Skip to main content

Multislice Applications and Examples

  • Chapter
  • First Online:
Advanced Computing in Electron Microscopy

Abstract

The multislice method of calculating electron microscope images and diffraction patterns of thicker specimen is applied to several different specimen. First, some simple examples are worked through to help understand how to use the method and then some more complicated specimens are investigated to illustrate the method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Atkinson A. C. The computer generation of Poisson random variable. J. Royal Statistical Society, Series C (Applied Statistics), 28:29–35, 1979.

    MATH  Google Scholar 

  2. L. J. Allen and C. J. Rossouw. Absorptive potentials due to ionization and thermal diffuse scattering by fast electrons in crystals. Phys. Rev. B, 42:11644–11654, 1990.

    Article  ADS  Google Scholar 

  3. A. Amali and P. Rez. Theory of lattice resolution in high-angle annular dark-field images. Microscopy and Microanalysis, 3:28–46, 1997.

    Article  ADS  Google Scholar 

  4. G. R. Anstis. The s-state analysis applied to high-angle, annular dark-field image interpretation when can we use it? Microscopy and Microanalysis, 10:4–8, 2004.

    Article  ADS  Google Scholar 

  5. G. R. Anstis, D. Q. Cai, and D. J. H. Cockayne. Limitations on the s-state approach to the interpretation of sub-angstrom resolution electron microscope images and microanalysis. Ultramicroscopy, 94:309–327, 2003.

    Article  Google Scholar 

  6. J. C. Barry. Semiquantitative image matching in HRTEM. In W. Krakow and M. O’Keefe, editors, Computer Simulation of Electron Microscope Diffraction and Images, pages 57–78, Warrendale, Penn., 1989. The Minerals, Metals and Materials Society.

    Google Scholar 

  7. J. C. Barry. Image-matching as a means of atomic structure evaluation in high resolution transmission electron microscopy. In P. W. Hawkes, editor, Signal and Image Processing in Microscopy and Microanalysis, Scanning Microscopy, Supplement 6, pages 209–221, Chicago, 1992. Scanning Microscopy Intern.

    Google Scholar 

  8. H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne. The protein data bank. Nucleic Acids Research, 28:235–242, 2000. www.rcsb.org.

    Article  Google Scholar 

  9. C. B. Boothroyd. Why don’t high-resolution simulations and images match? J. Microscopy, 190:99–108, 1998.

    Article  Google Scholar 

  10. B. F. Buxton, J. E. Loveluck, and J. W. Steeds. Bloch waves and their corresponding atomic and molecular orbitals in high energy electron diffraction. Philosophical Magazine A, 38:259–278, 1978.

    Article  ADS  Google Scholar 

  11. Yifan Cheng, Nikolaus Grigorieff, Pawel A. Penczek, and Thomas Waltz. A primer on single-particle cryo-electron microscopy. Cell, 161:439–449, 2015.

    Google Scholar 

  12. J. M. Cowley. Electron microscopy of crystals with time-dependent perturbations. Acta Cryst., A44:847–853, 1988.

    Article  Google Scholar 

  13. J. M. Cowley and R. J. Murray. Diffuse scattering in electron diffraction patterns, II. short-range order scattering. Acta Cryst., A24:329–336, 1968.

    Article  ADS  Google Scholar 

  14. J. M. Cowley and A. P. Pogany. Diffuse scattering in electron diffraction patterns, I. general theory and computational methods. Acta Cryst., A24:109–116, 1968.

    Article  Google Scholar 

  15. M. D. Croitoru, D. Van Dyck, S. Van Aert, S. Bals, and J. Verbeeck. An efficient way of including thermal diffuse scattering in simulation of scanning transmission electron microscope images. Ultramicroscopy, 106:933–940, 2006.

    Article  Google Scholar 

  16. C. Dinges and H. Rose. Simulation of filtered and unfiltered TEM images and diffraction patterns. Phys. Stat. Sol. (A), 150:23–30, 1995.

    Article  ADS  Google Scholar 

  17. C. Dwyer and J. Etheridge. Scattering of Å-scale electron probes in silicon. Ultramicroscopy, 96:343–360, 2003.

    Article  Google Scholar 

  18. A. Engel. Scanning transmission electron microscopy: Biological application. In P. W. Hawkes, editor, Adv. in Imaging and Electron Physics, vol. 159, pages 357–386. Academic Press, San Diego, 2009.

