Anisotropy of Anomalous Scattering: a tool for phase information

1998 ◽  
Vol 213 (6) ◽  
Author(s):  
A. Kirfel ◽  
R. Fischer
Keyword(s):  
Resonance Effect ◽  
Resonant Scattering ◽  
Anomalous Scattering ◽  
Phase Information ◽  
Partial Structure ◽  
Conventional Model ◽  
Present Contribution ◽  
Total Structure Factor ◽  
Total Structure ◽  
Centrosymmetric Structure

AbstractAnisotropy of Anomalous Scattering (AAS) is a resonance effect that can occur in the vicinity of an absorption edge of a bonded atom. The description of scattering requires a generalized scattering model showing that, in principle, all single crystal reflections become dependent on the rotation of the crystal about the scattering vector. In addition, it is well known that ’forbidden‘ reflections being systematically extinct in the conventional model can be excited and used to derive information about the absorbing element partial structure. The present contribution suggests for a centrosymmetric structure that also relative total structure factor sign information can be extracted from the intensity variations of allowed central lattice row reflections, provided the resonant scattering partial structure is known.

The structure of molten and glassy 2:1 binary systems: an approach using the Bhatia—Thornton formalism

1992 ◽  
Vol 437 (1901) ◽  
pp. 591-606 ◽  
Keyword(s):  
Structure Factor ◽  
Binary Systems ◽  
Range Order ◽  
Partial Structure ◽  
Systematic Analysis ◽  
Glass Forming ◽  
Structure Factors ◽  
Total Structure Factor ◽  
Diffraction Patterns ◽  
Total Structure

A systematic analysis of those liquid binary 2:1 systems (denoted MX 2 ), for which experimental partial structure factors are available from the isotopic substitution method in neutron diffraction, is made using the Bhatia-Thornton (BT) formalism.Particular attention is paid to the origin of the first sharp diffraction peak (FSDP ), which occurs in the measured diffraction patterns for some of the MX 2 systems, since it appears, from recent studies, that this feature is a signature of directional bonding. It is found that FSDPS can occur in all three BT partial structure factors S xB (k). A FSDP feature in the concentration-concentration partial structure factor S cc (k) is not, however, pronounced except in the case of MgCl 2 and the glass forming network melts ZnCl 2 and GeSe 2 . To the extent that these systems can be regarded as ionic melts a FSDP in S cc (k) implies a non-uniformity in the charge distribution on the scale of the intermediate-range order (IRO). The structure of molten GeSe 2 is compared with the structures of molten ZnCl 2 , glassy GeS 2 and glassy Si0 2 . Although the GeSe 2 and ZnCl 2 melts have different short-range order, there are similarities in the observed IRO which can be attributed to the arrangement of the electropositive species M. The essential features of the measured total structure factor for glassy GeS 2 can be reproduced by using the molten GeSe 2 S zB (k). This result lends support to the notion that the S zB (k) for liquid GeSe 2 (and ZnCl 2 ) are characteristic of both the liquid and glassy states of other network glass forming systems. The structures of molten GeSe 2 (or ZnCl 2 ) and glassy Si0 2 are, however, found to be different. The observed discrepancies are largest in the region of the FSDP which signifies pronounced differences in the nature of the IRO for these systems.

The Second Hydration Shell of Li+ in Aqueous LiI from X-Ray and MD Studies

1981 ◽  
Vol 36 (10) ◽  
pp. 1076-1082 ◽  
Author(s):  
T. Radnai ◽  
G. Pálinkás ◽  
Gy I. Szász ◽  
K. Heinzinger
Keyword(s):  
Hydration Shell ◽  
Distribution Functions ◽  
Dynamics Simulation ◽  
Scattering Data ◽  
Water Molecules ◽  
Radial Distribution Functions ◽  
Partial Structure ◽  
X Ray ◽  
Total Structure ◽  
First Hydration Shell

Indications from a molecular dynamics simulation of a 2.2 molal LiI solution of the existence of a second hydration shell of Li+ have been checked by an x-ray investigation of the same solution. The scattering data are analysed via partial structure functions and radial distribution functions which have been obtained from a model fitted to the total structure function. Experiment and simulation agree on first neighbor ion-water distances. An octahedral arrangement of six water molecules in the first hydration shell of Li+ and additional twelve water molecules in the second shell have been verified by the experiment.

The information available from anomalous scattering on fibres at different wavelengths

1987 ◽  
Vol 20 (4) ◽  
pp. 295-299 ◽  
Author(s):  
C. Nave
Keyword(s):  
Absorption Edge ◽  
Heavy Atom ◽  
Imaginary Component ◽  
Anomalous Scattering ◽  
Phase Problem ◽  
Phase Information ◽  
Helical Symmetry ◽  
X Ray ◽  
The Real ◽  
X Ray Scattering

The contribution of a particular atom in a molecule to the total X-ray scattering can be altered by varying the wavelength in the region of the absorption edge of the atom. It is shown that only the changes in the real part of the anomalous scattering of the atom provide significant changes in a pattern from a fibre containing molecules with helical symmetry. Changes due to the imaginary component are small and Friedel differences cannot be observed, owing to the fibre disorder. The information which can be obtained is equivalent to that given by a truly isomorphous heavy-atom derivative. For the general case this is not sufficient to provide unambiguous phase information. If a twofold axis is present at right angles to the fibre axis then the amplitudes are real and the phase problem can, in favourable cases, be solved.

