X-ray diffraction of bent crystals in Bragg geometry. I. Perfect-crystal modelling

Abstract

X-ray reflectivity, widths, centroid shifts and profiles for curved perfect crystals are calculated from a model. The crystal is approximated by a stack of perfectcrystal lamellae or blocks with a gradually changing (mean) orientation. A computer program has been developed to calculate the above quantities in the Johann geometry for the composite crystal from the dynamic theory of diffraction. Focusing and defocusing aberrations and the use of photographic detection methods are included. Correction of omissions from earlier theory and modelling is noted, together with observed effects. Incoherent scattering can give dramatic changes in diffracted intensities and significant shifts of final parameters. Effects of depth penetration on shifts, cosine ratios and other parameters are included. Assumptions of the model and implementation are detailed. It is shown that interference effects between waves of roughly equal amplitudes require use of lamellar thicknesses greater than those corresponding to the Darwin range. Internal tests demonstrate agreement with the literature at extremes. The theory is applied to first-and fourth-order spectra in differential Lyman ~ wavelength measurements. Resuits for pentaerythritol 002 crystals are presented. Paper II of this series extends this model to nonideally imperfect crystals and other crystals of interest and discusses experimental agreement.

Testing Three-Body Quantum Electrodynamics with TrappedTi20+Ions: Evidence for aZ-dependent Divergence Between Experiment and Calculation

“…Earlier work [8,[13][14][15] demonstrated that a thorough understanding of diffraction conditions, dispersion relations and source systematics can allow the determination of transition energies in highly charged ions to a precision limited by statistics [5,16].…”

“…Because inner shell neutral atomic lines are asymmetric due to underlying atomic processes [19,20], an extensive investigation of Kα peak shapes was undertaken to provide a robust fitting procedure [21] to accurately determine peak profile turning points as well as modelling the doublet as the sum of six Voigt functions. Finally, diffraction angles and detector positions were calculated using a curved crystal dynamical diffraction modelling code [13,14] to determine photon energy as a function of photon diffraction angle and detector position. Figure 1 shows the fitted helium-like Ti spectrum accumulated over several days of experimentation and weeks of calibration.…”

“…Systematic errors in the Ti spectral fit (v) were estimated by an extensive investigation of the effect of changing the assumed form of the fit function, weights, and r-line width in the fit. Statistics relating to the centroid determinations of the calibration lines (vi) and to the dynamical diffraction theory [13,14] and functional form of the dispersion relation (vii) are minor.…”

Simulation of X-ray diffraction profiles for bent anisotropic crystals

“…A detailed description of the assumptions of this method is in (Caciuffo et al, 1987) and (C.T. Chantler, 1990) and a good validation with experiments is in (Erola et al, 1990) …”

A status report on experimental tests of QED in medium-Z systems

“…When labelling a spectral line with a diffraction angle one must consider a modified Bragg law. Curved crystal diffraction modelling code (Chantler, 1992) allows us to quantify and reduce uncertainties of order 200 ppm in the dispersion function determination to around 5 ppm. It is not uncommon for published experimental results to contain no mention of uncertainties due to the spectrometer system used.…”