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  Home > JCE Print > Journal of Chemical Education > Issues > 2008  > January  >
In the Classroom
Use of the Primitive Unit Cell in Understanding Subtle Features of the Cubic Close-Packed Structure
John A. Hawkins and Jeffrey L. Rittenhouse
Walla Walla University, College Place, WA 99324

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

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

Cover
January 2008
Vol. 85 No. 1
p. 90
Abstract
One of the most important crystal structures adopted by metals is characterized by the abcabc… stacking of close-packed layers. This structure is commonly referred to in textbooks as the cubic close-packed (ccp) or face-centered cubic (fcc) structure, since the entire lattice can be generated by replication of a face-centered cubic unit cell containing exactly four atomic spheres. However, there is an inconsistency between the definition of unit cell generally applied in chemistry textbooks, as the smallest repeating structural unit, and the choice of the face-centered cube. The ccp structure may also be described by a primitive unit cell (containing one atom) that is a rhombohedron, where each face is a rhombus with acute angles of 60 degrees. While the fcc unit cell retains the symmetry of the ccp lattice, there are some clear pedagogical advantages in presenting the primitive rhombohedral unit cell that may help students gain greater insight into the nature of the ccp structure. We have compared the two unit cells and have performed calculations on the rhombohedral unit cell to determine the individual atomic sphere fraction enclosed by each of the vertices, which, as far as we have been able to determine, have not been previously reported.
Supplement
A computer animation of a rotating 3D "cutaway" model of the primitive rhombohedral unit cell for the ccp structure, paper templates for the construction of paper-and-glue models of the type developed by Birk and Yezierski (ref. 18), and Appendices A and B are available.
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Folder JCE2008p0090W containing JCE2008p0090W_1.doc and JCE2008p0090W_2.doc (Microsoft Word) and JCE2008p0090W.mov (QuickTime)
More Information
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Citation
Hawkins, John A.; Soper, Linda M.; Rittenhouse, Jeffrey L.; Rittenhouse, Robert C. J. Chem. Educ. 2008, 85, 90.
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Keywords
Crystals / Crystallography; Curriculum; First-Year Undergraduate / General; Hands-On Learning / Manipulatives; Inorganic Chemistry; Metals; Physical Chemistry; Second-Year Undergraduate; Solids; Textbooks / Reference Books; Upper-Division Undergraduate
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History
Created:
Last Updated:
12/4/2007
12/12/2007
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