Optimization of Stepsize in X-Ray Powder Diffractogram Collection

1988 ◽  
Vol 3 (1) ◽  
pp. 32-38 ◽  
Author(s):  
David G. Cameron ◽  
Ernest E. Armstrong
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
X Ray Diffraction ◽  
Step Size ◽  
Reasonable Estimate ◽  
X Ray ◽  
Fourier Transform Methods ◽  
Step Interval ◽  
The Fourier Transform ◽  
Selection Of

AbstractFourier transform methods of smoothing and interpolation are applied to X-ray diffraction data. It is shown that, frequently, too small a step size is used. Major gains are to be expected by selection of the optimum step size and use of these methods.A comparison of Fourier transforms of diffractograms of quartz measured between 67 and 69° 2θ, collected at varying step intervals (0.1 to 0.01° 2θ) was used to illustrate these applications. By examining the Fourier transform of the diffractogram and noting where it decays to die baseline, a reasonable estimate of the optimal step interval can be obtained. In addition, Fourier interpolation can be used to enhance the appearance of the diffractogram, approximating a continuous plot.

Weathering of biotite to vermiculite in Quaternary lahars from Monti Ernici, Central Italy

Clay Minerals ◽  
1992 ◽  
Vol 27 (2) ◽  
pp. 175-184 ◽  
Author(s):  
A. Pozzuoli ◽  
E. Vila ◽  
E. Franco ◽  
A. Ruiz-Amil ◽  
C. De La Calle
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Central Italy ◽  
Small Samples ◽  
X Ray Diffraction ◽  
Transform Methods ◽  
X Ray ◽  
Type Phase ◽  
Fourier Transform Methods ◽  
End Members

AbstractThe weathering of biotite in Quaternary lahars from Monti Ernici (Central Italy) via interstratification stages has been studied by X-ray diffraction of both the interstratified minerals and the initial (biotite) and final (vermiculite) end-members. The structure of the biotite and vermiculite is described by means of monodimensional Fourier series. The interstratified phases have been studied using the INTER program which permits an analysis of two interstratified components by Fourier transform methods. It is shown that in the alteration range for biotite to vermiculite even small samples have different spatial concentrations of biotite, vermiculite and an intermediate biotite-vermiculite-type phase. Hydrobiotite and a rare biotite-hydrobiotite with a tendency to regularity have also been documented. Chemically, the process involves considerable oxidation of Fe2+ and the removal of most of the elements, corresponding to a 34% loss in matter. The sequence of the element losses is: K+ > Fe2+ > F− > Mn2+ > Si4+ > Mg2+ > Al3+ > Ti4+. There are also some gains in the order: H+ > Ca2+ > Fe3+ > Na+.

A study of a long-spacing mica-like mineral

Clay Minerals ◽  
1966 ◽  
Vol 6 (4) ◽  
pp. 261-281 ◽  
Author(s):  
W. F. Cole
Keyword(s):  
Fourier Transform ◽  
Layer Structure ◽  
Compositional Variation ◽  
X Ray Diffraction ◽  
Transform Method ◽  
X Ray ◽  
Single Complex ◽  
New Interpretation ◽  
The Fourier Transform ◽  
Diffraction Effects

AbstractAn interstratified clay mineral from Surges Bay, Tasmania, described by Cole & Carthew (1953) as containing a random stacking of illite and montmorillonite in the ratio of 3:2 and a regular stacking of illite and montmorillonite in the ratio of 1 : 1 is re-examined, after purification, and a new interpretation is made of the X-ray diffraction effects in terms of a single complex stacking model. The Fourier transform method of analysis used with an appropriate layer structure factor shows that the interstratification is produced by a three component stacking of 18% single mica layers (A), 10% double mica layers (ĀĀ) and 72% allevardite-like layers (ĀB̄) in which the A and ĀĀ layers are never together. This leads to the conclusion that the near regular interstratification of the mineral is due to structural and/or compositional variation from layer to layer within the parent crystals as suggested by Sudo, Hayashi & Shimoda (1962) to explain similar mineral types occurring in Japan.

