High-accuracy measurements of the x-ray mass attenuation coefficients of molybdenum and tin

386 Pages·2006·6.9 MB·English

High-accuracy measurements of the
x-ray mass attenuation coefficients of
molybdenum and tin:
testing theories of photoabsorption
by
Martin D de Jonge
Submitted in total fulfilment of
the requirements for the degree of
Doctor of Philosophy
School of Physics
The University of Melbourne
Australia
August 25, 2005
Produced on acid-free paper

High-accuracy measurements of the
x-ray mass attenuation coefficients of molybdenum and tin:
testing theories of photoabsorption
by Martin D de Jonge
Supervised by Assoc. Prof. Christopher T Chantler
The x-ray atomic form-factor determines the x-ray optical properties of materials
and is a fundamental parameter for critical x-ray investigations. However, despite
uncertainty estimates of order 1%, differences of 2–10% between x-ray mass atten-
uation measurements render comparison with the various theoretical tabulations
meaningless. Moreover, such uncertainties impose limits on the accuracy of various
quantitative investigations.
We determine the imaginary component of the atomic form-factor from mea-
surements of the x-ray mass attenuation coefficient. With the exception of the
measurements of Tran et al. [Phys. Rev. A 64, 062506; 67, 042716; J. Phys. B 38,
89] with a 0.3% accuracy, previous work has been unable to achieve accuracies below
1%, and differences between results claiming this accuracy often exceed 6%.
We have developed a full-foil mapping technique which has improved the mea-
surement accuracy by an order of magnitude. This technique overcomes limitations
arising from absorber thickness variations, using the average integrated column den-
sityandattenuationmeasurementsacrosstheentiresurfaceoftheabsorber. Wehave
examined measurements obtained over a wide range of parameter space for system-
atic deviations indicative of experimental error. Among others, this has led to the
identification and correction of a 1% discrepancy arising from the x-ray bandwidth.
Resulting measurement accuracies for molybdenum are 0.02–0.15%. Preliminary re-
sults for tin suggest a final accuracy of 0.1–1%. We compare these measurements
with several commonly-used tabulations and identify a number of systematic dis-
crepancies whose causes are discussed.

This is to certify that
(i) the thesis comprises only my original work towards the PhD,
(ii) due acknowledgement has been made in the text to all other material used,
(iii) the thesis is less than 100,000 words in length, exclusive of tables, bibliogra-
phies, and appendices.
I authorise the Head of the School of Physics to make a copy of this thesis avail-
able to any person judged to have an acceptable reason for access to the information.
Martin D de Jonge
August 25, 2005

Responses to the referee’s comments
I thank the referees for their careful and close reading of this work. Their comments
have prompted several improvements, each of which is detailed here.
The reviewers have pointed out some typographical errors. In particular: refer-
ence [1] was incomplete; the upper limit of the energy range of the XCOM database
was reported as 1 GeV instead of 100 GeV (page 33), and; Delbru¨ck scattering dom-
inates the atomic scattering cross sections at energies above 100 MeV (page 27). In
addition, it was pointed out that the term ‘fluorescent radiation’ is somewhat re-
dundant, and so it is replaced by the term ‘fluorescence radiation’ (section 8.4).
A short discussion of the nuclear resonant contribution to the atomic scattering
cross section (page 28) implied that giant dipole resonances are limited to bound-
bound nuclear transitions. However, these resonances include the nuclear photo-
effect, which appears as a broad peak several MeV wide in the 10 MeV–40 MeV
region. The text has been updated, and references [2, 3, 4] have been added.
Section 2.8 discusses theoretical approaches to the calculation of mass attenua-
tion coefficients, observing that one approach [5] uses the Hartree-Fock renormalised
values of Scofield’s calculation of the photoelectric absorption cross sections [6], ex-
trapolating them over a further five orders of magnitude in energy, to 100 GeV
(page 31). We now mention in the text that the extrapolation was guided by the
theoretical high-energy results of Pratt [7]. While the extrapolation procedure en-
abled estimation of the photoelectric contribution to the total atomic cross section
(dominated at high energy by other processes), the extrapolated photoelectric cross
sections were not of high accuracy.
vii

