1. Optimization of Actinide Quantification by Electron Probe Microanalysis
Aurélien Moy
Claude Merlet (UM2/GM)
Xavier Llovet (Universitat de Barcelona/CCiTUB) Olivier Dugne (CEA/DEN)
June 24th, 2013

2. MOX fabrication and characterization Analysis of serious accidents
Context
EPMA uses in the nuclear field:  Quantitative characterization of actinides.
Actinides characterization in spent fuel
MOX fabrication and characterization
Conception of Gen IV fuel
Analysis of serious accidents
However, quantitative analysis is not always possible due to the lack of standard samples.
Solution: calculated standards.
To be reliable, these calculations require accurate atomic data and especially accurate x-ray production cross-section.
June 24th, 2013

3. Electron Probe Quantitation
a beam of electrons is fired at a sample
the beam causes each element in the sample to emit X-rays at a characteristic energy
characteristic x-ray intensities are proportional to the mass fraction of each emitting element present in the sample
For any element A in the sample:
𝐴 ∝ 𝐼 𝑚𝑒𝑎𝑠 𝐴 𝐼 𝑠𝑡𝑑 𝐴
𝐼 𝑠𝑡𝑑 (𝐴): intensity of characteristic X-rays from known composition (standard).
Standard intensity 𝐼 𝑠𝑡𝑑 (𝐴) must be determined with high accuracy.
June 24th, 2013

4. Standard intensity Standard intensity 𝑰 𝑠𝑡𝑑 is obtained by:
Direct measurement on samples of known composition Actinide standards are not always available (high radiotoxicity, short life- time, prohibitive cost, …) [1]
Numerical simulation (calculated standards)
Require the accurate knowledge of physical parameters.
Physical parameters are obtained:
- by measurements (when measurements are achievable)
- theoretically (from prediction of physical models)
[1] C. Walker, Electron probe microanalysis of irradiated nuclear fuel: an overview, J. Anal. At. Spectrom., 1999, 14,
June 24th, 2013

5. Calculated standard Number of target atoms per unit volume
Calculated intensity on a bulk sample can be expressed by :
𝑰 𝒊 𝑬 = 𝑵 𝟎 𝒏 𝒆 − 𝝈 𝑿 𝑬 𝟏+ 𝒇 𝒓 𝟏+ 𝒇 𝒄 𝜱 𝝆𝒛 𝒆 − 𝝁 𝝆 𝟏 𝒄𝒐𝒔 𝜽 𝝆𝒛 𝒅 𝝆𝒛 𝒅𝜽 𝚫𝜴 𝟒𝝅 𝜺
Number of target atoms per unit volume
Number of primary electrons reaching the target
X-ray production cross-section
Secondary fluorescence
Number of photon emerging from the sample
Spectrometer efficiency
𝝈 𝑿 𝑬
The x-ray production cross section is not well known especially for heavy elements and needs new evaluations.
June 24th, 2013

6. X-ray production cross-section
𝝈 𝑿 𝑬 : probability (per unit projectile flux) to emit an x-ray corresponding to the studied x-ray line.
L (resp. M) x-ray lines are emitted when a vacancy in the L (resp. M) shell is filled by an electron from an outer shell.

7. 𝝈 𝑿 𝑬 = 𝑰 𝒊 𝑬 𝑵 𝟎 𝒏 𝒆 − 𝒕 𝜟𝜴 𝟒𝝅 𝜺 Measurements method where
On a thin auto-supported sample, the equation reduces to:
𝝈 𝑿 𝑬 = 𝑰 𝒊 𝑬 𝑵 𝟎 𝒏 𝒆 − 𝒕 𝜟𝜴 𝟒𝝅 𝜺
where
𝑰 𝒊 𝑬 is the total measured intensity of x rays produced by the considered line by incident electrons with kinetic energy E,
𝑵 𝟎 is the number of target atoms per unit volume,
𝒏 𝒆 − is the number of primary electrons reaching the target,
𝒕 denotes the active film thickness,
and 𝜟𝜴 𝟒𝝅 𝜺 is the spectrometer efficiency.
June 24th, 2013

8. X-ray intensity measurement
Thin auto-supported sample were used: high signal-to-noise ratio no electron backscattering no photon absorption into the sample.
Samples composition: 1nm thick layer of the active material deposited on 5nm thick self-supporting carbon backing film.
To ensure a good counting statistic, x-ray intensities were recorded at 60 different positions during 600s.
𝒆 − 𝒉𝝂
Deposit
Auto-supported carbon layer
Grid
Faraday cage
Statistical uncertainties were about 4% or 5% for the lowest intense lines.
June 24th, 2013

9. X-ray intensity measurement
Intensity was measured at the top of the line and at each side of the line for background subtraction.
Total x-ray intensity 𝑰 𝒊 𝑬 : areas of several x-ray lines.
The considered spectrum line was fitted by a sum of pseudo-Voigt functions to obtain the total area.
June 24th, 2013

