1
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Farooq D, Potter ME, Stockenhuber S, Pritchard J, Vamvakeros A, Price SWT, Drnec J, Ruchte B, Paterson J, Peacock M, Beale AM. Chemical Imaging of Carbide Formation and Its Effect on Alcohol Selectivity in Fischer Tropsch Synthesis on Mn-Doped Co/TiO 2 Pellets. ACS Catal 2024; 14:12269-12281. [PMID: 39169906 PMCID: PMC11334103 DOI: 10.1021/acscatal.4c03195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2024] [Revised: 07/25/2024] [Accepted: 07/29/2024] [Indexed: 08/23/2024]
Abstract
X-ray diffraction/scattering computed tomography (XRS-CT) was used to create two-dimensional images, with 20 μm resolution, of passivated Co/TiO2/Mn Fischer-Tropsch catalyst extrudates postreaction after 300 h on stream under industrially relevant conditions. This combination of scattering techniques provided insights into both the spatial variation of the different cobalt phases and the influence that increasing Mn loading has on this. It also demonstrated the presence of a wax coating throughout the extrudate and its capacity to preserve the Co/Mn species in their state in the reactor. Correlating these findings with catalytic performance highlights the crucial phases and active sites within Fischer-Tropsch catalysts required for understanding the tunability of the product distribution between saturated hydrocarbons or oxygenate and olefin products. In particular, a Mn loading of 3 wt % led to an optimum equilibrium between the amount of hexagonal close-packed Co and Co2C phases resulting in maximum oxygenate selectivity. XRS-CT revealed Co2C to be located on the extrudates' periphery, while metallic Co phases were more prevalent toward the center, possibly due to a lower [CO] ratio there. Reduction at 450 °C of a 10 wt % Mn sample resulted in MnTiO3 formation, which inhibited carbide formation and alcohol selectivity. It is suggested that small MnO particles promote Co carburization by decreasing the CO dissociation barrier, and the Co2C phase promotes CO nondissociative adsorption leading to increased oxygenate selectivity. This study highlights the influence of Mn on the catalyst structure and function and the importance of studying catalysts under industrially relevant reaction times.
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Affiliation(s)
- Danial Farooq
- Department
of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K.
- Research
Complex at Harwell, Rutherford Appleton Laboratories, Harwell Science and Innovation Campus, Harwell,Didcot OX11 0FA, U.K.
| | - Matthew E. Potter
- Department
of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K.
- Research
Complex at Harwell, Rutherford Appleton Laboratories, Harwell Science and Innovation Campus, Harwell,Didcot OX11 0FA, U.K.
| | - Sebastian Stockenhuber
- Department
of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K.
- Research
Complex at Harwell, Rutherford Appleton Laboratories, Harwell Science and Innovation Campus, Harwell,Didcot OX11 0FA, U.K.
| | - Jay Pritchard
- Department
of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K.
- Research
Complex at Harwell, Rutherford Appleton Laboratories, Harwell Science and Innovation Campus, Harwell,Didcot OX11 0FA, U.K.
| | | | | | - Jakub Drnec
- European
Synchrotron Radiation Facility, ID 31 Beamline, BP 220, Grenoble CedexF-38043, France
| | - Ben Ruchte
- IXRF
Systems, 10421 Old Manchaca
Road, Suite 620, Austin, Texas 78748, United States
| | - James Paterson
- BP, Applied
Sciences, Innovation & Engineering, Saltend, Hull HU12 8DS, U.K.
| | - Mark Peacock
- BP, Applied
Sciences, Innovation & Engineering, Saltend, Hull HU12 8DS, U.K.
| | - Andrew M. Beale
- Department
of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K.
- Research
Complex at Harwell, Rutherford Appleton Laboratories, Harwell Science and Innovation Campus, Harwell,Didcot OX11 0FA, U.K.
- Finden, Building R71, Harwell Campus, Oxfordshire OX11 0QX, U.K.
