1. The Problem of Secondary Fluorescence in EPMA in the Application of the Ti-in-Zircon Geothermometer And the Utility of PENEPMA Monte Carlo Simulations
John H. Fournelle
Eugene Cameron Electron Microprobe Lab
Department of Geology and Geophysics University of Wisconsin
Madison, Wisconsin

2. Taking the Earth’s temperature
geologists can directly measure temperature of lava flows
but direct methods are not possible for most of deep Earth conditions …
so we use geochemical evidence -- element partitioning between coexisting minerals -- to infer conditions deep within the earth
these geothermometers and geobarometers have been developed with, and utilize, electron and ion probes for microanalysis of minerals and glasses.

3. Zircon…takes a licking, keeps on ticking…
ZrSiO4, small ~ microns, accessory mineral (~granites, rhyolites)
highly resistant to chemical changes
Th, U and Pb present: radiogenic decay
used for estimating earth conditions eons ago
oldest dated mineral on Earth is a zircon from Australia
its oxygen isotope value suggests Earth’s crust was cool and wet as long ago as 4.3 billion years.

4. A zircon thermometer?
Watson and Harrison* and Watson et al** experimentally determined that the amount of Ti incorporated in zircon (~1 to 1000s of ppm), coexisting with a high-Ti mineral (e.g., rutile TiO2 or ilmenite FeTiO3), was proportional to the temperature at which the zircon crystallized and could be a geothermometer.
* Watson and Harrison, 2005, Science, 308, ** Watson, Walk and Thomas, 2006, Contrib Mineral Petrol, 151, 413

5. Measuring tiny levels of Ti …..
SIMS
EPMA
Where the level of Ti is very low (1-100 ppm), the preferred method is ion probe (SIMS).
However, there are situations where EPMA is used:
for original validation of Ti in synthesized zircons (i.e., for SIMS standards),

6. Measuring tiny levels of Ti …..
SIMS
EPMA
Where the level of Ti is very low (1-100 ppm), the preferred method is ion probe (SIMS).
However, there are situations where EPMA is used:
for original validation of Ti in synthesized zircons (i.e., for SIMS standards),
by geologists who do not have ready access to SIMS, or

7. Measuring tiny levels of Ti …..
SIMS
EPMA
Where the level of Ti is very low (1-100 ppm), the preferred method is ion probe (SIMS).
However, there are situations where EPMA is used:
for original validation of Ti in synthesized zircons (i.e., for SIMS standards),
by geologists who do not have ready access to SIMS, or
where the large SIMS spot size (~25 microns) is prohibitive.

8. For EPMA of Ti at trace element levels,
However
For EPMA of Ti at trace element levels,
Secondary Fluorescence may be an issue

9. Secondary Fluorescence …
the electron beam’s interaction volume is small relative to the volume excited by both characteristic and continuum x-rays generated
what is the amount of secondary fluorescence that is measured during EPMA???
critical for trace element EPMA measurements

10. One alternative: model the effect the Monte Carlo way…
The PENEPMA Monte Carlo program, based upon PENELOPE, has been shown to accurately predict the extent of secondary fluorescence and has been recently modified to explicitly give characteristic peaks and also to give the SF intensity.
Energy total I error fluor I error
Ti Ka

11. 2 Cases Modeled with Penepma
Both 15 kV, 40° take off angles, with only continuum secondary fluorescence
Presence of rutiles (TiO2) in experimental runs for measuring Ti in zircon solubility (= relevant to original calibration of the geothermeter)
Zircons in rock samples with nearby ilmenite and biotite, Ti-bearing minerals (=relevant to actual application of the geothermometer)

12. Watson et al (2006) experimentally grew zircons where rutile (TiO2) were also present, and tried to minimize/account for secondary fluorescence (SF) …. I have tried here to model the SF effect magnitude by Monte Carlo simulations

13. Case 1: Zircon with Rutile — 7 Geometries Modeled
Geometry 1: 30 um zircon, no rutile, only Ti in surrounding silicate glass (6 wt% Ti) => 452 ppm SF Ti
30 um
Incident beam (15 kV) impacts center of round zircon here and in all cases
Cross Section
Plan View

14. Geometry 2: 30 um zircon, 5 large rutiles 15 um away, Ti in surrounding glass (6 wt% Ti) => 948 ppm SF Ti
Each rutile contributes ~100 ppm Ti to the level already present from the matrix glass.
Silicate glass with Ti

15. Geometry 3: 30 um zircon, 5 large rutiles 15 um away, NO Ti in surrounding glass, with Pb instead => 390 ppm SF Ti
This simulates what Watson et al did, dissolved the original Ti-bearing glass, replaced with Pb-bearing glass, to reduce SF — with moderate result
Silicate glass with Pb

