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Crystals
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Multivariate Analysis Applications to Crystallography
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Multivariate Analysis Applications to Crystallography

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Biomolecular Crystals".

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 30277

Special Issue Editors

Dr. Rocco Caliandro

E-Mail Website
Guest Editor
Institute of Crystallography, National Research Council of Italy, Via Amendola 122/O, 70126 Bari, Italy
Interests: protein crystallography; phasing methods; modulated enhanced diffraction; multivariate analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Marco Milanesio

E-Mail Website1 Website2
Co-Guest Editor
Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel 11, 15121 Alessandria, Italy
Interests: molecular and crystal structure of chemical compounds and materials; single-crystal and powder X-ray diffraction

Special Issue Information

Dear Colleagues,

The advent of next-generation X-ray sources, more sensitive and fast detectors, and multi-probe experimental setups enable deeper static and dynamic crystallographic investigations. The huge amount of data collected by multi-technique in situ or in operando experiments on powder samples or by serial crystallography experiments on single crystals demand advanced and fast methods of analysis. Multivariate analysis can efficiently process multiple measurements, by considering them as a whole data matrix and in a probe-independent way. This approach is fast, blind, unbiased, and complementary to the traditional approaches to process each measurement independently. It does not require a priori structural information, and can be used as on-site analysis to extract relevant trends in data. Multivariate methods such as principal component analysis and phase-sensitive detection have been used to detect subtle structural changes induced in situ by varying external parameters (temperature, light, etc.). In this context, theoretical frameworks for new techniques like modulated enhanced diffraction have been developed to achieve higher sensitivity and chemical selectivity in X-ray diffraction experiments. On the other hand, established statistical methods such as principal component analysis have been modified (constrained) to address issues related to X-ray diffraction and spectroscopic measurements. New procedures to reduce unwanted peak shifts due to lattice distortion, to automatically extract the structural kinetics, to selectively locate atoms responding to in situ stimulus have been developed and applied. As a new, exciting frontier, artificial intelligence is being applied to high-throughput crystallographic steps such as crystallization screening, indexing, and dataset merging.

This Special Issue will cover computational and experimental advancements related to the use of multivariate analysis in crystallography. Therefore, this Special Issue welcomes original research and review manuscripts on the following aspects of the processing of data collected in crystallographic experiments:

  • Data reduction, indexing, integration, and matching between different single-crystal datasets
  • Qualitative and quantitative analysis, classification of samples based on diffraction profiles
  • Combining data from multi-probe experiments
  • Fast extraction of reaction kinetics
  • High-sensitivity structural characterization by X-ray powder diffraction and pair distribution function measurements
  • Advancements in phasing methods
  • Improved interpretation of electron density maps, model validation

Dr. Rocco Caliandro
Prof. Marco Milanesio
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Crystals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2100 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Multivariate methods
  • Crystallography
  • Principal component analysis
  • Phase-sensitive detection
  • Modulated enhanced diffraction
  • On-site analysis

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Published Papers (8 papers)

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Editorial

Jump to: Research, Review

2 pages, 159 KiB  
Editorial
Multivariate Analysis Applications to Crystallography
by Rocco Caliandro and Marco Milanesio
Crystals 2021, 11(2), 166; https://doi.org/10.3390/cryst11020166 - 8 Feb 2021
Viewed by 1559
Abstract
The Special Issue contributions cover the main themes related to the applications of multivariate analysis to crystallography [...] Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)