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2
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Kjær ETS, Anker AS, Kirsch A, Lajer J, Aalling-Frederiksen O, Billinge SJL, Jensen KMØ. MLstructureMining: a machine learning tool for structure identification from X-ray pair distribution functions. DIGITAL DISCOVERY 2024; 3:908-918. [PMID: 38756225 PMCID: PMC11094694 DOI: 10.1039/d4dd00001c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Accepted: 03/27/2024] [Indexed: 05/18/2024]
Abstract
Synchrotron X-ray techniques are essential for studies of the intrinsic relationship between synthesis, structure, and properties of materials. Modern synchrotrons can produce up to 1 petabyte of data per day. Such amounts of data can speed up materials development, but also comes with a staggering growth in workload, as the data generated must be stored and analyzed. We present an approach for quickly identifying an atomic structure model from pair distribution function (PDF) data from (nano)crystalline materials. Our model, MLstructureMining, uses a tree-based machine learning (ML) classifier. MLstructureMining has been trained to classify chemical structures from a PDF and gives a top-3 accuracy of 99% on simulated PDFs not seen during training, with a total of 6062 possible classes. We also demonstrate that MLstructureMining can identify the chemical structure from experimental PDFs from nanoparticles of CoFe2O4 and CeO2, and we show how it can be used to treat an in situ PDF series collected during Bi2Fe4O9 formation. Additionally, we show how MLstructureMining can be used in combination with the well-known methods, principal component analysis (PCA) and non-negative matrix factorization (NMF) to analyze data from in situ experiments. MLstructureMining thus allows for real-time structure characterization by screening vast quantities of crystallographic information files in seconds.
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Affiliation(s)
- Emil T S Kjær
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Andy S Anker
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Andrea Kirsch
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Joakim Lajer
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | | | - Simon J L Billinge
- Department of Applied Physics and Applied Mathematics Science, Columbia University New York NY 10027 USA
| | - Kirsten M Ø Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
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3
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Lombardi J, Yang L, Farahmand N, Ruffino A, Younes A, Spanier JE, Billinge SJL, O'Brien S. Structure and phase transitions in niobium and tantalum derived nanoscale transition metal perovskites, Ba(Ti,MV)O3, M=Nb,Ta. J Chem Phys 2024; 160:134702. [PMID: 38573849 DOI: 10.1063/5.0192488] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/19/2024] [Indexed: 04/06/2024] Open
Abstract
The prospect of creating ferroelectric or high permittivity nanomaterials provides motivation for investigating complex transition metal oxides of the form Ba(Ti, MV)O3, where M = Nb or Ta. Solid state processing typically produces mixtures of crystalline phases, rarely beyond minimally doped Nb/Ta. Using a modified sol-gel method, we prepared single phase nanocrystals of Ba(Ti, M)O3. Compositional and elemental analysis puts the empirical formulas close to BaTi0.5Nb0.5O3-δ and BaTi0.5Ta0.5O3-δ. For both materials, a reversible temperature dependent phase transition (non-centrosymmetric to symmetric) is observed in the Raman spectrum in the region 533-583 K (260-310 °C); for Ba(Ti, Nb)O3, the onset is at 543 K (270 °C); and for Ba(Ti, Ta)O3, the onset is at 533 K (260 °C), which are comparable with 390-393 K (117-120 °C) for bulk BaTiO3. The crystal structure was resolved by examination of the powder x-ray diffraction and atomic pair distribution function (PDF) analysis of synchrotron total scattering data. It was postulated whether the structure adopted at the nanoscale was single or double perovskite. Double perovskites (A2B'B″O6) are characterized by the type and extent of cation ordering, which gives rise to higher symmetry crystal structures. PDF analysis was used to examine all likely candidate structures and to look for evidence of higher symmetry. The feasible phase space that evolves includes the ordered double perovskite structure Ba2(Ti, MV)O6 (M = Nb, Ta) Fm-3m, a disordered cubic structure, as a suitable high temperature analog, Ba(Ti, MV)O3Pm-3m, and an orthorhombic Ba(Ti, MV)O3Amm2, a room temperature structure that presents an unusually high level of lattice displacement, possibly due to octahedral tilting, and indication of a highly polarized crystal.
