High-throughput powder diffraction. IV. Cluster validation using silhouettes and fuzzy clustering

In two previous papers [Gilmore, Barr & Paisley (2004).J. Appl. Cryst.37, 231–242; Barr, Dong & Gilmore (2004).J. Appl. Cryst.37, 243–252], it was demonstrated how to generate a correlation matrix by comparing full powder diffraction patterns, and then partition the diffractograms into groups using multivariate statistics and associated classification procedures. For clustering the patterns into related sets, dendrograms, metric multidimensional scaling and three-dimensional principal-components analysis score plots are employed. However, sometimes cluster membership for certain patterns is not always very clear or other ambiguities may arise; this paper describes cluster validation techniques using silhouettes and fuzzy clustering. The two methods operate in a complementary way: in some cases silhouettes are the most useful, and in others fuzzy clustering is more applicable. These procedures are available as options in the commercial computer programPolySNAP.

Download Full-text

PolySNAP: a computer program for analysing high-throughput powder diffraction data

Journal of Applied Crystallography ◽

10.1107/s0021889804011173 ◽

2004 ◽

Vol 37 (4) ◽

pp. 658-664 ◽

Cited By ~ 32

Author(s):

Gordon Barr ◽

Wei Dong ◽

Christopher J. Gilmore

Keyword(s):

Computer Program ◽

Powder Diffraction ◽

High Throughput ◽

Three Dimensional ◽

Principal Component ◽

Visualization Tools ◽

Diffraction Patterns ◽

Pure Phases ◽

Related Compounds ◽

High Throughput Crystallography

In high-throughput crystallography experiments, it is possible to measure over 1000 powder diffraction patterns on a series of related compounds, often polymorphs or salts, in less than one week. The analysis of these patterns poses a difficult statistical problem. A computer program is presented that can analyse such data, automatically sort the patterns into related clusters or classes, characterize each cluster and identify any unusual samples containing, for example, unknown or unexpected polymorphs. Mixtures may be analysed quantitatively if a database of pure phases is available. A key component of the method is a set of visualization tools based on dendrograms and pie charts, as well as principal-component analysis and metric multidimensional scaling as a source of three-dimensional score plots. The procedures have been incorporated into the computer programPolySNAP, which is available commercially from Bruker-AXS.

Download Full-text

High-throughput powder diffraction. II. Applications of clustering methods and multivariate data analysis

Journal of Applied Crystallography ◽

10.1107/s0021889804000391 ◽

2004 ◽

Vol 37 (2) ◽

pp. 243-252 ◽

Cited By ~ 46

Author(s):

Gordon Barr ◽

Wei Dong ◽

Christopher J. Gilmore

Keyword(s):

Powder Diffraction ◽

High Throughput ◽

Inorganic Compounds ◽

Computer Software ◽

Principal Component ◽

Clustering Methods ◽

Visualization Tools ◽

Diffraction Patterns ◽

Pure Phases ◽

Related Compounds

In high-throughput crystallography, it is possible to accumulate over 1000 powder diffraction patterns on a series of related compounds, often polymorphs. A method is presented that can analyse such data, automatically sort the patterns into related clusters or classes, characterize each cluster and identify any unusual samples containing, for example, unknown or unexpected polymorphs. Mixtures may be analysed quantitatively if a database of pure phases is available. A key component of the method is a set of visualization tools based on dendrograms, cluster analysis, pie charts, principal-component-based score plots and metric multidimensional scaling. Applications to pharmaceutical data and inorganic compounds are presented. The procedures have been incorporated into thePolySNAPcommercial computer software.

