Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fourier map”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

How to correct relative voxel scale factors for calculations of vector-difference Fourier maps in cryo-EM

The atomic coordinates derived from cryo-electron microscopy (cryo-EM) maps can be inaccurate when the voxel scaling factors are not properly calibrated. Here, we describe a method for correcting relative voxel scaling factors between pairs of cryo-EM maps for the same or similar structures that are expanded or contracted relative to each other. We find that the correction of scaling factors reduces the amplitude differences of Fourier-inverted structure factors from voxel-rescaled maps by up to 20–30%, as shown by two cryo-EM maps of the SARS-CoV-2 spike protein measured at pH 4.0 and pH 8.0. This allows for the calculation of the difference map after properly scaling, revealing differences between the two structures for individual amino acid residues. Unexpectedly, the analysis uncovers two previously overlooked differences of amino acid residues in structures and their local structural changes. Furthermore, we demonstrate the method as applied to two cryo-EM maps of monomeric apo-photosystem II from the cyanobacteria Synechocystis sp. PCC 6803 and Thermosynechococcus elongatus. The resulting difference maps reveal many changes in the peripheral transmembrane PsbX subunit between the two species.

59 BASIC BIOLOGICAL SCIENCES↗

A hard X-ray study of a manganese-terpyridine catalyst in a chromium-based Metal Organic Framework

Hydrogen produced from water splitting is a promising source of clean energy. However, a robust catalyst is necessary to carry out the water oxidation step of water splitting. In this study, the catalyst studied was [(terpy)Mn(μ-O)2Mn(terpy)] 3+ (MnTD) synthesized in the Metal Organic Framework (MOF) MIL-101(Cr), and the method used for analysis was hard X-ray powder diffraction. The diffraction data was used to detect the presence of MOF in different catalytic stages, and lattice parameters were assigned to the samples containing MOF. Fourier maps were constructed with GSAS II to determine the contents of the MOF as preliminary studies suggested that MnTD may not be present. Results showed that MOF is present before catalysis occurs but disappears by the time 45 minutes of catalysis has ensued. Changes in the MOF’s lattice parameters and location of electron density in the Fourier maps suggest attractions between the MOF and catalyst that may lead to MOF degradation. Fourier maps also revealed limited, if any, amounts of MnTD, even before catalysis occurred. Molecular manganese oxide may be the source of the high rate of water oxidation catalysis in the studied system.

08 HYDROGEN↗

A revised partiality model and post-refinement algorithm for X-ray free-electron laser data

An updated partiality model and post-refinement algorithm for XFEL snapshot diffraction data is presented and confirmed by observing anomalous density for S atoms at an X-ray wavelength of 1.3 Å. Research towards using X-ray free-electron laser (XFEL) data to solve structures using experimental phasing methods such as sulfur single-wavelength anomalous dispersion (SAD) has been hampered by shortcomings in the diffraction models for X-ray diffraction from FELs. Owing to errors in the orientation matrix and overly simple partiality models, researchers have required large numbers of images to converge to reliable estimates for the structure-factor amplitudes, which may not be feasible for all biological systems. Here, data for cytoplasmic polyhedrosis virus type 17 (CPV17) collected at 1.3 Å wavelength at the Linac Coherent Light Source (LCLS) are revisited. A previously published definition of a partiality model for reflections illuminated by self-amplified spontaneous emission (SASE) pulses is built upon, which defines a fraction between 0 and 1 based on the intersection of a reflection with a spread of Ewald spheres modelled by a super-Gaussian wavelength distribution in the X-ray beam. A method of post-refinement to refine the parameters of this model is suggested. This has generated a merged data set with an overall discrepancy (by calculating the R{sub split} value) of 3.15% to 1.46 Å resolution from a 7225-image data set. The atomic numbers of C, N and O atoms in the structure are distinguishable in the electron-density map. There are 13 S atoms within the 237 residues of CPV17, excluding the initial disordered methionine. These only possess 0.42 anomalous scattering electrons each at 1.3 Å wavelength, but the 12 that have single predominant positions are easily detectable in the anomalous difference Fourier map. It is hoped that these improvements will lead towards XFEL experimental phase determination and structure determination by sulfur SAD and will generally increase the utility of the method for difficult cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Hard X-ray Study of a Manganese-Terpyridine Dimer Catalyst in a Chromium-based Metal Organic Framework - Oral Presentation [Slides]