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Affiliation(s)
- Julien Lombardi
- The CUNY Energy Institute, City University of New York, Steinman Hall, 160 Convent Avenue, The City College of New York, New York, New York 10031, USA
- Department of Chemistry and Biochemistry, The City College of New York, 1024 Marshak, 160 Convent Avenue, New York, New York 10031, USA
- Ph.D. Program in Chemistry, The Graduate Center, The City University of New York, New York, New York 10016, USA
| | - Long Yang
- School of Materials Science and Engineering, Tongji University, 4800 Caoan Road, Shanghai 201804, China
| | - Nasim Farahmand
- The CUNY Energy Institute, City University of New York, Steinman Hall, 160 Convent Avenue, The City College of New York, New York, New York 10031, USA
- Department of Chemistry and Biochemistry, The City College of New York, 1024 Marshak, 160 Convent Avenue, New York, New York 10031, USA
- Ph.D. Program in Chemistry, The Graduate Center, The City University of New York, New York, New York 10016, USA
| | - Anthony Ruffino
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Ali Younes
- Department of Chemistry, Hunter College of the City University of New York, 695 Park Ave., New York, New York 10065, USA
| | - Jonathan E Spanier
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA
- Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Simon J L Billinge
- Department of Applied Physics and Applied Mathematics, Columbia University, 500 West 120th Street, New York, New York 10027, USA
| | - Stephen O'Brien
- The CUNY Energy Institute, City University of New York, Steinman Hall, 160 Convent Avenue, The City College of New York, New York, New York 10031, USA
- Department of Chemistry and Biochemistry, The City College of New York, 1024 Marshak, 160 Convent Avenue, New York, New York 10031, USA
- Ph.D. Program in Chemistry, The Graduate Center, The City University of New York, New York, New York 10016, USA
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4
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Anker AS, Friis-Jensen U, Johansen FL, Billinge SJL, Jensen KMØ. ClusterFinder: a fast tool to find cluster structures from pair distribution function data. Acta Crystallogr A Found Adv 2024; 80:213-220. [PMID: 38420993 PMCID: PMC10913672 DOI: 10.1107/s2053273324001116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 02/01/2024] [Indexed: 03/02/2024] Open
Abstract
A novel automated high-throughput screening approach, ClusterFinder, is reported for finding candidate structures for atomic pair distribution function (PDF) structural refinements. Finding starting models for PDF refinements is notoriously difficult when the PDF originates from nanoclusters or small nanoparticles. The reported ClusterFinder algorithm can screen 104 to 105 candidate structures from structural databases such as the Inorganic Crystal Structure Database (ICSD) in minutes, using the crystal structures as templates in which it looks for atomic clusters that result in a PDF similar to the target measured PDF. The algorithm returns a rank-ordered list of clusters for further assessment by the user. The algorithm has performed well for simulated and measured PDFs of metal-oxido clusters such as Keggin clusters. This is therefore a powerful approach to finding structural cluster candidates in a modelling campaign for PDFs of nanoparticles and nanoclusters.
