GENEFP: a full-profile fitting program for X-ray powder patterns using the genetic algorithm

2006 ◽  
Vol 39 (4) ◽  
pp. 615-617 ◽  
Author(s):  
Zhen Jie Feng ◽  
Cheng Dong
Keyword(s):  
Genetic Algorithm ◽  
Grain Size ◽  
Least Squares ◽  
Global Extremum ◽  
X Ray ◽  
Fundamental Parameters ◽  
Profile Fitting ◽  
Full Profile ◽  
Integrated Intensities

GENEFPis a full-profile fitting program, employing a fundamental-parameters method, for Cu-target X-ray powder patterns. In this program, the Le Bail method is used to determine integrated intensities and the genetic algorithm is used to search for the proper fundamental parameters. When some parameters, such as the grain size, have large uncertainties, the genetic algorithm has an advantage over conventional least-squares methods in finding the global extremum.

A Minicomputer and Methodology for X-Ray Analysis

1979 ◽  
Vol 23 ◽  
pp. 313-316 ◽  
Author(s):  
W. Parrish ◽  
G. L. Ayers ◽  
T. C. Huang
Keyword(s):  
Thin Film ◽  
Quantitative Analysis ◽  
Data Reduction ◽  
Fluorescence Spectrometry ◽  
Small Computer ◽  
X Ray ◽  
Fundamental Parameters ◽  
Profile Fitting ◽  
Fitting Method ◽  
Integrated Intensities

AbstractThis paper outlines the use of an IBM Series/1 small computer for instrument automation and data reduction for X-ray polycrystalline diffractometry and wavelength dispersive X-ray fluorescence spectrometry. The profile fitting method is used to determine 2θ, d and relative peak and integrated intensities in diffraction, and the fundamental parameters method (LAMA program) is used for quantitative analysis of bulk and thin film samples. The methods are precise and rapid.

Crystal-structure refinement by profile fitting and least-squares analysis of powder diffractometer data

1983 ◽  
Vol 16 (6) ◽  
pp. 611-622 ◽  
Author(s):  
G. Will ◽  
W. Parrish ◽  
T. C. Huang
Keyword(s):  
Least Squares ◽  
Structure Refinement ◽  
Specimen Preparation ◽  
Crystal Structure Refinement ◽  
Instrument Function ◽  
X Ray ◽  
Profile Fitting ◽  
Fitting Method ◽  
The Individual ◽  
Integrated Intensities

The refinement of crystal structures using X-ray powder data in a two-stage method is described. (1) The integrated intensities of the individual reflections are derived by a profile fitting method in which the profile shapes are accurately defined using an experimentally determined instrument function and the sum of Lorentzian curves. (2) These values are then used in a powder least-squares refinement for structure determination. The results obtained with three simple structures (silicon, quartz and corundum) gave R(Bragg) values of 0.7 to 2.5%. The necessity of correcting for preferred orientation and the importance of proper specimen preparation are also discussed.

An Evaluation of Some Profile Models and the Optimization Procedures Used in Profile Fitting

1982 ◽  
Vol 26 ◽  
pp. 73-80 ◽  
Author(s):  
Scott A. Howard ◽  
Robert L. Snyder
Keyword(s):  
Least Squares ◽  
Efficient Method ◽  
Optimization Algorithm ◽  
Optimization Technique ◽  
Silicon Sample ◽  
X Ray Diffraction ◽  
Profile Function ◽  
X Ray ◽  
Profile Fitting ◽  
Time Required

AbstractThis paper examines some of the concerns regarding the development of an algorithm for the refinement of X-ray diffraction profiles. The object of the algorithm is to provide a time efficient method of refinement through the choice of a suitable profile function and optimization technique.Seven profile models were tested using a least-squares error criterion for refinement. Profile parameters were refined using non-linear Gauss-Newton, Marquardt and Simplex algorithms. The profiles were refined on a pattern digitally collected from an NBS 640A silicon sample.The results of this study indicate the repetitive function evaluations are not necessarily the time consuming step in the profile fitting process. As the number of parameters needed to evaluate the profile and the number of points in the profile increases, the time required to perform the mathematics in the Gauss-Newton and Marquardt algorithms increases. Although the Simplex was most memory and time efficient, our Gauss-Newton optimization algorithm provided a more consistent set of refined values which were not as dependent on the initial estimates of the parameters.The most favorable results were obtained by using the split Pearson VII profile with the alpha 2 reflection fixed in position and intensity with respect to the alpha 1 reflsction. This method generated the lowest residual error and was found to avoid some problems resulting from the alpha 1, alpha 2 line overlap.

