Christopher L. Farrow

Columbia University, New York City, New York, United States

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Publications (19)97.54 Total impact

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    ABSTRACT: In this work, the concept of complex modeling (CM) is tested by carrying out a co-refinement of the atomic pair distribution function and small-angle X-ray scattering data from CdS nanoparticles. It is shown that, compared with either single technique alone, the CM approach yields a more accurate and robust structural insight into the atomic structure and morphology of nanoparticles. This work opens the door for the application of CM to a wider class of nanomaterials and for the incorporation of additional experimental and theoretical techniques into these studies.
    Journal of Applied Crystallography 04/2014; 47(2). · 3.34 Impact Factor
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    Xiaohao Yang, Pavol Juhas, Christopher L. Farrow, Simon J. L. Billinge
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    ABSTRACT: PDFgetXgui is a software for Pair Distribution Function (PDF) transformation and data visualization. It provides a convenient GUI for PDF transformation and many functions that help user quickly obtaining PDF including real-time plotting for transformation parameters adjusting. It also has 2D and 3D plot modes for data visualization.
    02/2014;
  • Xiaohao Yang, Pavol Juhas, Christopher L. Farrow, Simon J. L. Billinge
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    ABSTRACT: The PDFgetXgui software program is described. It is for obtaining and visualizing atomic pair distribution functions (PDF) from X-ray powder diffraction data. It provides a convenient GUI for the PDFgetX3 program allowing the user to easily obtain PDFs from raw 1D powder diffraction patterns. It is specially useful for working with large numbers of datasets such as from high throughput measurements. The analysis of multiple datasets may be saved as projects and revisited later with the complete parameter state saved. Multiple datasets may be plotted in 2D waterfall and 3D modes. Plots and processed data may be saved as individual files for further processing. The software is written in Python and runs on multiple platforms.
    01/2014;
  • Simon J L Billinge, Christopher L Farrow
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    ABSTRACT: We examine the equations to obtain atomic pair distribution functions (PDFs) from x-ray, neutron and electron powder diffraction data with a view to obtaining reliable and accurate PDFs from the raw data using a largely ad hoc correction process. We find that this should be possible under certain circumstances that hold, to a reasonably good approximation, in many modern experiments. We describe a variational approach that could be applied to find data correction parameters that is highly automatable and should require little in the way of user inputs yet results in quantitatively reliable PDFs, modulo unknown scale factors that are often not of scientific interest when profile fitting models are applied to the data with scale factor as a parameter. We have worked on a particular implementation of these ideas and demonstrate that it yields PDFs that are of comparable quality to those obtained with the existing x-ray data reduction program PDFgetX2. This opens the door to rapid and highly automated processing of raw data to obtain PDFs.
    Journal of Physics Condensed Matter 11/2013; 25(45):454202. · 2.22 Impact Factor
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    ABSTRACT: Continual improvements in solar-to-fuels catalysis require a genuine understanding of catalyst structure-function relationships, not only with respect to local order, but also intermediate-range structure. We report the X-ray pair distribution function (PDF) analysis of the nanoscale order of an oxidic cobalt-based water splitting catalyst (Co-OEC) and uncover an electrolyte-dependence in the intermediate-range structure of catalyst films. Whereas catalyst films formed in borate electrolyte (CoBi) exhibit coherent domains consisting of 3-4 nm cobaltate clusters with up to 3 layers, films deposited in phosphate electrolyte (CoPi) comprise significantly smaller clusters that are not coherently stacked. These structural insights are correlated with marked differences in activity between CoPi and CoBi films.
