Support Options

Submit a Support Ticket

Home Groups ABACUS - Assembly of Basic Applications for Coordinated Understanding of Semiconductors Development Group Resources Teaching Materials Crystal Structures - Packing Efficiency Exercise About

Crystal Structures - Packing Efficiency Exercise

By Dragica Vasileska1, Gerhard Klimeck2

1. Arizona State University 2. Purdue University

Download (DOC)

Licensed according to this deed.

Published on


Consider the most efficient way of packing together equal-sized spheres and stacking close-packed atomic planes in three dimensions. For example, if plane A lies beneath plane B, there are two possible ways of placing an additional atom on top of layer B. If an additional layer was placed directly over plane A, this would give rise to the following series :

This type of crystal structure is known as hexagonal close packing (hcp).
If however, all three planes are staggered relative to each other and it is not until the fourth layer is positioned directly over plane A that the sequence is repeated, then the following sequence arises:

This type of crystal structure is known as cubic close packing (ccp).

The goal is to calculate the packing efficiency of hcp and ccp unit cell and compare to fcc lattice.

Cite this work

Researchers should cite this work as follows:

  • Dragica Vasileska; Gerhard Klimeck (2010), "Crystal Structures - Packing Efficiency Exercise,"

    BibTex | EndNote

Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.