Theory of X-ray scattering in the anomalous dispersion region and the problem of atomic-ternary-correlation-function determination in amorphous media

Abstract

A new method for x-ray atomic scattering factor (ASF) calculations in solids is proposedwhichenablesone toobtainimaginaryandrealpartsofthens~without Kramers-Kr6nig transformation in the anomalous dispersion region (both in XANES and EYAFS regions). Themethodproposedallowsfor the inclusionottheenvironmentalinikenceupon the ASF of the atoms in solids. Due to such influence, Asf in general becomes an anisotropic tensor. Asan example, the ASF tensor componentsofa boronatom ina hexagonal BNcrystal are calculated near the BK absorption edge. Imaginary parts of the ASF tensor components are employed to calculate the XANES which appears to be in reasonable agreement with experiment. The formulae for the intensity of x-ray diffraction from a homoatomic thin amorphous sample in a K-edge EMS region are obtained. The environmental influence upon the ASF causes the fine structure in the frequency dependence of the x-ray diffraction intensity. This fine structure together with the angular dependence of diffraction intensity is shown to provide valuable information about atomic ternary correlation functions of amorphous media.If the photon energy is close to the K absorption edge, the second term in (2) is small and the anomalous part of the ASF can be written as follows:where ro is the electron classical radius, m is the electron mass and c i s the velocity of light.

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

“…From Fig. 3, one also gets an impression of the quality of modern ASF calculations using the muffin-tin (MT, Vedrinskii et al, 1992) and full-potential (FP, Taillefumier et al, 2002) …”

“…Several codes have been developed for this type of calculation in the XANES region (Natoli et al, 1990;Vedrinskii et al, 1992;Ankudinov et al, 1998;Benfatto & Felici, 2001;Joly, 2001;Taillefumier et al, 2002), which, in principle, allow for a quantitative description of the ASF tensor (see examples below). However, in practice, this description must be improved with respect to the experimental energy profiles.…”

“…Inclusion of the possibility that both terms suffer the same thermal 'fall-off' caused by the Debye-Waller factor [expðÀ2MÞ] allowed the observations to be remarkably well fitted from 59 to 800 K. Thus, the phenomenological fitting gives a good explanation of the temperature effects, both for Ge and for ZnO, but it cannot describe the energy dependence. In recent contributions Dmitrienko et al, 2004;Ovchinnikova, Oreshko et al2005), numerical calculations were performed with the help of the codes developed by Vedrinskii et al (1992), Joly (2001) and Taillefumier et al (2002). These calculations, which allow for quantitative fitting of the experimental data, show the high sensitivity of ASF to atomic displacements.…”

Resonant diffraction inFeS2:Determination of the x-ray polarization anisotropy of iron atoms

“…Different approaches are suggested and implemented in computer codes. [31][32][33][34][35][36] Their application to a nontrivial object would be very interesting, but, for the beginning, for a case with a not too complicated structure. For this purpose, transition-metal disulfides with pyrite structure (FeS 2 , NiS 2 , CoS 2 , etc.͒ seem to be good candidates: they exhibit a wide variety of electronic, optical, magnetic, and chemical properties which have been subjects of many investigations, both fundamental and practical.…”

Resonant X-ray diffraction: Basic theoretical principles

“…Readers can find detailed description by Natoli and coworkers [31] or Brouder [25]. It is the main theory used in many codes as FEFF [16], MXAN [22] or KXQX [23] and one of the two used in FDMNES [30].…”