    Journal of the American Chemical Society 04/2013; · 10.68 Impact Factor
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    Pavol Juhas, Timur Davis, Christopher L. Farrow, Simon J. L. Billinge
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    ABSTRACT: PDFgetX3 is a new software application for converting X-ray powder diffraction data to atomic pair distribution function (PDF). PDFgetX3 has been designed for ease of use, speed and automated operation. The software can readily process hundreds of X-ray patterns within few seconds and is thus useful for high-throughput PDF studies, that measure numerous datasets as a function of time, temperature or other environment parameters. In comparison to the preceding programs, PDFgetX3 requires fewer inputs, less user experience and can be readily adopted by novice users. The live-plotting interactive feature allows to assess the effects of calculation parameters and select their optimum values. PDFgetX3 uses an ad-hoc data correction method, where the slowly-changing structure independent signal is filtered out to obtain coherent X-ray intensities that contain structure information. The outputs from PDFgetX3 have been verified by processing experimental PDFs from inorganic, organic and nanosized samples and comparing them to their counterparts from previous established software. In spite of different algorithm, the obtained PDFs were nearly identical and yielded highly similar results when used in structure refinement. PDFgetX3 is written in Python language and features well documented, reusable codebase. The software can be used either as standalone application or as a library of PDF-processing functions that can be called on from other Python scripts. The software is free for open academic research, but requires paid license for commercial use.
    J. Appl. Crystallogr. 11/2012; 46(2).
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    Christopher L. Farrow, Simon J. L. Billinge
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    ABSTRACT: We examine the equations to obtain atomic pair distribution functions (PDFs) from x-ray, neutron and electron powder diffraction data with a view to obtaining reliable and accurate PDFs from the raw data using a largely \emph{ad hoc} correction process. We find that this should be possible under certain circumstances that hold, to a reasonably good approximation, in many modern experiments. We describe a variational approach that could be applied to find data correction parameters that is highly automatable and should require little in the way of user inputs yet results in quantitatively reliable PDFs, modulo unknown scale factors that are often not of scientific interest when profile fitting models are applied to the data with scale-factor as a parameter. We have worked on a particular implementation of these ideas and demonstrate that it yields PDFs that are of comparable quality to those obtained with existing x-ray data reduction program PDFgetX2. This opens the door to rapid and highly automated processing of raw data to obtain PDFs.
    11/2012;
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    ABSTRACT: Manganese (Mn) oxides are among the most reactive natural minerals and play an important role in elemental cycling in oceanic and terrestrial environments. A large portion of naturally-occurring Mn oxides tend to be poorly-crystalline and/or nanocrystalline, with not fully resolved crystal structures. In this study, the crystal structures of their synthetic analogs including acid birnessite (AcidBir), δ-MnOâ, polymeric MnOâ (PolyMnOâ) and a bacteriogenic Mn oxide (BioMnOâ), have been revealed using atomic pair distribution function (PDF) analysis. Results unambiguously verify that these Mn oxides are layered materials. The best models that accurately allow simulation of pair distribution functions (PDFs) belong to the monoclinic C12/m1 space group with a disk-like shape. The single MnOâ layers in the average structures deviate significantly from hexagonal symmetry, in contrast to the results of previous studies based on X-ray diffraction analysis in reciprocal space. Manganese occupancies in MnOâ layers are estimated to be 0.936, 0.847, 0.930 and 0.935, for AcidBir, BioMnOâ, δ-MnOâ and PolyMnOâ, respectively; however, occupancies of interlayer cations and water molecules cannot be accurately determined using the models in this study. The coherent scattering domains (CSDs) of PolyMnOâ, δ-MnOâ and BioMnOâ are at the nanometer scale, comprising one to three MnOâ layers stacked with a high disorder in the crystallographic c-axis direction. Overall, the results of this study advance our understanding of the mineralogy of Mn oxide minerals in the environment.
    Geochimica et Cosmochimica Acta 03/2012; 81:39-55. · 3.88 Impact Factor
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    ABSTRACT: We have systematically studied the optimal real-space sampling of atomic pair distribution (PDF) data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we show that not only is the optimal sampling bounded by the Nyquist interval described by the Nyquist-Shannon (NS) sampling theorem as expected, but near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty estimates in the modeling. Surprisingly, we find that PDF refinements quickly become unstable for data on coarser grids. Although the Nyquist-Shannon sampling theorem is well known, it has not been applied to PDF refinements, despite the growing popularity of the PDF method and its adoption in a growing number of communities. Here, we give explicit expressions for the application of NS sampling theorem to the PDF case, and establish through modeling that it is working in practice, which lays the groundwork for this to become more widely adopted. This has implications for the speed and complexity of possible refinements that can be carried out many times faster than currently with no loss of information, and it establishes a theoretically sound limit on the amount of information contained in the PDF that will prevent over-parametrization during modeling.
