Measurement of the x-ray mass attenuation coefficient of copper using 8.85 – 20 keV synchrotron radiation C. T. Chantler, 1 C. Q. Tran, 1 Z. Barnea, 1 D. Paterson, 1 D. J. Cookson, 2 and D. X. Balaic 1 1 School of Physics, University of Melbourne, Victoria 3010, Australia 2 ANSTO, Private Mail Bag 1, Menai, NSW 2234, Australia and Chem-Mat-CARS-CAT (Sector 15, Bldg 434D), Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 Received 27 June 2001; published 19 November 2001 This work presents the x-ray extended range technique for measuring x-ray mass attenuation coefficients. This technique includes the use of multiple foil attenuators at each energy investigated, allowing independent tests of detector linearity and of the harmonic contributions to the monochromated synchrotron beam. Mea- surements over a wide energy range allow the uncertainty of local foil thickness to be minimized by the calibration of thin sample measurements to those of thick samples. The use of an extended criterion for sample thickness selection allows direct determination of dominant systematics, with an improvement of accuracies compared to previous measurements by up to factors of 20. Resulting accuracies for attenuation coefficients of copper 8.84 to 20 keV are 0.27–0.5 %, with reproducibility of 0.02%. We also extract the imaginary com- ponent of the form factor from the data with the same accuracy. Results are compared to theoretical calcula- tions near and away from the absorption edge. The accuracy challenges available theoretical calculations, and observed discrepancies of 10% between current theory and experiments can now be addressed. DOI: 10.1103/PhysRevA.64.062506 PACS numbers: 32.30.Rj, 32.80.Fb, 61.10.Ht, 61.10.Eq I. INTRODUCTION A precise understanding of the way x-ray photons interact with matter is important in atomic physics, crystallography, medical diagnosis, and surface and material sciences. Recent major developments have concentrated on applications for structural determination near absorption edges, including the use of Bijvoet ratios 1, multiple-wavelength anomalous dispersion MAD techniques 2, x-ray absorption fine structure XAFS investigations 3, and diffraction anoma- lous fine structure DAFS4. The complex form factor f the resonant scattering ampli- tude of x rays due to the charge distribution, is the funda- mental parameter for all optical devices. It specifies refrac- tive indices, permittivities, scattering, and attenuation coefficients, and hence the critical properties for mirrors, lenses, filters, and coatings. In the x-ray regime, the form factor becomes accessible to theoretical prediction on the basis of atomic physics and the atomic form factor 5. At intermediate x-ray energies, photons are primarily attenuated or elastically scattered by matter. Inelastic scattering be- comes dominant only at higher energies above 40 keV for copper. Current computations of theories vary by many quoted standard deviations from one another in important regions 6,7. In some cases this variation is due to a lack of conver- gence of the computation; in other cases it is due to inad- equate assumptions relating to the wave functions. This is a difficult area to compare directly with experiment, since ex- perimental data must be obtained to high accuracy over ex- tended ranges of energy and attenuation to observe both structural variation and possible offsets due to any given as- sumptions. This work presents the results of such an ex- tended investigation. The imaginary component of the form factor Im( f ) may be determined from studies of the full complex form factor using x-ray interferometry 8,9, reflection and refraction 10,11, diffraction intensities 12,13, and pendello ¨ sung fringes 14,15. Some difficulties of these approaches include the often narrow energy range covered by interferometric methods, the limited accuracy of separating the imaginary component of f from the real component in measurements of the full structure factor for a solid, and assumptions in using the Kramers-Kronig relation on a limited data set of Re( f ) measurements. Alternatively, Im( f ) denoted by f  or f 2 by various au- thors may be related directly to the photoelectric absorption coefficient and, equivalently, the photoelectric absorption cross section  PE , by the energy E, the classical electron radius r e , Planck’s constant h, and the speed of light c, Im f  = f   E  = f 2  E  = E  PE 2 hcr e . 1 Compilations of experimental data of  PE over the last decade show large variations of up to 30%, although many authors have claimed 1% precision or better using various experimental techniques 16,17. These variations are due to unresolved systematics relating to sample thickness determi- nation and purity, detector linearity, harmonic contamination of the x-ray beam, scattering, energy calibration, and beam divergence. The most reliable results quoted in the literature relate to the work of Creagh and Hubbell 17, Gerward 18, and Mika et al. and Chantler and Barnea 19. We have re- cently adapted the techniques of these authors and developed them to be appropriate for synchrotron research 16,20. The availability of modern synchrotron radiation brought near-edge absorption of x-rays within the reach of many fields of research. Previously, conventional x-ray diffraction PHYSICAL REVIEW A, VOLUME 64, 062506 1050-2947/2001/646/06250615/$20.00 ©2001 The American Physical Society 64 062506-1