    Google Scholar 

  19. A. Engel and C. Colliex. Application of scanning transmission electron microscopy to the study of biological structure. Current Opinion in Biotechnology, 4:403–411, 1993.

    Article  Google Scholar 

  20. S. J. Erasmus and K. C. A. Smith. An automatic focusing and astigmatism correction system for the SEM and CTEM. J. Microscopy, 127:185–199, 1982.

    Article  Google Scholar 

  21. G. Y. Fan. Multislice calculation of kikuchi patterns. In G. W. Bailey, editor, Proceedings of the 47th Annual Meeting of the Microscopy Society of America, pages 52–53. San Francisco Press, 1989.

    Google Scholar 

  22. S. D. Findlay and J. M. LeBeau. Detector non-uniformity in scanning transmission electron microscopy. Ultramicroscopy, 124:52–60, 2013.

    Article  Google Scholar 

  23. J. Frank. Three Dimensional Electron Microscopy of Macromolecular Assemblies. Oxford Univ. Press, New York, 2006.

    Book  Google Scholar 

  24. Harindarpal S. Gill and David Eisenberg. The crystal structure of phosphinothricin in the active site of glutamine synthetase illuminates the mechanism of enzymatic inhibition. Biochemistry, 40:1903–1912, 2001.

    Article  Google Scholar 

  25. C. R. Hall and P. B. Hirsch. Effect of thermal diffuse scattering on propagation of high energy electrons through crystals. Proc. Roy. Soc. London, A286:158–177, 1965.

    ADS  Google Scholar 

  26. S. Hillyard and J. Silcox. Detector geometry, thermal diffuse scattering and strain effects in ADF-STEM imaging. Ultramicroscopy, 58:6–17, 1995.

    Article  Google Scholar 

  27. R. Hovden, H. L. Xin, and D. A. Muller. Channeling of a subangstrom electron beam in a crystal mapped to two-dimensional molecular orbitals. Phys. Rev. B, 86:195415, 2012.

    Article  ADS  Google Scholar 

  28. M. J. Hÿtch and W. M. Stobbs. Quantitative comparison of high resolution TEM images with image simulation. Ultramicroscopy, 53:191–203, 1994.

    Article  Google Scholar 

  29. D. E. Jesson and S. J. Pennycook. Incoherent imaging of crystals using thermally scattered electrons. Proc. R. Soc. Lond. A, 449:273–293, 1995.

    Article  ADS  Google Scholar 

  30. C.-L. Jia, M. Lentzen, and K. Urban. High-resolution transmission electron microscopy using negative spherical aberration. Microsc. and Microanalysis, 10:174–184, 2004.

    Article  ADS  Google Scholar 

  31. K. Kambe, G. Lehmpfuhl, and F. Fujimoto. Interpretation of electron channeling by the dynamical theory of electron diffraction. Z. Naturforsch., 29 a:1034–1044, 1974.

    Google Scholar 

  32. Kibum Kang, Saien Xie, Lujie Huang, Yimo Han, Pinshane Y. Huang, Kin Fai Mak, Cheol-Joo Kim, David Muller, and Jiwoong Park. High-mobility three-atom-thick semiconducting films with wafer-scale homogeneity. Nature, 520:656–660, 2015.

    Article  ADS  Google Scholar 

  33. W. E. King and G. H. Campbell. Quantitative HREM using non-linear least-squares methods. Ultramicroscopy, 56:46–53, 1994.

    Article  Google Scholar 

  34. E. J. Kirkland. Z-contrast in a conventional TEM. In G. W. Bailey, R. V. W. Dimlich, K. B. Alexander, J. J. McCarthy, and T. P. Pretlow, editors, Proceedings Microscopy and Microanalysis 1997, pages 1147–1148, New York, 1997. Springer.

    Google Scholar 

  35. E. J. Kirkland. Some effects of electron channeling on electron energy loss spectroscopy. Ultramicroscopy, 102:199–207, 2005.