Research

Jump to: Editorial, Review

17 pages, 5800 KiB  
Article
Factor Analysis of XRF and XRPD Data on the Example of the Rocks of the Kontozero Carbonatite Complex (NW Russia). Part I: Algorithm
by Ekaterina Fomina, Evgeniy Kozlov and Ayya Bazai
Crystals 2020, 10(10), 874; https://doi.org/10.3390/cryst10100874 - 26 Sep 2020
Cited by 4 | Viewed by 2409
Abstract
This paper aims to develop a principle for selecting the most informative samples for geological research from extensive collections of rock material. As a tool for this selection, we chose an original method of statistical comparison of X-ray powder diffraction (XRPD) and X-ray [...] Read more.
This paper aims to develop a principle for selecting the most informative samples for geological research from extensive collections of rock material. As a tool for this selection, we chose an original method of statistical comparison of X-ray powder diffraction (XRPD) and X-ray fluorescence (XRF) data using factor analysis (FA). A collection of carbonatites and aluminosilicate rocks from the Kontozero Devonian carbonatite paleovolcano complex (198 samples) is presented to test our technique. The factors extracted during FA were successfully mineralogically interpreted according to peak positions on the graphs of factor loadings. For the studied rock collection, this approach allowed us to identify more than 20 rock-forming minerals based only on XRPD data. We also found about ten mineral phases, the lines of which are low-intensity, and/or which overlap with more intense peaks of other minerals in the diffraction patterns. The mineralogical interpretation of the factors of such hidden minerals can be performed through electron probe microanalysis (EPMA) of the samples previously selected using FA. In this study, we report on an algorithm that facilitates the selection of the rock samples exhibiting the greatest contrast in mineral and chemical composition and which contain the entire set of mineral phases occurring in the geological object under study. From the collection of Kontozero rocks we examined, the 30 most representative samples were selected, amounting to about 15% of the initial sample set. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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16 pages, 3849 KiB  
Article
Factor Analysis of XRF and XRPD Data on the Example of the Rocks of the Kontozero Carbonatite Complex (NW Russia). Part II: Geological Interpretation
by Evgeniy Kozlov, Ekaterina Fomina and Pavel Khvorov
Crystals 2020, 10(10), 873; https://doi.org/10.3390/cryst10100873 - 26 Sep 2020
Cited by 4 | Viewed by 2670
Abstract
Numerical comparison of mineralogical and geochemical data, which is required in a variety of geological applications, is a challenging task, especially when analyzing extensive sample collections. Herein, we apply factor analysis (FA) to a collection of 198 diffraction patterns of bulk rock samples [...] Read more.
Numerical comparison of mineralogical and geochemical data, which is required in a variety of geological applications, is a challenging task, especially when analyzing extensive sample collections. Herein, we apply factor analysis (FA) to a collection of 198 diffraction patterns of bulk rock samples from the Kontozero carbonatite complex. The mineralogical information hidden in the X-ray powder diffraction (XRPD) data is thereby squeezed down to a set of two dozen variables represented by factor scores (FS). The values of these FSs show a functional relationship with the contents of the minerals composing the rocks. Therefore, factor scores can be considered as a beneficial tool for rapid qualitative and semiquantitative analysis of the mineral composition of rocks. Supplementing principal component analysis (PCA) with FSs as independent variables characterizing the mineral content of rocks allows for the numerical comparison of mineralogical and geochemical data. By PCA, we reveal the main trends in the mineralogical and geochemical evolution of the investigated rocks of the Kontozero complex. Furthermore, the results are obtained in the very first stages of the research. This fact elucidates the potential use of the proposed technique in geological studies and mining. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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12 pages, 3037 KiB  
Article
Cocrystal Formation through Solid-State Reaction between Ibuprofen and Nicotinamide Revealed Using THz and IR Spectroscopy with Multivariate Analysis
by Sae Ishihara, Yusuke Hattori, Makoto Otsuka and Tetsuo Sasaki
Crystals 2020, 10(9), 760; https://doi.org/10.3390/cryst10090760 - 28 Aug 2020
Cited by 9 | Viewed by 3327
Abstract
Cocrystallisation can enhance the solubility and bioavailability of active pharmaceutical ingredients (APIs); this method may be applied to improve the availability of materials that were previously considered unsuitable. Terahertz (THz) spectroscopy provides clear, substance-specific fingerprint spectra; the transparency of the THz wave allows [...] Read more.
