### Least-squares refinement for powder diffraction data

These templates were created by Gary Novak and Alan Colville, 1989, American Mineralogist, v. 74, p. 488-490.

The templates are a set of Excel spreadsheets that calculate unit cell parameters (axis lengths and angles) from X-ray powder diffraction data using a least-squares best-fit fit procedure. The programs require 2Θ peak positions and {*hkl*} indexes for each peak. They also require that you know what mineral you are working on. There is one template for each of the six crystal systems (hexagonal and trigonal use the same template).

- The templates were developed using the Excel spreadsheet program.
- OPEN the template for the crystal system of interest to you (see below), then SAVE it to your computer and OPEN the saved version in Excel. It may not work properly if it is open direct from your web browser.
- Copy the first yellow row (light and dark yellow) down into exactly as many rows as you have indexed peaks.
- Index the peaks, that is, find {
*hkl*} values using the powder diffraction file database on the XRD computer, or the diffraction file books, or from the lab materials. - In the Excel template, replace the 2Θ and Miller index {
*hkl*} values with your own. Enter negative Miller indices (e.g., {*111*}) as negative numbers (e.g., {*1 -1 1*}). - For hexagonal and trigonal minerals, the formal Miller index values can take the form {
*hkil*}, as compared to {*hkl*} for the other crystal systems. However, because*h*+*k*+*i*= 0,*i*is redundant, so only*h*,*k*, and*l*are usually listed in diffraction indexes. - The best fit (refined) unit cell parameters are located in the blue area at the bottom of the spreadsheet.
- You MUST check your work. The
*observed and calculated d spacings should be similar*, and the*delta-d column values should generally be <0.01*. Axial lengths should generally be within 0.02Å of the book values. If your delta-d and axial length accuracy is much worse, carefully check the 2Θ angles you entered, and your Miller index assignments.

### Advanced notes

- If you picked the wrong crystal system, made a mistake choosing or typing in 2Θ angles or {
*hkl*} values, or use only peaks from a single zone (all parallel to an axis), you may see lots of error notations where you expect numbers. This is because a mathematically impossible result occurred somewhere in the calculations. Carefully check your work! - Change the Kα and Kα1 X-ray wavelengths if you are using a tube other than copper.
- Set the 2Θ Correction value if the 2Θ values are systematically incorrect by a known amount.
- If you are not using Kα1-stripped 2Θ values, set the Kα/Kα1 cut-over value to 50° 2Θ.