A NANOSTRUCTURED POLYMORPH OF μ-OXOBIS(PHTHALOCYANINATOIRON(III)) STUDIED BY ANGULAR AND ENERGY DISPERSIVE X-RAY DIFFRACTION

NANO ◽  
2007 ◽  
Vol 02 (02) ◽  
pp. 121-128 ◽  
Author(s):  
ROBERTO MATASSA ◽  
PAOLO BALLIRANO ◽  
MARIA PIA DONZELLO ◽  
CLAUDIO ERCOLANI ◽  
CLAUDIA SADUN ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Rietveld Method ◽  
Energy Dispersive ◽  
Structural Function ◽  
X Ray Diffraction ◽  
New Approach ◽  
X Ray ◽  
The Fourier Transform

A new approach of X-ray diffraction was used to investigate the nanostructured μ-Oxo(2) polymorph of μ-oxo-bis(phthalocyaninatoiron(III)), [ PcFe – O – FePc ]. The packing of the dinuclear units was determined by the Rietveld method on Angular Dispersive X-ray Diffraction (ADXD) data, whereas the intramolecular geometry was optimized by Energy Dispersive X-ray Diffraction (EDXD) exploiting the peculiar strength of those techniques. The dimension of the nanoparticles was estimated from the Fourier transform of the EDXD experimental structural function.

scholarly journals Regioselective Approach to Characterizing Increased Edge Availability in Layered Crystal Materials following Layer Expansion: Reaction of Kaolinite with Octadecyltrimethylammonium Salts

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 588
Author(s):  
Shingo Machida ◽  
Ken-ichi Katsumata ◽  
Atsuo Yasumori
Keyword(s):  
Fourier Transform ◽  
Mass Loss ◽  
Nitrogen Content ◽  
Infrared Spectra ◽  
Layered Crystal ◽  
X Ray Diffraction ◽  
X Ray ◽  
Thermogravimetric Curve ◽  
Diffraction Patterns ◽  
The Fourier Transform

In this paper, the regioselective reactions of kaolinite and methoxy-modified kaolinite (MeO-Kaol), methanol-expanded kaolinite, with octadecyltrimethylammonium salts are compared. This study mainly concerns the reactions of kaolinite or MeO-Kaol with octadecyltrimethylammonium chloride (C18TAC) in methanol and the subsequent exhaustive washing of the resultant products with ethanol. X-ray diffraction patterns of the products reveal no intercalation of C18TAC between pristine kaolinite layers. Additionally, intercalation and subsequent deintercalation of C18TAC proceed in the product using MeO-Kaol. In the Fourier-transform infrared spectra, the intensities of CH2 stretching bands of the product prepared using MeO-Kaol drastically increase compared to those using kaolinite. In addition, CH2 stretching bands of the product using kaolinite are hardly observed without enlarging the spectrum. The product using MeO-Kaol also displays mass loss in the range of 200–300 °C in the thermogravimetric curve and a nitrogen content with 0.15 mass% estimated using the CHN analysis. These results therefore demonstrate an increase in the available reactive edges in the layered crystal material following an expansion of the stacked layers.

Röntgen-Beugungsuntersuchungen an Bi-In-Schmelzen / X-Ray Diffraction Experiments with Bi-In-melts

1981 ◽  
Vol 36 (2) ◽  
pp. 150-153 ◽  
Author(s):  
R. Bek ◽  
E. Nold ◽  
S. Steeb
Keyword(s):  
Fourier Transform ◽  
Liquidus Temperature ◽  
X Ray Diffraction ◽  
X Ray ◽  
Coordination Numbers ◽  
Structure Factors ◽  
Concentration Dependency ◽  
The Fourier Transform

Abstract Using MoK α-radiation and a θ-θ diffractometer from molten In and Bi as well as six molten Bi-In alloys (8; 22; 27; 33.3; 50; and 77 at % Bi) intensity curves were obtained at 10 °C above the liquidus temperature. The measurements were performed in the q-region up to 14.5 Å-1. From the Fourier transform of the structure factors coordination numbers NItot and radii rItot were obtained. The concentration dependency of NItot and rItot leads to the conclusion, that the Bi-In melts belong to the compound forming melts.

scholarly journals Pitfalls in the Evaluation of X-ray Diffraction Line Shape

1988 ◽  
Vol 41 (2) ◽  
pp. 237 ◽  
Author(s):  
Gerhard Zorn
Keyword(s):  
Fourier Transform ◽  
Computer Simulations ◽  
Line Shape ◽  
Fourier Transformation ◽  
Step Width ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sampling Points ◽  
The Fourier Transform ◽  
Reliable Basis

The sources of errors in the analysis of X-ray diffraction profiles are described, and recipes are given to minimise or eliminate these errors. It is proposed that a sample at high temperatures is used as a standard. The influence of measurement statistics on the Fourier transform of deconvoluted functions is demonstrated through computer simulations. The necessity for smoothing procedures is stressed. It is shown how the parameter step width, number of sampling points, and position of origin for the Fourier transformation can be optimised, and thus a reliable basis can be created for the interpretation of the Fourier transform in terms of crystallite size, size distribution, and micros train.