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Affiliation(s)
- Andy S. Anker
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
| | - Ulrik Friis-Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
- Department of Computer Science, University of Copenhagen, 2100 Copenhagen Ø, Denmark
| | - Frederik L. Johansen
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
- Department of Computer Science, University of Copenhagen, 2100 Copenhagen Ø, Denmark
| | - Simon J. L Billinge
- Department of Applied Physics and Applied Mathematics Science, Columbia University, New York, NY 10027, USA
| | - Kirsten M. Ø. Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
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5
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Anker AS, Kjær ETS, Juelsholt M, Jensen KMØ. POMFinder: identifying polyoxometallate cluster structures from pair distribution function data using explainable machine learning. J Appl Crystallogr 2024; 57:34-43. [PMID: 38322723 PMCID: PMC10840315 DOI: 10.1107/s1600576723010014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Accepted: 11/16/2023] [Indexed: 02/08/2024] Open
Abstract
Characterization of a material structure with pair distribution function (PDF) analysis typically involves refining a structure model against an experimental data set, but finding or constructing a suitable atomic model for PDF modelling can be an extremely labour-intensive task, requiring carefully browsing through large numbers of possible models. Presented here is POMFinder, a machine learning (ML) classifier that rapidly screens a database of structures, here polyoxometallate (POM) clusters, to identify candidate structures for PDF data modelling. The approach is shown to identify suitable POMs from experimental data, including in situ data collected with fast acquisition times. This automated approach has significant potential for identifying suitable models for structure refinement to extract quantitative structural parameters in materials chemistry research. POMFinder is open source and user friendly, making it accessible to those without prior ML knowledge. It is also demonstrated that POMFinder offers a promising modelling framework for combined modelling of multiple scattering techniques.
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Affiliation(s)
- Andy S. Anker
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
| | - Emil T. S. Kjær
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
| | - Mikkel Juelsholt
- Department of Materials, University of Oxford, Parks Road, Oxford, Oxfordshire OX1 3PH, United Kingdom
| | - Kirsten M. Ø. Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen, 2100 Copenhagen Ø, Denmark
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6
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Anker AS, Butler KT, Selvan R, Jensen KMØ. Machine learning for analysis of experimental scattering and spectroscopy data in materials chemistry. Chem Sci 2023; 14:14003-14019. [PMID: 38098730 PMCID: PMC10718081 DOI: 10.1039/d3sc05081e] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 11/20/2023] [Indexed: 12/17/2023] Open
Abstract
The rapid growth of materials chemistry data, driven by advancements in large-scale radiation facilities as well as laboratory instruments, has outpaced conventional data analysis and modelling methods, which can require enormous manual effort. To address this bottleneck, we investigate the application of supervised and unsupervised machine learning (ML) techniques for scattering and spectroscopy data analysis in materials chemistry research. Our perspective focuses on ML applications in powder diffraction (PD), pair distribution function (PDF), small-angle scattering (SAS), inelastic neutron scattering (INS), and X-ray absorption spectroscopy (XAS) data, but the lessons that we learn are generally applicable across materials chemistry. We review the ability of ML to identify physical and structural models and extract information efficiently and accurately from experimental data. Furthermore, we discuss the challenges associated with supervised ML and highlight how unsupervised ML can mitigate these limitations, thus enhancing experimental materials chemistry data analysis. Our perspective emphasises the transformative potential of ML in materials chemistry characterisation and identifies promising directions for future applications. The perspective aims to guide newcomers to ML-based experimental data analysis.
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Affiliation(s)
- Andy S Anker
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Keith T Butler
- Department of Chemistry, University College London Gower Street London WC1E 6BT UK
| | - Raghavendra Selvan
- Department of Computer Science, University of Copenhagen 2100 Copenhagen Ø Denmark
- Department of Neuroscience, University of Copenhagen 2200 Copenhagen N Denmark
| | - Kirsten M Ø Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
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7
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Kløve M, Sommer S, Iversen BB, Hammer B, Dononelli W. A Machine-Learning-Based Approach for Solving Atomic Structures of Nanomaterials Combining Pair Distribution Functions with Density Functional Theory. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2208220. [PMID: 36630711 DOI: 10.1002/adma.202208220] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 11/25/2022] [Indexed: 06/17/2023]
Abstract
Determination of crystal structures of nanocrystalline or amorphous compounds is a great challenge in solid-state chemistry and physics. Pair distribution function (PDF) analysis of X-ray or neutron total scattering data has proven to be a key element in tackling this challenge. However, in most cases, a reliable structural motif is needed as a starting configuration for structure refinements. Here, an algorithm that is able to determine the crystal structure of an unknown compound by means of an on-the-fly trained machine learning model, which combines density functional theory calculations with comparison of calculated and measured PDFs for global optimization in an artificial landscape, is presented. Due to the nature of this landscape, even metastable configurations and stacking disorders can be identified.