    Article  Google Scholar 

  36. E. J. Kirkland. Fine tuning an aberration corrected ADF-STEM. Ultramicroscopy, 186:62–65, 2018.

    Article  Google Scholar 

  37. E. J. Kirkland, R. F. Loane, P. Xu, and J. Silcox. Multislice simulation of ADF-STEM and CBED images. In W. Krakow and M. O’Keefe, editors, Computer Simulation of Electron Microscope Diffraction and Images, pages 13–31, Warrendale, Penn., 1989. The Minerals, Metals and Materials Society.

    Google Scholar 

  38. E. J. Kirkland, B. M. Siegel, N. Uyeda, and Y. Fujiyoshi. Improved high resolution image processing of bright field electron micrographs II. experiment. Ultramicroscopy, 17:87–104, 1985.

    Article  Google Scholar 

  39. C. Kittel. Intro. to Solid State Physics. Wiley, New York, 7th edition, 1996.

    Google Scholar 

  40. D. O. Klenov, S. D. Findlay, L. J. Allen, and S. Stemmer. Influence of orientation on the contrast of high-angle annular dark-field images of silicon. Phys. Rev. B, 76:014111, 2007.

    Article  ADS  Google Scholar 

  41. Florian F. Krause, Knut Müller, Dennis Zillmann, Jacob Jansen, and Marco Schowalter. Comparison of intensity and absolute contrast of simulated and experimental high-resolution transmission electron microscopy images for different multislice simulation methods. Ultramicroscopy, 134:94–101, 2013.

    Article  Google Scholar 

  42. N. G. Krishna and D. B. Sirdeshmukh. Compilation of temperature factors of hexagonal close packed elements. Acta Cryst., A54:513–514, 1998.

    Article  Google Scholar 

  43. J. M. LeBeau, A. J. D’Alfonso, S. D. Findlay, S. Stemmer, and L. J. Allen. Quantitative comparisons of contrast in experimental and simulated bright-field scanning transmission electron microscopy images. Phys. Rev. B, 80:174106, 2009.

    Article  ADS  Google Scholar 

  44. J. M. LeBeau, S. D. Findlay, L. J. Allen, and S. Stemmer. Quantitative atomic resolution scanning transmission electron microscopy. Phys. Rev. Lett., 100:206101, 2008.

    Article  ADS  Google Scholar 

  45. J. M. LeBeau and S. Stemmer. Experimental quantification of annular dark-field images in scanning transmission electron microscopy. Ultramicroscopy, 108:1653–1658, 2008.

    Article  Google Scholar 

  46. Ming-Yang Li, Yumeng Shi, Chia-Chin Cheng, Li-Syuan Lu, Yung-Chang Lin, Hao-Lin Tang, Meng-Li Tsai, Chih-Wei Chu, Kung-Hwa Wei, Jr-Hau He, Wen-Hao Chang, Kazu Suenaga, and Lain-Jong Li. Epitaxial growth of a monolayer WSe2-MoS2 lateral p-n junction with an atomically sharp interface. Science, 349:524–528, 2015.

    Article  ADS  Google Scholar 

  47. Xinming Li, Li Tao, Zefeng Chen, Hui Fang, Xuesong Li, Xinran Wang, Jian-Bin Xu, and Hongwei Zhu. Graphene and related two-dimensional materials: Structure-property relationships for electronics and optoelectronics. Applied Physics Reviews, 4:021306, 2017.

    Article  ADS  Google Scholar 

  48. R. F. Loane, P. Xu, and J. Silcox. Thermal vibrations in convergent-beam electron diffraction. Acta Cryst., A47:267–278, 1991.

    Article  Google Scholar 

  49. R. F. Loane, P. Xu, and J. Silcox. Incoherent imaging of zone axis crystals with ADF STEM. Ultramicroscopy, 40:121–138, 1992.

    Article  Google Scholar 

  50. Andrew R. Lupini. The electron Ronchigram. In Stephen J. Pennycook and Peter D. Nellist, editors, Scanning Transmission Electron Microscopy, Imaging and Analysis, pages 117–482. Springer, New York, 2011.

