The X-ray standing wave (XSW) technique can be used to study the structure of surfaces and interfaces with high spatial resolution and chemical selectivity. Pioneered by B.W. Batterman in the 1960s,[1] the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.[2][3]
An X-ray standing wave (XSW) field is created by interference between an X-ray beam impinging on a sample and a reflected beam. The reflection may be generated at the Bragg condition for a crystal lattice or an engineered multilayer superlattice; in these cases, the period of the XSW equals the periodicity of the reflecting planes. X-ray reflectivity from a mirror surface at small incidence angles may also be used to generate long-period XSWs.[4]
The spatial modulation of the XSW field, described by the dynamical theory of X-ray diffraction, undergoes a pronounced change when the sample is scanned through the Bragg condition. Due to a relative phase variation between the incoming and reflected beams, the nodal planes of the XSW field shift by half the XSW period.[5] Depending on the position of the atoms within this wave field, the measured element-specific absorption of X-rays varies in a characteristic way. Therefore, measurement of the absorption (via X-ray fluorescence or photoelectron yield) can reveal the position of the atoms relative to the reflecting planes. The absorbing atoms can be thought of as "detecting" the phase of the XSW; thus, this method overcomes the phase problem of X-ray crystallography.
For quantitative analysis, the normalized fluorescence or photoelectron yield is described by [2][3]
,
where is the reflectivity and is the relative phase of the interfering beams. The characteristic shape of can be used to derive precise structural information about the surface atoms because the two parameters (coherent fraction) and (coherent position) are directly related to the Fourier representation of the atomic distribution function. Therefore, with a sufficiently large number of Fourier components being measured, XSW data can be used to establish the distribution of the different atoms in the unit cell (XSW imaging).[6]
Characteristic XSW yield (red lines) through the Bragg condition for an absorbing atom at position . The Bragg reflection, calculated by dynamical diffraction theory, is shown in green.
Experimental considerationsedit
XSW measurements of single crystal surfaces are performed on a diffractometer. The crystal is rocked through a Bragg diffraction condition, and the reflectivity and XSW yield are simultaneously measured. XSW yield is usually detected as X-ray fluorescence (XRF). XRF detection enables in situ measurements of interfaces between a surface and gas or liquid environments, since hard X-rays can penetrate these media. While XRF gives an element-specific XSW yield, it is not sensitive to the chemical state of the absorbing atom. Chemical state sensitivity is achieved using photoelectron detection, which requires ultra-high vacuum instrumentation.
Measurements of atomic positions at or near single crystal surfaces require substrates of very high crystal quality. The intrinsic width of a Bragg reflection, as calculated by dynamical diffraction theory, is extremely small (on the order of 0.001° under conventional X-ray diffraction conditions). Crystal defects such as mosaicity can substantially broaden the measured reflectivity, which obscures the modulations in the XSW yield needed to locate the absorbing atom. For defect-rich substrates such as metal single crystals, a normal-incidence or back-reflection geometry is used. In this geometry, the intrinsic width of the Bragg reflection is maximized. Instead of rocking the crystal in space, the energy of the incident beam is tuned through the Bragg condition. Since this geometry requires soft incident X-rays, this geometry typically uses XPS detection of the XSW yield.
^B. W. Batterman and H. Cole (1964). "Dynamical Diffraction of X Rays by Perfect Crystals". Reviews of Modern Physics. 36 (3): 681. doi:10.1103/RevModPhys.36.681.
^J. Als-Nielsen and D. McMorrow (2001). Elements of Modern X-ray Physics. John Wiley & Sons, Ltd. ISBN978-0471498582.
^L. Cheng, P. Fenter, M. J. Bedzyk, and N. J. Sturchio (2003). "Fourier-Expansion Solution of Atom Distributions in a Crystal Using X-Ray Standing Waves". Physical Review Letters. 90 (25): 255503. doi:10.1103/PhysRevLett.90.255503. PMID 12857143.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^P. Hoenicke; et al. (2010). "Depth profile characterization of ultra shallow junction implants". Analytical and Bioanalytical Chemistry. 396 (8): 2825–32. doi:10.1007/s00216-009-3266-y. PMID 19941133. S2CID 6443446.