16. Thought experiment: what if no surrounding glass, only epoxy?
Geometry 4: 30 um zircon, 5 large rutiles 15 um away, in epoxy => 1179 ppm SF Ti
Thought experiment: what if no surrounding glass, only epoxy?
Result suggests a balance of fluorescence and absorption involved — here fluorescence enhanced and absorption strongly eliminated
epoxy

17. Geometry 5: 30 um zircon, 5 large rutiles 60 um away, in Pb-glass => 25 ppm SF Ti
Silicate glass with Pb

18. 7 Experimental Geometries Modeled
Geometry 6: 30 um zircon, 5 tiny 4 um rutiles 0-1 um away, in epoxy => 61 ppm SF Ti
epoxy

19. Geometry 7: 30 um zircon, 10 tiny rutiles 0 um away, in epoxy => 120 ppm SF Ti

20. Conclusions
easy to get several hundred ppm of Ti if large Ti-rich phases are within tens of microns of analysis point
conceptually, “solid angle” that Ti-rich phases present to analysis point
continuum SF is not insignificant
analyst must consider/rule out/correct for secondary fluorescence to properly utilize Ti in zircon geothermometer

21. Case 2 examines the potential for secondary fluorescence in a rock where zircons are surrounded by ilmenite, hematite and biotite (suggested by C. Morisset, Univ. British Columbia). Here it is less easy to model a realistic geometry as the zircons are irregular in shape.

22. FeTiO3
Fe2O3
Biotite(Ti)
FeTiO3
Biotite(Ti)
The actual EPMA measurements of Ti in these zircons and temperatures from Watson et al’s geothermometer:
Zr1 162 ppm °C
Zr2 189 ppm °C
Zr3 264 ppm °C
Zr4 645 ppm °C
Zr ppm °C

23. Set up simple geometry for PENEPMA
ZIRCON
ZrSiO4
ILMENITE
FeTiO3
Run a traverse from 5 to 100 microns away from ilmenite boundary into zircon
2 cm

24. Results
ZIRCON
ZrSiO4
ILMENITE
FeTiO3
zircons within 5-40 microns of ilmenite can receive fictitious (SF) Ti counts ranging from 100 to 2000 ppm
for the 2 samples examined, the calculated temperatures are not correct

26. Size Can Matter in EPMA or….

27. Complications of Secondary Fluorescence: The “Size Discrepancy Issue”

28. Difference between small sample and large standard
Sample = 10 um polished sphere Cr2O3 embedded in plastic
Electron beam
Electron beam
Standard not to scale with unknown, would be much larger if true scale.
Standard = 2 mm polished sphere
PMM (plastic)
PMM (plastic)
In troubleshooting low totals, the question arose: if there is a several order magnitude size difference between unknowns (small grain separates) and standard (large), what could result?

29. Difference between small sample and large standard
Sample = 10 um polished sphere Cr2O3 embedded in plastic
Electron beam
Electron beam
Standard not to scale with unknown, would be much larger if true scale.
Standard = 2 mm polished sphere
PMM (plastic)
PMM (plastic)
If the primary electron “interaction volume” is confined within the material, and therefore the primary x-ray generation is also confined therein, is the lack of “additional” Cr x-ray counts resulting from secondary fluorescence outside the primary electron interaction volume of any importance in “normal” EPMA???

30. Set up a Penepma Monte Carlo simulation: Standard of “huge size”, 2 mm
Cr2O3
PMM (plastic)
Sample = 10 um polished sphere embedded in plastic
Standard = 2 mm polished sphere
Set up a Penepma Monte Carlo simulation:
Standard of “huge size”, 2 mm
Unknowns of much smaller size
Accelerating voltage of 20 kV, takeoff angle 40°

31. Yes, Secondary Fluorescence can cause problems
Standard=2000 mm Cr2O3 Unknown = smaller Cr2O3 4
Electron range (K-O): 1.7 micron Cr Ka X-ray range (A-H): 1.6 micron
A 100 mm grain of pure Cr2O3 will have 1% low Cr K-ratio, and a 10 mm grain will have a K-ratio 2.5% low.
(plots show K-ratios produced in centers of various discrete sized diameter cut-off spheres imbedded in epoxy simulations)

32. Conclusion
Discrepancies in size between unknown and standard can lead to small, but noticeable errors, because secondary fluorescence yields
additional x-rays beyond the primary electron impact-x-ray production volume in the same phase if the phase is large, or
a lack of additional x-rays if the phase is small and mounted in epoxy.

34. PENELOPE
created to model high energy radiation in bodies of complex geometries
simulates x-ray generation and x-ray absorption/secondary fluorescence
a new version developed for EPMA, with EDS-like spectral output
a FORTAN program, runs with G77 compiler under OS X, Linux, Windows
developed by Salvat, Llovet et al. of Universitat de Barcelona … and free