    Google Scholar 

  51. S. E. Maccagnano-Zacher, K. A. Mkhoyen, E. J. Kirkland, and J. Silcox. Effects of tilt on high-resolution ADF-STEM imaging. Ultramicroscopy, 108:718–726, 2008.

    Article  Google Scholar 

  52. Richard M. Martin. Electronic Structure, Basic Theory and Practice. Cambridge Univ. Press, New York, 2004.

    Book  Google Scholar 

  53. H. D. Megaw. Crystal Structures: A Working Approach. Saunders, Philadelphia, 1973.

    Google Scholar 

  54. J. C. Meyer, S. Kurasch, H. J. Park, V. Skakalova, D. Künzel, A. Groß, A. Chuvilin, G. Algara-Siller, S. Roth, T. Iwasaki, U. Starke, J. H. Smet, and U. Kaiser. Experimental analysis of charge redistribution due to chemical bonding by high-resolution transmission electron microscopy. Nature Materials, 10:209–215, 2011.

    Article  ADS  Google Scholar 

  55. K. Mitsuishi, M. Takeguchi, H. Yasuda, and K. Furuya. New scheme for calculation of annular dark-field STEM image including both elastically diffracted and TDS waves. J. Electron Microscopy, 50:157–162, 2001.

    Google Scholar 

  56. K. A. Mkhoyan, S. E. Maccagnano-Zacher, E. J. Kirkland, and J. Silcox. Effects of amorphous layers ADF-STEM imaging. Ultramicroscopy, 108:791–803, 2008.

    Article  Google Scholar 

  57. G. Möbus. Retrieval of crystal defect structures from HRTEM images by simulated evolution I. basic technique. Ultramicroscopy, 65:205–216, 1996.

    Article  Google Scholar 

  58. G. Möbus and G. Dehm. Retrieval of crystal defect structures from HRTEM images by simulated evolution II. experimental image evaluation. Ultramicroscopy, 65:217–228, 1996.

    Article  Google Scholar 

  59. G. Möbus, T. Gemming, and P. Gumbsch. The influence of phonon scattering on HREM images. Acta Cryst., A54:83–90, 1998.

    Article  Google Scholar 

  60. G. Möbus and M. Rühle. Structure determination of metal-ceramic interfaces by numerical contrast evaluation of HRTEM micrographs. Ultramicroscopy, 56:54–70, 1994.

    Article  Google Scholar 

  61. G. Möbus, R. Schweinfest, T. Gemming, T. Wagner, and M. Rühle. Iterative structure retrieval techniques in HREM: a comparative study and a modular program package. J. Microscopy, 190:109–130, 1998.

    Article  Google Scholar 

  62. D. A. Muller, B. Edwards, E. J. Kirkland, and J. Silcox. Detailed calculations of thermal diffuse scattering. In G. W. Bailey, R. V. W. Dimlich, K. B. Alexander, J. J. McCarthy, and T. P. Pretlow, editors, Proceedings Microscopy and Microanalysis 1997, pages 1153–1154, New York, 1997. Springer.

    Google Scholar 

  63. A. Ourmazd, F. H. Baumann, M. Bode, and Y. Kim. Quantitative chemical lattice matching: Theory and practice. Ultramicroscopy, 34:237–255, 1990.

    Article  Google Scholar 

  64. S. J. Pennycook and D. E. Jesson. High resolution Z-contrast imaging of crystals. Ultramicroscopy, 37:14–38, 1991.

    Article  Google Scholar 

  65. John S. Reid. Debye–Waller factors of zinc-blende-structure materials - a lattice dynamical comparison. Acta Cryst., A39:1–13, 1983.

    Article  Google Scholar 

  66. P. Rez, C. J. Humphreys, and M. J. Whelan. The distribution of intensity in electron diffraction patterns due to phonon scattering. Phil. Mag., 35:81–96, 1977.

    Article  ADS  Google Scholar 

  67. B. Schönfeld, J. J. Huang, and S. C. Moss. Anisotropic mean-square displacements (MSD) in single crystals of 2H- and 3R-MoS2. Acta Cryst. B, 39:404–407, 1983.

    Article  Google Scholar 

  68. M. Schowalter, A. Rosenauer, J. T. Titantah, and D. Lamoen. Computation and parametrization of the temperature dependence of Debye–Waller factors for group IV, III-V and II-VI semiconductors. Acta Cryst., A65:1–13, 2008.

