Bayesian approach to powder phase identification

2017 ◽  
Vol 50 (3) ◽  
pp. 776-786 ◽  
Author(s):  
Alexander Mikhalychev ◽  
Alex Ulyanenkov
Keyword(s):  
Phase Identification ◽  
X Ray Diffraction ◽  
X Ray ◽  
Prior Probabilities ◽  
Manual Search ◽  
Diffraction Patterns ◽  
Qualitative Phase ◽  
Established Technique ◽  
Standard Strategy ◽  
Powder Phase

Identification of unknown materials using X-ray powder diffraction patterns is a commonly used and well established technique with a number of proved implementations. Generally, qualitative phase analysis of X-ray diffraction data includes ranking of candidate phases on the basis of similarity of their diffraction patterns to the measured one. A standard strategy of such a ranking by algorithmization of manual search criteria may become inconvenient for modification and adaptation for problems that are not supported by our intuition. Here, the problem of providing physically grounded expressions for candidate phase ranking is addressed. The approach is based on calculation of Bayesian posterior probabilities of the phases' presence in the sample. The choice of the expressions for the prior probabilities for deviations of phases' diffraction patterns from database entries determines the degree of physical detailing and may be made according to the specifics of the problem being solved. It is shown that even for simple exponential expressions for prior probabilities the approach identifies the phases for IUCr round robin cases correctly, as well as ensuring sufficient robustness of the results with respect to diffraction peak shifts and intensity variations.

The Quality of X-ray Diffraction Standards for Phosphate Minerals and the Degree of Success in Computer Identification

1984 ◽  
Vol 28 ◽  
pp. 305-308
Author(s):  
Frank N. Blanchard
Keyword(s):  
Data Base ◽  
Powder Diffraction ◽  
Data Reduction ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Powder Diffraction File ◽  
X Ray ◽  
Diffraction Patterns ◽  
Computer Identification

Sixty-five years ago Hull first described X-ray powder diffraction as a means of phase identification, and 45 years ago Hannawalt and co-workers compiled the first catalogue of powder diffraction patterns, which has evolved into a file of about 44,000 patterns (the X-ray Powder Diffraction File or PDF). The Hannawalt method of manually searching the PDF is a time-tested, effective tool in seeking a match between an unknown pattern and its correct counterpart(s) in the PDF. Recently, computerized powder diffractometers with software to perform data reduction and search the PDF have become relatively common, and these systems offer tremendous potential for rapid and accurate phase identification in simple and complex systems where the data base may include 44,000 patterns.

scholarly journals Phase Identification by Rotation Electron Diffraction from Multiphasic Samples

2014 ◽  
Vol 70 (a1) ◽  
pp. C1080-C1080
Author(s):  
Yifeng Yun ◽  
Wei Wan ◽  
Faiz Rabbani ◽  
Jie Su ◽  
Sven Hovmöller ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Three Dimensional ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
X Ray ◽  
Space Groups ◽  
Transmission Electron ◽  
Diffraction Patterns ◽  
Five Phases ◽  
Oxide Sample

Electron Crystallography is an important technique for studying micro- and nano-sized crystals[1]. Crystals considered as powder by X-ray diffraction behave as single crystals by electron diffraction. Recently we developed a new method, Rotation Electron Diffraction (RED) for three-dimensional diffraction data collection by combining electron beam tilt with goniometer tilt on a transmission electron microscope (TEM)[2]. Here we apply the RED method on an unknown oxide sample in a Ni-Se-Cl-O system, which may show special physical properties, for example magnetic properties. The crystals in the sample were less than a few micrometers in sizes. Powder X-ray diffraction patterns of the sample could not be indexed by existing known phases. The sample was thus studied by TEM. Five 3D RED datasets were collected from five crystals with different morphologies using the software package RED. The data processing was also performed using the software RED-processing. The unit cell and space groups of all the five phases were obtained using RED and the structures of four of five phases were solved. Nearly all peaks in the powder X-ray diffraction pattern could be indexed using these five phases. To conclude, five phases from a powder sample have been identified using RED. RED is a powerful method for phase identification of multiphasic samples with nano-sized crystals.

scholarly journals Synchrotron radiation study of the surface impurities at Naica gypsum crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C881-C881
Author(s):  
Isai Castillo ◽  
Luis Fuentes-Cobas ◽  
Maria Montero-Cabrera ◽  
Maria Fuentes-Montero ◽  
Hilda Esparza-Ponce ◽  
...  
Keyword(s):  
Synchrotron Radiation ◽  
Grazing Incidence ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
X Ray ◽  
Image Mapping ◽  
Standard Procedures ◽  
Diffraction Patterns ◽  
Xrd Patterns ◽  
X Ray Absorption