    Physical review. B, Condensed matter 10/2011; 84(13). · 3.77 Impact Factor
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    ABSTRACT: In the two step synthesis of thiolate-monolayer protected clusters (MPCs), the first step of the reaction is a mild reduction of gold(III) by thiols that generates gold(I) thiolate complexes as intermediates. Using tiopronin (Tio) as the thiol reductant, the characterization of the intermediate Au(4)Tio(4) complex was accomplished with various analytical and structural techniques. Nuclear magnetic resonance (NMR), elemental analysis, thermogravimetric analysis (TGA), and matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS) were all consistent with a cyclic gold(I)-thiol tetramer structure, and final structural analysis was gathered through the use of powder diffraction and pair distribution functions (PDF). Crystallographic data has proved challenging for almost all previous gold(I)-thiolate complexes. Herein, a novel characterization technique when combined with standard analytical assessment to elucidate structure without crystallographic data proved invaluable to the study of these complexes. This in conjunction with other analytical techniques, in particular mass spectrometry, can elucidate a structure when crystallographic data is unavailable. In addition, luminescent properties provided evidence of aurophilicity within the molecule. The concept of aurophilicity has been introduced to describe a select group of gold-thiolate structures, which possess unique characteristics, mainly red photoluminescence and a distinct Au-Au intramolecular distance indicating a weak metal-metal bond as also evidenced by the structural model of the tetramer. Significant features of both the tetrameric and the aurophilic properties of the intermediate gold(I) tiopronin complex are retained after borohydride reduction to form the MPC, including gold(I) tiopronin partial rings as capping motifs, or "staples", and weak red photoluminescence that extends into the Near Infrared region.
    Inorganic Chemistry 11/2010; 49(23):10858-66. · 4.59 Impact Factor
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    ABSTRACT: SrRietveld is a highly automated software toolkit for Rietveld refinement. Compared to traditional refinement programs, it is more efficient to use and easier to learn. It is designed for modern high throughput diffractometers and capable of processing large numbers of data-sets with minimal effort. The new software currently uses conventional Rietveld refinement engines, automating GSAS and FullProf refinements. However, as well as automating and extending many tasks associated with these programs, it is designed in a flexible and extensible way so that in the future these engines can be replaced with new refinement engines as they become available. SrRietveld is an open source software package developed in Python. Comment: 14 pages, 3 figures, 2 tables
    Journal of Applied Crystallography 06/2010; · 3.34 Impact Factor
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    ABSTRACT: The pair distribution function (PDF) method provides detailed information about nanostructure and efficient software is available for refining PDF data to starting structures provided by the user. Starting structures may be developed using intuition, homologous structures from the literature, or by using ab-initio theoretical structures. However, in studies of nanoparticles good starting structures are hard to identify, particularly in systems where complex surface distortions occur. Moreover, refinement from random structures typically fails, or converges to unphysical structures. We quantify this problem through a systematic study of PDF refinement using starting structures that are randomly perturbed variants of the correct structures and identify the threshold perturbations beyond which refinement fails. To alleviate the difficulties in guessing or searching over starting structures it would be ideal if good starting structures could be found directly from PDF data. We outline our progress in this direction.
    03/2010;
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    ABSTRACT: In iron pnictides [1] presence of orbital degrees of freedom on the Fe site is one of the notable differences from cuprate superconductors (SC). The presence of an electron in a particular orbital directly influences the positions of the nearest neighbor ions and couples strongly to the lattice. The orbital degrees of freedom potentially strongly enhance the electron-phonon coupling, and could play a central role in the SC pairing mechanism. Understanding how this orbital occupancy evolves as a function of doping and temperature is of crucial importance. Probing orbital occupancy directly is difficult as the orbital order is expected to be ferro (identical from site to site), and thus not amenable to conventional scattering experiments. Doping towards the SC state destroys long range magnetic order, but the presence of short range ferro-orbital order is suspected. Results will be presented of a systematic x-ray total scattering based atomic pair distribution function study, to map out the local structure across the phase diagram of Ba1-xKxFe2As2 [2], and investigate the importance of the orbital degree of freedom in this new class of materials. [1] Y. Kamihara et al., J. Am. Chem. Soc. 130, 3296 (2008). [2] Y.J. Uemura, Nature Materials 8, 253 (2009). Supported by the DOE under Contract. No. DE-AC02-98CH10886.
