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Consider a hypothetical metal whose structure can be based on either of the following: Cell A, base-centered tetragonal for which a=0.2 nm and c=0.3...
1. Consider a hypothetical metal whose structure can be based on either of the following:
a. Cell A, base-centered tetragonal for which a=0.2 nm and c=0.3 nm;
b. Cell B, simple tetragonal.
Draw the two cells in the proper relation to one another (hint: start with Cell B and add points around it to form Cell A). Find values of a and c for Cell B. Determine simplified structure-factor equations (write in terms of the Miller indices and then give conditions of the Miller indices (to solve for the structure factor) for each cell and the positions (2values) of the first four lines that would be observed (F20) on a powder pattern made with Cu K radiation. Index these lines (write the d-spacing, diffraction angle, and structure factor for each Miller index) using Cell A and Cell B. Show that certain indices in both cells, other than obvious ones of the form {0 0 l}, refer to the same planes of atoms. Explain why it is possible to have a single structure indexed using the two cells.