The Cave of Swords was discovered in 1910 at Naica mine, Chihuahua, Mexico. Its crystals now are 0.1-0.3m long and their surface is opaque and ocher. For over 100 years these crystals continue to amaze and give us clues about their formation [1]. This work refers to the use of synchrotron radiation for phase identification on gypsum single crystals surfaces (GSCS). The experiments were performed at beamlines (BL) 11-3 and 2-3 of the Stanford Synchrotron Radiation Lightsource (SSRL). Synchrotron X-Ray micro-Fluorescence (μ-SXRF) and micro-X-ray absorption (μ-XANES) at BL 2-3, as well as Grazing Incidence X-ray Diffraction (GI-XRD) and Transmission X-ray Microscope (TXM) at BL 11-3, were employed for elemental and phase identification. For µ-SXRF spectroscopy at the Pb LIII absorption edge some region of interests were selected on each sample. In some samples Fe K-edge μ-XANES spectra were obtained. Spectra from BL 2-3 were analyzed by standard procedures of in-house software tools and using SMAK [2]. Ni, Cu, Co, V, K, Ti, Fe, Mn, Pb, Zn, Ca and S elements were identified. Hematite phase was identified by μ-XANES. All GI-XRD and TXM 2D X-ray diffraction patterns (2D-XRD) were calibrated using standard procedures developed at BL 11-3. 2D-XRD data were analyzed by ANAELU [3], Wfdiff [2] and FindIt codes. Figure shows above a TXM image, mapping where 2D-XRD patterns were recorded. Impurities in the sample increase from left to right, as was observed by direct inspection. Below, 2D-XRD patterns show at left the single crystal spots and at right the mosaic tracks of gypsum crystals. It was concluded that the crystal structure is affected by impurities. Hematite, chalcopyrite, sphalerite, cuprite, galena, and alabandite phases were determined by GI-XRD at GSCS. Acknowledgment: Stanford Synchrotron Radiation Lightsource, Harvard Museum of Natural History and CONACYT CB-183706.

The potential of multivariate analysis to phase identification based on X-ray diffraction patterns

2014 ◽  
Vol 135 ◽  
pp. 126-132 ◽  
Author(s):  
G. Balcerowska-Czerniak ◽  
A. Wronkowski ◽  
A.J. Antończak ◽  
Ł. Skowroński ◽  
A.A. Wronkowska
Keyword(s):  
Multivariate Analysis ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Patterns

scholarly journals Enhancing deep-learning training for phase identification in powder X-ray diffractograms

IUCrJ ◽  
2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Jan Schuetzke ◽  
Alexander Benedix ◽  
Ralf Mikut ◽  
Markus Reischl
Keyword(s):  
Deep Learning ◽  
Training Data ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Data Set ◽  
X Ray ◽  
Cell Parameters ◽  
Training Samples ◽  
Reliable Performance ◽  
Diffraction Patterns

Within the domain of analyzing powder X-ray diffraction (XRD) scans, manual examination of the recorded data is still the most popular method, but it requires some expertise and is time consuming. The usual workflow for the phase-identification task involves software for searching databases of known compounds and matching lists of d spacings and related intensities to the measured data. Most automated approaches apply some iterative procedure for the search/match process but fail to be generally reliable yet without the manual validation step of an expert. Recent advances in the field of machine and deep learning have led to the development of algorithms for use with diffraction patterns and are producing promising results in some applications. A limitation, however, is that thousands of training samples are required for the model to achieve a reliable performance and not enough measured samples are available. Accordingly, a framework for the efficient generation of thousands of synthetic XRD scans is presented which considers typical effects in realistic measurements and thus simulates realistic patterns for the training of machine- or deep-learning models. The generated data set can be applied to any machine- or deep-learning structure as training data so that the models learn to analyze measured XRD data based on synthetic diffraction patterns. Consequently, we train a convolutional neural network with the simulated diffraction patterns for application with iron ores or cements compounds and prove robustness against varying unit-cell parameters, preferred orientation and crystallite size in synthetic, as well as measured, XRD scans.

An Application of Calculated X-Ray Diffraction Patterns in the Analysis of Reference Powder Data: Trivalent Metal Sulfates

1992 ◽  
Vol 7 (4) ◽  
pp. 215-218 ◽  
Author(s):  
Sidney S. Pollack ◽  
Gregory J. McCarthy ◽  
Jean M. Holzer
Keyword(s):  
Powder Diffraction ◽  
Structure Data ◽  
The Other ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Trivalent Metal ◽  
Powder Diffraction File ◽  
X Ray ◽  
Cell Parameters ◽  
Diffraction Patterns

AbstractPowder diffraction patterns have been calculated for nine isostructural rhombohedral M2(SO4)3 (M = Sc, Ti, V, Cr, Fe, Ga, Y, Rh, In) phases, and for four isostructural monoclinic M2(SO4)3 (M = V, Fe, In, Tl) phases. The pattern for monoclinic Fe2(SO4)3 is the first reported for this phase. Because structure data are available only for the two Fe2(SO4)3 polymorphs, the powder patterns of the other trivalent metal sulfates were approximated using the structure data of the isostructural Fe phases with the scattering factors and previously determined cell parameters of the various metal sulfates. These calculated patterns are termed an approximation by isostruduralism.The calculated patterns were used to evaluate reference powder data for these phases in the Powder Diffraction File (PDF). All but two of the PDF patterns were found to differ substantially from the calculated patterns in the stronger peaks used for identification, and to be missing weak peaks that may be confused for impurities during phase identification.

