Solution

ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1/1/b/solution

Reduce the supplied fractional coordinates modulo one. The rutile structure has Ti at with height and at with height . The oxygen projections are at , and at . Include equivalent corner sites to show the boundary of a complete unit cell; the cell edges are along and .
Figure 1.
Rutile unit-cell projection along the tetragonal axis
. Original plan constructed from the fractional coordinates. Labels give height as a fraction of ; circle sizes distinguish species rather than ionic radii. Details.

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