Kα₁–Kα₂characteristic of a parabolic graded multilayer

Abstract

Line shapes of the K 1 ±K 2 doublet beam re¯ected from a parabolic graded multilayer (PGM) were analysed by ray tracing and rocking-curve measurements using an Si(400)¯at single crystal. The integrated intensity and the intensity ratio of K 2 to K 1 of the re¯ected beam vary with the angle of incidence at the PGM. The rates of these variations are considered to increase with increasing spectral resolution of the PGM. The K 1 and K 2 beams are re¯ected from the PGM in slightly different directions. Therefore, the angular separation between the K 1 and K 2 peaks of the observed diffraction pro®le of a sample becomes smaller than that calculated from the two wavelengths for K 1 and K 2 when the PGM and the sample are arranged in the (+ À) setting, and vice versa when they are in the (++) setting. The magnitude of the shift of the angular separation is close to the experimental uncertainty in the determination of the peak positions when the PGM consists of W/Si bilayers, whereas it is estimated to be three times as large when a PGM of high spectral resolution is used.

Fundamental parameters line profile fitting in laboratory diffractometers

“…The inclusion of a parabolic multilayer mirror in the incident beam of a diffractometer can also introduce a distortion into the wavelength spectrum [42]. This happens because the Kα 1 and Kα 2 components of the spectrum reflect off the mirror in slightly different directions as shown in Fig.…”

“…30, the separation ∆2θ Kα21 is smaller than the value expected from the known Kα 1 and Kα 2 wavelengths by an amount corresponding to the difference ∆ψ in the directions of the two incident beams on to the specimen. According to Toraya and Hibina [42] the difference δψ for a conventional long fine focus x-ray with a projected target width of 0.04 mm can rise to 0.0017° for a high resolution mirror, but decreases to a negligible level for low resolution mir- rors. In any high accuracy lattice parameter determination using this type of diffractometer it is necessary to incorporate the wavelength dependent zero error into the analysis.…”

Profile Analysis

“…Parabolic multilayer mirrors in the incident beam of a diffractometer can also distort the wavelength spectrum (Toraya and Hibino, 2000). As different wavelengths reflect off the mirror in slightly different directions as shown in Figure 4.6 for the K α 1 and K α 2 components, an inhomogeneous spread in wavelength across the specimen in the equatorial plane will be obtained.…”

Application of Single and Dual Multilayer Optics for Powder X‐Ray Diffraction

“…Ray tracing calculations for prediction of intensities and diffraction geometries by Toraya and Hibino [9] as well as by Gutman and Verman [3] demonstrate that one should expect a shift in the α 1 and α 2 peak separations as a result of slightly different diffraction angles from the multilayer. Of course, the different diffraction angles for the α 1 and α 2 radiation are not an issue if one employs a channel-cut monochromator to further condition the beam.…”

“…Of these measurements, powder diffraction, thin film diffraction, and reflectivity are routinely performed using Θ-2Θ diffractometers with appropriate attachments and optics. The incorporation of parabolic multilayer optics for powder diffraction has been studied by several groups, with varied results that depend upon the particular application [1][2][3][4][5][6][7][8][9]. Research to date has focused mainly on the use of a parabolic multilayer in the incident beam to collimate the beam, with diffracted-side optics that include either a long soller parallel-plate collimator or collimator with crystal combination [4,6,8,10,11].…”