Cleaner forms of energy are needed, and H 2 produced from water splitting is a possible source. However, a robust catalyst is necessary to carry out the water oxidation reaction. Plants utilize Photosystem II to catalyze water oxidation as a part of photosynthesis, and many synthetic water oxidation catalysts use Photosystem II as a model. In this study, the catalyst of interest was [(terpy)Mn(μ-O)2Mn(terpy)]3+ (MnTD), which was synthesized in a chromium-based Metal Organic Framework (MOF) to avoid degradation of MnTD molecules. Hard X-ray powder diffraction was the primary method of analysis. The diffraction data was used to detect the presence of MOF in samples at different catalytic stages, and lattice parameters were assigned to the samples containing MOF. Fourier maps were constructed to determine the contents of the MOF as preliminary studies suggested that MnTD may not be present. Results showed that MOF is present before catalysis occurs, but disappears in the initial stages of catalysis. Changes in the MOF’s lattice parameters suggest attractive interactions between the MOF and catalyst; these interactions may lead to the observed MOF degradation. Fourier maps also reveal limited, if any, amounts of MnTD in the system. Molecular manganese oxide may be the source of the high rate of water oxidation catalysis in the studied system.

08 HYDROGEN↗

Structure resolution by electron diffraction tomography of the complex layered iron-rich Fe-2234-type Sr{sub 5}Fe{sub 6}O{sub 15.4}

The crystal structure of the strontium ferrite Sr{sub 5}Fe{sub 6}O{sub 15.4}, was solved by direct methods on electron diffraction tomography data acquired on a transmission electron microscope. The refined cell parameters are a=27.4047(3) Å, b=5.48590(7) Å and c=42.7442(4) Å in Fm2m symmetry. Its structure is built up from the intergrowth sequence between a quadruple perovskite-type layer with a complex rock-salt (RS)-type block. In the latter iron atoms are found in two different environments : tetragonal pyramid and tetrahedron. The structural model was refined by Rietveld method based on the powder X-ray diffraction pattern. - Highlights: • Complex structure of Sr{sub 5}Fe{sub 6}O{sub 15.4} solved by electron diffraction tomography. • Observed Fourier maps allow determining missing oxygen atoms in the structure. • Structural model refined from powder X-ray diffraction data. • Intergrowth between quadruple perovskite layer with double rock-salt-type layer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure Characterization and Properties of K-Containing Copper Hexacyanoferrate

Copper hexacyanoferrate, Cu II [Fe III (CN) 6 ] 2/3 nH 2 O, was synthesized, and varied amounts of K + ions were inserted via reduction by K 2 S 2 O 3 (aq). Ideally, the reaction can be written as Cu II [Fe III (CN) 6 ] 2/3 ∙ nH 2 O + 2x/3K + + 2x/3e⁻ ↔K 2x/3 Cu II [Fe II x Fe III 1- x (CN) 6 ] 2/3 nH 2 O. Infrared, Raman, and Mössbauer spectroscopy studies show that Fe III is continuously reduced to Fe II with increasing x, accompanied by a decrease of the a-axis of the cubic F$m\bar{3}$m unit cell. Elemental analysis of K by inductively coupled plasma shows that the insertion only begins when a significant fraction, ~20% of the Fe III , has already been reduced. Thermogravimetric analysis shows a fast exchange of water with ambient atmosphere and a total weight loss of ~26 wt % upon heating to 180 °C, above which the structure starts to decompose. The crystal structures of Cu II [Fe III (CN) 6 ] 2/3 ∙ nH 2 O and K 2/3 Cu[Fe(CN) 6 ] 2/3 ∙ nH 2 O were refined using synchrotron X-ray powder diffraction data. In both, one-third of the Fe(CN) 6 groups are vacant, and the octahedron around Cu II is completed by water molecules. In the two structures, difference Fourier maps reveal three additional zeolitic water sites (8c, 32f, and 48g) in the center of the cavities formed by the Cu N C Fe framework. In conclusion, the K-containing compound shows an increased electron density at two of these sites (32f and 48g), indicating them to be the preferred positions for the K + ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lipidic cubic phase injector is a viable crystal delivery system for time-resolved serial crystallography

