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Bibliography
Further Reading
C. C. Ahn, Ed.: Transmission Electron Energy Loss Spectroscopy in MaterialsScience and the EELS Atlas (Wiley–VCH, Weinheim 2004). An updated 2ndedition of the Disko, Ahn and Fultz book by the same name. A practicalreference covering EELS instrumentation, quantification, fine structure, andapplications to the different classes of materials. Includes a CD ROM withthe EELS Atlas.C. C. Ahn and O. L. Krivanek: EELS Atlas (Gatan, Inc., Pleasanton, CA1983). The standard reference presenting EELS spectra of nearly all the ele-ments in the periodic table and some compounds.S. Amelinckx, R. Gevers and J. Van Landuyt: Diffraction and Imaging Tech-niques in Materials Science (North–Holland, Amsterdam 1978). Excellentchapters on kinematical and dynamical electron diffraction, the WBDF tech-nique, computed electron micrographs, Kikuchi diffraction and defects in ma-terials.Leonid V. Azaroff: Elements of X-Ray Crystallography (McGraw–Hill, NewYork 1968), reprinted by TechBooks, Fairfax, VA. Emphasizes crystal struc-ture and symmetry determination by x-ray diffractometry.B. W. Batterman and H. Cole: Rev. Mod. Phys. 36, 681-717 (1964). A sys-tematic presentation of the dynamical theory of x-ray diffraction based onMaxwell’s equations.J. M. Cowley: Diffraction Physics, 2nd edn. (North–Holland Publishing, Am-sterdam 1975). Thorough but concise presentation of the physical opticsapproach to diffraction and imaging, scattering of radiation by atoms andcrystals, kinematical and dynamical diffraction, and applications to selectedtopics.B. D. Cullity and S. R. Stock: Elements of X-Ray Diffraction (Prentice–Hall, Upper Saddle River, NJ 2001). A popular introductory text on x-raydiffraction – provides physical explanations of many topics.M. De Graef: Introduction to Conventional Transmission Electron Microscopy(Cambridge University Press, Cambridge 2003). Much more than an intro-duction, this textbook provides excellent and thorough coverage of electron
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optics, crystallography, and defect contrast in dynamical theory. Computa-tional methods are presented with an accompanying website.M. M. Disko, C. C. Ahn and B. Fultz, Eds.: Transmission Electron EnergyLoss Spectroscopy in Materials Science (Minerals, Metals & Materials Soci-ety, Warrendale, PA 1992). A practical reference covering EELS instrumen-tation, quantification, fine structure, and applications to the different classesof materials.J. A. Eades: ‘Convergent-Beam Diffraction’. In: Electron Diffraction Tech-niques, Volume 1, ed. by J. M. Cowley (International Union of Crystallog-raphy, Oxford University Press, Oxford 1992). Good overall review of thesubject.J. W. Edington: Practical Electron Microscopy in Materials Science, 1. TheOperation and Calibration of the Electron Microscope (Philips Technical Li-brary, Eindhoven 1974). Easy to understand discussion of the optics, align-ment and calibration of the TEM.J. W. Edington: Practical Electron Microscopy in Materials Science, 2. Elec-tron Diffraction in the Electron Microscope (Philips Technical Library, Eind-hoven 1975). Thorough discussion of electron diffraction patterns, Kikuchilines, and their use in the TEM. Has a good appendix on stereographic pro-jections.J. W. Edington: Practical Electron Microscopy in Materials Science, 3. Inter-pretation of Transmission Electron Micrographs (Philips Technical Library,Eindhoven 1975). Excellent discussion of diffraction contrast and quantitativedefect analysis in the TEM with many useful examples.J. W. Edington: Practical Electron Microscopy in Materials Science, 4. Typi-cal Electron Microscope Investigations (Philips Technical Library, Eindhoven1976). A number of illustrative examples of diffraction and imaging analysesin the TEM.T. Egami and S. J. L. Billinge: Underneath the Bragg Peaks: Structural Analy-sis of Complex Materials (Pergamon Materials Series, Elsevier, Oxford 2003).A book on modern powder diffraction experiments, with emphasis on totalscattering measurements and pair distribution function analysis. Clear andthorough coverage of theory and practice of experiments with synchrotronradiation and neutron scattering for identifying nanoscale structures and dis-order in hard condensed matter.R. F. Egerton: Electron Energy-Loss Spectroscopy in the Electron Microscope,2nd edn. (Plenum Press, New York 1996). Thorough, scholarly and rigorouscoverage of EELS instrumentation, electron scattering theory, quantitativeEELS analysis, and examples in materials research.C. T. Forwood and L. M. Clarebrough: Electron Microscopy of Interfaces inMetals and Alloys (Adam Hilger IOP Publishing Ltd., Bristol 1991). Excellentreference on computed electron micrographs of interfaces in materials.
Bibliography 679
P. J. Goodhews and F. J. Humphreys: Electron Microscopy and Microanalysis(Taylor & Francis Ltd., London 1988). Easy-to-follow discussions of electronoptics in the TEM, electron beam-specimen interactions, electron diffractionand imaging, and microanalysis.P. Grivet: Electron Optics, revised by A. Septier, translated by P. W. Hawkes(Pergamon, Oxford, 1965). The electromagnetics of electron optics, with em-phasis on electron lenses and the TEM.C. Hammond: The Basics of Crystallography and Diffraction (InternationalUnion of Crystallography, Oxford University Press, Oxford 1977). Simple andunderstandable introduction to crystallography and diffraction techniques,with worked examples of structure factor calculations and diffraction analy-ses.A. K. Head, P. Humble, L. M. Clarebrough, A. J. Morton and C. T. Forwood:Computed Electron Micrographs and Defect Identification (North–HollandPublishing Company, Amsterdam 1973). Excellent reference on computedelectron micrographs based on the Howie-Whelan two-beam theory of diffrac-tion, including applications and limitations of the technique.P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan:Electron Microscopy of Thin Crystals (R. E. Krieger, Malabar, Florida 1977).A reprinted early book on conventional TEM. Excellent discussions of kine-matical and dynamical electron diffraction theory and application to defectanalysis in materials. It offers a broad coverage of experimental technique,and for many years was the essential text on the subject. Includes workedproblems.J. J. Hren, J. I. Goldstein and D. C. Joy, Eds.: Introduction to AnalyticalElectron Microscopy (Plenum Press, New York 1979). Good overall book onTEM, providing treatment of electron optics, EDS, EELS, CBED, STEM.The International Union of Crystallography publishes the International Ta-bles for X-ray Crystallography (Kynock Press, Birmingham, England, 1952-),which contain the standard tables of crystal symmetry plus a wealth of tabu-lated data on scattering factors, dispersion corrections, and other details andprinciples of x-ray data analysis.O. Johari and G. Thomas: The Stereographic Projection and Its Applications(Interscience Publishers, John Wiley & Sons, New York 1969). Provides stere-ographic projections and presents their applications to problems in materialsscience.D. C. Joy, A. D. Romig, Jr. and J. I. Goldstein, Eds.: Principles of AnalyticalElectron Microscopy (Plenum Press, New York 1986). Provides a good intro-duction to electron scattering and electron optics, with emphasis on EDS andEELS spectroscopy. Contains worked examples.R. J. Keyse, A. J. Garratt-Reed, P. J. Goodhew and G. W. Lorimer: Introduc-tion to Scanning Transmission Electron Microscopy (Springer BIOS Scientific
