Session W9: X-ray, Light, and Particle Scattering and Diffraction

Strain maps with ppm resolution for single crystal wafers obtained from x-ray rocking curve maps

A double crystal (+, -) x-ray technique has been used to obtain separate maps of strain and tilt across single crystal samples of high crystalline perfection. Rocking curves were obtained for each pixel of a CCD detector and from these data angular shifts of the rocking curve center were mapped. By using data for two azimuthal rotations, that is, by combining data from two diffraction conditions separated by 180\r{ } rotation around the diffraction vector, we obtained separately the tilt and the strain. Data for diamonds has been obtained to demonstrate the technique in the case of a symmetric reflection[1]. Extensions of the method to asymmetric reflections in order to also extract strains parallel to the surface[2] will be discussed. Also a correction for wavelength dispersion in the case of different d-spacings for first and second crystals will be discussed. This work was supported by DOE Basic Energy Sciences-Materials Science, under contract No. W-31-109-ENG-38 and by NSF under contract No. EAR-0421020. [1] A.T. Macrander et al., Applied Physics Letters, 87, 194113 (2003). [2] V. Swaminathan and A.T. Macrander, ``Materials Aspects of GaAs and InP Based Structures'', Prentice Hall, 1991, ISBN 0-13-346826-7.   

Is Resonant X-ray Scattering Sensitive to the Electronic Structure of the CDW State?

The strong ``white-line'' observed at the Ta L$_{III}$ x-ray absorption edge (9.881KeV) in 1$T$-TaS$_{2}$ indicates resonance with the 2p $\to $ 5d atomic transition. Theories of the charge density wave (CDW) state in TaS$_{2}$ highlight the special role played by the 5d states of the thirteen Ta atoms in each unit cell of the super-lattice in forming the reconstructed conduction bands of the CDW state. By measuring the resonant diffraction at the CDW satellites, we combine this additional periodicity with the resonant scattering to amplify and isolate the x-ray signal from the CDW. Then, by studying the behavior as the system goes through the incommensurate-commensurate transition, we probe the sensitivity of this resonant x-ray scattering technique to changes in the electronic structure near the Fermi surface.   

Diffraction by Distorted Object -- a Unified Description of Coherent X-ray Diffraction and Imaging.

It is well-known that a diffracted or scattered wave by an object can be simply described by a Fourier transform of the electron density distribution of the object. This, in principle, is true only in the so-called far-field regime. In the near-field regime, evaluations of wave field amplitudes become more complicated and Fresnel diffraction and imaging effects have to be taken into account. In this paper, we present a unified diffraction theory that is valid in both far-field and near-field regime. Using the concept of a `phase-chirped' distorted object, where Fresnel-zone construction is embedded on an original object, we show that the Fourier transform of this distorted object can be used to evaluate Fresnel coherent diffraction images or phase-contrast images from objects. This approach is valid continuously from the near-field to the far-field regimes. In addition, the distorted-object approach extends the applicability of Fourier-based iterative phasing algorithm that is already established for far-field diffraction into the near-field holographic regime where phase retrieval had been difficult in high-resolution structural imaging of noncrystalline specimens. Imaging in near-field also possesses the advantage that it can eliminate twin image ambiguity that may exist in far-field diffraction.   

Recovering Ancient Inscriptions by X-ray Fluorescence Imaging

For many ancient cultures including those of the Mediterranean, carved stone inscriptions provide our most detailed historical record. Over the ages the surfaces of many of these inscriptions have been eroded so that the original text can no longer be distinguished. A method that allowed at least partial recovery of this lost text would provide a major breakthrough for the study of these cultures. The scope of analytical techniques that can be applied to stone tablets is limited by their large size and weight. We have applied X-ray fluorescence imaging to study the text of ancient stone inscriptions [1]. This method allows the concentrations of trace elements, including those introduced during inscription and painting, to be measured and mapped. The images created in this way correspond exactly to the published text of the inscription, both when traces of letters are visible with the naked eye and when they are barely detectable. [1] J. Powers et al., Zeitschrift f\"{u}r Papyrologie und Epigraphik 152: 221-227 (2005).   

