X-Ray Measurement of the Static Lattice Distortion in the Solid Solution of Oxygen in Titanium*

1962 ◽  
Vol 6 ◽  
pp. 136-141
Author(s):  
F. R. L. Schoening ◽  
F. Witt
Keyword(s):  
Single Crystal ◽  
Oxygen Concentration ◽  
Waller Factor ◽  
Interstitial Oxygen ◽  
Exponential Factor ◽  
X Ray ◽  
X Ray Scattering ◽  
Lattice Strains ◽  
Debye Waller Factor ◽  
Oxygen Atoms

AbstractOxygen was introduced into a single crystal of titanium in successive stages. The intensities of the h00 and 00l reflections were measured with a single-crystal diffractometer. The observed variation of the intensities with oxygen concentration was attributed to three factors: (1) the additional scattering from the oxygen atoms, (2) a change in the Debye-Waller factor, and (3) an exponential factor originating from the distortion around the oxygen atom. The theory of X-ray scattering from crystals containing centers of distortion was applied to the hexagonal titanium containing interstitial oxygen atoms. Using the variation of the lattice constant with oxygen concentration, it was possible to predict the intensity reduction due to lattice strains. It was concluded that it would have been possible to obtain an estimate of the defect concentration from the X-ray measurements of lattice expansion and intensity reduction.

In Situ Observation of the Oxygen Nucleation in Silicon with X-Ray Single Crystal Diffraction

2011 ◽  
Vol 178-179 ◽  
pp. 353-359 ◽  
Author(s):  
Johannes Will ◽  
Alexander Gröschel ◽  
Christoph Bergmann ◽  
Andreas Magerl
Keyword(s):  
Single Crystal ◽  
Waller Factor ◽  
Dynamical Theory ◽  
Mean Value ◽  
Single Crystal Diffraction ◽  
X Ray ◽  
Float Zone ◽  
Debye Waller Factor ◽  
The Mean

The measurement of Pendellösungs oscillations was used to observe the time dependent nucleation of oxygen in a Czochralski grown single crystal at 750°C. It is shown, that the theoretical approach of the statistical dynamical theory describes the data well. Within the framework of this theory it is possible to determine the static Debye-Waller-factor as a function of the annealing time by evaluating the mean value of the Bragg intensity and the period length. The temperature influence on the Pendellösungs distance was corrected for by measurement of a Float-zone sample at the same temperature.

Interference Effects in Neutron and X Ray Scattering

1974 ◽  
Vol 52 (22) ◽  
pp. 2281-2298 ◽  
Author(s):  
H. R. Glyde
Keyword(s):  
Phonon Scattering ◽  
Sum Rules ◽  
Waller Factor ◽  
Interference Term ◽  
Scattering Intensity ◽  
X Ray ◽  
X Ray Scattering ◽  
Debye Waller Factor ◽  
The One ◽  
Ray Scattering

The properties of interference between the one and multiphonon contributions to the dynamic and static scattering functions, S(Q, ω) and S(Q), first considered by Ambegaokar et al., are discussed in detail for b.c.c 3He and 4He for comparison with recent neutron and proposed X ray scattering experiments. Calculations of interference for Na and of the Debye temperature appropriate to the Debye–Waller factor in b.c.c 3He are also presented. In all cases the on shell interference term which alters the one phonon scattering intensity is found to be more important than the off shell term which alters the one phonon line shape. This is characteristic of systems in which anharmonic effects produce a large phonon frequency shift but in which the phonon lifetimes remain long. The difficulty in establishing the one phonon sum rules experimentally in the presence of interference is emphasized. As noted by Horner, existing unusual variations of scattering intensity observed in solid 4He can be satisfactorily explained by taking account of interference and this difficulty without introducing an anomolous Debye–Waller factor. Comparisons with liquid 4He suggest a similar difficulty in establishing the sum rules there.

Diffuse x-ray scattering study of single crystal alpha-AgI

1983 ◽  
Vol 9-10 ◽  
pp. 1347-1351 ◽  
Author(s):  
R.J Cava ◽  
R.M Fleming ◽  
E.A Rietman
Keyword(s):  
Single Crystal ◽  
X Ray ◽  
X Ray Scattering ◽  
Scattering Study ◽  
Ray Scattering

scholarly journals Atomic structure and phason modes of the Sc–Zn icosahedral quasicrystal

IUCrJ ◽  
2016 ◽  
Vol 3 (4) ◽  
pp. 247-258 ◽  
Author(s):  
Tsunetomo Yamada ◽  
Hiroyuki Takakura ◽  
Holger Euchner ◽  
Cesar Pay Gómez ◽  
Alexei Bosak ◽  
...  
Keyword(s):  
Atomic Structure ◽  
Diffuse Scattering ◽  
Waller Factor ◽  
Close Packing ◽  
Icosahedral Quasicrystal ◽  
X Ray Diffraction ◽  
X Ray ◽  
Large Atom ◽  
Debye Waller Factor ◽  
The Difference