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Publishers Ltd., New York 1998). Practical explanation of optics, diffraction,imaging and microanalysis – specifically for the STEM.Harold P. Klug and Leroy E. Alexander: X-Ray Diffraction Procedures(Wiley–Interscience, New York 1974). Provides an encyclopedic coverage ofexperimental methods and many principles of x-ray diffraction.M. A. Krivoglaz: Theory of X-Ray and Thermal Neutron Scattering by RealCrystals (Plenum, New York 1969). An elegant and formal treatment of scat-tering from fluctuations with analysis of their correlation functions.M. H. Lorretto: Electron Beam Analysis of Materials (Chapman and Hall,London 1984). Concise discussion of most TEM topics, including electrondiffraction and imaging, CBED, and microanalysis.A. J. F. Metherell: ‘Diffraction of Electrons by Perfect Crystals’, in ElectronMicroscopy in Materials Science II, ed. by U. Valdre and E. Ruedl (CECBrussels 1975) pp. 387. This is probably the most detailed and comprehen-sive article written on materials analysis using the Bloch wave approach todynamical electron diffraction.I. C. Noyan and J. B. Cohen: Residual Stress (Springer–Verlag, New York1987). A thorough development of the experiment and theory connecting con-tinuum mechanics to x-ray diffractometry. Includes x-ray lineshape analysis.S. J. Pennycook, D. E. Jesson, M. F. Chisholm, N. D. Browning, A. J. McGib-bon, and M. M. McGibbon: ‘Z-Contrast Imaging in the Scanning Transmis-sion Electron Microscope’, J. Micros. Soc. Amer. 1, 234 (1995). An overviewof the principles and practice of Z-contrast imaging in the STEM, with em-phasis on chemical and structural information on the atomic scale.H. Raether: Excitations of Plasmons and Interband Transitions by Electrons(Springer–Verlag, Berlin and New York 1980). An in-depth treatment of thelow-loss part of EELS spectra.L. Reimer, Ed.: Energy-Filtering Transmission Electron Microscopy (Springer–Verlag, Berlin 1995). Contains detailed theoretical discussions of electron-specimen interactions, EELS instrumentation, spectroscopic diffraction andimaging techniques.L. Reimer: Transmission Electron Microscopy: Physics of Image Formationand Microanalysis, 4th edn. (Springer–Verlag, New York 1997). Comprehen-sive, scholarly, and rigorous coverage of TEM instrumentation, imaging anddiffraction techniques. Strong emphasis on the underlying physics. Extensivereferences to recent research.P. Schattschneider: Fundamentals of Inelastic Electron Scattering (Springer–Verlag, Vienna, New York 1986). The theoretical physics of low-loss EELSspectra, with emphasis on the quantum mechanics of scattering using many-body theory.L. H. Schwartz and J. B. Cohen: Diffraction from Materials (Springer–Verlag,Berlin 1987). Provides a thorough treatment of x-ray theory and experiment,including crystallography.
Bibliography 681
F. G. Smith and J. H. Thomson: Optics, 2nd edn. (John Wiley & Sons, NewYork 1988). Although this book is concerned with light optics, it providesexcellent coverage on the subjects of wave propagation, geometrical optics,interference and diffraction, resolution, and phase-amplitude diagrams.J. C. H. Spence: Experimental High-Resolution Electron Microscopy, 2nd edn.(Oxford Univ. Press, New York 1988). Wide-ranging coverage of the theoryand practice of TEM, emphasizing HRTEM.J. C. H. Spence and J. M. Zuo: Electron Microdiffraction (Plenum Press,New York 1992). Excellent discussion of dynamical electron diffraction andconvergent-beam electron diffraction.G. L. Squires: Introduction to the Theory of Thermal Neutron Scattering(Dover, Mineola, New York 1996). A broad coverage of the theoretical physicsof neutron scattering, developed elegantly and concisely.J. W. Steeds: ‘Convergent Beam Electron Diffraction’. In: Introduction toAnalytical Electron Microscopy, ed. by J. J. Hren, J. I. Goldstein, D. C. Joy(Plenum Press, New York 1979) p. 401. Good overall discussion of CBEDtechnique and application to materials.J. W. Steeds and R. Vincent: ‘Use of High-Symmetry Zone Axes in ElectronDiffraction in Determining Crystal Point and Space Groups’, J. Appl. Cryst.16, 317 (1983). Provides a useful sequence of steps for determining crystalpoint and space groups from high-symmetry zone axes.M. Tanaka and M. Terauchi: Convergent-Beam Electron Diffraction (JEOLLtd., Nakagami, Tokyo 1985). M. Tanaka, M. Terauchi and T. Kaneyama,Convergent-Beam Electron Diffraction II (JEOL Ltd., Musashino 3-chome,Tokyo 1988). These compilations provide a thorough summary of CBEDprocedures such as point and space group determination, lattice parametermeasurement, etc.G. Thomas and M. J. Goringe: Transmission Electron Microscopy of Ma-terials (Wiley–Interscience, New York 1979). Good general discussion ofTEM techniques, including kinematical and dynamical electron diffractionand imaging. Many examples of TEM images of defects in materials withdiscussion of practice. Includes worked problems.B. E. Warren: X-Ray Diffraction (Addison–Wesley, Reading, MA 1969), isnow a best buy as a Dover reprint (Dover, New York, 1990). It provides arigorous coverage of concepts in x-ray powder diffractometry of imperfectcrystals.D. B. Williams: Practical Analytical Electron Microscopy in Materials Science(Philips Electron Instruments, Inc., Mahwah, NJ 1984). In-depth discussionof alignment and calibration of the TEM, quantitative x-ray microanalysisand EELS spectrometry with many useful examples.D. B. Williams and C. B. Carter: Transmission Electron Microscopy: A Text-book for Materials Science (Plenum Press, New York 1996). Probably the
682 Bibliography
most comprehensive current book on TEM available, covering almost all as-pects of the technique. Includes both theory and practical examples.
References and Figures
Chapter 1 title photograph of Inel Corp. CPS-120 x-ray diffractometer withlarge-angle position-sensitive detector. Radiation shielding not shown.
1.1 International Centre for Diffraction Data, 12 Campus Boulevard New-town Square, PA 19073-3273 USA. http://www.icdd.com
1.2 H. G. J. Moseley: Philos. Mag. 27, 713 (1914).1.3 F. Richtmyer and E. Kennard: Introduction to Modern Physics (McGraw–
Hill, New York 1947).1.4 A partial list of web sites for synchrotron sources includes (prefixed
with http:// ): aps.anl.gov/, www.esrf.eu/, www.spring8.or.jp/,www-hasylab.desy.de/, slac.stanford.edu/, www.srs.ac.uk/srs/www.bessy.de/, www.nsls.bnl.gov/, www.als.lbl.gov/, ssrc.inp.nsk.su/
1.5 Leonid V. Azaroff: Elements of X-Ray Crystallography (McGraw–Hill,New York 1968). Figure reprinted with the courtesy of TechBooks,Fairfax, VA.
1.6 National Institute of Standards and Technology, Standard ReferenceMaterials Program, Bldg. 202, Rm 204, Gaithersburg, MD 20899.http://ts.nist.gov/srm
1.7 J. Nelson and D. Riley: Proc. Phys. Soc. (London) 57, 160 (1945).1.8 Harold P. Klug and Leroy E. Alexander: X-Ray Diffraction Procedures
(Wiley–Interscience, New York 1974). Figure reprinted with the cour-tesy of John Wiley–Interscience.
Chapter 2 title drawing of JEOL JEM-2010F. Figure reprinted with the cour-tesy of JEOL Ltd., Tokyo.
2.1 B. Demczyk: Ultramicros., 47, 433 (1993). Figure reprinted with thecourtesy of Elsevier Science Publishing B.V.
2.2 J. M. Howe, W. E. Benson, A. Garg and Y. C. Chang: Mater. Sci.Forum, 189-90, 255 (1995). Figure reprinted with the courtesy of TransTech Publications Ltd.
2.3 Near the year 2007, manufacturers of TEM instruments include JEOL,FEI, Hitachi and Zeiss. A partial list of web sites for manufacturers ofTEM instruments includes: www.jeol.com/, www.fei.com/,www.hitachi-hta.com/, www.smt.zeiss.com/
2.4 Figure reprinted with the courtesy of FEI Company.2.5 P. J. Goodhew and F. J. Humphreys: Electron Microscopy and Analy-
sis, 2nd edn. (Taylor & Francis, Ltd., London 1975). Figure reprintedwith the courtesy of Taylor & Francis, Ltd.
