Indexing of powder diffraction patterns for low-symmetry lattices by the successive dichotomy method

1991 ◽  
Vol 24 (6) ◽  
pp. 987-993 ◽  
Author(s):  
A. Boultif ◽  
D. Louër
Keyword(s):  
Success Rate ◽  
Powder Diffraction ◽  
Input Parameter ◽  
Mathematical Treatment ◽  
Monoclinic Symmetry ◽  
Unit Cells ◽  
Rate Calculation ◽  
Diffraction Patterns ◽  
Low Symmetry ◽  
Very High

The dichotomy method for indexing powder diffraction patterns for low-symmetry lattices is studied in terms of an optimization of bound relations used in the comparison of observed data with the calculated patterns generated at each level of the analysis. A rigorous mathematical treatment is presented for monoclinic and triclinic cases. A new program, DICVOL91, has been written, working from the cubic end of the symmetry sequence to triclinic lattices. The search of unit cells is exhaustive within input parameter limits, although a few restrictions for the hkl indices of the first two diffraction lines have been introduced in the study of triclinic symmetry. The efficiency of the method has been checked by means of a large number of accurate powder data, with a very high success rate. Calculation times appeared to be quite reasonable for the majority of examples, down to monoclinic symmetry, but were less predictable for triclinic cases. Applications to all symmetries, including cases with a dominant zone, are discussed.

Design and use of a prototype long-wavelength powder diffractometer

1993 ◽  
Vol 8 (2) ◽  
pp. 84-88
Author(s):  
Ron Jenkins ◽  
J. A. Nicolosi
Keyword(s):  
Powder Diffraction ◽  
Poor Quality ◽  
Inorganic Materials ◽  
Large Unit ◽  
X Ray ◽  
Long Wavelength ◽  
Angle Data ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Low Symmetry

The analysis of crystalline organic phases by X-ray powder diffraction presents special problems, beyond those typically associated with inorganic materials. The large unit cells often associated with organic compounds, combined with the low symmetry of the structures, give rather complicated diffraction patterns that contain many low angle lines. The Bragg–Brentano geometric arrangement employed in most commercial diffractometers gives maximum (d-spacing error at low diffraction angles. This geometry, in turn, means that not only can the large (d-spacing data be of poor quality, but also that much of the low angle data required for the indexing of the pattern is subject to large errors.

Automatic Structure-Sensitive Searching in X-Ray Powder Diffraction

1990 ◽  
Vol 5 (4) ◽  
pp. 181-185 ◽  
Author(s):  
S.D. Kirik ◽  
S.A. Kovyazin ◽  
A.M. Fedotov
Keyword(s):  
Crystal Structures ◽  
Powder Diffraction ◽  
Search System ◽  
X Ray ◽  
Automatic Structure ◽  
Structure Sensitive ◽  
Unit Cells ◽  
Low Symmetry

AbstractThe resemblance between powder patterns because of similarity of crystal structures is well known and widely used. This phenomenon facilitates the determination of unit cells and is frequently used to predict crystal structures of new substances. At present the matching of diffraction analogues is done mainly by hand. Some approaches have been considered in this paper for applying a computer to the problem. Four numerical criteria for resemblance of powder patterns are suggested. Powder patterns are matched with patterns in a database by making use of a computer program based on these criteria.The procedure results in a short list of powder patterns to be examined by the expert. The efficiency of the program is illustrated by examples of calculations for substances of both high and low symmetry. The search system may find an important application in X-ray powder diffraction analysis for the identification of solid solutions, of substances documented under unusual conditions, of structure analogues and for classification of patterns in a database.

Systematic crystallographic refinement of triclinic unit cells

1998 ◽  
Vol 13 (1) ◽  
pp. 22-31
Author(s):  
Ludo K. Frevel
Keyword(s):  
Powder Diffraction ◽  
Unit Cell ◽  
Simultaneous Equations ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Triclinic Phase ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Limits Of Error

Combining the exhaustive indexing of triclinic powder diffraction patterns with a crystallographic determination of unit cell parameters from pinacoid and prism reflections yields unit cell parameters with realistic limits of error. Additionally a referee method has been developed by which the six reciprocal cell parameters of a triclinic phase are determined by solving an exhaustive set of linear simultaneous equations in six unknowns.