Serial femtosecond crystallography (SFX) using X-ray free-electron laser sources is an emerging method with considerable potential for time-resolved pump-probe experiments. Here we present a lipidic cubic phase SFX structure of the light-driven proton pump bacteriorhodopsin (bR) to 2.3 Å resolution and a method to investigate protein dynamics with modest sample requirement. Time-resolved SFX (TR-SFX) with a pump-probe delay of 1 ms yields difference Fourier maps compatible with the dark to M state transition of bR. Importantly, the method is very sample efficient and reduces sample consumption to about 1 mg per collected time point. Accumulation of M intermediate within the crystal lattice is confirmed by time-resolved visible absorption spectroscopy. Furthermore, this study provides an important step towards characterizing the complete photocycle dynamics of retinal proteins and demonstrates the feasibility of a sample efficient viscous medium jet for TR-SFX.

59 BASIC BIOLOGICAL SCIENCES↗

Solving the structure of Lgl2, a difficult blind test of unsupervised structure determination

In the companion paper by Ufimtsev and Levitt [Ufimtsev IS, Levitt M (2019) Proc Natl Acad Sci USA , 10.1073/pnas.1821512116], we presented a method for unsupervised solution of protein crystal structures and demonstrated its utility by solving several test cases of known structure in the 2.9- to 3.45-Å resolution range. Here we apply this method to solve the crystal structure of a 966-amino acid construct of human lethal giant larvae protein (Lgl2) that resisted years of structure determination efforts, at 3.2-Å resolution. The structure was determined starting with a molecular replacement (MR) model identified by unsupervised refinement of a pool of 50 candidate MR models. This initial model had 2.8-Å RMSD from the solution. The solved structure was validated by comparison with a model subsequently derived from an alternative crystal form diffracting to higher resolution. This model could phase an anomalous difference Fourier map from an Hg derivative, and a single-wavelength anomalous dispersion phased density map made from these sites aligned with the refined structure.

59 BASIC BIOLOGICAL SCIENCES↗

Towards phasing using high X-ray intensity

X-ray free-electron lasers (XFELs) show great promise for macromolecular structure determination from sub-micrometre-sized crystals, using the emerging method of serial femtosecond crystallography. The extreme brightness of the XFEL radiation can multiply ionize most, if not all, atoms in a protein, causing their scattering factors to change during the pulse, with a preferential `bleaching' of heavy atoms. This paper investigates the effects of electronic damage on experimental data collected from a Gd derivative of lysozyme microcrystals at different X-ray intensities, and the degree of ionization of Gd atoms is quantified from phased difference Fourier maps. In conclusion, a pattern sorting scheme is proposed to maximize the ionization contrast and the way in which the local electronic damage can be used for a new experimental phasing method is discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

Kashi, Aditya↗

Crystal structure solution and high-temperature thermal expansion in NaZr 2 (PO 4 ) 3 -type materials

The NaZr 2 P 3 O 12 family of materials have shown low and tailorable thermal expansion properties. In this study, SrZr 4 P 6 O 24 (SrO·4ZrO 2 ·3P 2 O 5 ), CaZr 4 P 6 O 24 (CaO·4ZrO 2 ·3P 2 O 5 ), MgZr 4 P 6 O 24 (MgO·4ZrO 2 ·3P 2 O 5 ), NaTi 2 P 3 O 12 [½(Na 2 O·4TiO 2 ·3P 2 O 5 )], NaZr 2 P 3 O 12 [½(Na 2 O·4ZrO 2 ·3P 2 O 5 )], and related solid solutions were synthesized using the organic–inorganic steric entrapment method. The samples were characterized by in-situ high-temperature X-ray diffraction from 25 to 1500°C at the Advanced Photon Source and National Synchrotron Light Source II. The average linear thermal expansion of SrZr 4 P 6 O 24 and CaZr 4 P 6 O 24 was between −1 × 10 −6 per °C and 6 × 10 −6 per °C from 25 to 1500°C. The crystal structures of the high-temperature polymorphs of CaZr 4 P 6 O 24 and SrZr 4 P 6 O 24 with R 3 c symmetry were solved by Fourier difference mapping and Rietveld refinement. This polymorph is present above ∼1250°C. This work measured thermal expansion coefficients to 1500°C for all samples and investigated the differences in thermal expansion mechanisms between polymorphs and between compositions.

