Array-type universal profile function for powder pattern fitting

1990 ◽  
Vol 23 (6) ◽  
pp. 485-491 ◽  
Author(s):  
H. Toraya
Keyword(s):  
Peak Position ◽  
Powder Pattern ◽  
Mathematical Form ◽  
X Rays ◽  
Unknown Parameters ◽  
Profile Function ◽  
Accurate Analysis ◽  
Array Type ◽  
Profile Fitting ◽  
Fitting In

An array-type universal profile function for powder-pattern fitting is described. It is defined as an array of unknown parameters representing the profile heights at discrete angular steps. The unknown parameters are determined during least-squares fitting together with the integrated intensity, the peak position, the peak width and background parameters. The function has been applied to profile fitting in a small 20 range, and has better R-factors than the pseudo-Voigt and Pearson VII functions. This new function has some important advantages: it can model any complex profile shape, which would be difficult to describe by a smoothly varying analytical-type function; it generally gives a better fit and thus more precise and accurate analysis than currently used analytical-type functions; and it can be applied to the data of all radiation sources including conventional X-rays, synchrotron radiation and time-of-flight and fixed-wavelength neutrons without changing the mathematical form. The optimized use of the function and the accuracy of deduced parameters are also discussed.

Powder pattern indexing with the dichotomy method

2004 ◽  
Vol 37 (5) ◽  
pp. 724-731 ◽  
Author(s):  
Ali Boultif ◽  
Daniel Louër
Keyword(s):  
Input Parameter ◽  
Zero Point ◽  
Absolute Error ◽  
Peak Position ◽  
Powder Pattern ◽  
X Rays ◽  
Cell Analysis ◽  
Input File ◽  
A Cell ◽  
Difficult Cases

The efficiency of the successive dichotomy method for powder diffraction pattern indexing [Louër & Louër (1972).J. Appl. Cryst.5, 271–275] has been proved over more than 30 years of usage. Features implemented in the new version of the computer programDICVOL04 include (i) a tolerance to the presence of impurity (or inaccurately measured) diffraction lines, (ii) a refinement of the `zero-point' position, (iii) a reviewing of all input lines from the solution found from, generally, the first 20 lines, (iv) a cell analysis, based on the concept of the reduced cell, to identify equivalent monoclinic and triclinic solutions, and (v) an optional analysis of input powder data to detect the presence of a significant `zero-point' offset. New search strategies have also been introduced,e.g.each crystal system is scanned separately, within the input volume limits, to limit the risk of missing a solution characterized by a metric lattice singularity. The default values in the input file have been extended to 25 Å for the linear parameters and 2500 Å3for the cell volume. The search is carried out exhaustively within the input parameter limits and the absolute error on peak position measurements. Many tests with data from the literature and from powder data of pharmaceutical materials, collected with the capillary technique and laboratory monochromatic X-rays, have been performed with a high success rate, covering all crystal symmetries from cubic to triclinic. Some examples reported as `difficult' cases are also discussed. Additionally, a few recommendations for the correct practice of powder pattern indexing are reported.

Profile Fitting in Residual Stress Determination

1985 ◽  
Vol 29 ◽  
pp. 89-101
Author(s):  
T. J. Devine ◽  
J. B. Cohen
Keyword(s):  
Residual Stress ◽  
Cross Correlation ◽  
Bragg Peak ◽  
Stress Measurement ◽  
Peak Position ◽  
Stress Determination ◽  
Profile Fitting ◽  
Least Squares Fit ◽  
Fitting In

Of major importance in the determination of residual stress via diffraction is the accuracy of the measurement of the scattering angle (2 θp) of a Bragg peak. This determines the accuracy of the interplanar (d) spacing and hence the strain and stress. In the U.S., the most commonly accepted method of determining peak position is a parabolic fit near the top of a peak. (While a diffraction peak is not parabolic, this is a satisfactory function near the maximum.) The error in this procedure has been derived and tested, and it has been shown that a multipoint fit with a least 7 points is rapid and as precise or more precise than the centroid, the bisector of the half width, or cross correlation, except for sharp peaks in which case the centroid or cross correlation are slightly better. Thus a parabolic fit is generally useful and, since a least-squares fit to this function is readily carried out on modem micro-processors, automatical of a stress measurement is possible, including evaluation of errors.