Schallgeschwindigkeitsmessung in Bi-Cu Schmelzen zur Bestimmung der Kompressibilität und der partiellen Strukturfaktoren / Sound Velocity, Compressibility, und Partial Structure Factors (q = 0) in Bi-Cu Melts

1974 ◽  
Vol 29 (12) ◽  
pp. 1890-1897 ◽  
Author(s):  
Helmut Ebert ◽  
Jochen Höhler ◽  
Siegfried Steeb
Keyword(s):  
Sound Velocity ◽  
Linear Combination ◽  
Transition Region ◽  
Density Fluctuations ◽  
Partial Structure ◽  
Cu Alloys ◽  
Structure Factors ◽  
Velocity Of Ultrasound ◽  
Total Structure ◽  
Versus Concentration

The adiabatic velocity of ultrasound in molten Bi-Cu alloys was measured at various concentrations and temperatures. For the alloys with concentrations between 40 and 80 a/0 Cu the μ(T)- curves consist of two linear regions with a transition region. Within the concentration range mentioned ⊿u/⊿T and the compressibility show respectively positive and negative deviations from linearity. The deviations can be detected at temperatures up to 1200 C. The total structure factors I(O) for Bi and Cu as well as the partial structure factors aij(O) were obtained. aCuCu(O) shows rather high values, indicating the existence of inhomogeneities containing mainly Cu-atoms. The slope of ⊿Nj' [which is a linear combination of the aij (O)] versus concentration is negative. From this fact follows that segregation must exist in these melts. This also follows from the rather large density fluctuations given by the partial factors SCC(O) obtained in this work.

Determination of anomalous scattering factors from X-ray resonant-scattering-induced Pendellösung fringes: Ge

1990 ◽  
Vol 46 (12) ◽  
pp. 945-948 ◽  
Author(s):  
T. Fukamachi ◽  
M. Yoshizawa ◽  
K. Ehara ◽  
T. Kawamura ◽  
T. Nakajima
Keyword(s):  
Resonant Scattering ◽  
Anomalous Scattering ◽  
X Ray

Anomalous dispersion techniques

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Refractive Index ◽  
Field Strength ◽  
Natural Frequencies ◽  
Resonance Effect ◽  
Anomalous Dispersion ◽  
Index Of Refraction ◽  
Primary Beam ◽  
Negative Slope ◽  
Anomalous Scattering ◽  
Atomic Electrons

The term anomalous scattering originates from the first research on light dispersion in transparent materials. It was found that, in general, the index of refraction increases when the wavelength decreases (this was considered to be normal). It was also found that, close to the absorption edges, the refractive index shows a negative slope, and this effect was called anomalous. Today, it is clear that anomalous dispersion is a resonance effect. Indeed, atomic electrons may be considered to be oscillators with natural frequencies; they are bound to the nucleus by forces which depend on the atomic field strength and on the quantum state of the electron. If the frequency of the primary beam is near to some of these natural frequencies, resonance will take place (the concept of dispersion involves a change of property with frequency).

Isotopic quantum effects in the structure of liquid ethanol

2002 ◽  
Vol 80 (9) ◽  
pp. 1059-1068 ◽  
Author(s):  
B Tomberli ◽  
C J Benmore ◽  
J Neuefeind ◽  
P A Egelstaff
Keyword(s):  
Room Temperature ◽  
Gamma Ray ◽  
Ambient Pressure ◽  
High Energy ◽  
Radiation Scattering ◽  
Structure Factors ◽  
Structural Differences ◽  
Order Of Magnitude ◽  
Total Structure Factor ◽  
Total Structure

High-energy electromagnetic-radiation-scattering techniques have been used to measure the structural differences between five isotopic samples of ethanol (CH3CH2OH, CD3CD2OD, CD3CH2OH, CH3CH2OD, and CH3CD2OH) at room temperature and ambient pressure. The differences in the X-ray structure factors between several pairs of isotopes, ΔSX(Q), are shown to have maximum amplitudes that are on the order of a few percent compared to the total structure factor for CH3CH2OH. Our uncertainties are an order of magnitude smaller than those of early gamma-ray measurements on methanol (C.J. Benmore and P.A. Egelstaff. J. Phys. Condens. Matter, 8, 9429 (1996)). These studies have shown that isotopic structural differences in room-temperature ethanol vary as a function of substitution site and are in qualitative agreement with similar differences found in liquid methanol. PACS Nos.: 61.20-p, 61.25E, 61.10-E

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