    03/2010;
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    Christopher L. Farrow, Chong-Yu Ruan, Simon J L Billinge
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    ABSTRACT: We describe the quantitative refinement of nanoparticle structures from gold nanoparticles probed by ultrafast electron crystallography (UEC). We establish the equivalence between the modified radial distribution function employed in UEC and the atomic pair distribution function (PDF) used in x-ray and neutron powder diffraction analysis. By leveraging PDF refinement techniques, we demonstrate that UEC data are of sufficient quality to differentiate between cuboctahedral, decahedral and icosahedral nanoparticle models. Furthermore, we identify the signatures of systematic errors that may occur during data reduction and show that atomic positions refined from UEC are robust to these errors. This work serves as a foundation for reliable quantitative structural analysis of time-resolved laser-excited nanoparticle states.
    Physical review. B, Condensed matter 10/2009; 81(13). · 3.77 Impact Factor
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    Christopher L Farrow, Simon J L Billinge
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    ABSTRACT: The relationship between the equations used in the atomic pair distribution function (PDF) method and those commonly used in small-angle-scattering (SAS) analyses is explicitly shown. The origin of the sloping baseline, -4pirrho0, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The nonlinear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles.
    Acta crystallographica. Section A, Foundations of crystallography 06/2009; 65(Pt 3):232-9. · 49.93 Impact Factor
  • C. L. Farrow, S. J. L. Billinge
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    ABSTRACT: The exact relationship between the atomic pair distribution function and small-angle-scattering equations is established and discussed. This has implications for the structural modeling of nanoparticles.
    Acta Crystallographica Section A Foundations of Crystallography 05/2009; · 2.24 Impact Factor
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    ABSTRACT: Atomic pair distribution functions (PDFs) obtained from high energy x-ray synchrotron radiation and x-ray absorption fine structure measurements were performed on 18 closely spaced compositions of chalcogenide glasses ( GexSe1-x with 0.15
    Physical review. B, Condensed matter 01/2008; 77(9). · 3.77 Impact Factor
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    ABSTRACT: PDFfit2 is a program as well as a library for real-space refinement of crystal structures. It is capable of fitting a theoretical three-dimensional (3D) structure to atomic pair distribution function data and is ideal for nanoscale investigations. The fit system accounts for lattice constants, atomic positions and anisotropic atomic displacement parameters, correlated atomic motion, and experimental factors that may affect the data. The atomic positions and thermal coefficients can be constrained to follow the symmetry requirements of an arbitrary space group. The PDFfit2 engine is written in C++ and is accessible via Python, allowing it to inter-operate with other Python programs. PDFgui is a graphical interface built on the PDFfit2 engine. PDFgui organizes fits and simplifies many data analysis tasks, such as configuring and plotting multiple fits. PDFfit2 and PDFgui are freely available via the Internet.
    Journal of Physics Condensed Matter 08/2007; 19(33):335219. · 2.22 Impact Factor
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    ABSTRACT: The size-dependent structure of CdSe nanoparticles, with diameters ranging from 2 to 4 nm, has been studied using the atomic pair distribution function (PDF) method. The core structure of the measured CdSe nanoparticles can be described in terms of the wurtzite atomic structure with extensive stacking faults. The density of faults in the nanoparticles ~50% . The diameter of the core region was extracted directly from the PDF data and is in good agreement with the diameter obtained from standard characterization methods suggesting that there is little surface amorphous region. A compressive strain was measured in the Cd-Se bond length that increases with decreasing particle size being 0.5% with respect to bulk CdSe for the 2 nm diameter particles. This study demonstrates the size-dependent quantitative structural information that can be obtained even from very small nanoparticles using the PDF approach. Comment: 10 pages, 7 figures and 3 tables. Phys. Rev. B, submitted (2007)
    Physical review. B, Condensed matter 04/2007; · 3.77 Impact Factor