JCE 2006 (83) 175 [Jan] Filling in the Hexagonal Close-Packed Unit Cell


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Home > JCE Print > Journal of Chemical Education > Issues > 2006 > January >

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Filling in the Hexagonal Close-Packed Unit Cell

Robert C. Rittenhouse
Department of Chemistry, Walla Walla College, College Place, WA 99324

Linda M. Soper
Department of Mathematics, Kalispell Community College, Kalispell, MT 59901

Jeffrey L. Rittenhouse
Walla Walla Valley Academy, College Place, WA 99324

January 2006
Vol. 83 No. 1
p. 175

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Abstract

The hexagonal close-packed (hcp) structure is one of the most common and important crystal structures adopted by metals and other atomic solids. Despite its prominence in nature, the hcp structure has not been treated at the same level of geometric rigor as the common cubic structures. The illustrations of the hcp unit cell that are used in textbooks at all levels and also in crystallography and solid-state reference works are incomplete, in that they fail to include fractions of middle layer atomic spheres with centers lying outside of the unit cell. These fractions are necessary to properly determine the number of atoms enclosed in the unit cell. Though it seems unlikely that the middle layer fractions of atomic spheres have not been previously determined, we have found no evidence of this in our survey of textbooks and reference works. We have shown how these fractions may be determined using the solids-of-revolution method and have prepared animated 3D "cutaway" computer models and templates for paper and glue models to more accurately illustrate the hcp unit cell.

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Citation	Rittenhouse, Robert C.; Soper, Linda M.; Rittenhouse, Jeffrey L. J. Chem. Educ. 2006 83 175.
Keywords	Crystals / Crystallography; First-Year Undergraduate / General; Inorganic Chemistry; Metals; Multimedia-Based Learning; Physical Chemistry; Second-Year Undergraduate; Solids; Textbooks / Reference Books; Upper-Division Undergraduate
History	Created: Last Updated:	12/1/2005 12/7/2005


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