Multiple-Energy X-Ray Holography: Atomic Images of Hematite (F<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:ma

Gog, T.; Len, P.M.; Materlik, G.; Bahr, David F.; Fadley, C. S.; Sánchez-Hanke, Cecilia

doi:10.1103/physrevlett.76.3132

Cited by 247 publications

(131 citation statements)

References 22 publications

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“…This image assumes maxima at atomic positions, but is distorted because of interference between the scattered waves. The interference artifacts can be suppressed by summing multiple energy XFH data [2]. However, the resulting image differs significantly from the true charge density of a material.…”

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confidence: 99%

“…The indirect XFH can be depolarized by summing the holograms measured with two perpendicular polarization directions, and . With · r · r k · r 1 , the depolarized indirect XFH also can be represented by (2). The following discussions apply to both direct XFH and depolarized indirect XFH, as described by equation (2).…”

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confidence: 99%

“…Unlike standard x-ray diffraction (XRD) methods that measure only the magnitude of the structure factors and require significant a priori knowledge of the crystal structure for generating a solution, XFH is sensitive to both the amplitude and phase of the structure factor. However, even though the first experimental XFH measurement was realized fifteen years ago [1,2], and data collection procedures have greatly improved with the advent of high flux third generation synchrotron sources, there still are no effective methods for retrieving quantitative structural information from x-ray holograms.…”

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confidence: 99%

“…. Chukhovskii et al [2,3] defined a scattering function connecting the XFH hologram function to the structure factors. Using standard least square methods, they retrieved a set of structure factors from an XFH hologram simulated with the same set of structure factors.…”

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Direct extraction of quantitative structural information from x-ray fluorescence holograms using spherical-harmonic analysis

2012

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Direct extraction of quantitative structural information from x-ray fluorescence holograms using spherical-harmonic analysis

2012

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“…The measurement was performed by rotating the sample at high speed in a spiral motion [22]: the azimuth at 3600 degrees per second, and the polar at 2 degrees per second and varying from 0 (perpendicular to the surface) to 80 degrees. The detector was placed close to the sample to average the "inside source" holo- gram, resulting in an "inside-detector" measurement in holographic terminology [9]. The azimuth stepper motor pulses were used to synchronize the data acquisition allowing us to collect a full pattern of 3.2 10 5 pixels in about 40 seconds.…”

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Holographic analysis of diffraction structure factors

et al. 2002

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We combine the theory of inside-source/inside-detector x-ray fluorescence holography and Kossel lines/x ray standing waves in kinematic approximation to directly obtain the phases of the diffraction structure factors. The influence of Kossel lines and standing waves on holography is also discussed. We obtain partial phase determination from experimental data obtaining the sign of the real part of the structure factor for several reciprocal lattice vectors of a vanadium crystal.PACS numbers: 61.10.-i, 07.85.-m, 42.20.-i The phase determination of diffracted beams is the central problem of x-ray crystallography. Several methods exist to obtain this information, such as direct methods [1], 3-beam diffraction [2], anomalous diffraction, heavy atom or molecular replacement [3] and x-ray standing waves or Kossel lines [4,5,6]. Despite the many advances in these methods, not all problems can be solved. Direct methods fail when the unit cell contains a large number of atoms. Anomalous diffraction and related methods are among the most successful methods for biological crystallography, but they often require chemical modification of the molecules. Multiple beam diffraction, x-ray standing waves and Kossel lines have usually been applied only to high-quality crystals of relatively simple structures, or to the localization of dopants in high quality crystals [7].Kossel lines are formed when a source of short wavelength radiation (∼ 1Å) is located on a crystallographic site: they result from the Bragg scattering of outgoing fluorescent x-rays from various sets of planes in the lattice. In the notation of holography, this is an "insidesource" experiment. The fine structure of these lines has been explained by the dynamical theory of x-ray diffraction via the reciprocity theorem used in optics [4]. A proper analysis of the KL fine structure allows the determination of the phases of reflections [5,6,8,10,11]. In parallel to this work on KL, the x-ray standing wave (XSW) method has been developed [5,6,7,10]. In this case, the source and the detector are interchanged as compared to the KL method: the atoms are subject to the changing wave-field in the crystal as the incident beam goes through a Bragg reflection, and fluorescent radiation proportional to the field at the atom is generated. This constitutes the "inside-detector" configuration in holography [8]. Besides the fine structure of the KL or XSW produced when the crystal orientation satisfies a Bragg or Laue condition, tails are formed far from the Bragg angle. These coarse features, also formed by poorer-quality mosaic crystals provide information on the real and imaginary part of the structure factor [10,11].Unlike standard imaging methods, holography offers the possibility of extracting both intensity and phase information. X-ray fluorescence holography (XFH) is thus a very promising new method for obtaining a direct image in real space of the local environments of different atomic species in reasonably well-ordered crystals or molecular ensembles. Long-range transl...

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