Bibliography 683
2.6 Figure reprinted with the courtesy of Prof. M. K. Hatalis.2.7 M. Bilaniuk and J. M. Howe: Interface Sci., 6, 328 (1998). Figure
reprinted with the courtesy of Kluwer Academic Publishers.2.8 D. B. Williams: Practical Analytical Electron Microscopy in Materi-
als Science (Philips Electron Optics Publishing Group, Mahwah, NJ1984). Figure reprinted with the courtesy of FEI Company.
2.9 Figure courtesy of Dr. Simon Nieh.2.10 L. Reimer: Transmission Electron Microscopy: Physics of Image For-
mation and Microanalysis, 4th edn. (Springer–Verlag, New York 1997).Figure reprinted with the courtesy of Springer–Verlag.
2.11 F. W. Sears and M. W. Zemansky: University Physics, 4th edn.(Addison– Wesley–Longman Publishing, Reading, MA 1973). Figurereprinted with the courtesy of Addison–Wesley–Longman Publishing.
2.12 J. W. Edington: Practical Electron Microscopy in Materials Science,1. The Operation and Calibration of the Electron Microscope (PhilipsTechnical Library, Eindhoven 1975). Figure reprinted with the courtesyof FEI Company.
Chapter 3 title image conveys the important concept of Fig. 3.7.
3.1 Figure reproduced with the courtesy of the Huntington Library, ArtCollections, and Botanical Gardens, San Marino, CA.
3.2 J. C. H. Spence: Acta Cryst. A49, 231 (1993).3.3 J. M. Zuo, M. Kim, M. O’Keefe, and J. C. H. Spence: Nature 401, 49
(1999). Figure reproduced with the courtesy of Nature and J. C. H.Spence.
3.4 U. Kriplani: Kinematical Mossbauer Diffraction from Polycrystalline57Fe. Ph.D. Thesis, California Institute of Technology, California (2000).
Chapter 4 title drawing of Gatan 666 EELS spectrometer. Figure reprintedwith the courtesy of Dr. C. C. Ahn.
4.1 D. H. Pearson: Measurements of White Lines in Transition Metalsand Alloys using Electron Energy Loss Spectrometry. Ph.D. Thesis,California Institute of Technology, California (1991). Figure reprintedwith the courtesy of Dr. D. H. Pearson.
4.2 M. M. Disko: ‘Transmission Electron Energy-Loss Spectrometry in Ma-terials Science’. In: Transmission Electron Energy Loss Spectroscopy inMaterials Science, ed. by M. M. Disko, C. C. Ahn and B. Fultz (Min-erals, Metals & Materials Society, Warrendale, PA 1992). Reprintedwith courtesy of The Minerals, Metals & Materials Society.
4.3 J. K. Okamoto: Temperature-Dependent Extended Electron EnergyLoss Fine Structure Measurements from K, L23, and M45 Edges inMetals, Intermetallic Alloys, and Nanocrystalline Materials. Ph.D.
684 Bibliography
Thesis, California Institute of Technology, California (1993). Figurereprinted with the courtesy of Dr. J. K. Okamoto.
4.4 A. Hightower: Lithium Electronic Environments in Rechargeable Bat-tery Electrodes. Ph.D. Thesis, California Institute of Technology, Cal-ifornia (2000).
4.5 R. F. Egerton: Electron Energy-Loss Spectroscopy in the Electron Mi-croscope, 2nd edn. (Plenum Press, New York 1996). Figures reprintedwith the courtesy of Plenum Press.
4.6 D. B. Williams and C. B. Carter: Transmission Electron Microscopy: ATextbook for Materials Science (Plenum Press, New York 1996). Figurereprinted with the courtesy of Plenum Press.
4.7 R. D. Leapman: ‘EELS Quantitative Analysis’. In: Transmission Elec-tron Energy Loss Spectroscopy in Materials Science, ed. by M. M.Disko, C. C. Ahn and B. Fultz (Minerals, Metals & Materials Soci-ety, Warrendale, PA 1992). Reprinted with courtesy of The Minerals,Metals & Materials Society.
4.8 Figure reprinted with the courtesy of K. T. Moore.4.8 D. B. Williams: Practical Analytical Electron Microscopy in Materi-
als Science (Philips Electron Optics Publishing Group, Mahwah, NJ1984). Figure reprinted with the courtesy of FEI Company.
4.10 E. H. S. Burhop: The Auger Effect and Other Radiationless Transi-tions (Cambridge University Press 1952). Figure reprinted with thepermission of Cambridge University Press.
4.11 Figure reprinted with the courtesy of Dr. K. M. Krishnan.4.12 Figure reprinted with the courtesy of C. M. Garland.4.13 C. Nockolds, M. J. Nasir, G. Cliff and G. W. Lorimer, In: Electron
Microscopy and Analysis - 1979, ed. by T. Mulvey (The Institute ofPhysics, Bristol and London, 1980) p. 417.
4.14 J. M. Howe and R. Gronsky: Scripta Metall., 20, 1168 (1986). Figurereprinted with the courtesy of Elsevier Science Ltd.
Chapter 5 title image of electron diffraction pattern from precipitates in anAl-Cu-Li alloy.
5.1 The International Union of Crystallography: International Tables forX-ray Crystallography (Kynock Press, Birmingham, England, 1952-).
5.2 Figure reprinted with the courtesy of Dr. S. R. Singh.5.3 Y. C. Chang: Crystal Structure and Nucleation Behavior of {111} Pre-
cipitates in an Al-3.9Cu-0.5Mg-0.5Ag Alloy. Ph.D. Thesis, CarnegieMellon University, Pittsburgh, PA (1993). Figure reprinted with thecourtesy of Dr. Y. C. Chang.
5.4 R. J. Rioja and D. E. Laughlin: Metall. Trans., 8A, 1259 (1977). Figurereprinted with the courtesy of The Minerals, Metals and MaterialsSociety.
Bibliography 685
5.5 G. Thomas and M. J. Goringe: Transmission Electron Microscopy ofMaterials (Wiley–Interscience, New York 1979). Figure reprinted withthe courtesy of Wiley–Interscience.
5.6 Figure and problem reprinted with the courtesy of Prof. D. E. Laughlin.5.7 F. K. LeGoues, H. I. Aaronson, Y. W. Lee and G. J. Fix: In: Proceedings
of the International Conference on Solid-Solid Phase Transformationsed. by H. I. Aaronson, D. E. Laughlin, R. F. Sekerka and C. M. Way-man (TMS-AIME, Warrendale, PA 1982) p. 427. Figure reprinted withthe courtesy of The Minerals, Metals and Materials Society.
Chapter 6 title image of Kikuchi map of bcc crystal. G. Thomas and M. J.Goringe: Transmission Electron Microscopy of Materials (Wiley–Interscience,New York 1979). Figure reprinted with the courtesy of Wiley–Interscience.
6.1 G. Thomas and M. J. Goringe: Transmission Electron Microscopy ofMaterials (Wiley–Interscience, New York 1979). Figure reprinted withthe courtesy of Wiley–Interscience.
6.2 J. W. Edington: Practical Electron Microscopy in Materials Science,2. Electron Diffraction in the Electron Microscope (Philips TechnicalLibrary, Eindhoven 1975). Figure reprinted with the courtesy of FEICompany.
6.3 Dr. J.-S. Chen, unpublished results.6.4 M. Tanaka and M. Terauchi: Convergent-Beam Electron Diffraction
(JEOL Ltd., Nakagami, Tokyo 1985). Figures reprinted with the cour-tesy of JEOL, Ltd. Worked thickness example on pp. 38-39.
