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No abstract

Anomalous scattering factors Δf′ and Δf″ have been calculated relativistically for Cr, Fe, Cu, Mo, and Ag Kα radiations for the atoms Li through Cf. An interpolation scheme for other wavelengths is included in a separate report. Relativistic calculations of the photoelectric cross section have been made and the integral for the principal contribution to Δf′ has been evaluated numerically without approximation to the form of the cross section-vs-energy curve, as has been done in previous calculations. Many of the results are significantly different from previous calculations. Where experimental values exist, agreement for Δf″ is improved. For the rare gases, except for xenon, agreement between Δf′ and experiment is improved. Because of the more rigorous evaluation of Δf′ from cross-section information, it is presumed that the present Δf′ values are more accurate than previous calculated values. Calculated mass absorption coefficients for the elements are included as incidental information.

Tabulations are presented of the atomic form factor, F(x,Z), and the incoherent scattering function, S(x,Z), for values of x (=sin (IJ/2)/X,) from 0.005 A-I to 10 9 A-1, for all elements Z=l to 100. These tables are constructed from available state-of-the-art theoretical data, including the Pirenne formulas for Z = 1, configuration-interaction results by Brown using Brown-Fontana and Weiss correlated wavefunctions for Z=2 to 6, non-relativistic Hartree-Fock results by Cromer for Z=7 to 100, and a relativistic K-shell analytic expression for F(x,Z) by Bethe and Levinger for x> 10 A-I for all elements Z =2 to 100. These tabulated values are graphically compared with available photon scattering angular distribution measurements. Tables of coherent (Rayleigh) and incoherent (Compton) total scattering cross sections, obtained by numerical integration over combinations of F2(X.z) with the Thomson formula and S (x,Z) with the Klein-Nishina formula, respectively, are presented for all elements Z= I to 100, for photon energies 100 eV (1..=124 A)lto 100 MeV (0.000124 A). The incoherent scattering cross sections also include the radiative and double-Compton corrections as given by Mork. Similar tables are presented for the special cases of terminally-bonded hydrogen and for the H2 molecule, interpolated and extrapolated from values calculated by Stewart et al. and by Bentley and Stewart using Kolos-Roothaan wavefunctions.

Using powder data obtained with a Norelco X-ray diffractometer, the crystal structures of anatase and rutile have been determined with greater precision than has been previously reported. The cell parameters are for rutile a = 4.5929 ± 0.0005 and c = 2.9591 ± 0.0003 Á.; for anatase a = 3.785 ± 0.001 and c = 9.514 ± 0.006 Á. The oxygen parameter for rutile is 0.3056 ± 0.0006 and for anatase is 0.2066 ± 0.0009. There are four Ti-0 distances of 1.946 ± 0.003 A. and two Ti-O distances of 1.984 ± 0.004 Á. in rutile. In anatase there are four Ti-0 distances of 1.937 ± 0.003 and two Ti-0 distances of 1.964 ± 0.009 Á. These results are qualitatively correlated with the color differences of the two materials.