Cocrystallisation can enhance the solubility and bioavailability of active pharmaceutical ingredients (APIs); this method may be applied to improve the availability of materials that were previously considered unsuitable. Terahertz (THz) spectroscopy provides clear, substance-specific fingerprint spectra; the transparency of the THz wave allows us to probe inside a sample to identify medicinal materials. In this study, THz and infrared (IR) spectroscopy were used to characterise cocrystallisation in solid-phase reactions between ibuprofen and nicotinamide. Multivariate curve resolution with alternating least squares (MCR-ALS) was applied to both time-dependent THz and IR spectra to identify the intermolecular interactions between these cocrystallising species. The analytical results revealed cocrystal formation through a two-step reaction, in which the steps were dominated by thermal energy and water vapour, respectively. We infer that the presence of water molecules significantly lowered the activation energy of cocrystal formation. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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16 pages, 869 KiB  
Article
Principal Component Analysis (PCA) for Powder Diffraction Data: Towards Unblinded Applications
by Dmitry Chernyshov, Iurii Dovgaliuk, Vadim Dyadkin and Wouter van Beek
Crystals 2020, 10(7), 581; https://doi.org/10.3390/cryst10070581 - 5 Jul 2020
Cited by 13 | Viewed by 4171
Abstract
We analyze the application of Principal Component Analysis (PCA) for untangling the main contributions to changing diffracted intensities upon variation of site occupancy and lattice dimensions induced by external stimuli. The information content of the PCA output consists of certain functions of Bragg [...] Read more.
We analyze the application of Principal Component Analysis (PCA) for untangling the main contributions to changing diffracted intensities upon variation of site occupancy and lattice dimensions induced by external stimuli. The information content of the PCA output consists of certain functions of Bragg angles (loadings) and their evolution characteristics that depend on external variables like pressure or temperature (scores). The physical meaning of the PCA output is to date not well understood. Therefore, in this paper, the intensity contributions are first derived analytically, then compared with the PCA components for model data; finally PCA is applied for the real data on isothermal gas uptake by nanoporous framework γ –Mg(BH 4 ) 2 . We show that, in close agreement with previous analysis of modulation diffraction, the variation of intensity of Bragg lines and the displacements of their positions results in a series of PCA components. Every PCA extracted component may be a mixture of terms carrying information on the average structure, active sub-structure, and their cross-term. The rotational ambiguities, that are an inherently part of PCA extraction, are at the origin of the mixing. For the experimental case considered in the paper, the extraction of the physically meaningful loadings and scores can only be achieved with a rotational correction. Finally, practical recommendations for non-blind applications, i.e., what boundary conditions to apply for the the rotational correction, of PCA for diffraction data are given. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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17 pages, 13337 KiB  
Article
In Situ X-ray Diffraction Study of Xe and CO2 Adsorption in Y Zeolite: Comparison between Rietveld and PCA-Based Analysis
by Eleonora Conterosito, Mattia Lopresti and Luca Palin
Crystals 2020, 10(6), 483; https://doi.org/10.3390/cryst10060483 - 5 Jun 2020
Cited by 7 | Viewed by 3729
Abstract
New very fast and efficient detectors, installed both on laboratory instruments and synchrotron facilities, allow the monitoring of solid-state reactions from subsecond to minute scales with the production of large amounts of data. Traditional “one-by-one” pattern refinement needs complementary approaches, useful to handle [...] Read more.
New very fast and efficient detectors, installed both on laboratory instruments and synchrotron facilities, allow the monitoring of solid-state reactions from subsecond to minute scales with the production of large amounts of data. Traditional “one-by-one” pattern refinement needs complementary approaches, useful to handle hundreds to thousands of X-ray patterns. Principal-component analysis (PCA) has been applied to these fields in the last few years to speed up analysis with the specific goals of assessing data quality, identifying patterns where a reaction occurs, and extracting the kinetics. PCA is applied to the adsorption/desorption of Xe and CO2 within a Y zeolite. CO2 sequestration is a key issue in relation to climate change, while Xe is a critical raw material, and its purification is an important topic for the industry. At first, results were compared to traditional sequential Rietveld refinement. CO2-Y data were also compared with in situ single crystal data to investigate the different potentialities of PCA in the two cases. Two CO2 adsorption sites were confirmed, while three Xe sites were identified. CO2 showed a more linear adsorption trend with decreasing temperature, while Xe showed a more sigmoidal-like trend. Xe only showed site-dependent behavior in adsorption. Finally, PCA and correlation analysis, applied to analyze the parameters obtained from Rietveld refinement, highlighted finer details: in particular, this approach showed that the Y zeolite framework responded differently to CO2 and Xe adsorption. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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Review