Indexing of Powder Diffraction Patterns

1962 ◽  
Vol 6 ◽  
pp. 1-17 ◽  
Author(s):  
P. M. de Wolff
Keyword(s):  
Powder Diffraction ◽  
Initial Phase ◽  
Complete Solution ◽  
Powder Pattern ◽  
X Ray ◽  
Physical Limit ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Influence Of Impurities

AbstractDespite the advances of the electron mtcrodiflraction technique, the determination of unit cells of microcrystalline compounds still depends in many cases on the interpretation of the X-ray powder pattern. The feasibility of this interpretation depends strongly un the precision of the data, the present-day level of which is far from its physical limit. It could be improved by application of monochromators in diflractometry. Some possible methods are discussed. With regard to interpretation, a survey of existing methods is given (Lipson, Ito, de Wolff, Szoldos). Some of these techniques are suitable for computers, at least in the initial phase of the procedure. This is illustrated by application of a zone-finding program for the complete solution of a given pattern. Finally, the influence of impurities and other disturbing factors is discussed.

Notizen: Ternäre Gamma-Messing Phasen in den Systemen Calcium-MIB(IIB)-Quecksilber / New Ternary Gamma-Brass Phases in the Systems Ca-MIB(IIB)-Hg

1980 ◽  
Vol 35 (12) ◽  
pp. 1594-1595 ◽  
Author(s):  
Z. Ban ◽  
M. Pušelj
Keyword(s):  
Intermetallic Compounds ◽  
Powder Diffraction ◽  
Structure Type ◽  
Density Measurements ◽  
X Ray ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Ternary Intermetallic Compounds

Abstract A series of new ternary intermetallic compounds of the general composition Ca16M18IB(IIB)-Hg18 (M = Zn, Cd, Hg, Cu, Ag and Au) has been identified. The X-ray powder diffraction patterns were indexed on a basis of primitive cubic unit cells.From the X-ray data and density measurements it is concluded that these phases belong to the partially disordered (MIB(IIB) and Hg) gamma-brass structure type D83.

New Directions in the X-Ray Diffraction Analysis of Organic Materials

1991 ◽  
Vol 35 (A) ◽  
pp. 653-660
Author(s):  
Ron Jenkins
Keyword(s):  
Poor Quality ◽  
Inorganic Materials ◽  
X Ray Diffraction ◽  
Large Unit ◽  
X Ray ◽  
Angle Data ◽  
New Directions ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Low Symmetry

AbstractThe analysis of crystalline organic phases by X-ray powder diffraction presents special problems, beyond those typically associated with inorganic materials. The large unit cells often associated with organic compounds, combined with the low symmetry of the structures, give rather complicated diffraction patterns which contain many low angle lines. The Bragg-Brentano geometric arrangement employed in most commercial diffractometers gives maximum d-spacing error at low diffraction angles. This, in turn, means that not only can the large d-spacing data be of poor quality, but also that much of the low angle data required for the indexing of the pattern is subject to large errors.

Computing X-Ray Powder Diffraction Intensities and Bragg Angles Using a Microcomputer

1986 ◽  
Vol 30 ◽  
pp. 439-446
Author(s):  
P. Sujjayakorn ◽  
H. H. Stadelmaier ◽  
J. C. Russ
Keyword(s):  
Powder Diffraction ◽  
Visual Display ◽  
Apple Computer ◽  
Disk Drives ◽  
X Ray Diffraction ◽  
X Ray ◽  
Unit Cells ◽  
Jcpds Powder Diffraction File ◽  
Diffraction Patterns ◽  
Symmetry Relations

Programs exist to compute X-ray diffraction patterns (angles and intensities) for specified atomic arrangements using mainframe computers. We report here a microcomputer version (in Basic, to n m on a standard Apple ][ computer with two disk drives and optionally a printer). Additionally, the program offers considerable flexibility in entering atomic positions and using symmetry relations to simplify the input for complex unit cells, and provides a visual display of the unit cell in any orientation.There are a variety of search-match algorithms that compare measured powder diffraction patterns to previously determined standards, such as the JCPDS powder diffraction file. These have been implemented on computers ranging from mainframes to microcomputers, with tradeoffs in the practical size of the standards file and the speed of the search.

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