1. The Significance of Refractive Index “K” Values LSMs, or, Why Long Wavelength Peak Markers Don’t Line Up Correctly John Fournelle* and K. Bolger*, J. Cook*, M. Herrick*, K. Kimme**, P. Lancaster*, M. Riederer*, C. Santhaweeesuk**, E. Shullenberger* and C. Zhang** (students of 2005 UW EPMA Class) *Department of Geology & Geophysics, University of Wisconsin, Madison, WI **Department of Materials Science, University of Wisconsin, Madison, WI

2. High count rates Depressed n>1 counts But ….. rather wide peaks … Many electron probes now have layered synthetic material diffractors, very useful for light element detection

3. … How well can n>1 interferences be accurately identified if markers not correctly aligned? C Ka ?

4. One researcher asked me to prove that the LSM actually suppressed the 3rd order P K  that falls very close to F K  So I scanned first on TAP -- the 3rd order P K  is just to the right of F K  … 3 P K  F K 

5. And then scanned the sample with 60 Å LSM … no 3rd order P K  obvious like before … …but the 3rd order P K  marker now just to the left of F K  ….? 3 P K  F K 

6. 3 P KaF Ka Sin  F Ka 3 P Ka F K  = 18.32 Å P K  = 6.157Å 3 P K  = 18.471Å The 3rd order P K  should be to the right of F K  (in Å or sin  units) … but it’s not. Why?

7. Back to basics … suggested by Carl Henderson (U. Michigan) A query posted to the sx50-users listed produced a reply …

8. After the Braggs published their results in 1913-14, Siegbahn, Stenstrom and Hjalmar found that higher resolution spectroscopy indicated that while Braggs’ equation was very close for 1st order lines, there were systematic deviations with higher order line locations.

9. Or replacing d’ we have the familiar equation n = 2d sin  (1-k/n 2 ) k is refraction factor, n is order of diffraction

10. Somewhat counterintuitively, the greatest deviation is for the 1st order peak! --> using first order peaks to determine the 2d for LSMs which have significant K factors, will give the greatest error n = 2d sin  (1-k/n 2 ) k is refraction factor, n is order of diffraction

11. Consider the nominal 60 Å LSM (PC1) and calculations of 2d if first order peak alone evaluated: First order average = 60.9

12. But when higher orders evaluated: PC1 (nominal 60 Å) First order average = 60.9 Second order average = 61.8 3rd order average = 62.1 4th order average = 62.1

13. From survey of 15 probe labs Presumably many LSMs are supplied by same manufacturer (e.g. Osmic/Ovionx) … so how could they have such differences?

14. 1.Evaluate periodic table and select elements with 3rd or 4th orders that fall in wavelengths of the LSM 2.Find material with both first order (e.g. O Ka) and higher orders 3.Scan 4.Iteratively find best fit for 2d and K values Class project: determination of correct 2d and K values for our nominal 45, 60, 100 and 200 Å LSMs

15. 45 Å : ZnO: n=2 Zn La, O Ka; GaN: n=1, 2 Ga La; N Ka; F topaz: n=2 Al Ka, n=2 Si Ka 60 Å : pure or alloy metals: Al, Mn, Co, Ni, Zn (3rd order Al Ka, Ni La, Zn La; 4th order Al Ka and Zn La) 100 Å : Carbon coated MgO: n=2 O Ka; n=3,4 Mg Ka; C Ka Carbon coated ZnO: n=2 Ka; n=2,3 Zn La; C Ka 200 Å : MgO: n=3 and 5 O Ka Materials Used for 2d, K determinations

16. Display incorrectly labeled spectrum for n>1 C Ka

17. … after several iterations of 2d and K C Ka

18. EPMA empirical determination of LSM 2ds without consideration of the K factor will yield erroneous 2d calculations. Example: PC1 (60 A) First order average = 60.9 Second order average = 61.8 3rd order average = 62.1 4th order average = 62.1

19. Old vs New 45 Å, 0.01483 44 Å, 0.01 61 Å, 0.01 62.1 Å, 0.02 95.2 Å, 0.013 98.5 Å, 0.033 200 Å, 0.01 204 Å, 0.04 (for UW Madison SX51 #485)

20. Conclusion If you utilize the LSMs very much, and need to identify higher order interferences with a high degree of certainty, determining the 2d and K factors for your LSMs is recommended, and can be done relatively easily

21. Also, somewhat complicating the issue is the fact that the wavelength of B, C, O, N, F - used for these determinations - is not “fixed” (chemical shifts) and various tables give different values …. A minor issue though…