Recovering local structure information from high-pressure total scattering experiments

High pressure is a powerful thermodynamic tool for exploring the structure and the phase behaviour of the crystalline state, and is now widely used in conventional crystallographic measurements. High-pressure local structure measurements using neutron diffraction have, thus far, been limited by the presence of a strongly scattering, perdeuterated, pressure-transmitting medium (PTM), the signal from which contaminates the resulting pair distribution functions (PDFs). Here, a method is reported for subtracting the pairwise correlations of the commonly used 4:1 methanol:ethanol PTM from neutron PDFs obtained under hydrostatic compression. The method applies a molecular-dynamics-informed empirical correction and a non-negative matrix factorization algorithm to recover the PDF of the pure sample. Proof of principle is demonstrated, producing corrected high-pressure PDFs of simple crystalline materials, Ni and MgO, and benchmarking these against simulated data from the average structure. Finally, the first local structure determination of α-quartz under hydrostatic pressure is presented, extracting compression behaviour of the real-space structure.

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Total scattering experiments on glass and crystalline materials at the ESRF on the ID11 Beamline

Powder Diffraction ◽

10.1017/s0885715614001304 ◽

2014 ◽

Vol 30 (S1) ◽

pp. S2-S8 ◽

Cited By ~ 9

Author(s):

Andrea Bernasconi ◽

Jonathan Wright ◽

Nicholas Harker

Keyword(s):

High Energy ◽

Real Space ◽

European Synchrotron Radiation Facility ◽

Small Sample ◽

Distribution Functions ◽

Total Scattering ◽

Crystalline Materials ◽

Space Resolution ◽

Atomic Pair ◽

Counting Statistics

ID11 is a multi-purpose high-energy beamline at the European Synchrotron Radiation Facility (ESRF). Owing to the high-energy X-ray source (up to 140 keV) and flexible, high-precision sample mounting which allows small sample–detector distances to be achieved, experiments such as total scattering in transmission geometry are possible. This permits the exploration of a wide Q range and so provides high real-space resolution. A range of samples (glasses and crystalline powders) have been measured at 78 keV, first putting the detector as close as possible to the sample (~10 cm), and then moving it vertically and laterally with respect to the beam in order to have circular and quarter circle sections of diffraction rings, with consequent QMAX at the edge of the detector of about 16 and 28 Å−1, respectively. Data were integrated using FIT2D, and then normalized and corrected with PDFgetX3. Results have been compared to see the effects of Q-range and counting statistics on the atomic pair distribution functions of the different samples. A Q of at least 20 Å−1 was essential to have sufficient real-space resolution for both type of samples while statistics appeared more important for glass samples rather than for crystalline samples.

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Relationship between low-Q peak and long-range ordering of ionic liquids revealed by high-energy X-ray total scattering

Physical Chemistry Chemical Physics ◽

10.1039/c5cp01760b ◽

2015 ◽

Vol 17 (27) ◽

pp. 17838-17843 ◽

Cited By ~ 15

Author(s):

Kenta Fujii ◽

Shinji Kohara ◽

Yasuhiro Umebayashi

Keyword(s):

Ionic Liquids ◽

Long Range ◽

High Energy ◽

Real Space ◽

Space Structure ◽

Total Scattering ◽

X Ray ◽

Peak Intensity ◽

Long Range Ordering

A new function, SQpeak(r); a connection between low-Q peak intensity with real space structure.

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Peculiarities in the high-pressure phase behaviour of binary mixtures of nitrogen with methane, helium and water

Journal of Physics Condensed Matter ◽

10.1088/0953-8984/6/23a/027 ◽

1994 ◽

Vol 6 (23A) ◽

pp. A187-A192 ◽

Cited By ~ 3

Author(s):

J A Schouten ◽

M G E van Hinsberg ◽

M I M Scheerboom ◽

J P J Michels

Keyword(s):

High Pressure ◽

Binary Mixtures ◽

Phase Behaviour ◽

High Pressure Phase ◽

Pressure Phase

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NanoPDF64: software package for theoretical calculation and quantitative real-space analysis of powder diffraction data of nanocrystals

Journal of Applied Crystallography ◽

10.1107/s1600576717013152 ◽

2017 ◽

Vol 50 (6) ◽

pp. 1821-1829 ◽

Cited By ~ 6

Author(s):

Kazimierz Skrobas ◽

Svitlana Stelmakh ◽

Stanislaw Gierlotka ◽

Bogdan F. Palosz

Keyword(s):

Powder Diffraction ◽

Diffraction Data ◽

Analytical Formula ◽

Real Space ◽

Distribution Functions ◽

Powder Diffraction Data ◽

Space Analysis ◽

Atomic Vibrations ◽

Hexagonal Close Packed Structure ◽

Diffraction Patterns

NanoPDF64is a tool designed for structural analysis of nanocrystals based on examination of powder diffraction data with application of real-space analysis. The program allows for fast building of models of nanocrystals consisting of up to several hundred thousand atoms with either cubic or hexagonal close packed structure. The nanocrystal structure may be modified by introducing stacking faults, density modulation waves (i.e.the core–shell model) and thermal atomic vibrations. The program calculates diffraction patterns and, by Fourier transform, the reduced pair distribution functionsG(r) for the models. ExperimentalG(r)s may be quantitatively analyzed by least-squares fitting with an analytical formula.

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Crystallography and Diffraction

Principles of Materials Characterization and Metrology ◽

10.1093/oso/9780198830252.003.0004 ◽

2021 ◽

pp. 220-276

Author(s):

Kannan M. Krishnan

Keyword(s):

Rotational Symmetry ◽

Reciprocal Lattice ◽

Real Space ◽

Crystalline Materials ◽

Space Groups ◽

Ewald Sphere ◽

Point Groups ◽

Diffraction Patterns ◽

Point Line ◽

Periodic Arrangement

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

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