Preface
The work reported in this thesis has resulted in a number of written and oral pre-
sentations. These are detailed here for reference.
Publications resulting directly from this thesis
The following publications have arisen directly from this work. They are reprinted
in full in Appendix D.
• M D de Jonge, C Q Tran, C T Chantler, Z Barnea, B B Dhal, D J Cookson,
W-K Lee, and A Mashayekhi. Measurement of the x-ray mass attenuation
coefficient and determination of the imaginary component of the atomic form
factor of molybdenum over the 13.5–41.5-keV energy range. Physical Review
A 71(3), 2004.
• M D de Jonge, Z Barnea, C T Chantler, and C Q Tran. Bandwidth: deter-
mination by on-edge absorption and effect on various experiments. Physical
Review A 69(2), 2004.
• MDdeJonge, ZBarnea, CQTran, andCTChantler. Full-foilx-raymapping
of integrated column density applied to the absolute determination of mass
attenuation coefficients. Measurement Science and Technology 15, 1811–22,
2004.
Publications related to this thesis
The author has made significant contributions to the writing, development, and/or
analysis presented in the following works.
• CQTran,MDdeJonge,ZBarnea,andCTChantler. Absolutedetermination
of the effect of scattering and fluorescence on x-ray attenuation measurements.
Journal of Physics B 37, 3163–76, 2004.
ix
• C Q Tran, Z Barnea, M D de Jonge, B B Dhal, Paterson D, D J Cookson, and
CTChantler. Quantitativedeterminationofmajorsystematicsinsynchrotron
x-ray experiments: seeing through harmonic components X-Ray Spectrometry
32, 69–74, 2003.
• CQTran,ZBarnea,CTChantler,andMDdeJonge. Accuratedetermination
of the thickness or mass per unit area of thin foils and single-crystal wafers
for x-ray attenuation measurements. Review of Scientific Instruments 75(9),
2943–9, 2004.
• C Q Tran, C T Chantler, Z Barnea, M D de Jonge, B B Dhal, C T Y Chung, D
Paterson, and J Wang. Measurement of the x-ray mass attenuation coefficient
of silver using the x-ray-extended range technique. Journal of Physics B:
Atomic, Molecular, and Optical Physics 38(1), 89–107, 2005.
• CQTran, MDdeJonge, ZBarnea, BBDhal, andChantlerCT.Quantitative
determination of the effect of the harmonic component in monochromatised
synchrotron x-ray beam experiments. Developments in Quantum Physics,
Nova Science. Eds. F Columbus and V Krasnoholovets, 2004.
Conference proceedings
• M D de Jonge, C Q Tran, C T Chantler, and Z Barnea. Improved techniques
for measuring x-ray mass attenuation coefficients. Proc. SPIE: Optical con-
stants of materials for UV to x-ray wavelengths, Eds. R Soufli and J F Seely,
5538, 96–106, Oct. 2004.
• CQTran, MDdeJonge, ZBarnea, BBDhal, andChantlerCT.Quantitative
determination of the effect of the harmonic component in monochromatised
synchrotron x-ray beam experiments. 19th International conference on x-ray
and inner-shell processes, Frascati Physics Series, Vol. XXXII, Eds. S Bian-
coni, A Marcelli, and N L Santini, 335–42, 2003.
Conference abstracts
• MDdeJonge,CQTran,ZBarnea,BBDhal,DJCookson,andCTChantler.
X-ray extended-range technique for precision measurement of the x-ray mass
attenuationcoefficientand Im(f)formolybdenum usingsynchrotron radiation.
Acta Crystallographica, Section A 58, section 1, p. C82, 2002.
x