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Affiliation(s)
- Magnus Kløve
- Center for Integrated Materials Research, Department of Chemistry and iNano, Aarhus University, Aarhus, 8000, Denmark
| | - Sanna Sommer
- Center for Integrated Materials Research, Department of Chemistry and iNano, Aarhus University, Aarhus, 8000, Denmark
| | - Bo B Iversen
- Center for Integrated Materials Research, Department of Chemistry and iNano, Aarhus University, Aarhus, 8000, Denmark
| | - Bjørk Hammer
- Center for Interstellar Catalysis, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus, C 8000, Denmark
| | - Wilke Dononelli
- MAPEX Center for Materials and Processes, Bremen Center for Computational Materials Science and Hybrid Materials Interfaces Group, Bremen University, 28359, Bremen, Germany
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8
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Kjær ETS, Anker AS, Weng MN, Billinge SJL, Selvan R, Jensen KMØ. DeepStruc: towards structure solution from pair distribution function data using deep generative models. DIGITAL DISCOVERY 2023; 2:69-80. [PMID: 36798882 PMCID: PMC9923795 DOI: 10.1039/d2dd00086e] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 11/28/2022] [Indexed: 11/29/2022]
Abstract
Structure solution of nanostructured materials that have limited long-range order remains a bottleneck in materials development. We present a deep learning algorithm, DeepStruc, that can solve a simple monometallic nanoparticle structure directly from a Pair Distribution Function (PDF) obtained from total scattering data by using a conditional variational autoencoder. We first apply DeepStruc to PDFs from seven different structure types of monometallic nanoparticles, and show that structures can be solved from both simulated and experimental PDFs, including PDFs from nanoparticles that are not present in the training distribution. We also apply DeepStruc to a system of hcp, fcc and stacking faulted nanoparticles, where DeepStruc recognizes stacking faulted nanoparticles as an interpolation between hcp and fcc nanoparticles and is able to solve stacking faulted structures from PDFs. Our findings suggests that DeepStruc is a step towards a general approach for structure solution of nanomaterials.
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Affiliation(s)
- Emil T S Kjær
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Andy S Anker
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Marcus N Weng
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Simon J L Billinge
- Department of Applied Physics and Applied Mathematics Science, Columbia University New York NY 10027 USA
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory Upton NY 11973 USA
| | - Raghavendra Selvan
- Department of Computer Science, University of Copenhagen 2100 Copenhagen Ø Denmark
- Department of Neuroscience, University of Copenhagen 2200 Copenhagen N Denmark
| | - Kirsten M Ø Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
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9
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Zimmerli NK, Müller CR, Abdala PM. Deciphering the structure of heterogeneous catalysts across scales using pair distribution function analysis. TRENDS IN CHEMISTRY 2022. [DOI: 10.1016/j.trechm.2022.06.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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10
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Thatcher Z, Liu CH, Yang L, McBride BC, Thinh Tran G, Wustrow A, Karlsen MA, Neilson JR, Ravnsbæk DB, Billinge SJL. nmfMapping: a cloud-based web application for non-negative matrix factorization of powder diffraction and pair distribution function datasets. ACTA CRYSTALLOGRAPHICA SECTION A FOUNDATIONS AND ADVANCES 2022; 78:242-248. [DOI: 10.1107/s2053273322002522] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2021] [Accepted: 03/04/2022] [Indexed: 11/10/2022]
Abstract
A cloud-hosted web-based software application, nmfMapping, for carrying out a non-negative matrix factorization of a set of powder diffraction or atomic pair distribution function datasets is described. This application allows structure scientists to find trends rapidly in sets of related data such as from in situ and operando diffraction experiments. The application is easy to use and does not require any programming expertise. It is available at https://pdfitc.org/.
