Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T09:26:00.510Z Has data issue: false hasContentIssue false
  • English
  • Français

FFT Multislice Method—The Silver Anniversary

Published online by Cambridge University Press:  22 January 2004

Kazuo Ishizuka
Kazuo Ishizuka
Affiliation:
HREM Research Inc., Higashimatsuyama, Saitama 355-0055 Japan and National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan
Get access

Abstract

The first paper on the FFT multislice method was published in 1977, a quarter of a century ago. The formula was extended in 1982 to include a large tilt of an incident beam relative to the specimen surface. Since then, with advances of computing power, the FFT multislice method has been successfully applied to coherent CBED and HAADF-STEM simulations. However, because the multislice formula is built on some physical approximations and approximations in numerical procedure, there seem to be controversial conclusions in the literature on the multislice method. In this report, the physical implication of the multislice method is reviewed based on the formula for the tilted illumination. Then, some results on the coherent CBED and the HAADF-STEM simulations are presented.

Keywords

multislicedynamical diffractionFFTCBEDSTEMHAADFtilted illuminationinclined surface
Type
Research Article
Information
Microscopy and Microanalysis , Volume 10 , Issue 1 , February 2004 , pp. 34 - 40
Copyright
© 2004 Microscopy Society of America

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Allen, L.J., Findlay, S.D., Oxley, M.P., & Rossouw, C.J. (2003). Lattice-resolution contrast from a focused coherent electron probe I. Ultramicroscopy 96, 47–63.Google Scholar
Anstis, G.R. & Cockayne, D.J.G. (1979). The calculation and interpretation of high-resolution electron microscope images of lattice defects. Acta Cryst A 35, 511–524.Google Scholar
Brigham, E.O. (1974). The Fast Fourier Transform, Englewood Cliffs, NJ: Prentice-Hill.
Chen, J.H., Op de Beeck, M., & van Dyck, D. (1996). Can the multislice method be used to calculate HOLZ reflections in high-energy diffraction and imaging? Microsc Microanal Microstruct 7, 27–47.Google Scholar
Chen, J.H., Van Dyck, D., & Op de Beeck, M. (1997a). Multislice method for large beam tilt with application to HOLZ effects in triclinic and monoclinic crystals. Acta Cryst A 53, 576–589.Google Scholar
Chen, J.H., Van Dyck, D., Op de Beeck, M., & Van Landuyt, J. (1997b). Computational comparison between the conventional multislice method and the third-order multislice method for calculating high-energy electron diffraction and imaging. Ultramicroscopy 69, 219–240.Google Scholar
Cowley, J.M. & Moodie, A.F. (1957). The scattering of electrons by atoms and crystals. I. A new theoretical approach. Acta Cryst 10, 609–619.Google Scholar
Goodman, P. & Moodie, A.F. (1974). Numerical evaluations of N-beam wave functions in electron scattering by the multi-slice method. Acta Cryst A 30, 280–290.Google Scholar
Howie, A. (1978). The theory of high energy electron diffraction. In Diffraction and Imaging Techniques in Material Science, Amelinckx, S., Gevers, R. & van Landuyt, J. (Eds.), pp. 457–509. Amsterdam: North-Holland.
Howie, A. (1979). Image contrast and localized signal selection techniques. J Microsc 117, 11–23.Google Scholar
Ishizuka, K. (1982). Multislice formula for inclined illumination. Acta Cryst A 38, 773–779.Google Scholar
Ishizuka, K. (1985). Comments on the computation of electron wave propagation in the slice method. J Microsc 137, 233–239.Google Scholar
Ishizuka, K. (1998). Multislice implementation for inclined illumination and convergent-beam electron diffraction. In Proceedings of the International Symposium on Hybrid Analysis for Functional Nanostructure, Shiojiri, M. & Nishio, K. (Eds.), pp. 69–72. Kyoto: Nakanishi Printing Co.
Ishizuka, K. (2001). Prospects of atomic resolution imaging with an aberration-corrected STEM. J Electron Microsc 50, 291–305.Google Scholar
Ishizuka, K. (2002). A practical approach for STEM image simulation based on the FFT multislice method. Ultramicroscopy 90, 71–83.Google Scholar
Ishizuka, K. & Taftø, J. (1984). Quantitative analysis of CBED to determine polarity and ionicity of ZnS-type crystals. Acta Cryst B 40, 332–337.Google Scholar
Ishizuka, K. & Uyeda, N. (1977). A new theoretical and practical approach to the multislice method. Acta Cryst A 33, 740–749.Google Scholar
Kilaas, R. & Gronsky, R. (1983). Real space image simulation in high resolution electron microscopy. Ultramicroscopy 11, 289–298.Google Scholar
Kilaas, R., O'Keefe, M.A., & Krishnan, K.M. (1987). On the inclusion of upper Laue layers in computational methods in high resolution transmission electron microscopy. Ultramicroscopy 21, 47–62.Google Scholar
Kirkland, E.J., Loane, R.F., & Silcox, J. (1987). Simulation of annular dark field STEM images using a modified multislice method. Ultramicroscopy 23, 77–96.Google Scholar
Lynch, D.F. (1971). Out-of-zone effects in dynamical electron diffraction intensities from gold. Acta Cryst A 27, 399–407.Google Scholar
Nishio, K., Isshiki, T., Saijo, H., & Sahiojiri., M. (1994). Multi-slice calculation for InP crystals using different slices. Ultramicroscopy 54, 301–309.Google Scholar
Pennycook, S.J. & Boatner, L.A. (1988). Chemically sensitive structure imaging with a scanning transmission electron microscope. Nature 336, 565–567.Google Scholar
Pennycook, S.J. & Jesson, D.E. (1991). High-resolution Z-contrast imaging of crystals. Ultramicroscopy 37, 14–38.Google Scholar
Qin, L.C. & Urban, K. (1990). Electron diffraction and lattice image simulations with the inclusion of HOLZ reflections. Ultramicroscopy 33, 159–166.Google Scholar
Self, P.G. (1982). Observations on the real space computation of dynamical electron diffraction intensities. J Microsc 127, 293–299.Google Scholar
Self, P.G., O'Keefe, M.A., Buseck, P.R., & Spargo, A.E.C. (1983). Practical computation of amplitudes and phases in electron diffraction. Ultramicroscopy 11, 35–52.Google Scholar
Spence, J.C.H. & Cowley, J.M. (1978). Lattice imaging in STEM. Optik 50, 129.Google Scholar
Van Dyck, D. (1980). Fast computational procedure for the simulation of structure images in complex or disordered crystals: A new approach. J Microsc 119, 141–152.Google Scholar
Wang, Z.L. (1995). Elastic and Inelastic Scattering in Electron Diffraction and Imaging. New York: Prenum Press.