10. Target thickness determination
 measurement of the k-ratio (ratio between the emitted x-ray intensity from the sample and from a tick standard target) versus electron beam energy.
 analysis of the k-ratio by the EPMA software X-film.
Uncertainty on the determination of the thinnest target thickness (1.94µg/cm²) < 5%.
June 24th, 2013

11. Spectrometer efficiency
Spectrometer efficiency: ratio between the bremsstrahlung produced on a thick C or Ni sample and the bremsstrahlung calculated by Monte Carlo simulation.
𝜀 𝜆 𝑖 ΔΩ= 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑏𝑟𝑒𝑚𝑠𝑠𝑡𝑟𝑎ℎ𝑙𝑢𝑛𝑔 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑏𝑟𝑒𝑚𝑠𝑠𝑡𝑟𝑎ℎ𝑙𝑢𝑛𝑔
Spectrometer efficiency’s uncertainty < 5%.
June 24th, 2013

12. Results: uranium L-shell x-ray production cross section
Lα x-ray production cross section was recorded from the ionization threshold up to 38 keV.
No experimental data were found for comparison.
Total uncertainties for the Lα line was estimated to be 10%.
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13. Results: lead L-shell x-ray production cross sections
Lα and Lβ x-ray production cross sections were recorded from the ionization threshold up to 36 keV [2].
Experimental results were compared with the only set of experimental data found in the literature [3].
Total uncertainties were estimated to be 7% and 7.5% for the Lα and Lβ lines, respectively.
[2] A. Moy, C. Merlet, X. Llovet and O. Dugne, 2013, J. Phys. B: At. Mol. Opt. Phys. 46,
[3] Y. Wu, Z. An, Y. M. Duan, M. T. Liu et C. H. Tang, 2007, J. Phys. B: At. Mol. Opt. Phys. 40, 735.
June 24th, 2013

14. DWBA cross-section
𝝈 𝑳𝜷 = 𝜞 𝑳 𝟑 𝑵 𝟏,𝟒,𝟓 + 𝜞 𝑳 𝟑 𝑶 𝟏,𝟒,𝟓 𝜞 𝑳 𝟑 𝒕𝒐𝒕𝒂𝒍 𝝎 𝑳 𝟑 𝝈 𝑳 𝟑 + 𝒇 𝟐𝟑 𝝈 𝑳 𝟐 + 𝒇 𝟏𝟑 + 𝒇 𝟏𝟐 𝒇 𝟐𝟑 + 𝒇′ 𝟏𝟑 𝝈 𝑳 𝟏 + 𝜞 𝑳 𝟐 𝑴 𝟒 𝜞 𝑳 𝟐 𝒕𝒐𝒕𝒂𝒍 𝝎 𝑳 𝟐 𝝈 𝑳 𝟐 + 𝒇 𝟏𝟐 𝝈 𝑳 𝟏 + 𝜞 𝑳 𝟏 𝑴 𝟐,𝟑 𝜞 𝑳 𝟏 𝒕𝒐𝒕𝒂𝒍 𝝎 𝑳 𝟏 𝝈 𝑳 𝟏
Theoretical ionization cross sections were calculated by Bote et al. [4] into the distorted-wave Born approximation (DWBA) theory.
Ionization cross sections were converted into x-ray production cross sections with atomic relaxation data extracted from the Evaluated Atomic Data Library (EADL).
[4] D. Bote, F. Salvat, A. Jablonski and C. J. Powell, 2009, At. Data Nucl. Data Tables 96, 871.
June 24th, 2013

15. Results: lead M-shell x-ray production cross sections
Mα and Mβ x-ray production cross sections were recorded from the ionization threshold up to 38keV.
Grey shaded areas represent the uncertainty bands of the converted Bote et al. DWBA calculation.
Total uncertainties were estimated to be 6.5% and 7% for the Mα and Mβ lines, respectively.
June 24th, 2013

16. Results: lead M-shell x-ray production cross sections
The shape of the experimental curve is in good agreement with the DWBA calculation.
Total uncertainty was estimated to be 12% for the Mg line.
June 24th, 2013

17. Results: uranium
Experimental results are in very good agreement with theoretical DWBA cross sections in shape and magnitude.
Total uncertainties were estimated to be 9.5% and 8.5% for the Mα and Mβ lines, respectively.
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18. Results: uranium
Mg experimental results agree with the theoretical DWBA cross-section.
Total uncertainty was estimated to be 15% for the Mg line.
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19. Conclusion and perspectives
L and M x-ray production cross sections are in good agreement  with other experimental data (Pb L-shells)  with converted theoretical DWBA cross sections.
DWBA model  good candidate to calculate x-ray production cross sections for the conception of calculated standards (standardless analysis).
The x-ray production cross-section represents one term in the calculated standard intensity  To obtain absolute intensity, other terms have to be carefully evaluated.
X-ray production cross sections for Th will be measured  prediction of the DWBA model will also be tested.
Virtual standards will be set up  intensity predictions for Pu, Np and Am will be tested (with measured intensity) to asses the reliability.
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20. Thank you for your attention
June 24th, 2013