A-B-A-B stacking sequence, and Cubic Close Packing (CCP), which is equivalent to Face-Centered Cubic (FCC), with an A-B-C-A-B-C stacking sequence.

Both HCP and CCP have a coordination number of 12 and a maximum packing efficiency of 74%. When layers are stacked, two types of voids are formed: tetrahedral voids (surrounded by 4 spheres) and octahedral voids (surrounded by 6 spheres).

For 'N' atoms in a close-packed structure, there are 'N' octahedral voids and '2N' tetrahedral voids. Understanding these structures is vital for predicting material properties and the stoichiometry of compounds formed by occupying these voids.

Important Differences

vs Cubic Close Packing (CCP)

Aspect	This Topic	Cubic Close Packing (CCP)
Stacking Sequence	A-B-A-B-A-B...	A-B-C-A-B-C...
Unit Cell Type	Hexagonal	Face-Centered Cubic (FCC)
Coordination Number	12	12
Packing Efficiency	74%	74%
Number of Atoms per Unit Cell	6	4
Examples	Mg, Zn, Ti, Cd	Cu, Ag, Au, Al, Ni

While both Hexagonal Close Packing (HCP) and Cubic Close Packing (CCP) represent the most efficient ways to arrange identical spheres, sharing the same coordination number (12) and packing efficiency (74%), they differ fundamentally in their stacking sequence and resulting unit cell geometry. HCP exhibits an A-B-A-B layer stacking, leading to a hexagonal unit cell. In contrast, CCP follows an A-B-C-A-B-C stacking, which is structurally equivalent to a face-centered cubic (FCC) unit cell. This difference in long-range order influences properties like the number of slip planes, affecting material ductility and malleability.