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11
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Terban MW, Billinge SJL. Structural Analysis of Molecular Materials Using the Pair Distribution Function. Chem Rev 2022; 122:1208-1272. [PMID: 34788012 PMCID: PMC8759070 DOI: 10.1021/acs.chemrev.1c00237] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Indexed: 12/16/2022]
Abstract
This is a review of atomic pair distribution function (PDF) analysis as applied to the study of molecular materials. The PDF method is a powerful approach to study short- and intermediate-range order in materials on the nanoscale. It may be obtained from total scattering measurements using X-rays, neutrons, or electrons, and it provides structural details when defects, disorder, or structural ambiguities obscure their elucidation directly in reciprocal space. While its uses in the study of inorganic crystals, glasses, and nanomaterials have been recently highlighted, significant progress has also been made in its application to molecular materials such as carbons, pharmaceuticals, polymers, liquids, coordination compounds, composites, and more. Here, an overview of applications toward a wide variety of molecular compounds (organic and inorganic) and systems with molecular components is presented. We then present pedagogical descriptions and tips for further implementation. Successful utilization of the method requires an interdisciplinary consolidation of material preparation, high quality scattering experimentation, data processing, model formulation, and attentive scrutiny of the results. It is hoped that this article will provide a useful reference to practitioners for PDF applications in a wide realm of molecular sciences, and help new practitioners to get started with this technique.
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Affiliation(s)
- Maxwell W. Terban
- Max
Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Simon J. L. Billinge
- Department
of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
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12
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Schlesinger C, Habermehl S, Prill D. Structure determination of organic compounds by a fit to the pair distribution function from scratch without prior indexing. J Appl Crystallogr 2021; 54:776-786. [PMID: 34188612 PMCID: PMC8202035 DOI: 10.1107/s1600576721002569] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 03/08/2021] [Indexed: 11/20/2022] Open
Abstract
A method for the ab initio crystal structure determination of organic compounds by a fit to the pair distribution function (PDF), without prior knowledge of lattice parameters and space group, has been developed. The method is called 'PDF-Global-Fit' and is implemented by extension of the program FIDEL (fit with deviating lattice parameters). The structure solution is based on a global optimization approach starting from random structural models in selected space groups. No prior indexing of the powder data is needed. The new method requires only the molecular geometry and a carefully determined PDF. The generated random structures are compared with the experimental PDF and ranked by a similarity measure based on cross-correlation functions. The most promising structure candidates are fitted to the experimental PDF data using a restricted simulated annealing structure solution approach within the program TOPAS, followed by a structure refinement against the PDF to identify the correct crystal structure. With the PDF-Global-Fit it is possible to determine the local structure of crystalline and disordered organic materials, as well as to determine the local structure of unindexable powder patterns, such as nanocrystalline samples, by a fit to the PDF. The success of the method is demonstrated using barbituric acid as an example. The crystal structure of barbituric acid form IV solved and refined by the PDF-Global-Fit is in excellent agreement with the published crystal structure data.
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Affiliation(s)
- Carina Schlesinger
- Institut für Anorganische und Analytische Chemie, Goethe Universität, Max-von-Laue-Strasse 7, Frankfurt am Main, 60437, Germany
| | - Stefan Habermehl
- Institut für Anorganische und Analytische Chemie, Goethe Universität, Max-von-Laue-Strasse 7, Frankfurt am Main, 60437, Germany
| | - Dragica Prill
- Institut für Anorganische und Analytische Chemie, Goethe Universität, Max-von-Laue-Strasse 7, Frankfurt am Main, 60437, Germany
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13
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Liu CH, Wright CJ, Gu R, Bandi S, Wustrow A, Todd PK, O'Nolan D, Beauvais ML, Neilson JR, Chupas PJ, Chapman KW, Billinge SJL. Validation of non-negative matrix factorization for rapid assessment of large sets of atomic pair distribution function data. J Appl Crystallogr 2021. [DOI: 10.1107/s160057672100265x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
The use of the non-negative matrix factorization (NMF) technique is validated for automatically extracting physically relevant components from atomic pair distribution function (PDF) data from time-series data such as in situ experiments. The use of two matrix-factorization techniques, principal component analysis and NMF, on PDF data is compared in the context of a chemical synthesis reaction taking place in a synchrotron beam, applying the approach to synthetic data where the correct composition is known and on measured PDFs from previously published experimental data. The NMF approach yields mathematical components that are very close to the PDFs of the chemical components of the system and a time evolution of the weights that closely follows the ground truth. Finally, it is discussed how this would appear in a streaming context if the analysis were being carried out at the beamline as the experiment progressed.