The detailed atomic structure of the binary icosahedral (i) ScZn7.33quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33and i-YbCd5.7was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constantsK2/K1= −0.53,i.e.close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye–Waller factor, which explains the vanishing of `high-Qperp' reflections.

scholarly journals IYCr Open Factory: Inviting Young Crystallographers to Europe – Status & Outlook

2014 ◽  
Vol 70 (a1) ◽  
pp. C1802-C1802
Author(s):  
Martin Fark ◽  
Jens Richter ◽  
Christian Brönnimann ◽  
Clemens Schulze-Briese ◽  
Peter Høghøj ◽  
...  
Keyword(s):  
Single Crystal ◽  
Small Angle ◽  
Practical Training ◽  
X Ray ◽  
Intensive Training ◽  
High Interest ◽  
X Ray Scattering ◽  
The Status ◽  
Future Events

The STOE DECTRIS Xenocs OpenFactory will take place from 10 to 19 September 2014. Participants receive seven days of intensive training by STOE, DECTRIS and Xenocs staff and guest scientists in cooperation with the IUCr. The training will focus on teaching participants the relevant theoretical skillset as well as giving practical training. In Grenoble, the delegates will spend significant time at the ESRF (European Synchrotron) and will be trained in Small Angle X-ray scattering at Xenocs' headquarters. In Darmstadt, the participants will be trained in Single Crystal and Powder XRD at STOE's headquarter. Delegates will have the opportunity to visit beamlines and interact with scientists at ESRF. Starting on 18 September, all OpenFactory participants will join the STOE annual user meeting. The user meeting is a platform for the exchange of ideas among its participants as well as speeches to highlight recent research results. It will be a unique opportunity for OpenFactory participants to interact with highly experienced XRD users and to build up relevant networks. This presentation and poster will highlight the activity, the focus of the program and present the selected participants for the OpenFactory event. The intention is to update on the status of the OpenFactory, but even more important, to encourage similar activities within and after the International Year of Crystallography. In this context, the presenter will discuss any insights from the applications received, i.e. geographies with particular high interest in the OpenFactory, which could be used to follow up on the OpenFactory with future events.

scholarly journals Phase transitions in Zr-rich lead zirconate-titanate studied by single-crystal diffuse and inelastic X-ray scattering

2019 ◽  
Vol 75 (a2) ◽  
pp. e429-e429
Author(s):  
Daria Andronikova ◽  
Iurii Bronwald ◽  
Alexei Bosak ◽  
Dmitry Chernyshov ◽  
Alexey Filimonov ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Single Crystal ◽  
Lead Zirconate Titanate ◽  
Lead Zirconate ◽  
X Ray ◽  
X Ray Scattering ◽  
Zirconate Titanate ◽  
Ray Scattering

Absorption Coefficients of Inelastic Dynamic X-Ray Diffraction

2014 ◽  
pp. 483-502
Keyword(s):  
Absorption Coefficient ◽  
Inelastic Scattering ◽  
Waller Factor ◽  
Time Dependent ◽  
X Ray Diffraction ◽  
Absorption Coefficients ◽  
X Ray ◽  
Charge Current ◽  
Dispersion Equations ◽  
Debye Waller Factor

The X-ray inelastic scattering phenomena during the time-dependent perturbations are described with the aid of dynamical dispersion equations coupled with charge current in the Maxwell equations towards the appearance of the Debye-Waller factor driving the absorption coefficient, either for inelastic thermal diffusion and the Compton scattering, respectively.

Two Modifications of Hg5Re2O10

1995 ◽  
Vol 50 (9) ◽  
pp. 1335-1339 ◽  
Author(s):  
Marietta S. Schriewer-Pöttgen ◽  
Wolfgang Jeitschko
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Elemental Mercury ◽  
Oxidation States ◽  
X Ray ◽  
Structure Factors ◽  
Oxygen Atoms

AbstractThe previously reported mercury perrhenate Hg5Re2O10, prepared hydrothermally, has now been obtained by reaction of HgO with the mercury(II) metaperrhenate Hg(ReO4)2 in sealed silica tubes. A second modification of this compound can be obtained by reaction of elemental mercury with Hg(ReO 4)2 also in sealed silica tubes. Its crystal structure has been determined from single-crystal X-ray data: P21/c, a - 861.5(1), b = 1200.9(2), c = 1203.9(2) pm, β = 97.15(1)°, Z = 4, R = 0.024 for 1733 structure factors and 105 variables. Both modifications may be represented by the formula Hg2+-2Hg2O - 2ReO4-, indicating that mercury occurs in oxidation states I and II. In both modifications the mercury and some oxygen atoms form two-dimensionally infinte, puckered, cationic nets of the composition (Hg2+-2Hg2O)n , which are separated by the ReO4- tetrahedra. In the modification reported earlier the mercury oxygen nets consist of condensed 16-membered rings, while the nets of the present modification contain 10- and 22-membered rings.

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