The analytical calculation of absorption in multifaceted crystals

Abstract

The optimal c~ and/3 values can be calculated then as ot= v/u, fl= 1/u 2.In the vicinity of u = B -l/z, v = O, Q(u, v) = (-lnB -1) -2B(u --B-I/2) zso if ~ < 0 this point is the maximum point, but if > 0 this is a saddle point and the maximum is attained at a point corresponding to the nontrivial solution of G(t) = 0. A2. Mathematical analysisWe exclude from the analysis the singular case when there exists a scale factor ). such that Fi °bs = 2F~ °~ for all the reflections, i.e. the model is ideal.The function G(t) is even, so we can consider it for t > 0 only.It is easy to see that G(t) -0 always has the trivial solution t --0, i.e. v = O, u --B -i/2 or a = 0, t5 = B.Using asymptotic formulae for the modified Bessel functions, we can obtain, for small values of t,and, for large t, lim(1/t)G(t) = 2[(AB) !/2 -C].(33)The value of (AB) 1/2 -C is always positive owing to Cauchy inequality, so G(t) = 0 has at least one nontrivial solution if the value I2 = D -ABis positive. It is possible to show, too, that the function Q(u, v) tends to -o~ when the point (u, v) tends to infinity. So, the maximum value is attained at an inner point. AbstractThe exact analytic method of evaluating the absorption during scattering in multifaceted convex crystals is developed in a way that permits efficient computation.

Structural and thermodynamic properties of molecular complexes of aluminum and gallium trihalides with bifunctional donor pyrazine: decisive role of Lewis acidity in 1D polymer formation

“…Either semi-empirical 37 or analytical absorption corrections from crystal faces 38 were applied. The structures were solved by direct and chargeflipping methods, respectively.…”

Synthesis, Characterization, and Biological Evaluation of New Ru(II) Polypyridyl Photosensitizers for Photodynamic Therapy

“…The selected suitable single crystal was mounted using polybutene oil on a flexible loop fixed on a goniometer head and immediately transferred to the diffractometer. Pre-experiment, data collection, data reduction and analytical absorption correction 96 were performed with the program suite CrysAlisPro. 97 Using Olex2, 98 (Gibco) with 5% fetal calf serum (FCS, Gibco), 100 U/ml penicillin, 100 μg/ml streptomycin at 37°C and 5% CO2.…”

Refinement of iron ore sinter phases: a silico-ferrite of calcium and aluminium (SFCA) and an Al-free SFC, and the effect on phase quantification by X-ray diffraction

“…Subsequent integration and data reduction was performed with the CrysAlis Pro software package (Agilent 2012). Data reduction included Lorentz and polarization corrections and an analytical absorption correction using accurately measured external faces based on the procedure of Clark and Reid (1995). For the calculation of the linear absorption coefficient the results from the chemical analysis were used.…”