36 MATERIALS SCIENCE↗

FEM: Feature-enhanced map

A method is presented that modifies a 2 m F obs - D F model σ A -weighted map such that the resulting map can strengthen a weak signal, if present, and can reduce model bias and noise. The method consists of first randomizing the starting map and filling in missing reflections using multiple methods. This is followed by restricting the map to regions with convincing density and the application of sharpening. The final map is then created by combining a series of histogram-equalized intermediate maps. In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2 m F obs - D F model σ A -weighted map.

36 MATERIALS SCIENCE↗

Impedance-Based Detection of NO 2 Using Ni-MOF-74: Influence of Competitive Gas Adsorption

Chemically robust, low-power sensors are needed for the direct electrical detection of toxic gases. Metal–organic frameworks (MOFs) offer exceptional chemical and structural tunability to meet this challenge, though further understanding is needed regarding how coadsorbed gases influence or interfere with the electrical response. To probe the influence of competitive gases on trace NO 2 detection in a simulated flue gas stream, a combined structure–property study integrating synchrotron powder diffraction and pair distribution function analyses was undertaken, to elucidate how structural changes associated with gas binding inside Ni-MOF-74 pores correlate with the electrical response from Ni-MOF-74-based sensors. Data were evaluated for 16 gas combinations of N 2 , NO 2 , SO 2 , CO 2 , and H 2 O at 50 °C. Fourier difference maps from a rigid-body Rietveld analysis showed that additional electron density localized around the Ni-MOF-74 lattice correlated with large decreases in Ni-MOF-74 film resistance of up to a factor of 6 × 10 3 , observed only when NO 2 was present. These changes in resistance were significantly amplified by the presence of competing gases, except for CO 2 . Without NO 2 , H 2 O rapidly (<120 s) produced small (1–3×) decreases in resistance, though this effect could be differentiated from the slower adsorption of NO 2 by the evaluation of the MOF’s capacitance. Furthermore, samples exposed to H 2 O displayed a significant shift in lattice parameters toward a larger lattice and more diffuse charge density in the MOF pore. Evaluating the Ni-MOF-74 impedance in real time, NO 2 adsorption was associated with two electrically distinct processes, the faster of which was inhibited by competitive adsorption of CO 2 . Together, this work points to the unique interaction of NO 2 and other specific gases (e.g., H 2 O, SO 2 ) with the MOF’s surface, leading to orders of magnitude decrease in MOF resistance and enhanced NO2 detection. Finally, understanding and leveraging these coadsorbed gases will further improve the gas detection properties of MOF materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗

Synthesis and structure of a stuffed derivative of α-quartz, Mg 0.5 AlSiO 4

A structural derivative of quartz with the composition Mg 0.5 AlSiO 4 has been grown from glass and characterized using synchrotron X-ray diffraction (XRD), transmission electron microscopy (TEM), and 29 Si nuclear magnetic resonance (NMR) spectroscopy. Rietveld analysis of the XRD data indicates that the framework of Mg 0.5 AlSiO 4 is isostructural with α-quartz, rather than β-quartz, as is consistent with previous theoretical modeling (Sternitzke and Müller 1991). Al and Si exhibit long-range disorder over the framework tetrahedral sites, indicated by the absence of the superlattice reflections corresponding to the doubling of c relative to that of quartz. Nevertheless, 29 Si NMR measurements show that Al and Si exhibit partial short-range order with an ordering degree of 56%. Electron diffraction reveals superlattice reflections indicative of doubled periodicities along the a-axes. In conclusion, Fourier electron density maps show that Mg occupies channel sites that each are bonded to six O atoms, in contrast to the tetrahedral coordination of Li in the β-quartz-type framework for β-eucryptite, LiAlSiO 4 . Furthermore, the concentrations of Mg in adjacent channels are different, resulting in framework distortions that generate the superstructures along a.

36 MATERIALS SCIENCE↗