A fundamental parameters approach to X-ray line-profile fitting

1992 ◽  
Vol 25 (2) ◽  
pp. 109-121 ◽  
Author(s):  
R. W. Cheary ◽  
A. Coelho
Keyword(s):  
Line Profile ◽  
Incident Beam ◽  
Slit Width ◽  
Multilinear Regression ◽  
Double Crystal ◽  
X Ray ◽  
Fundamental Parameters ◽  
Emission Profile ◽  
Profile Fitting ◽  
Slit Length

A convolution approach to X-ray powder line-profile fitting is developed in which the line shape is synthesized from the Cu Kα emission profile, the dimensions of the diffractometer and the physical variables of the specimen. In addition to the integrated intensities and 2θ positions of the line profiles, the parameters that may be fitted include the receiving-slit width, the receiving-slit length, the X-ray-source size, the angle of divergence of the incident beam, the X-ray attenuation coefficient of the specimen and the crystallite size. This is a self-consistent approach to fitting as the instrumental parameters are usually known by direct measurement. To minimize correlation between refined instrumental parameters, profiles at high and low 2θ values should be fitted simultaneously. The Cu Kα emission profile used in this work is based on recent monolithic double-crystal spectrometer measurements that have identified a doublet structure in both the Kα 1 and Kα 2 components. Fast and accurate convolution procedures have been developed and a mixture of multilinear regression and Gauss–Newton non-linear least squares with numerical differentials is used for fitting the profiles. The method is evaluated by fitting powder diffraction data from well crystallized specimens of MgO and Y3Al5O12 (YAG). Testing has also been carried out by examining the changes in the fitted values after altering various instrumental parameters (e.g. receiving-slit width, detector defocus, receiving-slit length and inclusion of a monochromator).

scholarly journals Crystal structure of a new HfO(OH)2 oxyhydroxide

2013 ◽  
Vol 28 (S2) ◽  
pp. S510-S518
Author(s):  
N.V. Tarakina ◽  
A.P. Tyutyunnik ◽  
Ya.V. Baklanova ◽  
L.G. Maksimova ◽  
T.A. Denisova ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Pair Distribution Function ◽  
Direct Method ◽  
X Ray ◽  
Ion Exchange Reaction ◽  
Atomic Pair Distribution Function ◽  
Profile Fitting ◽  
Atomic Pair ◽  
Full Profile ◽  
A Direct Method

The crystal structure of a new hafnium oxyhydroxide obtained by an ion-exchange reaction from a Li2HfO3 precursor has been solved by a direct method and refined using Rietveld full profile fitting based on X-ray powder diffraction data. HfO(ОН)2 crystallizes in a P21/c monoclinic unit cell (a = 5.5578(5) Å, b = 9.0701(10) Å, c = 5.7174(5) Å, β = 119.746(5)°); its structure can be described as a framework formed by edge-sharing HfO6 octahedra connected to each other via vertices. In addition, an analysis of the atomic pair distribution function obtained using synchrotron radiation was used to confirm the model and to describe fine-structure features.

Comments on determining X-ray diffraction-based volume fractions of retained austenite in steels

2001 ◽  
Vol 16 (4) ◽  
pp. 198-204 ◽  
Author(s):  
C. K. Lowe-Ma ◽  
W. T. Donlon ◽  
W. E. Dowling
Keyword(s):  
Retained Austenite ◽  
Volume Fraction ◽  
X Ray Diffraction ◽  
Experimental Conditions ◽  
X Ray ◽  
Profile Fitting ◽  
Diffraction Peaks ◽  
Diffraction Patterns ◽  
Heat Treatment Regimes ◽  
Integrated Intensities

Retained austenite is an important characteristic of properly heat-treated steel components, particularly gears and shafts, that will be subjected to long-term use and wear. Normally, either X-ray diffraction or optical microscopy techniques are used to determine the volume percent of retained austenite present in steel components subjected to specific heat-treatment regimes. As described in the literature, a number of phenomenological, experimental, and calculation factors can influence the volume fraction of retained austenite determined from X-ray diffraction measurements. However, recent disagreement between metallurgical properties, microscopy, and service laboratory values for retained austenite led to a re-evaluation of possible reasons for the apparent discrepancies. Broad, distorted X-ray peaks from un-tempered martensite were found to yield unreliable integrated intensities whereas diffraction peaks from tempered samples were more amenable to profile fitting with standard shape functions, yielding reliable integrated intensities. Retained austenite values calculated from reliable integrated intensities were found to be consistent with values obtained by Rietveld refinement of the diffraction patterns. The experimental conditions used by service laboratories combined with a poor choice of diffraction peaks were found to be sources of retained austenite values containing significant bias.

Conformations of Bridged Diphenyls. VIII. Crystal Structure of 2-(2′,6′-Dinitrophenoxy)-t-butyIbenzene

1975 ◽  
Vol 53 (14) ◽  
pp. 2093-2101 ◽  
Author(s):  
Kapil Gurtu ◽  
W. David Chandler ◽  
Beverly E. Robertson
Keyword(s):  
Crystal Structure ◽  
Oxygen Atom ◽  
Least Squares ◽  
Steric Effects ◽  
Monoclinic Space Group ◽  
X Ray Diffraction ◽  
X Ray ◽  
R Factor ◽  
Independent Molecules ◽  
Integrated Intensities

The crystal structure of 2-(2′,6′-dinitrophenoxy)-t-butylbenzene, C16HI5N2O5, has been determined by X-ray diffraction. The crystals are monoclinic, space group P21/c: a = 13.949(9), b = 9.652(6), c = 23.806(12) Å, β = 93.82(5), Z = 8. The integrated intensities of 6811 reflections were recorded with a four circle automated diffractometer at 20 °C; 3334 of these reflections were used in the refinement of the structure to a least-squares weighted residual of 0.057 and a traditional R factor of 0.057.The two crystallographically independent molecules both have the skew-t-butyl-distal conformation, suggesting that the steric effects of the two ortho-nitro groups play a greater role in determining the conformation than does conjugation with the bridging oxygen atom.

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