Line profile analysis: pattern modellingversusprofile fitting

2006 ◽  
Vol 39 (1) ◽  
pp. 24-31 ◽  
Author(s):  
Paolo Scardi ◽  
Matteo Leoni
Keyword(s):  
Line Profile ◽  
Powder Diffraction ◽  
Profile Analysis ◽  
Domain Size ◽  
Systematic Errors ◽  
Powder Pattern ◽  
Line Profile Analysis ◽  
Microstructural Parameters ◽  
Profile Fitting ◽  
Transmission Electron

Powder diffraction data collected on a nanocrystalline ceria sample within a round robin conducted by the IUCr Commission on Powder Diffraction were analysed by two alternative approaches: (i) whole-powder-pattern modelling based upon a fundamental microstructural parameters approach, and (ii) a traditional whole-powder-pattern fitting followed by Williamson–Hall and Warren–Averbach analysis. While the former gives results in close agreement with those of transmission electron microscopy, the latter tends to overestimate the domain size effect, providing size values about 20% smaller. The origin of the discrepancy can be traced back to a substantial inadequacy of profile fitting with Voigt profiles, which leads to systematic errors in the following line profile analysis by traditional methods. However, independently of the model, those systematic errors seem to have little effect on the volume-weighted mean size.

Enhancing XRPD Pattern Quality With Line-Profile-Fitting in Multiphase Systems

1994 ◽  
pp. 95-99
Author(s):  
G. Kimmel ◽  
J. Sariel ◽  
I. Dahan ◽  
S. Nathan ◽  
U. Admon
Keyword(s):  
Line Profile ◽  
Profile Fitting ◽  
Multiphase Systems ◽  
Fitting In ◽  
Xrpd Pattern

Plasma Diagnostics of Microflares observed by STIX and AIA

2021 ◽  
Author(s):  
Jonas Saqri ◽  
Astrid Veronig ◽  
Ewan Dickson ◽  
Säm Krucker ◽  
Andrea Francesco Battaglia ◽  
...  
Keyword(s):  
Solar Flares ◽  
Magnetic Energy ◽  
Emission Measure ◽  
Transport Processes ◽  
X Rays ◽  
Solar Dynamics Observatory ◽  
Energy Bands ◽  
Accurate Analysis ◽  
Great Opportunity ◽  
Wide Range

<p>Solar flares are generally thought to be the impulsive release of magnetic energy giving rise to a wide range of solar phenomena that influence the heliosphere and in some cases even conditions of earth. Part of this liberated energy is used for particle acceleration and to heat up the solar plasma. The Spectrometer/Telescope for Imaging X-rays (STIX) instrument onboard the Solar Orbiter mission launched on February 10th 2020 promises advances in the study of solar flares of various sizes. It is capable of measuring X-ray spectra from 4 to 150 keV with 1 keV resolution binned into 32 energy bins before downlinking. With this energy range and sensitivity, STIX is capable of sampling thermal plasma with temperatures of≳10 MK, and to diagnose the nonthermal bremsstrahlung emission of flare-accelerated electrons. During the spacecraft commissioning phase in the first half of the year 2020, STIX observed 68 microflares. Of this set, 26 events could clearly be identified in at least two energy channels, all of which originated in an active region that was also visible from earth. These events provided a great opportunity to combine the STIX observations with the multi-band EUV imagery from the Atmospheric Imaging Assembly (AIA) instrument on board the earth orbiting Solar Dynamics Observatory (SDO). For the microflares that could be identified in two STIX science energy bands, it was possible to derive the temperature and emission measure (EM) of the flaring plasma assuming an isothermal source. For larger events where more detailed spectra could be derived, a more accurate analysis was performed by fitting the spectra assuming various thermal and nonthermal sources. These results are compared to the diagnostics derived from AIA images. To this aim, the Differential EmissionMeasure (DEM) was reconstructed from AIA observations to infer plasma temperatures and EM in the flaring regions. Combined with the the relative timing between the emission seen by STIX and AIA, this allows us to get deeper insight into the flare energy release and transport processes.</p>

scholarly journals INFLUENCE OF DEATH CRITERIA ON THE X-RAY SURVIVAL CURVES OF THE FUNGUS, NEUROSPORA

1934 ◽  
Vol 17 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Fred M. Uber ◽  
David R. Goddard
Keyword(s):  
Survival Curve ◽  
X Rays ◽  
Survival Curves ◽  
Single Spore ◽  
Accurate Analysis ◽  
Single Well ◽  
Growth Production ◽  
Multiple Hit ◽  
Neurospora Tetrasperma ◽  
Ascospore Production

1. When ascospores of Neurospora tetrasperma were irradiated with 11 kv. X-rays, the single spore cultures obtained displayed a wide variety of mutated forms. 2. Control germinations of ascospores showed uniform behavior, ranging from 92–95 per cent germination. 3. The shape of the survival curves was found to be a function of the criterion of death. The following criteria were used: germination, growth, production of mature ascospores, and the production of normal perithecia. 4. The germination survival curve exhibited a rhythmic variation with dosage. Germination is not a significant criterion of death. 5. Half-survival dosages for growth and ascospore production were approximately 30,000 and 20,000 roentgens, respectively. 6. Multiple hit-to-kill relations were found on the basis of the quantum hit theory; no accurate analysis was possible. 7. The studies indicate that ascospore death does not result from a single well defined reaction, but rather from the integrated effects of several deleterious processes initiated by the radiation.