6.5 R. Ayer: J. Electron Micros. Tech. 13, 16 (1989). Figure reprinted withthe courtesy of Alan R. Liss, Inc.
6.6 S. J. Rozeveld: Measurement of Residual Stress in an Al-SiCw Compos-ite by Convergent-Beam Electron Diffraction, Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA (1991). Figure reprinted with thecourtesy of Dr. S. J. Rozeveld.
6.7 B. F. Buxton, et al.: Proc. Roy. Soc. London A281, 188 (1976). B.F. Buxton, et al.: Phil. Trans. Roy. Soc. London, A281, 171 (1976).Tables reprinted with the courtesy of The Royal Society, London.
6.8 M. Tanaka, H. Sekii and T. Nagasawa: Acta Cryst. A39, 825 (1983).Figure reprinted with the courtesy of the International Union of Crys-tallography.
6.9 M. Tanaka, R. Saito and H. Sekii: Acta Cryst. A39, 359 (1983). Figurereprinted with the courtesy of International Union of Crystallography.
6.10 J. M. Howe, M. Sarikaya and R. Gronsky: Acta Cryst. A42, 371 (1986).Figure reprinted with the courtesy of International Union of Crystal-lography.
6.11 The International Union of Crystallography: International Tables forX-ray Crystallography (Kynock Press, Birmingham, England, 1952-).
686 Bibliography
6.12 J. W. Steeds and R. Vincent: ‘Use of High-Symmetry Zone Axes inElectron Diffraction in Determining Crystal Point and Space Groups’,J. Appl. Cryst. 16 317 (1983).
6.13 J. Gjønnes and A. F. Moodie: Acta Cryst. 19, 65 (1965).6.14 M. J. Kaufman and H. L. Fraser: Acta Metall. 33, 194 (1985). Figure
reprinted with the courtesy of Elsevier Science Ltd.
Chapter 7 title image of dislocations in Al.
7.1 P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J.Whelan: Electron Microscopy of Thin Crystals (R. E. Krieger, Malabar,Florida 1977). Figure reprinted with the courtesy of R. E. Krieger.
7.2 J. W. Edington: Practical Electron Microscopy in Materials Science,3. Interpretation of Transmission Electron Micrographs (Philips Tech-nical Library, Eindhoven 1975). Figure reprinted with the courtesy ofFEI Company.
7.3 Figure reprinted with the courtesy of Dr. Y. C. Chang.7.4 G. Thomas and M. J. Goringe: Transmission Electron Microscopy of
Materials (Wiley–Interscience, New York 1979). Figure reprinted withthe courtesy of Wiley–Interscience.
7.5 Figure reprinted with the courtesy of Dr. S. R. Singh.7.6 J. M. Howe, H. I. Aaronson and R. Gronsky: Acta Metall. 33, 641
(1985). Figure reprinted with the courtesy of Elsevier Science Ltd.7.7 P. B. Hirsch, A. Howie and M. J. Whelan: Phil. Trans. Royal Soc.
(London) 252A, 499 (1960).7.8 D. J. H. Cockayne, I. L. F. Ray, and M. J. Whelan: Philos. Mag. 20,
1265 (1969). D. J. H. Cockayne, M. L. Jenkins, and I. L. F. Ray: Philos.Mag. 24, 1383 (1971).
7.9 L. Reimer: Transmission Electron Microscopy: Physics of Image For-mation and Microanalysis, 4th edn. (Springer–Verlag, New York 1997).Figure reprinted with the courtesy of Springer–Verlag.
7.10 A. Garg and J. M. Howe: Acta Metall. Mater. 39, 1934 (1991). A.Garg, Y. C. Chang and J. M. Howe: Acta Metall. Mater. 41, 240(1993). Figures reprinted with the courtesy of Elsevier Science Ltd.
7.11 J. W. Edington: Practical Electron Microscopy in Materials Science,3. Interpretation of Transmission Electron Micrographs (Philips Tech-nical Library, Eindhoven 1975) p. 40. R. Gevers, A. Art and S.Amelinckx: Phys. Stat. Sol. 3, 1563 (1963).
7.12 N. Prabhu and J. M. Howe: Philos. Mag. A 63, 650 (1991). Figurereprinted with the courtesy of Taylor & Francis, Ltd.
7.13 M. F. Ashby and Brown: Philos. Mag. 8, 1083 (1963).7.14 H. P. Degischer: Philos. Mag. 26, 1147 (1972). Figure reprinted with
the courtesy of Taylor & Francis, Ltd.7.15 M. Hwang, D. E. Laughlin and I. M. Bernstein: Acta Metall. 28, 629
(1980). Figure reprinted with the courtesy of Elsevier Science Ltd.
Bibliography 687
7.16 Figure reprinted with the courtesy of Dr. A. Garg.
Chapter 8 title figure of (400)fcc diffraction from a nanocrystalline iron alloy(Mo Kα radiation).
8.1 H. P. Klug and L. E. Alexander: X-Ray Diffraction Procedures (Wiley–Interscience, New York 1974) pp. 687-692.
8.2 H. P. Klug and L. E. Alexander: X-Ray Diffraction Procedures (Wiley–Interscience, New York 1974) pp. 655-665.
8.3 B. E. Warren: X-Ray Diffraction (Dover, New York, 1990) pp. 251-275.8.4 H. Frase: Vibrational and Magnetic Properties of Mechanically Attr-
ited Ni3Fe Nanocrystals. Ph.D. Thesis, California Institute of Technol-ogy, California (1998).
Chapter 9 title image conveys the important concept of Fig. 9.3.
9.1 B. E. Warren: X-Ray Diffraction (Dover, New York, 1990) pp. 178-193.9.2 F. Ducastelle: Order and Phase Stability in Alloys (North–Holland,
Amsterdam 1991) pp. 439-442. This “relaxation energy” is importantfor the thermodynamics of many alloys.
9.3 J. A. Rodriguez, S. C. Moss, J. L. Robertson, J. R. D. Copley, D. A.Neumann and J. Major: Phys. Rev. B 74, 104115 (2006).
9.4 B. E. Warren: X-Ray Diffraction (Dover, New York, 1990) pp. 206-250.9.5 L. H. Schwartz and J. B. Cohen: Diffraction from Materials (Springer–
Verlag, Berlin 1987) pp. 407-409.9.6 J. M. Cowley: Diffraction Physics, 2nd edn. (North–Holland Publish-
ing, Amsterdam 1975) pp. 152-154.9.7 A. Williams: Atomic Structure of Transition Metal Based Metallic
Glasses. Ph.D. Thesis, California Institute of Technology, California(1981).
9.8 H. P. Klug and L. E. Alexander: X-Ray Diffraction Procedures (Wiley–Interscience, New York 1974) pp. 791-859.
9.9 T. Egami: ‘PDF Analysis Aplied to Crystalline Materials’, in: LocalStructure from Diffraction, ed. by S. J. L. Billinge and M. F. Thorpe(Plenum, New York 1998) pp. 1-21.
9.10 A. Guinier: X-Ray Diffraction in Crystals, Imperfect Crystals, andAmorphous Bodies (Dover, New York 1994) pp. 344-349.
Chapter 10 title image of Pb precipitate in Al. Figure reprinted with thecourtesy of U. Dahmen.
10.1 J. M. Cowley and A. F. Moodie: Acta Cryst. 10, 609 (1957). Ibid. 12,353, 360, 367 (1959).
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10.2 M. A. O’Keefe: ‘Electron image simulation; a complementary process-ing technique’. In: Proceedings of the 3rd Pfeffercorn Conference onElectron Optical Systems, Ocean City, MD ed. by J. J. Hren, F. A.Lenz, E. Munro, P. B. Sewell, and S. A. Bhatt (Scanning ElectronMicroscopy, Inc., Illinois 1984) pp. 209-220.
10.3 R. R. Meyer, J. Sloan, R. E. Dunin-Borkowski, A. I. Kirkland, M. C.Novotny, S. R. Bailey, J. L. Hutchison and M. L. H. Green: Science 289,1324 (2000). Figure reproduced with the courtesy of J. L. Hutchisonand the American Association for the Advancement of Science.