Site specific valence band structure of SrTiO$_{3}$ determined with X-ray standing waves

Structure and chemical composition define the properties of materials, notably band structure and electronic characteristics of solids. Ab initio calculations deliver frequently reliably predictions, which are, however, difficult to verify, in particular in view of the direct relationship between atomic and electronic structure. Combining the x-ray standing wave (XSW) technique with X-ray photoelectron spectroscopy (XPS) is a unique tool in this sense. It is used here to identify unambiguously parts of the valence band of SrTiO$_{3}$, which can be assigned to Sr, Ti, or O-sites of the lattice. The XSW/XPS measurements were performed in UHV at the ID32 insertion device beamline at the ESRF using a (001) oriented, atomically clean SrTiO$_{3}$ crystal. Traversing the (111) and (112) Bragg reflections and recording the valence band for different standing wave positions within the lattice unit cell, the site specific contributions could directly be identified. Obtained experimental results are in very good agreement with theory, by utilizing as adjustable parameters the X-ray absorption cross sections of the valence electrons.   

CMR Manganite Sensors for Total Energy Measurements of the Linear Coherent Light Source Pulsed X-ray Laser

We are developing CMR manganite thin film bolometric sensors for total energy measurements of the Linear Coherent Light Source (LCLS) pulsed free electron x-ray laser (FEL). This application requires the sensor array to be fabricated on a low Z substrate capable of withstanding the pulse impact of 2 mJ in $\sim $ 200 femtoseconds, without the thermal expansion exceeding the yield strength, when the back side of the substrate is irradiated. Si is a potential candidate for meeting this requirement though its stability for long term exposure is a concern that needs to be tested. Optimal operating temperature of the sensor is estimated to be $\sim $ 100 K-200 K, based on finite element simulations of the temperature evolution in the sensor pixel. Our initial work has identified Nd $_{1-x}$ Sr$_{x}$ MnO$_{3}$ as the manganite material suitable for the LCLS sensor. We will present our materials development efforts towards LCLS sensor design as well as simulations of the sensor response.   

Verification and Application of a New Analysis Method for X-ray Diffraction Microscopy

X-ray diffraction microscopy has been used to determine microstructure maps of bulk polycrystalline material. Data are collected at the Advanced Photon Source beamline 1-ID using line focused 50keV x-rays. Diffracted beams are imaged with a CCD camera and are tracked through space so that orientation, point-of-origin, and shape of individual grains are encoded. Analysis uses a computer simulation of the measurement and sample to generate calculated diffraction patterns; orientations of sample space area elements are adjusted to obtain a match to the data. We illustrate data and analysis using a thin silicon wafer sample. We then show images of several layers of an aluminum polycrystal. The ability to obtain such images in a non-destructive way opens the possibility of measurements of the response to external stimuli of ensembles of individual grains. Our analysis is amenable to inclusion of complex scattering rules such as will be needed to study defected materials.   

Nanometer Focusing X-rays With Multiple Kinoform Lenses

It has been suggested that for refractive optics operating at photon energies of order 10 keV, that the resolution is limited to the wavelength divided by the critical angle. Using a compound kinoform lens consisting of individually optimized kinoform lenses, we investigate the possibility of exceeding this limit. Single-dimensional, kinoform lens stacks in deep-etched silicon have been fabricated that in principle can exceed the critical angle limit. These optics have been tested and the results will be presented. Additionally we present calculations that show that the resolution of radially-symmetric kinoform lenses is limited only by x-ray wavelength.   

