Christopher L. Farrow

Columbia University, New York, New York, United States

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Publications (27)

  • Pavol Juhás · Christopher L. Farrow · Xiaohao Yang · [...] · Simon J. L. Billinge
    [Show abstract] [Hide abstract] ABSTRACT: A strategy is described for regularizing ill posed structure and nanostructure scattering inverse problems ( i.e. structure solution) from complex material structures. This paper describes both the philosophy and strategy of the approach, and a software implementation, DiffPy Complex Modeling Infrastructure ( DiffPy-CMI ).
    Article · Nov 2015 · Acta Crystallographica Section A: Foundations and Advances
  • [Show abstract] [Hide abstract] ABSTRACT: A method of using electron diffraction to obtain PDFs from crystalline, nanocrystalline, and amorphous inorganic, organic, and organometallic compound.
    Patent · Dec 2014
  • Simon Billinge · Christopher Farrow · Tatiana E. Gorelik · [...] · Martin U. Schmidt
    [Show abstract] [Hide abstract] ABSTRACT: A method of using electron diffraction to obtain PDFs from crystalline, nanocrystalline, and amorphous inorganic, organic, and organometallic compound.
    Patent · Dec 2014
  • Article: Ab-initio.
    S R Gujarathi · C L Farrow · C Glosser · [...] · P M Duxbury
    [Show abstract] [Hide abstract] ABSTRACT: Reconstruction of complex structures is an inverse problem arising in virtually all areas of science and technology, from protein structure determination to bulk heterostructure solar cells and the structure of nanoparticles. We cast this problem as a complex network problem where the edges in a network have weights equal to the Euclidean distance between their endpoints. We present a method for reconstruction of the locations of the nodes of the network given only the edge weights of the Euclidean network. The theoretical foundations of the method are based on rigidity theory, which enables derivation of a polynomial bound on its efficiency. An efficient implementation of the method is discussed and timing results indicate that the run time of the algorithm is polynomial in the number of nodes in the network. We have reconstructed Euclidean networks of about 1000 nodes in approximately 24 h on a desktop computer using this implementation. We also reconstruct Euclidean networks corresponding to polymer chains in two dimensions and planar graphene nanoparticles. We have also modified our base algorithm so that it can successfully solve random point sets when the input data are less precise.
    Article · May 2014
  • S. R. Gujarathi · C. L. Farrow · C. Glosser · [...] · P. M. Duxbury
    [Show abstract] [Hide abstract] ABSTRACT: Reconstruction of complex structures is an inverse problem arising in virtually all areas of science and technology, from protein structure determination to bulk heterostructure solar cells and the structure of nanoparticles. We cast this problem as a complex network problem where the edges in a network have weights equal to the Euclidean distance between their endpoints. We present a method for reconstruction of the locations of the nodes of the network given only the edge weights of the Euclidean network. The theoretical foundations of the method are based on rigidity theory, which enables derivation of a polynomial bound on its efficiency. An efficient implementation of the method is discussed and timing results indicate that the run time of the algorithm is polynomial in the number of nodes in the network. We have reconstructed Euclidean networks of about 1000 nodes in approximately 24 h on a desktop computer using this implementation. We also reconstruct Euclidean networks corresponding to polymer chains in two dimensions and planar graphene nanoparticles. We have also modified our base algorithm so that it can successfully solve random point sets when the input data are less precise.
    Article · May 2014 · Physical Review E
  • Source
    Christopher L. Farrow · Chenyang Shi · Pavol Juhás · [...] · Simon J. L. Billinge
    [Show abstract] [Hide abstract] 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.
    Full-text Article · Apr 2014 · Journal of Applied Crystallography
  • Xiaohao Yang · Pavol Juhas · Christopher L. Farrow · Simon J. L. Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Feb 2014
  • Xiaohao Yang · Pavol Juhas · Christopher L. Farrow · Simon J. L. Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Jan 2014
  • Simon J L Billinge · Christopher L Farrow
    [Show abstract] [Hide abstract] 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.
    Article · Nov 2013 · Journal of Physics Condensed Matter
  • Christopher L Farrow · Daniel Kwabena Bediako · Yogesh Surendranath · [...] · Simon J L Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Apr 2013 · Journal of the American Chemical Society
  • Pavol Juhas · Timur Davis · Christopher L. Farrow · Simon J. L. Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Nov 2012 · Journal of Applied Crystallography
  • Christopher L. Farrow · Simon J. L. Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Nov 2012
  • Source
    MQ Zhu · CL Farrow · Jeffrey E. Post · [...] · DL Sparks
    [Show abstract] [Hide abstract] 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.
    Full-text Article · Mar 2012 · Geochimica et Cosmochimica Acta
  • Christopher L. Farrow · Margaret Shaw · Hyunjeong Kim · [...] · Simon J. L. Billinge
    [Show abstract] [Hide abstract] ABSTRACT: We have systematically studied the optimal real-space sampling of atomic pair distribution data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we demonstrate that the optimal sampling is bounded by the Nyquist interval described by the Nyquist-Shannon sampling theorem. Near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty prediction. Furthermore, refinements using sparsely sampled data may run many times faster than using oversampled data. This investigation establishes a theoretically sound limit on the amount of information contained in the PDF, which has ramifications towards how PDF data are modeled.
    Article · Oct 2011 · Physical review. B, Condensed matter
  • P. Juhas · C. L. Farrow · J. Liu · [...] · S. J. L. Billinge
    Article · Aug 2011 · Acta Crystallographica Section A Foundations of Crystallography
  • Source
    Carrie A Simpson · Christopher L Farrow · Peng Tian · [...] · David E Cliffel
    [Show abstract] [Hide abstract] 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.
    Full-text Article · Nov 2010 · Inorganic Chemistry
  • [Show abstract] [Hide abstract] 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 is capable of processing large numbers of data sets with minimal effort. The 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.
    Article · Jun 2010 · Journal of Applied Crystallography
  • Corey Musolff · Christopher Farrow · Phillip Duxbury · [...] · Pavol Juhas
    [Show abstract] [Hide abstract] 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.
    Article · Mar 2010
  • E. Bozin · C. Farrow · J. Liu · [...] · S. Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Mar 2010
  • Christopher L. Farrow · Chong-Yu Ruan · Simon J L Billinge
    [Show abstract] [Hide abstract] 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.
    Article · Oct 2009 · Physical review. B, Condensed matter