Evaluation of Freezing Methods by Low Temperature X-Ray Diffraction

1977 ◽  
Vol 35 ◽  
pp. 330-333
Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello
Keyword(s):  
Biological Materials ◽  
Molecular Organization ◽  
X Ray Diffraction ◽  
Glass Capillary ◽  
X Ray ◽  
Rate Dependent ◽  
Before And After ◽  
Freeze Etching ◽  
Diffraction Patterns ◽  
Set Up

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.

Examination of Rabbit Fc Crystals

1968 ◽  
Vol 26 ◽  
pp. 140-141
Author(s):  
J. P. Robinson ◽  
P. G. Lenhert
Keyword(s):  
Molecular Weight ◽  
Flat Plate ◽  
Phosphate Buffer ◽  
Asymmetric Unit ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutral Ph ◽  
Small Crystals ◽  
Carbon Coated ◽  
Diffraction Patterns

Crystallographic studies of rabbit Fc using X-ray diffraction patterns were recently reported. The unit cell constants were reported to be a = 69. 2 A°, b = 73. 1 A°, c = 60. 6 A°, B = 104° 30', space group P21, monoclinic, volume of asymmetric unit V = 148, 000 A°3. The molecular weight of the fragment was determined to be 55, 000 ± 2000 which is in agreement with earlier determinations by other methods.Fc crystals were formed in water or dilute phosphate buffer at neutral pH. The resulting crystal was a flat plate as previously described. Preparations of small crystals were negatively stained by mixing the suspension with equal volumes of 2% silicotungstate at neutral pH. A drop of the mixture was placed on a carbon coated grid and allowed to stand for a few minutes. The excess liquid was removed and the grid was immediately put in the microscope.

Control of the phase composition of advanced calcium phosphates using an x-ray diffractometer with a curved position-sensitive detector

2020 ◽  
Vol 86 (6) ◽  
pp. 29-35
Author(s):  
V. P. Sirotinkin ◽  
O. V. Baranov ◽  
A. Yu. Fedotov ◽  
S. M. Barinov
Keyword(s):  
Phase Composition ◽  
Calcium Phosphates ◽  
Position Sensitive Detector ◽  
Sensitive Detector ◽  
X Ray Diffraction ◽  
X Ray ◽  
Impurity Phases ◽  
Position Sensitive ◽  
Diffraction Peaks ◽  
Diffraction Patterns

The results of studying the phase composition of advanced calcium phosphates Ca10(PO4)6(OH)2, β-Ca3(PO4)2, α-Ca3(PO4)2, CaHPO4 · 2H2O, Ca8(HPO4)2(PO4)4 · 5H2O using an x-ray diffractometer with a curved position-sensitive detector are presented. Optimal experimental conditions (angular positions of the x-ray tube and detector, size of the slits, exposure time) were determined with allowance for possible formation of the impurity phases during synthesis. The construction features of diffractometers with a position-sensitive detector affecting the profile characteristics of x-ray diffraction peaks are considered. The composition for calibration of the diffractometer (a mixture of sodium acetate and yttrium oxide) was determined. Theoretical x-ray diffraction patterns for corresponding calcium phosphates are constructed on the basis of the literature data. These x-ray diffraction patterns were used to determine the phase composition of the advanced calcium phosphates. The features of advanced calcium phosphates, which should be taken into account during the phase analysis, are indicated. The powder of high-temperature form of tricalcium phosphate strongly adsorbs water from the environment. A strong texture is observed on the x-ray diffraction spectra of dicalcium phosphate dihydrate. A rather specific x-ray diffraction pattern of octacalcium phosphate pentahydrate revealed the only one strong peak at small angles. In all cases, significant deviations are observed for the recorded angular positions and relative intensity of the diffraction peaks. The results of the study of experimentally obtained mixtures of calcium phosphate are presented. It is shown that the graphic comparison of experimental x-ray diffraction spectra and pre-recorded spectra of the reference calcium phosphates and possible impurity phases is the most effective method. In this case, there is no need for calibration. When using this method, the total time for analysis of one sample is no more than 10 min.

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