Download Full-text

Ambiguities in the structure determination of antimony tellurides arising from almost homometric structure models and stacking disorder

Journal of Applied Crystallography ◽

10.1107/s0021889810032644 ◽

2010 ◽

Vol 43 (5) ◽

pp. 1012-1020 ◽

Cited By ~ 14

Author(s):

Matthias N. Schneider ◽

Markus Seibald ◽

Patrick Lagally ◽

Oliver Oeckler

Keyword(s):

Powder Diffraction ◽

Three Dimensional ◽

Basic Structure ◽

Initial Structure ◽

Data Sets ◽

Layered Chalcogenides ◽

Potential Applications ◽

Diffraction Patterns ◽

Characteristic Layers ◽

Stacking Disorder

Ambiguities in the interpretation of both single-crystal and powder diffraction data can lead to wrong conclusions concerning the structure analysis of layered chalcogenides with interesting physical properties and potential applications. This is illustrated for binary and Pb-doped phases of the homologous series (Sb2)k(Sb2Te3)m. Almost homometric structure models for 39R-Sb10Te3[R\bar 3m,a = 4.2874 (6),c = 64.300 (16) Å,R1 = 0.0298] have been derived from initial structure solutions and crystal chemical considerations. The variation of the electron density on certain positions may further reduce the differences between the calculated diffraction patterns of non-congruent structure models as exemplified by the new compound 33R-[Sb0.978(3)Pb0.022(3)]8Te3[R\bar 3m,a = 4.2890 (10),c = 75.51 (2) Å,R1 = 0.0615]. Both compounds are long-range ordered, and in either case both `almost homometric' models can be refined equally well on experimental data sets. The models can only be distinguished by chemical analysis, as reasonable atom assignments lead to different compositions for each model. Interestingly, all structure solution attempts led to the wrong models in both cases. In addition, it is shown that stacking disorder of characteristic layers may lead to powder diffraction patterns that can be misinterpreted in terms of three-dimensional randomly disordered almost isotropic structures with a simple α-Hg-type basic structure.

Download Full-text

High-throughput powder diffraction. III. The application of full-profile pattern matching and multivariate statistical analysis to round-robin-type data sets

Journal of Applied Crystallography ◽

10.1107/s0021889804013743 ◽

2004 ◽

Vol 37 (4) ◽

pp. 635-642 ◽

Cited By ~ 13

Author(s):

Gordon Barr ◽

Wei Dong ◽

Christopher Gilmore ◽

John Faber

Keyword(s):

Pattern Matching ◽

Powder Diffraction ◽

Fuzzy Clustering ◽

Round Robin ◽

Original Form ◽

X Rays ◽

Multivariate Statistical ◽

Data Set ◽

Diffraction Patterns ◽

Matching Techniques

Powder pattern matching techniques, using all the experimentally measured data points, coupled with cluster analysis, fuzzy clustering and multivariate statistical methods are used, with appropriate visualization tools, to analyse a set of 27 powder diffraction patterns of alumina collected at seven different laboratories on different instruments as part of an International Center for Diffraction Data Grant-in-Aid program. In their original form, the data factor into six distinct clusters. However, when a non-linear shift of the form \Delta \left({2\theta } \right)\, = \,a_0 \, + \,a_1 \sin \theta (wherea0anda1are refinable constants) is applied to optimize the correlations between patterns, clustering produces a large 25-pattern set with two outliers. The first outlier is a synchrotron data set at a different wavelength from the other data, and the second is distinguished by the absence ofKα2lines,i.e.it uses Ge-monochromated incident X-rays. Fuzzy clustering, in which samples may belong to more than one cluster, is introduced as a complementary method of pinpointing problematic diffraction patterns. In contrast to the usual methodology associated with the analysis of round-robin data, this process is carried out in a routine way, with minimal user interaction or supervision, using thePolySNAPsoftware.

Download Full-text

XRD peak migration and apparent shift of cell-edge lengths of nano-sized hematite, goethite and lepidocrocite

Clay Minerals ◽

10.1180/0009855023740065 ◽

2002 ◽

Vol 37 (4) ◽

pp. 629-638 ◽

Cited By ~ 10

Author(s):

H. Stanjek

Keyword(s):

Powder Diffraction ◽

Three Dimensional ◽

Reciprocal Space ◽

Regression Equations ◽

Cell Edge ◽

X Ray ◽

Structure Factors ◽

Diffraction Patterns ◽

Apparent Shift

AbstractX-ray powder diffraction patterns were simulated for nano-sized hematite, goethite and lepidocrocite by three-dimensional integration in reciprocal space. The cell-edge lengths were refined together with the size parameters X and Xe of the Thompson-Cox-Hastings function, which for orthorhombic structures was extended by a biaxial broadening parameter Xo. Variations of the structure factors across broad peaks resulted in apparent peak shifts and concomitant shifts in celledge lengths, which were significantly correlated with the size parameters for hematite and partially correlated for goethite and lepidocrocite. Regression equations are given for correcting cell-edge lengths obtained from Rietveld fits for size-induced shifts.