^Z. Feng, C.-Y. Kim, J.W. Elam, Q. Ma, Z. Zhang, M.J. Bedzyk (2009). "Direct Atomic-Scale Observation of Redox-Induced Cation Dynamics in an Oxide-Supported Monolayer Catalyst: WOx/α-Fe2O3(0001)". Journal of the American Chemical Society. 131 (51): 18200–18201. doi:10.1021/ja906816y. PMID 20028144.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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The X ray standing wave XSW technique can be used to study the structure of surfaces and interfaces with high spatial resolution and chemical selectivity Pioneered by B W Batterman in the 1960s 1 the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science 2 3 Contents 1 Basic principles 2 Experimental considerations 3 Selected applications 4 See also 5 References 6 Further readingBasic principles edit nbsp Principle of X ray standing wave measurements An X ray standing wave XSW field is created by interference between an X ray beam impinging on a sample and a reflected beam The reflection may be generated at the Bragg condition for a crystal lattice or an engineered multilayer superlattice in these cases the period of the XSW equals the periodicity of the reflecting planes X ray reflectivity from a mirror surface at small incidence angles may also be used to generate long period XSWs 4 The spatial modulation of the XSW field described by the dynamical theory of X ray diffraction undergoes a pronounced change when the sample is scanned through the Bragg condition Due to a relative phase variation between the incoming and reflected beams the nodal planes of the XSW field shift by half the XSW period 5 Depending on the position of the atoms within this wave field the measured element specific absorption of X rays varies in a characteristic way Therefore measurement of the absorption via X ray fluorescence or photoelectron yield can reveal the position of the atoms relative to the reflecting planes The absorbing atoms can be thought of as detecting the phase of the XSW thus this method overcomes the phase problem of X ray crystallography For quantitative analysis the normalized fluorescence or photoelectron yield Y p displaystyle Y p nbsp is described by 2 3 Y p W 1 R 2 C R f H cos n 2 p P H displaystyle Y p Omega 1 R 2C sqrt R f H cos nu 2 pi P H nbsp where R displaystyle R nbsp is the reflectivity and n displaystyle nu nbsp is the relative phase of the interfering beams The characteristic shape of Y p displaystyle Y p nbsp can be used to derive precise structural information about the surface atoms because the two parameters f H displaystyle f H nbsp coherent fraction and P H displaystyle P H nbsp coherent position are directly related to the Fourier representation of the atomic distribution function Therefore with a sufficiently large number of Fourier components being measured XSW data can be used to establish the distribution of the different atoms in the unit cell XSW imaging 6 nbsp Characteristic XSW yield red lines through the H h k l displaystyle mathbf H hkl nbsp Bragg condition for an absorbing atom at position H r displaystyle mathbf H cdot mathbf r nbsp The Bragg reflection calculated by dynamical diffraction theory is shown in green Experimental considerations editXSW measurements of single crystal surfaces are performed on a diffractometer The crystal is rocked through a Bragg diffraction condition and the reflectivity and XSW yield are simultaneously measured XSW yield is usually detected as X ray fluorescence XRF XRF detection enables in situ measurements of interfaces between a surface and gas or liquid environments since hard X rays can penetrate these media While XRF gives an element specific XSW yield it is not sensitive to the chemical state of the absorbing atom Chemical state sensitivity is achieved using photoelectron detection which requires ultra high vacuum instrumentation Measurements of atomic positions at or near single crystal surfaces require substrates of very high crystal quality The intrinsic width of a Bragg reflection as calculated by dynamical diffraction theory is extremely small on the order of 0 001 under conventional X ray diffraction conditions Crystal defects such as mosaicity can substantially broaden the measured reflectivity which obscures the modulations in the XSW yield needed to locate the absorbing atom For defect rich substrates such as metal single crystals a normal incidence or back reflection geometry is used In this geometry the intrinsic width of the Bragg reflection is maximized Instead of rocking the crystal in space the energy of the incident beam is tuned through the Bragg condition Since this geometry requires soft incident X rays this geometry typically uses XPS detection of the XSW yield Selected applications editApplications which require ultra high vacuum conditions Physisorption and chemisorption studies 2 3 Diffusion of dopants in crystals 7 Superlattices and Quasi crystal characterization Applications which do not require ultra high vacuum conditions Langmuir Blodgett films Self assembled monolayers Model heterogeneous catalysts 8 Buried interfacesSee also editList of surface analysis methodsReferences edit B W Batterman and H Cole 1964 Dynamical Diffraction of X Rays by Perfect Crystals Reviews of Modern Physics 36 3 681 doi 10 1103 RevModPhys 36 681 a b c J Zegenhagen 1993 Surface structure determination with X ray standing waves Surface Science Reports 18 7 8 202 271 doi 10 1016 0167 5729 93 90025 K a b c D P Woodruff 2005 Surface structure determination using x ray standing waves Reports on Progress in Physics 68 4 743 doi 10 1088 0034 4885 68 4 R01 S2CID 122085105 M J Bedzyk G M Bommarito J S Schildkraut 1989 X ray standing waves at a reflecting mirror surface Physical Review Letters 62 12 1376 1379 doi 10 1103 PhysRevLett 62 1376 PMID 10039658 J Als Nielsen and D McMorrow 2001 Elements of Modern X ray Physics John Wiley amp Sons Ltd ISBN 978 0471498582 L Cheng P Fenter M J Bedzyk and N J Sturchio 2003 Fourier Expansion Solution of Atom Distributions in a Crystal Using X Ray Standing Waves Physical Review Letters 90 25 255503 doi 10 1103 PhysRevLett 90 255503 PMID 12857143 a href Template Cite journal html title Template Cite journal cite journal a CS1 maint multiple names authors list link P Hoenicke et al 2010 Depth profile characterization of ultra shallow junction implants Analytical and Bioanalytical Chemistry 396 8 2825 32 doi 10 1007 s00216 009 3266 y PMID 19941133 S2CID 6443446 Z Feng C Y Kim J W Elam Q Ma Z Zhang M J Bedzyk 2009 Direct Atomic Scale Observation of Redox Induced Cation Dynamics in an Oxide Supported Monolayer Catalyst WOx a Fe2O3 0001 Journal of the American Chemical Society 131 51 18200 18201 doi 10 1021 ja906816y PMID 20028144 a href Template Cite journal html title Template Cite journal cite journal a CS1 maint multiple names authors list link Further reading editZegenhagen Jorg Kazimirov Alexander 2013 The X Ray Standing Wave Technique World Scientific doi 10 1142 6666 ISBN 978 981 2779 00 7 Retrieved from https en wikipedia org w index php title X ray standing waves amp oldid 1169096336, wikipedia, wiki, book, books, library,
