Measurement of coherent x-ray scatter form factors for amorphous materials using diffractometers

Abstract

The feasibility of measuring the coherent x-ray scatter form factors of amorphous materials using powder diffractometers has been assessed. A five-step procedure was developed: (i) Low-angle background, consisting of a portion of the incident x-ray beam that passes directly to the detector, is measured using a specially designed replacement for the sample holder which absorbs most of the photons that otherwise would scatter off the sample holder cavity. (ii) Angle-dependent effects including monochromator efficiency and projected beam area are characterized by extracting the incoherent signal from the diffraction pattern of powdered graphite. The incoherent signal divided by the calculated incoherent cross section gives a correction factor as a function of scattering angle θ. (iii) Diffraction patterns are measured for the samples for θ = 2°–150°. (iv) The scattering data are corrected for background and then for angle-dependent effects. (v) The data are normalized to calculated free atom form factors at high θ, and the coherent form factor extracted. The method was implemented on two diffractometers at different energies (Co Kα and Cu Kα), and the results compared for water and plastics. Over the range 0.117 < x < 5.39 nm−1, where x = λ−1 sin(θ/2), the average form factor ratio for water was 0.93. Systematic errors are difficult to eliminate. While this x-ray powder diffractometer technique suffices for a survey measurement of the form factor of a material, its accuracy is probably insufficient for detailed studies.