Download Full-text

High-throughput powder diffraction V: the use of Raman spectroscopy with and without X-ray powder diffraction data

Journal of Applied Crystallography ◽

10.1107/s0021889809022924 ◽

2009 ◽

Vol 42 (4) ◽

pp. 706-714 ◽

Cited By ~ 6

Author(s):

Gordon Barr ◽

Gordon Cunningham ◽

Wei Dong ◽

Christopher J. Gilmore ◽

Takashi Kojima

Keyword(s):

Raman Spectroscopy ◽

Powder Diffraction ◽

High Throughput ◽

Diffraction Data ◽

Powder Diffraction Data ◽

Large Numbers ◽

Individual Differences Scaling ◽

Diffraction Patterns ◽

The Individual ◽

Related Compounds

In high-throughput crystallography it is possible to accumulate large numbers of powder diffraction patterns on a series of related compounds, often polymorphs, salts or co-crystals. In previous papers [Gilmore, Barr & Paisley (2004).J. Appl. Cryst.37, 231–242; Barr, Dong & Gilmore (2004).J. Appl. Cryst.37, 243–252] it has been shown how such data can be analysed by generating an (n×n) correlation matrix,ρ, by correlatingnfull powder diffraction patterns, point by point. Theρmatrix is used as a source of dendrograms and metric multidimensional plots in three or more dimensions which classify the patterns into sets related by similarity. In this paper, it is shown how Raman spectroscopy data can be used by themselves or as an adjunct to powder diffraction data by combining the two techniques using the individual differences scaling method (INDSCAL) of Carroll & Chang [Psychometria, (1970),35, 283–319]. The method is very robust, and can be extended to other forms of spectroscopy. It is available as an option in the commercialPolySNAP3computer program.

Download Full-text

Cryomicroscopy of crotoxin complex crystals at 400 KV

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100156109 ◽

1989 ◽

Vol 47 ◽

pp. 826-827

Author(s):

Jaap Brink ◽

Wah Chiu

Keyword(s):

Signal To Noise Ratio ◽

3D Structure ◽

Three Dimensional ◽

Carbon Films ◽

Depth Of Field ◽

Basic Subunit ◽

Ewald Sphere ◽

Diffraction Patterns ◽

Complex Crystals ◽

Acidic Subunit

The crotoxin complex is a potent neurotoxin composed of a basic subunit (Mr = 12,000) and an acidic subunit (M = 10,000). The basic subunit possesses phospholipase activity whereas the acidic subunit shows no enzymatic activity at all. The complex's toxocity is expressed both pre- and post-synaptically. The crotoxin complex forms thin crystals suitable for electron crystallography. The crystals diffract up to 0.16 nm in the microscope, whereas images show reflections out to 0.39 nm2. Ultimate goal in this study is to obtain a three-dimensional (3D-) structure map of the protein around 0.3 nm resolution. Use of 100 keV electrons in this is limited; the unit cell's height c of 25.6 nm causes problems associated with multiple scattering, radiation damage, limited depth of field and a more pronounced Ewald sphere curvature. In general, they lead to projections of the unit cell, which at the desired resolution, cannot be interpreted following the weak-phase approximation. Circumventing this problem is possible through the use of 400 keV electrons. Although the overall contrast is lowered due to a smaller scattering cross-section, the signal-to-noise ratio of especially higher order reflections will improve due to a smaller contribution of inelastic scattering. We report here our preliminary results demonstrating the feasability of the data collection procedure at 400 kV.Crystals of crotoxin complex were prepared on carbon-covered holey-carbon films, quench frozen in liquid ethane, inserted into a Gatan 626 holder, transferred into a JEOL 4000EX electron microscope equipped with a pair of anticontaminators operating at −184°C and examined under low-dose conditions. Selected area electron diffraction patterns (EDP's) and images of the crystals were recorded at 400 kV and −167°C with dose levels of 5 and 9.5 electrons/Å, respectively.

Download Full-text