Comparison of polycapillary and curved crystal optics for convergent beam powder x-ray diffraction

Comparisons were made of diffracted ring width, ring uniformity, system resolution and diffracted beam intensity for convergent beam powder diffraction using two different types of x-rays optics, doubly curved crystal optics$^{2}$ and polycapillary x-ray optics.$^{3,4}$ Measurements were made using very low power microfocus sources for small inorganic and organic standard samples. Detailed source and optics characterizations were performed to develop comparisons with theoretical calculations. Resolution and intensity were in good agreement with those obtained from simple geometrical calculations. \newline \newline $^{2}$Z. W. Chen, N. Mail, F.Z. Wei, C. A. MacDonald, W. M. Gibson ``Total reflection x-ray fluorescence with low power sources coupled to doubly curved crystal optics,'' Spectrochimica. Acta. B, 60 (4), pp.471-8, 2005. \newline $^{3}$C.A. MacDonald and W.M. Gibson, ``Applications and Advances In Polycapillary Optics'', X-ray Spectrometry, \textbf{\textit{32 (}}\textit{3), 2003, pp 258-268.} \newline $^{4}$C.A. MacDonald, S.M. Owens, and W.M. Gibson, ``Polycapillary X-Ray Optics for Microdiffraction,'' Journal of Applied Crystallography, \textbf{\textit{32}}\textit{, pp160-7, 1999.}   

Light diffraction from a metallic bigrating.

The diffraction of $\pi $- and $\sigma $- polarized electromagnetic plane waves from metallic bigratings is studied theoretically. The reduced Rayleigh equations are solved using a perturbation approach. The diffracted amplitudes are calculated until second order on the surface height profile. Numerical results of the diffraction orders and Near-Field are obtained using both, two-dimensional sinusoidal and semicircular profiles.   

Electron structure factor: a unique quantity in probing material's properties.

Electron diffraction is very sensitive to valence charge distribution compared with x-ray at small scattering angles due to the near cancellation of the scattering from the positively charged nucleus and the negatively charged electrons. Thus, small changes in electron density can lead to considerable variations in the scattering amplitude. The well known divergence at small scattering vector for Coulomb scattering leads to strong measurable scattered intensities. However, the advantage of the accurate measurement using quantitative electron diffraction has not been well appreciated. We propose here that the accurate measured electron structure factor can be a unique quantity in probing properties of materials. We demonstrate this by examining the sensitivity of electron structure factor to valence charge distribution, chemical composition variations, and charge / orbital orderings in many functional materials. We also show that the accurately measured low-order electron structure factors can be used to test first principles theories, especially to optimize exchange-correlation functionals.   

$^{3}$\textbf{He neutron spin filters for polarized neutron scattering}.

Polarized neutron scattering (PNS) is a powerful tool that probes the magnetic structures in a wide variety of magnetic materials. Polarized $^{3}$He gas, produced by optical pumping, can be used to polarize or analyze neutron beams because of the strong spin dependence of the neutron absorption cross section for $^{3}$He. Polarized $^{3}$He neutron spin filters (NSF) have been of great interest in PNS community due to recent significant improvement of their performance. Here I will discuss successful applications using $^{3}$He NSFs in polarized neutron reflectometry (PNR) and triple-axis spectrometry (TAS). In PNR, a $^{3}$He NSF in conjunction with a position-sensitive detector allows for efficient polarization analysis of off-specular scattering over a broad range of reciprocal space. In TAS, a $^{3}$He NSF in combination with a double focusing pyrolytic graphite monochromator provides greater versatility and higher intensity compared to a Heusler polarizer. Finally I will present the results from patterned magnetically-coupled thin films in PNR and our first ``proof-of-principle'' experiment in TAS, both of which were performed using $^{3}$He NSF(s) at the NIST Center for Neutron Research.   

A low and hyperthemal energy UHV ion beamline for surface scattering spectroscopies

We are using a differentially pumped beamline to provide well- collimated, monoenergetic beams of noble gas and alkali-metal ions that range in energy from $<$10eV to 10keV. These ion beams are scattered from a surface (e.g. Cu(001)) to study charge transfer effects, energy loss, and the excitation of surface phonons and excitons. The ion beam is focused into a UHV scattering chamber that possesses capabilities for studying and characterizing samples using LEED, Auger spectroscopy, and a Kelvin probe for work function measurements. Recent additions to this setup include replacing diffusion pumps with turbo pumps as well as the addition of a fast entry load-lock sample exchange system. Our current research is focused on developing a source to produce an ion beam of C$_{60} $ as well as studying charge transfer and energy loss effects at the low and hyperthermal energy range. Also, we are investigating chemicurrents associated with Schottky diodes in this energy regime.