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21 pages, 2777 KiB  
Review
Multivariate Analysis Applications in X-ray Diffraction
by Pietro Guccione, Mattia Lopresti, Marco Milanesio and Rocco Caliandro
Crystals 2021, 11(1), 12; https://doi.org/10.3390/cryst11010012 - 25 Dec 2020
Cited by 16 | Viewed by 5264
Abstract
Multivariate analysis (MA) is becoming a fundamental tool for processing in an efficient way the large amount of data collected in X-ray diffraction experiments. Multi-wedge data collections can increase the data quality in case of tiny protein crystals; in situ or operando setups [...] Read more.
Multivariate analysis (MA) is becoming a fundamental tool for processing in an efficient way the large amount of data collected in X-ray diffraction experiments. Multi-wedge data collections can increase the data quality in case of tiny protein crystals; in situ or operando setups allow investigating changes on powder samples occurring during repeated fast measurements; pump and probe experiments at X-ray free-electron laser (XFEL) sources supply structural characterization of fast photo-excitation processes. In all these cases, MA can facilitate the extraction of relevant information hidden in data, disclosing the possibility of automatic data processing even in absence of a priori structural knowledge. MA methods recently used in the field of X-ray diffraction are here reviewed and described, giving hints about theoretical background and possible applications. The use of MA in the framework of the modulated enhanced diffraction technique is described in detail. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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Graphical abstract

46 pages, 9355 KiB  
Review
Spectral Decomposition of X-ray Absorption Spectroscopy Datasets: Methods and Applications
by Andrea Martini and Elisa Borfecchia
Crystals 2020, 10(8), 664; https://doi.org/10.3390/cryst10080664 - 1 Aug 2020
Cited by 27 | Viewed by 6099
Abstract
X-ray absorption spectroscopy (XAS) today represents a widespread and powerful technique, able to monitor complex systems under in situ and operando conditions, while external variables, such us sampling time, sample temperature or even beam position over the analysed sample, are varied. X-ray absorption [...] Read more.
X-ray absorption spectroscopy (XAS) today represents a widespread and powerful technique, able to monitor complex systems under in situ and operando conditions, while external variables, such us sampling time, sample temperature or even beam position over the analysed sample, are varied. X-ray absorption spectroscopy is an element-selective but bulk-averaging technique. Each measured XAS spectrum can be seen as an average signal arising from all the absorber-containing species/configurations present in the sample under study. The acquired XAS data are thus represented by a spectroscopic mixture composed of superimposed spectral profiles associated to well-defined components, characterised by concentration values evolving in the course of the experiment. The decomposition of an experimental XAS dataset in a set of pure spectral and concentration values is a typical example of an inverse problem and it goes, usually, under the name of multivariate curve resolution (MCR). In the present work, we present an overview on the major techniques developed to realize the MCR decomposition together with a selection of related results, with an emphasis on applications in catalysis. Therein, we will highlight the great potential of these methods which are imposing as an essential tool for quantitative analysis of large XAS datasets as well as the directions for further development in synergy with the continuous instrumental progresses at synchrotron sources. Full article
(This article belongs to the Special Issue Multivariate Analysis Applications to Crystallography)
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