K-alpha : believe your eyes
or trust mathematics ?
Arguments developed in the context of a discussion about "how to purchase a high resolution diffractometer".
See the SDPD Mailing List at : http://www.egroups.com/list/sdpd/

The 3 "if" :

  1. If really the Kalpha-2 component was at an exactly known position relative to Kalpha-1.
  2. If the alpha1/alpha2 ratio was exactly known.
  3. If the Kalpha-2 profile shape was exactly the same as the Kalpha-1 profile.

Then we could simulate a Kalpha-1 powder pattern, add to it some statistical noise, then simulate the Kalpha-2 component, then add the two patterns and compare...

Mathematically, the two patterns should be equivalent, because of the 3 "if" above (a coded text can be exactly decoded - without any information loss - if you have the code key), and a Rietveld refinement on both patterns should lead to equivalent results.

Let us try.

The calculation of the 2 powder patterns was done by the Fullprof program on a small-size orthorhombic cell, that of GaOOH :


See the refinement results in the Fullprof .sum file. Download the .dat file and the .pcr file.


See the refinement results in the Fullprof .sum file. Download the .dat file and the .pcr file.


So what ? Compare the Fullprof .sum files above, do you find any clear difference in the refinements ? There is not. Try a larger cell with thousand reflections will not change anything, if the 3 "if" above are really mathematically/physically true.

Of course, the problem here is that the 3 "if" above are not completely true...

However, this is not a reason for trusting only your eyes, telling that Kalpha-1 is so much better, this would also not be completely the truth.

If the 3 "if" were true, we could perfectly remove the Kalpha-2 component (in case of extremely good statistics, anyway), but we cannot. Nevertheless, we can almost do it, with only some ripple problems, right ? And this is why we prefer to make the Rietveld refinement on the original pattern, but not on the pattern corrected from the Kalpha-2 component : less errors occur when adding the alpha-1 and alpha-2 calculated contributions than when stripping alpha-2 from the observed pattern. Anyway, a primary beam monochromator is nothing else than a Kalpha-2 stripping hardware. Some are not better in that exercise than certain Kalpha-2 stripping software, and may let up to 1.5% of alpha-2 residue on your experimental powder pattern. Of course, if you want your Kalpha-2 stripping sofware to make well the job, you should have a high-resolution pattern, with a counting step sufficiently small, and a quite good counting statistics.

A Kalpha-1 pattern and a Kalpha pattern are almost equivalent. You will not obtain easier indexation from a Kalpha-1 pattern than from a Kalpha pattern corrected from the Kalpha-2 component. And the final Rietveld refinements would be quite similar, in spite of what say your eyes.

Do not believe only your eyes.

Armel Le Bail
October 2000