10.4 S. D. Hudson, H. T. Jung, V. Percec, W. D. Cho, G. Johansson, G.Ungar, V. S. K. Balagurusamy: Science 278, 449 (1997). Figure repro-duced with the courtesy of S. D. Hudson and the American Associationfor the Advancement of Science.
10.5 S. R. Singh and J. M. Howe: Philos. Mag. A 66, 746 (1992). Figurereprinted with the courtesy of Taylor & Francis, Ltd.
10.6 S. Das, J. M. Howe and J. H. Perepezko: Metall. Mater. Trans. 27A,1627 (1996). Figure reprinted with the courtesy of The Minerals, Met-als & Materials Society.
10.7 G. Rao, J. M. Howe and P. Wynblatt, unpublished research.10.8 U. Dahmen: Micros. Soc. Amer. Bull. 24, 341 (1994). Figure reprinted
with the courtesy of Microscopy Society of America.10.9 Figure reprinted with the courtesy of R. Gronsky and D. Acklund.10.10 J. M. Howe and S. J. Rozeveld: J. Micros. Res. Tech. 23, 233 (1992).
Reprinted with the courtesy of Wiley–Liss, Inc.10.11 M. M. Tsai: Determination of the Growth Mechanisms of TiH in
Ti Using High-Resolution and Energy-Filtering Transmission ElectronMicroscopy. Ph.D. Thesis, University of Virginia, Charlottesville, VA(1997). Figure reprinted with the courtesy of Dr. M. M. Tsai.
10.14 such as Gatan Digital MicrographTM or NIH Image.10.15 B. Laird and J. M. Howe, unpublished research.10.16 R. Kilaas and R. Gronsky: Ultramicros. 16, 193 (1985). Figure reprinted
with the courtesy of Elsevier Science Publishing B.V.10.17 J.O. Malm and M.A. O’Keefe: Ultramicros. 68, 13 (1997).10.18 S.-C.Y. Tsen, P.A. Crozier and J. Liu: Ultramicros. 98, 63 (2003).
Chapter 11 title figure shows HAADF images acquired with a Cs-correctedinstrument. The images were acquired at different values of defocus as labeled.Together with other measurements and computational support, the imagesshow how that La atoms segregate to sites on the surfaces of an Al2O3 crystal,which correspond to defocus values of 0 and −8 nm. Bar length is 1 nm. AfterS. Wang, A.Y. Borisevich, S.N. Rashkeev, M.V. Glazoff, K. Sohlberg, S.J.Pennycook, and S.T. Pantelides: Nature Materials 3, 143 (2004).
Bibliography 689
11.1 After N. D. Browning, D. J. Wallis, P. D. Nellist and S. J. Pennycook:Micron 28, 334 (1997). Reprinted with the courtesy of Elsevier ScienceLtd.
11.2 S. J. Pennycook, D. E. Jesson, M. F. Chisholm, N. D. Browning, A. J.McGibbon, and M. M. McGibbon: J. Micros. Soc. Amer. 1, 234 (1995).Reprinted with the courtesy of Microscopy Society of America.
11.3 A. Amali and P. Rez: Microsc. and Microanal. 3, 28 (1997).11.4 A.R. Lupini and S. J. Pennycook: Ultramicroscopy 96, 313 (2003).11.5 P. M. Voyles and D. A. Muller, private communication. See also P. M.
Voyles, D. A. Muller, J. L. Grazul, P. H. Citrin, and H-.J. L. Gossmann:Nature 416, 826 (2002).
11.6 O.L. Krivanek, N. Dellby, and A.R. Lupini: Ultramicroscopy 78, 1(1999).
11.7 S. Uhlemann and M. Haider: Ultramicroscopy 72, 109 (1998).11.8 Q.M. Ramasse and A.L. Bleloch, Ultramicroscopy 106, 37 (2005).11.9 H. Muller, S. Uhlemann, P. Hartel and M. Haider: Microsc. and Mi-
croanal. 12, 442 (2006).11.10 M. Lentzen: Microsc. Microanal. 12, 191 (2006).11.11 A.Y. Borisevich, A.R. Lupini and S.J. Pennycook: Proc. Nat. Acad.
Sci. 103, 3044 (2006).11.12 K. van Benthem, A.R. Lupini, M. Kim, K.-S. Baik, S. Doh, J.-H. Lee,
M.P. Oxley, S.D. Findlay, L.J. Allen, J.T. Luck and S. J. Pennycook:Appl. Phys. Lett. 87, 034104 (2005). Reprinted with the courtesy ofthe American Institute of Physics.
11.13 N.D. Browning, R.P. Erni, J.C. Idrobo, A. Ziegler, C.F. Kisielowski,R.O. Ritchie: Microsc. Microanal. 11 (Suppl 2), 1434 (2005).
Chapter 12 title figure is an enlargement of Fig. 12.15.
12.1 Figure reprinted with the courtesy of Dr. Y. C. Chang.12.2 P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J.
Whelan: Electron Microscopy of Thin Crystals (R. E. Krieger, Malabar,Florida 1977) pp. 222-242.
12.3 N. Prabhu and J. M. Howe: Philos. Mag. A 63, 650 (1991). Figurereprinted with the courtesy of Taylor & Francis, Ltd.
12.4 A. W. Wilson: Microstructural Examination of NiAl Alloys. Ph.D.Thesis, University of Virginia, Charlottesville, VA (1999). Figure re-printed with the courtesy of Dr. A. W. Wilson.
12.5 Peter Rez, private communication of academic course notes.
A. Appendix
A.1 Indexed Powder Diffraction Patterns
Fig. A.1. Indices of peaks in powder diffraction patterns from simple cubic, face-centered cubic, body-centered cubic, diamond cubic, and hexagonal close-packedcrystals.
692 A. Appendix
Table A.1. Mass attenuation coefficients for characteristic Kα x-rays [cm2/g]
Z Cr Co Cu Mo Z Cr Co Cu Mo
1 H 0.412 0.397 0.391 0.373 48 Cd 626 329 222 27.82 He 0.498 0.343 0.292 0.202 49 In 663 349 236 29.53 Li 1.30 0.693 0.500 0.198 50 Sn 691 364 247 31.04 Be 3.44 1.67 1.11 0.256 51 Sb 723 383 259 32.75 B 7.59 3.59 2.31 0.368 52 Te 740 394 267 33.86 C 15.0 7.07 4.51 0.576 53 I 796 425 288 36.77 N 24.7 11.7 7.44 0.845 54 Xe 721 440 299 38.28 O 37.8 18.0 11.5 1.22 55 Cs 760 465 317 40.79 F 51.5 24.7 15.8 1.63 56 Ba 570 480 325 42.310 Ne 74.1 35.8 22.9 2.35 57 La 225 507 348 44.911 Na 94.9 46.2 29.7 3.03 58 Ce 238 535 368 47.712 Mg 126 61.9 40.0 4.09 59 Pr 238 565 390 50.713 Al 155 76.4 49.6 5.11 60 Nd 251 505 404 53.014 Si 196 97.8 63.7 6.64 61 Pm 294 400 426 56.315 P 230 115 75.5 7.97 62 Sm 279 440 434 57.816 S 281 142 93.3 9.99 63 Eu 309 153 434 60.917 Cl 316 161 106 11.5 64 Gd 298 161 403 62.618 Ar 342 176 116 12.8 65 Tb 332 180 321 65.819 K 421 218 145 16.2 66 Dy 325 176 362 68.320 Ca 490 255 170 19.3 67 Ho 347 187 129 71.321 Sc 516 269 180 20.8 68 Er 352 191 132 74.422 Ti 590 291 200 23.4 69 Tm 386 206 140 77.923 V 74.7 325 219 26.0 70 Yb 387 206 142 80.424 Cr 86.8 408 247 29.9 71 Lu 431 229 156 84.025 Mn 97.5 393 270 33.1 72 Hf 425 227 155 86.926 Fe 113 57.2 302 37.6 73 Ta 432 231 158 90.427 Co 124 63.2 321 41.0 74 W 457 246 168 93.828 Ni 144 73.5 48.8 46.9 75 Re 501 268 187 97.429 Cu 153 78.0 51.8 49.1 76 Os 499 268 184 10030 Zn 171 87.1 57.9 54.0 77 Ir 520 278 191 10431 Ga 183 93.4 62.1 57.0 78 Pt 541 276 188 10732 Ge 199 102 67.9 61.2 79 Au 551 295 201 11233 As 219 112 74.7 66.1 80 Hg 541 273 188 11534 Se 234 120 80.0 69.5 81 Tl 597 331 226 11835 Br 260 133 89.0 75.6 82 Pb 643 343 235 12236 Kr 277 142 95.2 79.3 83 Bi 666 355 244 12637 Rb 303 156 104 85.1 84 Po 691 370 254 13238 Sr 328 170 113 90.6 85 At 680 363 248 11739 Y 358 185 124 97.0 86 Rn 734 392 267 10840 Zr 386 200 139 16.3 87 Fr 758 403 277 87.041 Nb 416 216 145 17.7 88 Ra 743 398 273 88.042 Mo 442 230 154 18.8 89 Ac 739 461 317 90.843 Tc 474 247 166 20.4 90 Th 768 406 306 96.544 Ru 501 262 176 21.7 91 Pa 738 394 271 10145 Rh 536 280 189 23.3 92 U 766 420 288 10246 Pd 563 295 199 24.7 93 Np 800 430 314 42.247 Ag 602 316 213 26.5 94 Pu 760 408 280 39.9
Example: calculate the fraction, I/I0, of Mo Kα x-rays transmitted through0.01 cm of metallic Ag (having density 10.5 g cm−3):
I/I0 = exp(−26.5 cm2g−1 10.5 g cm−3 0.01 cm) = e−2.78 = 0.062 .
