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A New Perspective on Rutile James K. Beattie School of Chemistry, University of Sydney, NSW 2006, Australia
Most textbooks, and the cover of the Journal of Chemical Education (August 1982) (Fig. 1), give a misleading representation of the unit cell structure of rutile (TiO 2). The diagrams suffer from a distortion of perspective that leads to the impression that the fourfold (42 ) axis is horizontal instead of vertical; that is, that the square face is on the side and not on the top of the unit cell. Consequently, when our students have been asked to construct a model of the unit cell, those who work exclusively from these textbook diagrams frequently build an incorrect structure. A few authors have conveyed more of the sense of a square face for the top of the unit cell, but at the expense of shortening the c-axis and
distorting the octahedral coordination of the central titanium atom. We have been unable to generate an entirely satisfactory view, either with plotting programs or by photographing a model. One of the more acceptable perspectives is shown in Figure 2, which is a view more from the top and closer to 45° to the x-axis than the conventional representations. This perspective shows the square top face of the unit cell and emphasizes the equivalence of the two side faces. One way to specify the structure unambiguously is to describe the “floor plan” of the unit cell (Fig. 3). This is the projection of the unit cell contents onto the ab plane with the fractional c coordinate specified for each atom. Together with the aspect ratio c/a (2.98 Å/4.58 Å = 0.65 for rutile), this enables the unit cell to be constructed. Perhaps “floor-plan” diagrams, together with space-filling or stereo drawings, should replace the misleading unit cell pictures now used. Whatever methods are employed, the availability of modern computer techniques means that textbook publishers and readers should no longer accept outmoded and misleading drawings. Acknowledgments This work began in collaboration with Helga Fiedler, Mervyn Cooper, and Julia James at the University of Sydney.
Figure 1. Classic view (after Wells) of the unit cell of rutile as it appeared on the cover of Journal of Chemical Education, August 1982.
Figure 2. An alternative view of the unit cell of rutile.
Figure 3. “Floor plan” projection of the unit cell contents onto the ab plane.
JChemEd.chem.wisc.edu • Vol. 75 No. 5 May 1998 • Journal of Chemical Education
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