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Z Dependence of Electron Scattering by Single Atoms into Annular Dark-Field Detectors

  • Michael M.J. Treacy (a1)

A simple parameterization is presented for the elastic electron scattering cross sections from single atoms into the annular dark-field (ADF) detector of a scanning transmission electron microscope (STEM). The dependence on atomic number, Z, and inner reciprocal radius of the annular detector, q0, of the cross section σ(Z,q0) is expressed by the empirical relation

where A(q0) is the cross section for hydrogen (Z = 1), and the detector is assumed to have a large outer reciprocal radius. Using electron elastic scattering factors determined from relativistic Hartree-Fock simulations of the atomic electron charge density, values of the exponent n(Z,q0) are tabulated as a function of Z and q0, for STEM probe sizes of 1.0 and 2.0 Å.

Comparison with recently published experimental data for single-atom scattering [Krivanek et al. (2010). Nature464, 571–574] suggests that experimentally measured exponent values are systematically lower than the values predicted for elastic scattering from low-Z atoms. It is proposed that this discrepancy arises from the inelastic scattering contribution to the ADF signal. A simple expression is proposed that corrects the exponent n(Z,q0) for inelastic scattering into the annular detector.

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Amali A. & Rez P. (1997). Theory of lattice resolution in high-angle annular dark-field images. Microsc Microanal 3, 2846.
Amali A., Rez P. & Cowley J.M. (1997). High angle annular dark field imaging of stacking faults. Micron 28, 8994.
Cosslett V.E. (1965). Possibilities and limitations for the differentiation of elements in the electron microscope. In Quantitative Electron Microscopy (Proceedings at Armed Forces Inst. Path., Washington, DC, 1964), Bahr G.F. & Zeitler E.H. (Eds.), pp. 271281. Baltimore, MD: The Williams and Wilkins Company.
Crewe A.V., Langmore J.P. & Isaacson M.S. (1975). Resolution and contrast in the STEM. In Physical Aspects of Electron Microscopy and Microbeam Analysis, Siegel B.M. & Beaman D.R. (Eds.), pp. 4762. NY: John Wiley & Sons.
Crewe A.V., Wall J. & Langmore J.P. (1970). Visibility of single atoms. Science 168, 13381340.
Donald A.M. & Craven A.J. (1979). Study of grain-boundary segregation in Cu-Bi alloys using STEM. Philos Mag A 39, 111.
Doyle P.A. & Turner P.S. (1968). Relativistic Hartree-Fock X-ray and electron scattering factors. Acta Crystallogr A 24, 390397.
Gibson J.M. & Howie A. (1979). Investigation of local-structure and composition in amorphous solids by high-resolution electron-microscopy. Chem Scripta 14, 109116.
Howie A. (1979). Image-contrast and localized signal selection techniques. J Microsc 117, 1123.
Humphreys C.J., Hart-Davis A. & Spencer J.P. (1974). Optimizing the signal/noise in the dark field imaging of single atoms. In Proc. 8th Intl. Congress on Electron Microscopy, Sanders J.V. & Goodchild D.J. (Eds.), pp. 248249. Canberra, Australia: Australian Academy of Science.
Kirkland E.J. (1998). Advanced Computing in Electron Microscopy. New York, London: Plenum Press.
Kirkland E.J., Loane R.F. & Silcox J. (1987). Simulation of annular dark field STEM images using a modified multislice method. Ultramicroscopy 23, 7796.
Krivanek O., Chisholm M.F., Nicolosi V., Pennycook T.J., Corbin G.J., Dellby N., Murfitt M.F., Own C.S., Szilagyi Z.S., Oxley M.P., Pantelides S.T. & Pennycook S.J. (2010a). Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571574.
Krivanek O.L., Dellby N., Murfitt M.F., Chisholm M.F., Pennycook T.J., Suenaga K. & Nicolosi V. (2010b). Gentle STEM: ADF imaging and EELS at low primary energies. Ultramicroscopy 110, 935945.
Langmore J.P., Wall J. & Isaacson M.S. (1973). Collection of scattered electrons in dark field electron-microscopy. 1. Elastic-scattering. Optik 38, 335350.
Lenz F. (1954). Zur streuung mittelschneller elektronen in kleinst winkel. Z Naturforsch 9A, 185204.