A.3 Atomic Form Factors for X-Rays 693
Table
A.2
.A
tom
icfo
rmfa
ctors
for
hig
h-e
ner
gy
x-r
ays
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
6.0
He
2.0
01.9
61.8
41.6
61.4
61.2
61.0
60.8
90.7
40.5
10.3
50.2
50.1
80.1
30.1
00.0
50.0
30.0
20.0
10.0
10.0
00.0
00.0
00.0
00.0
0
Li+
12.0
01.9
81.9
41.8
61.7
61.6
51.5
21.4
01.2
71.0
30.8
20.6
40.5
10.4
00.3
20.2
00.1
30.0
90.0
60.0
40.0
20.0
10.0
00.0
00.0
0Li
3.0
02.7
12.2
21.9
01.7
41.6
31.5
11.3
91.2
71.0
30.8
30.6
50.5
10.4
10.3
20.2
10.1
40.0
90.0
60.0
50.0
20.0
10.0
00.0
00.0
0
Be+
22.0
01.9
91.9
71.9
31.8
71.8
01.7
31.6
41.5
51.3
71.1
81.0
10.8
50.7
20.6
00.4
30.3
00.2
20.1
60.1
20.0
60.0
30.0
10.0
10.0
0B
e4.0
03.7
13.0
72.4
72.0
61.8
31.6
91.6
01.5
21.3
61.2
01.0
30.8
80.7
40.6
20.4
40.3
10.2
20.1
60.1
20.0
60.0
30.0
10.0
10.0
0B
5.0
04.7
34.0
63.3
22.7
02.2
71.9
81.8
01.6
81.5
31.4
01.2
81.1
51.0
20.9
00.6
90.5
30.4
00.3
00.2
30.1
30.0
70.0
30.0
10.0
1C
6.0
05.7
55.1
24.3
33.5
72.9
62.5
02.1
81.9
51.6
91.5
41.4
31.3
21.2
21.1
20.9
20.7
40.5
90.4
70.3
70.2
20.1
30.0
50.0
20.0
1N
7.0
06.7
86.1
85.3
94.5
73.8
33.2
22.7
52.4
01.9
41.7
01.5
51.4
51.3
51.2
71.0
90.9
20.7
70.6
40.5
30.3
30.2
10.0
90.0
40.0
2O
8.0
07.8
07.2
56.4
75.6
34.8
14.0
93.4
93.0
12.3
41.9
51.7
21.5
71.4
61.3
81.2
21.0
70.9
30.7
90.6
80.4
40.2
90.1
40.0
70.0
4O−
19.0
08.7
17.9
26.8
95.8
44.8
94.1
03.4
72.9
82.3
21.9
41.7
11.5
71.4
61.3
81.2
21.0
70.9
20.7
90.6
70.4
40.2
90.1
30.0
70.0
4
O−
210.0
09.5
98.5
47.2
25.9
64.9
04.0
63.4
22.9
42.3
01.9
31.7
11.5
71.4
71.3
81.2
21.0
70.9
20.7
90.6
70.4
40.2
90.1
30.0
70.0
3F
9.0
08.8
28.3
07.5
66.7
15.8
65.0
64.3
63.7
62.8
82.3
11.9
61.7
41.5
91.4
81.3
31.1
91.0
60.9
30.8
10.5
70.3
90.1
90.1
00.0
6
F−
110.0
09.7
39.0
28.0
46.9
85.9
85.0
94.3
53.7
42.8
52.2
91.9
51.7
31.5
91.4
81.3
21.1
91.0
50.9
30.8
10.5
60.3
90.1
90.1
00.0
6N
e10.0
09.8
39.3
58.6
57.8
16.9
36.0
95.3
14.6
33.5
42.8
02.3
01.9
71.7
61.6
11.4
21.2
81.1
61.0
40.9
30.6
80.4
90.2
50.1
40.0
8N
a+
110.0
09.8
89.5
59.0
38.3
87.6
56.9
06.1
75.4
84.3
03.4
02.7
62.3
12.0
01.7
91.5
31.3
71.2
51.1
41.0
30.7
90.5
90.3
30.1
80.1
1N
a11.0
010.5
79.7
69.0
38.3
47.6
26.8
96.1
65.4
84.3
03.4
02.7
62.3
12.0
01.7
91.5
31.3
71.2
51.1
41.0
30.7
90.5
90.3
20.1
90.1
1M
g+
210.0
09.9
19.6
69.2
78.7
68.1
67.5
26.8
66.2
25.0
34.0
53.2
92.7
32.3
22.0
31.6
61.4
61.3
31.2
21.1
20.8
90.6
90.4
00.2
30.1
4M
g12.0
011.5
110.4
89.5
18.7
48.0
87.4
56.8
26.2
05.0
44.0
73.3
02.7
32.3
22.0
31.6
61.4
61.3
31.2
21.1
20.8
90.6
90.4
00.2
40.1
4A
l+3
10.0
09.9
39.7
49.4
39.0
28.5
37.9
87.4
16.8
35.7
04.7
03.8
73.2
12.7
12.3
31.8
51.5
81.4
11.2
91.2
00.9
80.7
80.4
80.2
90.1
8A
l13.0
012.4
411.2
310.0
69.1
68.4
77.8
87.3
26.7
75.7
04.7
23.8
93.2
32.7
22.3
41.8
41.5
71.4
11.2
91.2
00.9
80.7
80.4
80.2
90.1
8Si
14.0
013.4
412.1
510.7
89.6
88.8
68.2
47.7
07.2
16.2
55.3
24.4
83.7
63.1
72.7
12.0
81.7
21.5
11.3
71.2
71.0
60.8
70.5
60.3
50.2
2P
15.0
014.4
613.1
411.6
310.3
39.3
48.6
08.0
37.5
56.6
85.8
45.0
34.2
93.6
63.1
32.3
71.9
11.6
31.4
51.3
41.1
20.9
40.6
30.4
20.2
7S
16.0
015.4
814.1
812.5
811.1
19.9
39.0
48.3
87.8
67.0
26.2
65.5
14.8
04.1
53.5
82.7
12.1
41.7
81.5
61.4
11.1
81.0
10.7
10.4
80.3
2C
l17.0
016.5
115.2
413.6
012.0
010.6
49.5
88.7
98.1
97.3
16.6
05.9
25.2
54.6
24.0
33.0
82.4
11.9
71.6
91.5
01.2
41.0
70.7
70.5
40.3
7
Cl−
118.0
017.3
615.7
613.8
112.0
210.5
99.5
38.7
58.1
67.3
16.6
15.9
35.2
64.6
24.0
33.0
82.4
11.9
71.6
91.5
01.2
41.0
70.7
70.5
40.3
7A
r18.0
017.5
416.3
014.6
612.9
611.4
510.2
39.2
88.5
77.5
86.8
86.2
65.6
55.0
44.4
73.4
72.7
22.2
01.8
51.6
21.3
01.1
20.8
40.6
00.4
3
K+
118.0
017.6
516.6
815.3
013.7
712.2
910. 9
89.9
19.0
67.8
97.1
36.5
35.9
75.4
14. 8
73.8
63.0
52.4
62.0
41.7
51.3
71.1
80.9
00.6
60.4
8K
19.0
018.2
116.7
415.2
513.7
412.2
810.9
99.9
29.0
77.9
07.1
36.5
35.9
75.4
14.8
73.8
63.0
52.4
62.0
41.7
51.3
71.1
80.8
90.6
60.4
8C
a+
218.0
017.7
216.9
415.7
814.4
213.0
311. 7
210.5
99.6
48.2
77.4
06.7
