1 OPTIMIZATION OF ACTINIDE QUANTIFICATION BY ELECTRON PROBE MICROANALYSIS Aurélien Moy Claude Merlet (UM2/GM) Xavier Llovet (Universitat de Barcelona/CCiTUB)

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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

Context• EPMA uses in the nuclear field: Quantitative characterization of actinides.

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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.

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Electron Probe Quantitation

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For any element A in the sample:

: intensity of characteristic X-rays from known composition (standard).

• 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

• Standard intensity must be determined with high accuracy.

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Standard intensity

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Standard intensity 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, 447-454.

Calculated standard

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The x-ray production cross section is not well known especially for heavy elements and needs new evaluations.

Calculated intensity on a bulk sample can be expressed by :

𝑰 𝒊 (𝑬 )=𝑵𝟎𝒏𝒆−𝝈𝑿 (𝑬 ) (𝟏+ 𝒇 𝒓 ) (𝟏+ 𝒇 𝒄 )∫𝜱 (𝝆 𝒛 )𝒆− 𝝁𝝆

𝟏𝒄𝒐𝒔 (𝜽 )

𝝆𝒛𝒅 (𝝆 𝒛 )𝒅𝜽 𝚫𝜴

𝟒𝝅𝜺

Number of target atoms per unit volumeNumber of primary electrons reaching the target X-ray production cross-sectionSecondary fluorescenceNumber of photon emerging from the sampleSpectrometer efficiency

𝝈𝑿 (𝑬 )

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X-ray production cross-section

: probability (per unit projectile flux) to emit an x-ray corresponding to the studied x-ray line.

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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.

Measurements method

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𝝈𝑿 (𝑬 )=𝑰 𝒊 (𝑬 )

𝑵 𝟎𝒏𝒆−𝒕𝜟𝜴𝟒𝝅

𝜺

where is the total measured intensity of x rays produced by the considered line

by incident electrons with kinetic energy E,

is the number of target atoms per unit volume,

is the number of primary electrons reaching the target,

denotes the active film thickness,

and is the spectrometer efficiency.

On a thin auto-supported sample, the equation reduces to:

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X-ray intensity measurement

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Thin auto-supported sample were used:high signal-to-noise rationo electron backscatteringno 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

DepositAuto-supported carbon layer

Grid

Faraday cage

Statistical uncertainties were about 4% or 5% for the lowest intense lines.

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X-ray intensity measurement

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Intensity was measured at the top of the line and at each side of the line for background subtraction.

Total x-ray intensity : areas of several x-ray lines.The considered spectrum line was fitted by a sum of pseudo-Voigt functions to obtain the total area.

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Target thickness determination

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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%.

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Spectrometer efficiency

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Spectrometer efficiency: ratio between the bremsstrahlung produced on a thick C or Ni sample and the bremsstrahlung calculated by Monte Carlo simulation.

Spectrometer efficiency’s uncertainty < 5%.

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Results: uranium L-shell x-ray production cross section

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Total uncertainties for the Lα line was estimated to be 10%.

Lα x-ray production cross section was recorded from the ionization threshold up to 38 keV.No experimental data were found for comparison.

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Results: lead L-shell x-ray production cross sections

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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, 115202.[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.

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].

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DWBA cross-section

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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.

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Results: lead M-shell x-ray production cross sections

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Total uncertainties were estimated to be 6.5% and 7% for the Mα and Mβ lines, respectively.

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.

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Results: lead M-shell x-ray production cross sections

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Total uncertainty was estimated to be 12% for the Mg line.

The shape of the experimental curve is in good agreement with the DWBA calculation.

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Results: uranium

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Total uncertainties were estimated to be 9.5% and 8.5% for the Mα and Mβ lines, respectively.

Experimental results are in very good agreement with theoretical DWBA cross sections in shape and magnitude.

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Results: uranium

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Total uncertainty was estimated to be 15% for the Mg line.

M g experimental results agree with the theoretical DWBA cross-section.

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Conclusion and perspectives

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• 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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Thank you for your attention

June 24th, 2013