    Google Scholar 

  69. V. F. Sears and S. A. Shelley. Debye-Waller factor for elemental crystals. Acta Cryst., A47:441–446, 1991.

    Article  Google Scholar 

  70. J. C. H. Spence and J. M. Cowley. Lattice imaging in STEM. Optik, 50:129–142, 1978.

    Google Scholar 

  71. A. Thust. High-resolution transmission electron microscopy on an absolute contrast scale. Phys. Rev. Lett., 102:220801, 2009.

    Article  ADS  Google Scholar 

  72. A. Thust and K. Urban. Quantitative high-speed matching of high-resolution electron microscopy images. Ultramicroscopy, 45:23–42, 1992.

    Article  Google Scholar 

  73. K. Tillmann, A. Thust, and K. Urban. Spherical aberration correction in tandem with exit-plane wave function reconstruction: Interlocking tools for atomic scale imaging of lattice defects in GaAs. Microsc. and Microanalysis, 10:185–198, 2004.

    Article  ADS  Google Scholar 

  74. K. Urban. Studying atomic structures by aberration-corrected transmission electron microscopy. Science, 321:506–510, 2008.

    Article  ADS  Google Scholar 

  75. B. K. Vainshtein. Modern Crystallography I, Fundamentals of Crystals. Springer-Verlag, Berlin, 2nd edition, 1994.

    Google Scholar 

  76. B. K. Vainshtein, V. M. Fridkin, and V. L. Indenbom. Modern Crystallography II, Structure of Crystals. Springer-Verlag, Berlin, 1982.

    Book  Google Scholar 

  77. M. van Heel. Similarity measures between images. Ultramicroscopy, 21:95–100, 1987.

    Article  Google Scholar 

  78. J. Wall. Simulation of coherent scattering in STEM. In P. Kotula, M. Marko, J.-H. Scott, R. Gauvin, D. Beniac, G. Lucas, S. McKernan, and J. Shields, editors, Microscopy and Microanalysis 2006, volume 12, suppl. 2, pages 1350–1351, Cambridge, UK, 2006. Cambridge Univ. Press.

    Google Scholar 

  79. Z. L. Wang. Dynamics of thermal diffuse scattering in high-energy electron diffraction and imaging: Theory and experiments. Phil. Mag., B65:559–587, 1992.

    Article  ADS  Google Scholar 

  80. Z. L. Wang. An optical potential approach to incoherent multiple thermal diffuse scattering in quantitative HRTEM. Ultramicroscopy, 74:7–26, 1998.

    Article  Google Scholar 

  81. Z. L. Wang and J. M. Cowley. Simulating high-angle annular dark-field STEM images including inelastic thermal diffuse scattering. Ultramicroscopy, 31:437–454, 1989.

    Article  Google Scholar 

  82. Z. L. Wang and J. M. Cowley. Dynamical theory of high-angle annular dark-field STEM lattice images for a Ge/Si interface. Ultramicroscopy, 32:275–289, 1990.

    Article  Google Scholar 

  83. B. E. Warren. X-ray Diffraction. Dover, New York, 1969,1990.

    Google Scholar 

  84. A. R. Wilson, A. E. C. Spargo, and D. J. Smith. The characterisation of instrumental parameters in high resolution electron microscopy. Optik, 61:63–78, 1982.

    Google Scholar 

  85. R. W. G. Wyckoff. Crystal Structures, Vol. 1 and 2. Wiley, New York, 2nd edition, 1963,64.

    Google Scholar 

  86. H. Zhang, L. D. Marks, Y. Y. Wang, H. Zhang, V. P. Dravid, P. Han, and D. A. Payne. Structure of planar defects in (Sr0.9Ca0.3)1.1Cuo2 infinite-layer superconductors by quantitative high-resolution electron microscopy. Ultramicroscopy, 57:103–111, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kirkland, E.J. (2020). Multislice Applications and Examples. In: Advanced Computing in Electron Microscopy. Springer, Cham. https://doi.org/10.1007/978-3-030-33260-0_7

Download citation

Publish with us

Policies and ethics