Loane R.F., Kirkland E.J. & Silcox J. (1986). Visibility of single heavy atoms on thin crystalline silicon in simulated annular dark-field STEM images. Acta Crystallogr A 44, 912927.
Molina S.I., Sales D.L., Galindo P.L., Fuster D., González Y., Alén B., González L., Varela M. & Pennycook S.J. (2009). Column-by-column compositional mapping by Z-contrast imaging. Ultramicroscopy 109, 172176.
Motz J.W., Olsen H. & Koch H.W. (1964). Electron scattering without atomic or nuclear excitation. Rev Modern Phys 36, 881928.
Nellist P.D., Chisholm M.F., Dellby N., Krivanek O.L., Murfitt M.F., Szilagyi Z.S., Lupini A.R., Borisevich A., Sides W.H. & Pennycook S.J. (2004). Direct sub-angstrom imaging of a crystal lattice. Science 305, 1741.
Nellist P.D. & Pennycook S.J. (1996). Direct imaging of the atomic configuration of ultradispersed catalysts. Science 274, 413415.
Pennycook S.J., Berger S.J. & Culbertson R.J. (1986). Elemental mapping with elastically scattered electrons. J Microsc 144, 229249.
Pennycook S.J. & Boatner L.A. (1988). Chemically sensitive structure-imaging with a scanning transmission electron microscope. Nature 336, 565567.
Pennycook S.J. & Jesson D.E. (1990). High-resolution incoherent imaging of crystals. Phys Rev Lett 64, 938941.
Pennycook S.J., Varela M., Lupini A.R., Oxley M.P. & Chisholm M.F. (2009). Atomic-resolution spectroscopic imaging: Past, present and future. J Elec Microsc 58, 8797.
Rez D., Rez P. & Grant I. (1994). Dirac-Fock calculations of X-ray scattering factors and contributions to the mean inner potential for electron scattering. Acta Crystallogr A 50, 481497.
Rice S.B., Koo J.Y., Disko M.M. & Treacy M.M.J. (1990). On the imaging of Pt atoms in zeolite frameworks. Ultramicroscopy 34, 108118.
Ritchie R.H. & Howie A. (1977). Electron excitation and the optical potential in electron microscopy. Philos Mag A 36, 463481.
Robb P.D. & Craven A.J. (2008). Column ratio mapping: A processing technique for atomic resolution high angle annular dark field (HAADF) images. Ultramicroscopy 109, 6169.
Treacy M.M.J. (1982). Optimising atomic number contrast in annular dark field images of thin films in the scanning transmission electron microscope. J Microsc Spectrosc Electron 7, 511523.
Treacy M.M.J. (1999). Deactivation of Pt/KL reforming catalysts by Pt agglomeration and entombment. J Micropor Mesopor Mater 28, 271292.
Treacy M.M.J. & Gibson J.M. (1982). On the detection of point-defects in crystals using high-angle diffuse-scattering in the STEM. In J Inst Phys Conf Ser No. 61, Goringe M.J. (Ed.), pp. 263266. London: The Institute of Physics.
Treacy M.M.J. & Gibson J.M. (1993). Coherence and multiple scattering in “Z”-contrast images. Ultramicroscopy 52, 3153.
Treacy M.M.J. & Gibson J.M. (1996). Variable coherence microscopy: A rich source of structural information from disordered materials. Acta Crystallogr A 52, 212220.
Treacy M.M.J., Gibson J.M., Short K.T. & Rice S.B. (1988). Channeling effects from impurity atoms in the high angle annular detector of the STEM. Ultramicroscopy 26, 133142.
Treacy M.M.J., Howie A. & Pennycook S.J. (1980). Contrast effects in the transmission electron-microscopy of supported crystalline catalyst particles. In J Inst Phys Conf Ser No. 52, Mulvey T. (Ed.), pp. 261265. London: The Institute of Physics.
Treacy M.M.J., Howie A. & Wilson C.J. (1978). Z contrast of platinum and palladium catalysts. Philos Mag A 38, 569585.
Treacy M.M.J. & Rice S.B. (1989). Catalyst particle sizes from Rutherford scattered intensities. J Microsc 156, 211234.
Varela M., Findlay S.D., Lupini A.R., Christen H.M., Borisevich A.Y., Dellby N., Krivanek O.L., Nellist P.D., Oxley M.P. & Allen L.J. (2004). Spectroscopic imaging of single atoms within a bulk solid. Phys Rev Lett 92, 95502.
Voyles P.M., Grazul J.L. & Muller D.A. (2003). Imaging individual atoms inside crystals with ADF-STEM. Ultramicroscopy 96, 251273.
Wall J.S. & Hainfeld J.F. (1986). Mass mapping with the scanning-transmission electron-microscope. Ann Rev Biophys Biophys Chem 15, 355376.
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Microscopy and Microanalysis
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