Possible Models of Murein and Their Fourier Transforms

1982 ◽  
Vol 37 (3-4) ◽  
pp. 226-235 ◽  
Author(s):  
Helmut Formanek
Keyword(s):  
Fourier Transform ◽  
Cell Walls ◽  
Fourier Transforms ◽  
Elementary Cell ◽  
Two Dimensional ◽  
Density Measurements ◽  
X Ray ◽  
Rigid Layer ◽  
The Fourier Transform ◽  
Almost All

Abstract Murein, Models, Fourier Transforms Murein, the rigid layer of the cell walls of almost all bacteria can be regarded as derivative of chitin. Within the sterically allowed region its polysaccharide chain can perform conformations with two-to threefold screw axes. Two dimensional Fourier transforms calculated from different possible conformations have been compared with data of density measurements, X-ray and electron diffraction. The Fourier transform of murein with a chitin-like conformation of the poly­ saccharide chain and an elementary cell of 4.5 × 10.4 × 21.5 Å3 provides the best agreement with the experimental results.

Thermal and Structural of Methyl Cellulose

2014 ◽  
Vol 979 ◽  
pp. 307-310 ◽  
Author(s):  
W. Siriprom ◽  
S. Kongsriprapan ◽  
K. Teanchai
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Thermo Gravimetric Analysis ◽  
Methyl Cellulose ◽  
Gravimetric Analysis ◽  
X Ray Diffraction ◽  
Biodegradable Film ◽  
Thermo Gravimetric ◽  
X Ray ◽  
The Fourier Transform

The present study aims to investigate the physicochemical properties of the methyl cellulose. The information of this investigate has been used to reference in preparing biodegradable film. It was observed that the Fourier Transform Infrared Spectroscopy (FTIR) spectroscopy show the hydrogen bond’s formation and the Energy Dispersive X-Ray Fluorescence (EDXRF) show the chemical and level of the composition element, which Copper (Cu) has the highest accumulate. Another that, the XRD spectra which investigated by X-Ray Diffraction (XRD) show the methyl cellulose had lowered crystalline. Another that, the Thermo-Gravimetric Analysis (TGA) was used to investigate the effect of heating and influence of thermal.

PREPARATION AND STRUCTURAL CHARACTERIZATION OF NANOCRYSTALLINE Zn–Cu–Cr FERRITES WITH Gd SUBSTITUTION

2010 ◽  
Vol 24 (27) ◽  
pp. 5409-5416 ◽  
Author(s):  
JING JIANG ◽  
CHAOCHAO CHEN ◽  
LUNHONG AI
Keyword(s):  
Fourier Transform ◽  
Spinel Structure ◽  
Remanent Magnetization ◽  
Phase Reaction ◽  
X Ray Diffraction ◽  
Reaction Method ◽  
X Ray ◽  
Magnetic Parameters ◽  
The Fourier Transform

Nanocrystalline spinel Zn – Cu – Cr ferrites with Gd substitution were prepared by a rheological phase reaction method. By means of the Fourier transform infrared (FTIR) spectra, Raman spectra, and X-ray diffraction (XRD), the cubic spinel structure of samples had been confirmed. The magnetic parameters such as saturation magnetization, remanent magnetization and coercivity can be tailored by controlling the content of substituting Gd ions.

Multicomponent Analysis Using Fourier Transform Infrared and UV Spectra

1988 ◽  
Vol 42 (2) ◽  
pp. 353-359 ◽  
Author(s):  
Steven M. Donahue ◽  
Chris W. Brown ◽  
Robert J. Obremski
Keyword(s):  
Factor Analysis ◽  
Fourier Transform ◽  
Fourier Transforms ◽  
Uv Spectra ◽  
Data Sets ◽  
Transform Method ◽  
Multicomponent Analysis ◽  
P Matrix ◽  
The Fourier Transform ◽  
Selection Of

Two- and three-component mixtures of methylated benzenes were analyzed with the use of both infrared and UV spectra. The spectra of known mixtures were Fourier transformed and coefficients from the transforms selected to form coordinates of vectors. The resulting vectors were subjected to factor analysis to obtain representations for multicomponent analysis. A total of eight data sets were analyzed by factor analysis after preprocessing by taking the Fourier transforms of the spectra. The eight data sets were also analyzed by the P-matrix method (inverse Beer's law) in the spectral domain after preprocessing of the data to allow selection of the optimum analytical wavenumbers. This spectral method was compared to the Fourier transform method using cross-validation, in which one sample at a time was left out of the standards and treated as an unknown. The Standard Error of Prediction (SEP) was calculated for the two methods for all possible numbers of vectors and numbers of wavenumbers, starting with the number equal to the number of components and increasing up to a total number of standards or some reasonable cut-off value. Processing in the Fourier domain clearly produced the best results for seven of the data sets and equal results for the other set.

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