76.2
45.7
35. 2
24.2
43.4
02.7
42.2
61.9
11.4
51.2
30.9
50.7
20.5
3C
a20.0
019.0
917.3
415.7
314.3
112. 9
711.7
210.6
09.6
68.2
87.4
06.7
76.2
35.7
25.2
24.2
43.4
02.7
42.2
51.9
11.4
51.2
30.9
50.7
20.5
3Sc
21.0
020.1
318.3
616.6
515.1
413.7
412.4
311.2
510.2
48.7
07.6
97.0
06. 4
75.9
85.5
14.5
83.7
33.0
32.4
92.1
01.5
41.2
81.0
00.7
80.5
8
Ti+
418.0
017.8
117.2
616.4
215.3
614.2
013. 0
111.8
810.8
59.2
08.0
57.2
66.6
96.2
25. 7
84.9
14.0
83.3
52.7
62.3
11.6
41.3
41.0
40.8
20.6
4T
i22.0
021.1
719.4
117.6
416.0
514.5
813.2
111.9
610.8
69.1
68.0
27.2
56. 6
86.2
15.7
64.8
84.0
53.3
22.7
42.3
01.6
41.3
41.0
40.8
30.6
3
V+
518.0
017.8
417.3
716.6
315.7
014.6
513. 5
412.4
611.4
39.7
08.4
47.5
56.9
26.4
36. 0
05.1
94.3
93.6
53.0
32.5
41.7
71.4
11.0
90.8
70.6
9V
23.0
022.2
120.4
818.6
617.0
015.4
714.0
312.7
111.5
49.6
78.3
87.5
16. 9
06.4
15.9
85.1
54.3
43.6
13.0
02.5
11.7
61.4
11.0
90.8
70.6
8
Cr+
420.0
019.8
019.2
318.3
417.2
315.9
814. 6
813.4
212.2
510.2
78.8
37.8
47.1
46.6
26. 1
95.4
04.6
33.9
13.2
82.7
51.9
01.4
81.1
30.9
10.7
3
694 A. Appendix
Table
A.2
.(c
ontinued
)
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
6.0
Cr
24.0
023.3
321.7
920.0
218.2
516.5
614.9
713.5
212.2
410.1
98.7
77.8
07.1
26.6
16.1
85.3
84.6
13.8
83.2
52.7
31.8
91.4
81.1
30.9
20.7
3
Mn+
223.0
022.7
121.8
720.6
319.1
317.5
215.9
214.4
213.0
610.8
49.2
48.1
47.3
76.8
16.3
75.5
94.8
64.1
53.5
12.9
72.0
41.5
71.1
70.9
60.7
8M
n25.0
024.2
822.6
120.7
619.0
117.3
615.8
114.3
613.0
410.8
59.2
58.1
57.3
86.8
16.3
75.5
94.8
64.1
53.5
12.9
72.0
41.5
71.1
70.9
60.7
8
Fe+
224.0
023.7
122.8
921.6
520.1
418.5
116.8
715.3
213.8
911.5
09.7
58.5
17.6
57.0
36.5
55.7
85.0
84.3
93.7
63.2
02.2
01.6
61.2
21.0
00.8
2Fe
26.0
025.3
023.6
821.8
320.0
518.3
516.7
515.2
413.8
511.5
19.7
68.5
27.6
57.0
36.5
55.7
85.0
84.4
03.7
63.2
02.2
01.6
61.2
11.0
00.8
2
Co+
225.0
024.7
223.9
022.6
721.1
719.5
217.8
516.2
414.7
512.2
210.3
08.9
37.9
67.2
66.7
55.9
65.2
84.6
23.9
93.4
32.3
71.7
71.2
61.0
30.8
6C
o27.0
026.3
324.7
522.9
021.1
019.3
717.7
116.1
514.7
012.2
210.3
28.9
47.9
67.2
76.7
55.9
65.2
84.6
24.0
03.4
32.3
71.7
71.2
61.0
40.8
6
Ni+
226.0
025.7
224.9
223.7
022.2
020.5
418.8
517.2
015.6
512.9
710.9
19.3
98.3
07.5
26.9
56.1
35.4
64.8
24.2
23.6
52.5
51.8
81.3
11.0
70.9
0N
i28.0
027.3
625.8
123.9
822.1
620.4
018.7
017.0
915.5
912.9
710.9
29.4
08.3
17.5
36.9
56.1
25.4
64.8
34.2
23.6
62.5
51.8
81.3
11.0
70.9
0
Cu+
227.0
026.7
325.9
424.7
423.2
421.5
819.8
618.1
716.5
713.7
711.5
69.9
08.6
97.8
17.1
86.2
95.6
25.0
14.4
23.8
62.7
32.0
11.3
61.1
10.9
4C
u29.0
028.3
826.8
725.0
523.2
221.4
419.7
118.0
616.5
013.7
611.5
79.9
18.7
07.8
27.1
86.2
95.6
35.0
24.4
33.8
72.7
32.0
11.3
61.1
10.9
4
Zn+
228.0
027.7
326.9
625.7
724.2
922.6
220.8
919.1
717.5
214.6
012.2
510.4
59.1
18.1
47.4
26.4
65.7
85.1
94.6
14.0
72.9
12.1
41.4
21.1
40.9
7Zn
30.0
029.4
027.9
326.1
324.3
022.4
920.7
419.0
517.4
414.5
812.2
510.4
69.1
28.1
47.4
36.4
65.7
85.1
94.6
24.0
72.9
22.1
41.4
21.1
40.9
7G
a31.0
030.3
028.6
726.7
924.9
423.1
921.5
019.8
718.3
015.4
313.0
211.0
99.6
28.5
27.7
16.6
45.9
35.3
54.8
04.2
73.1
12.2
81.4
81.1
81.0
0G
e32.0
031.2
829.5
327.5
025.5
723.8
022.1
520.5
819.0
716.2
513.7
911.7
610.1
78.9
58.0
46.8
46.0
85.5
04.9
74.4
53.2
92.4
31.5
51.2
21.0
3A
s33.0
032.2
730.4
628.3
026.2
324.3
922.7
421.2
019.7
517.0
114.5
612.4
610.7
69.4
38.4
17.0
66.2
45.6
45.1
24.6
33.4
82.5
91.6
21.2
61.0
7Se
34.0
033.2
731.4
429.1
626.9
525.0
023.3
021.7
720.3
517.7
115.2
913.1
711. 3
89.9
48.8
27.3
16.4
05.7
85.2
74.7
93.6
72.7
51.7
11.3
01.1
0B
r35.0
034.2
932.4
530.0
927.7
525.6
623.8
722.3
020.8
918.3
315.9
813.8
612. 0
210.5
09.2
87.5
96.5
85.9
25.4
14.9
43.8
42.9
21.8
01.3
41.1
3B
r−1
36.0
035.1
232.9
130.2
427.7
325.6
123.8
222.2
720.8
818.3
315.9
913.8
612.0
210.5
09.2
87.5
96.5
85.9
25.4
14.9
43.8
42.9
21. 8
01.3
41.1
3K
r36.0
035.3
133.4
731.0
728.6
126.3
824.4
722.8
421.4
118.8
916.6
114.5