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14
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Yang L, Culbertson EA, Thomas NK, Vuong HT, Kjær ETS, Jensen KMØ, Tucker MG, Billinge SJL. A cloud platform for atomic pair distribution function analysis: PDFitc. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2021; 77:2-6. [PMID: 33399126 PMCID: PMC7842210 DOI: 10.1107/s2053273320013066] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 09/26/2020] [Indexed: 11/21/2022]
Abstract
A new web platform is presented for the pair distribution function (PDF) community to use and share advanced PDF analysis software in the cloud. A cloud web platform for analysis and interpretation of atomic pair distribution function (PDF) data (PDFitc) is described. The platform is able to host applications for PDF analysis to help researchers study the local and nanoscale structure of nanostructured materials. The applications are designed to be powerful and easy to use and can, and will, be extended over time through community adoption and development. The currently available PDF analysis applications, structureMining, spacegroupMining and similarityMapping, are described. In the first and second the user uploads a single PDF and the application returns a list of best-fit candidate structures, and the most likely space group of the underlying structure, respectively. In the third, the user can upload a set of measured or calculated PDFs and the application returns a matrix of Pearson correlations, allowing assessment of the similarity between different data sets. structureMining is presented here as an example to show the easy-to-use workflow on PDFitc. In the future, as well as using the PDFitc applications for data analysis, it is hoped that the community will contribute their own codes and software to the platform.
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Affiliation(s)
- Long Yang
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
| | - Elizabeth A Culbertson
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
| | - Nancy K Thomas
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
| | - Hung T Vuong
- Department of Chemistry, Columbia University, New York, NY 10027, USA
| | - Emil T S Kjær
- Department of Chemistry and Nanoscience Center, University of Copenhagen, Copenhagen, DK 2100, Denmark
| | - Kirsten M Ø Jensen
- Department of Chemistry and Nanoscience Center, University of Copenhagen, Copenhagen, DK 2100, Denmark
| | - Matthew G Tucker
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
| | - Simon J L Billinge
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
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Christiansen TL, Cooper SR, Jensen KMØ. There's no place like real-space: elucidating size-dependent atomic structure of nanomaterials using pair distribution function analysis. NANOSCALE ADVANCES 2020; 2:2234-2254. [PMID: 36133369 PMCID: PMC9418950 DOI: 10.1039/d0na00120a] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 05/05/2020] [Indexed: 05/25/2023]
Abstract
The development of new functional materials builds on an understanding of the intricate relationship between material structure and properties, and structural characterization is a crucial part of materials chemistry. However, elucidating the atomic structure of nanomaterials remains a challenge using conventional diffraction techniques due to the lack of long-range atomic order. Over the past decade, Pair Distribution Function (PDF) analysis of X-ray or neutron total scattering data has become a mature and well-established method capable of giving insight into the atomic structure in nanomaterials. Here, we review the use of PDF analysis and modelling in characterization of a range of different nanomaterials that exhibit unique atomic structure compared to the corresponding bulk materials. A brief introduction to PDF analysis and modelling is given, followed by examples of how essential structural information can be extracted from PDFs using both model-free and advanced modelling methods. We put an emphasis on how the intuitive nature of the PDF can be used for understanding important structural motifs, and on the diversity of applications of PDF analysis to nanostructure problems.
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Affiliation(s)
| | - Susan R Cooper
- Department of Chemistry and Nanoscience Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Kirsten M Ø Jensen
- Department of Chemistry and Nanoscience Center, University of Copenhagen 2100 Copenhagen Ø Denmark
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