Probing a crystal's short‐range structure and local orbitals by Resonant X‐ray Diffraction methods

Abstract

Diffraction Anomalous Fine Structure (DAFS) combines the long‐range, crystallographic sensitivity of X‐ray diffraction with the short‐range sensitivity of X‐ray Absorption Spectroscopy (XAS). In comparison to other spectroscopic methods, DAFS can additionally distinguish phases of different translational symmetry by choice of momentum transfer, or isolate spectra from chemically identical atoms on various Wyckoff sites of a crystal's structure using crystallographic weights. The Anisotropy of Anomalous Scattering (AAS) extends the concept of isotropically scattering atoms to a more general case, where the atom's scattering characteristics depend on the polarization as well as the wavevector of the incident and scattered X‐rays. These can be written as tensors that reflect the local site symmetries of the resonant atom. Forbidden Reflection Near‐Edge Diffraction (FRED) is an elegant way to measure AAS by using reflections that are extinguished in the special case of isotropically scattering atoms. They can only be observed due to the non‐isotropic contributions at photon energies in the vicinity of an absorption edge where electronic transitions occur. Combining the site selectivity of DAFS with the information accessible through AAS allows probing the short‐range order and local orbitals of selected atoms in a crystal structure of a chosen phase. The present condensed review gives a brief overview on the pioneer work, the theory and sensitivities as well as selected recent applications of these powerful and promising Resonant X‐ray Diffraction (RXD) methods. Additionally, some recent work of the authors is included exemplarily for the model structure rutile TiO2 presenting the progress in measurement and interpretation.

Harmonic Principles of Elemental Crystals—From Atomic Interaction to Fundamental Symmetry

“…The presented considerations may give rise to optimization of pair potentials beyond the scope of the Standard Morse Potential, which is widely used, e.g., in Molecular Dynamic Simulations [33] and Bond Valence Methods [34]. Enhanced potentials with a broad flexibility, which can be determined from structural data of large structure databases like the ICSD [35], may then present a convenient way to tackle free internal parameters in structure determination, without computationally expensive quantum-electronic calculations like density functional theory (DFT, see e.g., [36]) or modern synchrotron methods like Resonant X-ray Diffraction [37,38]. Table 2.…”

Picometer polar atomic displacements in strontium titanate determined by resonant X-ray diffraction

“…Today, the field of resonant X-ray diffraction (RXD) spans a set of techniques based on the different dependencies in the resonant atomic scattering amplitude 1 , 2 . The variation in its real and imaginary part is used for contrast enhancement of atoms with similar 3 or even equal 4 number of electrons, or to solve the phase problem in crystallography 5 , 6 .…”

Sample chamber for synchrotron based in-situ X-ray diffraction experiments under electric fields and temperatures between 100 K and 1250 K

“…For instance, the low-temperature regime allows the separation of thermal-motion-induced contributions (Ovchinnikova et al, 2005(Ovchinnikova et al, , 2010 and point-defect-induced contributions (Dmitrienko & Ovchinnikova, 2003;Ovchinnikova et al, 2005) to the reflection intensity. This separation is particularly important while measuring RXD at 'forbidden' reflections, which is a powerful technique to study atomic displacements (Richter et al, 2014(Richter et al, , 2018 and the local electronic structure of selected atomic positions in crystals (Zschornak et al, 2014).…”

“…For instance, we can determine pyroelectric coefficients using the Sharp- Garn method (Sharp & Garn, 1982;Garn & Sharp, 1982) or characterize ferroelectric hysteresis loops (Sawyer & Tower, 1930), by implementing well defined, alternating temperature and/or electrical functions. In parallel, crystal structure analysis is possible via standard XRD or in combination with resonant techniques like X-ray absorption fine structure, and resonant X-ray diffraction (RXD) (Zschornak et al, 2014;Richter et al, 2018) comprising various kinds of scans such as energy, azimuthal, and rocking scans. For instance, a simultaneous structural and electrical characterization of pyroelectrics was discussed recently, where the spontaneous polarization is determined from structure as a function of temperature using a semi-theoretical approach based on Born effective charges from density functional theory calculations (Weigel, 2016).…”