Oxygen Concentration Determination in Silicon Single Crystals by Precision Lattice Parameter Measurement

1990 ◽  
Vol 34 ◽  
pp. 577-586
Author(s):  
H. Ohmori ◽  
M. Tomita ◽  
N. Tsuchiya ◽  
Y. Matsushita
Keyword(s):  
Single Crystals ◽  
Oxygen Concentration ◽  
Diffraction Method ◽  
Lattice Parameter ◽  
Peak Position ◽  
Silicon Wafers ◽  
Parameter Measurement ◽  
Lattice Parameter Measurement ◽  
Precise Adjustment ◽  
Fitting In

AbstractPrecision lattice parameter measurement by the X-ray diffraction method of Bond [1] has been examined as a substitutional method for IR in determining the oxygen concentration in silicon single crystals. Asymmetric 444 CuKai reflections were measured for undoped (100) oriented silicon wafers to obtain the correlation curve between the silicon lattice parameter and oxygen concentration. Precise adjustment of the optical system and computer fitting in determining the peak position allow a minute lattice dilation of silicon due to oxygen to be detected by the Bond method. The precision of this measurement system was of the order of 10-6. The lattice expansion of silicon by dissolved oxygen was determined to be at the rate of 3.2X10-24 atoms of oxygen per cm3. Furthermore, the oxygen concentrations of heavily Sb-doped silicon wafers were determined nondestructively.

X-ray Diffractometric Determination of Lattice Misfit Between γ and γ' Phases in Ni-Base Superalloys

1988 ◽  
Vol 32 ◽  
pp. 365-375 ◽  
Author(s):  
Katsumi Ohno ◽  
Hirosi Harada ◽  
Toshihiro Yamagata ◽  
Michio Yamazaki ◽  
Kazumasa Ohsumi
Keyword(s):  
Lattice Misfit ◽  
Least Square Method ◽  
Least Square ◽  
X Rays ◽  
Deconvolution Method ◽  
X Ray ◽  
Window Functions ◽  
Profile Fitting ◽  
Overlapping Peaks

AbstractThe lattice misfits between γ and γ' phases in Ni-base superalloys (single crystal) were accurately determined for filings of specimens by using both a conventional X-ray tube focusing diffractometer(CXRFD) and a synchrotron-radiation parallel beam X-ray diffractometer (SRPXRD). All reflection peaks measured with the CXRFD were in a cluster of overlapping peaks because of the very small differences in the lattice parameters of both phases and the instrumental broadening due to X-ray optics including the spectral distribution of Xray source such as CuKα doublet. The deconvolution method was applied to remove the instrumental broadening from the peaks measured with the CXRFD. The window functions for the deconvolution method were calculated from CuKα doublet reflection of Si standard by a nonlinear least-square method.The instrumental broadening of SRPXRD was much smaller than that of CXRFD since the monochromatic X-rays produced single peak profiles and constant profile shape over a wide 2θ range. A profile fitting with a pseudo-Voigt function was used to determine 2θ angles to 0.0005 deg. for the synchrotron powder data. The peak angle and shape reflected from γ' phases in γ-matrix and those fron electrochemically extracted γ'-phase were significantly different.

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 Gaussian–Hermite polynomials function for X-ray diffraction profile fitting

1999 ◽  
Vol 32 (4) ◽  
pp. 730-735 ◽  
Author(s):  
F. Sánchez-Bajo ◽  
F. L. Cumbrera
Keyword(s):  
Hermite Polynomials ◽  
Gaussian Function ◽  
Shape Functions ◽  
X Ray Diffraction ◽  
Stabilized Zirconia ◽  
Profile Function ◽  
Diffraction Profile ◽  
X Ray ◽  
Profile Fitting ◽  
Diffraction Peaks

In recent years, several profile-shape functions have been successfully used in X-ray powder diffraction studies. Here, a new profile function for approximating the X-ray diffraction peaks is proposed. This model, based on a Gaussian function multiplied by a correction factor in the form of a series expansion in Hermite polynomials, can be employed in the cases where there are peak asymmetries. The function has been tested by using samples of α-Al2O3and 9-YSZ (yttria-stabilized zirconia), yielding generally satisfactory results.

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