1. Detection Limits N no longer >> N B at low concentration What value of N-N B can be measured with statistical significance? Liebhafsky limit: Element is present if counts exceed 3X precision of background: N > 3(N B ) 1/2 Ziebold approximation: C DL > 3.29a / [(nτP)(P/B)] 1/2 τ = measurement time n = # of repetitions of each measurement P = pure element count rate B = background count rate (on pure element standard) a = relates composition to intensity

2. Or 3.29 (wt.%) / I P [(τ i) / I B ] 1/2 I P = peak intensity I B = background intensity τ = acquisition time i = current Ave Z = 79 Ave Z = 14 Ave Z = 14, 4X counts as b

3. Where Detection limit (Ancey) α : Risk of considering that C>0 when it is in fact C=0 β : Risk of considering that C=0 when it is in fact C>0 By default, we will use α = β = 5%.

4. Detection limit for Pb PbMα measured on VLPET 200nA, 800 sec

5. Can increase current and / or count time to come up with low detection limits and relatively high precision But is it right?

6. Accuracy All results are approximations Many factors Level 1 quality and characterization of standards precision matrix corrections mass absorption coefficients ionization potentials backscatter coefficients ionization cross sections dead time estimation and implementation Evaluate by cross checking standards of known composition (secondary standards)

7. Level 2 – the sample Inhomogeneous excitation volume Background estimation Peak positional shift Peak shape change Polarization in anisotropic crystalline solids Changes in Φ(ρZ) shape with time Measurement of time Time-integral effects Measurement of current, including linearity is a nanoamp a nanoamp? Depends on measurement – all measurements include errors!

8. Time-integral acquisition effects drift in electron optics, measurement circuitry dynamic X-ray production non-steady state absorbed current / charge response in insulating materials beam damage compositional and charge distribution changes surface contamination

9. Overall accuracy is the combined effect of all sources of variance…. σ T 2 = σ C 2 +σ I 2 +σ O 2 +σ S 2 +σ M 2 σ T = total error σ C = counting error σ I = instrumental error σ O = operational error σ S = specimen error σ M = miscellaneous error Each of which can consist of a number of other summed terms Becomes more critical for more sensitive analyses - trace element analysis

10. Sources of measurement error – Time-integral measurements and sample effects

11. Time (min) Cps/nA 2σ counting statistics 051015202530

12. Cps/nA Wavelength (sinθ)

13. ideal

14. Beam damage Monazite LGG246-5 Lower Granite Gorge - Grand Canyon 15kV, 200nA, 30 min

15. Sources of measurement error: Current and dead-time

17. Sources of measurement error: Extracting accurate intensities – peak and background measurements Background shape depends on Bremsstrahlung emission Spectrometer efficiency

19. PHA effects relating to trace analysis

20. Detector gas type and pressure

21. GdPO4 Pb region (PET) PbMα

28. Sources of measurement error - Peak shifts Wavelength may shift between standard and sample (or between samples) if X-ray transition involves valance electrons Example: Y Lγ 2,3 transitions from N2 (4p 1/2 ) and N3 (4p 3/2 ) levels Critical in Pb measurement in monazite: PbMα - YLγ overlap YPO 4 (tetragonal) Monazite (monoclinic) O coordination8-fold9-fold Ave REE-O bond length (Å)2.3462.559

30. YPO4

31. Calculate peak wavelength shift of - 4.5x10 -3 Å in monazite relative to YPO 4 Results in overestimation of overlap: 36ppm Pb / wt.%Y