312.6
711.0
89.7
77.9
16.7
86.0
65.5
45.0
84.0
13.0
81.8
91.3
91.1
6R
b+
136.0
035.4
433.9
031.7
529.4
127.1
625.1
723.4
421.9
519.4
117.1
915.1
513.2
911.6
710.2
98.2
77.0
16.2
25.6
65.2
14.1
83.2
52. 0
01.4
41.1
9R
b37.0
035.9
533.9
131.6
929.3
827.1
625. 1
823.4
521.9
519.4
117.1
915.1
513.2
911. 6
710.2
98.2
77.0
16.2
25.6
65.2
14.1
83.2
52.0
01.4
41.1
9Sr+
236.0
035.5
334.2
032.2
930.1
027.9
125.8
824.0
822.5
219.9
217.7
215.7
313.9
012.2
510.8
28.6
57.2
66.3
85.7
95.3
34.3
33.4
12. 1
11.5
01.2
3Sr
38.0
036.8
034.4
732.1
830.0
027.8
825.8
924.1
122.5
419.9
217.7
215.7
213.8
912.2
510.8
38.6
67.2
66.3
85.7
95.3
34.3
33.4
12.1
01.5
01.2
3Y
+3
36.0
035.5
934.4
432.7
230.7
028.5
926.5
724.7
423.1
220.4
318.2
216.2
714.4
712.8
311.3
79.0
77.5
46.5
75.9
35.4
54.4
73.5
72. 2
21.5
61.2
7Y
39.0
037.8
235.3
732.9
130.6
528.5
026.5
124.7
023.1
020.4
318.2
316.2
714.4
712.8
311.3
79.0
77.5
46.5
75.9
35.4
54.4
73.5
72.2
21.5
61.2
6
Zr+
436.0
035.6
434.6
233.0
831.2
129.2
127.2
325.3
923.7
220.9
518.7
116.7
715.0
113.3
811.9
19.5
17.8
56.7
86.0
75.5
74.6
03.7
22. 3
41.6
21.3
1Zr
40.0
038.8
536.3
633.7
631.3
729.1
627.1
125.2
723.6
320.9
218.7
216.8
015. 0
313.3
911.9
19.5
17.8
56.7
86.0
75.5
74.6
03.7
22.3
41.6
31.3
0
Nb+
536.0
035.6
834.7
733.3
731.6
529.7
627.8
426.0
124.3
321.4
819.1
917.2
515.5
113.9
012.4
39.9
78.1
97.0
16.2
35.6
94.7
33.8
72. 4
71.7
01.3
5N
b41.0
039.9
737.5
934.9
032.3
029.8
927.7
125.7
824.1
121.3
719.1
817.3
015. 5
613.9
512.4
69.9
78.1
97.0
16.2
35.6
94.7
23.8
62.4
61.7
01.3
4
Mo+
636.0
035.7
234.9
033.6
232.0
330.2
528.4
126.6
124.9
322.0
219.6
717.7
115.9
914.4
112.9
410.4
38.5
57.2
66.4
05.8
24.8
44.0
12. 5
91.7
71.3
9M
o42.0
041.0
038.6
435.8
933.1
830.6
628.3
926.3
824.6
421.8
219.6
217.7
516. 0
614.4
712.9
910.4
58.5
67.2
66.4
15.8
24. 8
34.0
02.5
91.7
71.3
8R
u44.0
043.0
640.7
737.9
635.0
932.3
629.8
827.6
825.7
722.7
320.4
318.5
816. 9
515.4
414.0
011.4
29.3
57.8
56.8
16.1
15. 0
54.2
52.8
41.9
41.4
8R
h45.0
044.0
941.8
439.0
236.0
933.2
830.6
928.3
926.3
923.2
020.8
318.9
617. 3
615.8
814.4
711.9
09.7
78.1
77.0
56.2
85.1
54.3
62.9
62.0
31.5
4
Pd+
244.0
043.4
641.9
339.6
737.0
234.2
731.6
229.2
227.1
023.7
121.2
219.3
217.7
316.2
814.9
212.3
710.2
18.5
27.3
16.4
65.2
54.4
73. 0
92.1
21.6
0P
d46.0
045.2
343.1
840.3
737.3
134.3
131.5
529.1
126.9
923.6
521.2
119.3
217.7
416.3
014.9
312.3
810.2
18.5
27.3
16.4
65.2
54.4
73.0
92.1
21.5
9
Ag+
245.0
044.4
642.9
540.7
038.0
335.2
332.5
130.0
127.7
924.2
321.6
319.6
818.0
816.6
715.3
312.8
310.6
48.8
97.5
86.6
65.3
64.5
73. 2
22.2
11.6
6A
g47.0
046.1
443.9
741.1
738.1
735.2
232.4
429.9
427.7
324.2
021.6
319.6
818. 0
916.6
715.3
412.8
410.6
48.8
97.5
86.6
65.3
64.5
73.2
12.2
11.6
6
A.3 Atomic Form Factors for X-Rays 695
Table
A.2
.(c
ontinued
)
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
6.0
Cd+
246.0
045.4
743.9
841.7
439.0
636.2
133.4
330.8
428.5
324.7
822.0
520.0
318.4
217.0
215.7
313.2
811.0
89.2
77.8
86.8
85.4
74.6
73.3
42.3
11.7
2C
d48.0
047.0
944.8
141.9
438.9
536.0
333.2
830.7
528.4
924.8
122.0
920.0
518.4
217.0
215.7
213.2
711.0
89.2
77.8
86.8
85.4
74.6
73.3
42.3
11.7
2In
49.0
047.9
745.5
242.6
039.6
636.8
034.0
931.5
729.2
825.4
522.5
720.4
318.7
617.3
516.0
713.6
911.5
19.6
68.2
07.1
25.5
94.7
73.4
52.4
21.7
9Sn
50.0
048.9
246.3
343.2
940.3
137.4
934.8
332.3
430.0
526.1
223.1
020.8
319.0
917.6
616.4
014.0
811.9
410.0
58.5
37.3
85.7
14.8
63.5
72.5
21.8
6Sb
51.0
049.9
047.2
144.0
240.9
538.1
235.5
033.0
530.7
826.8
123.6
721.2
719.4
417.9
816.7
214.4
512.3
410.4
58.8
87.6
65.8
54.9
53.6
82.6
31.9
3Te
52.0
050.8
948.1
444.8
141.6
138.7
236.1
133.7
131.4
727.5
024.2
621.7
419.8
118.2
917.0
214.7
912.7
310.8
59.2
37.9
55.9
95.0
53.7
92.7
32.0
1I
53.0
051.9
049.1
345.6
942.3
439.3
436.7
034.3
132.1
128.1
724.8
822.2
520.2
118.6
217.3
115.1
113.1
011.2
49.6
08.2
66.1
55.1
43.9
02.8
42.0
9I−
154.0
052.6
949.5
045.7
542.2
839.2
936.6
634.3
032.1
128.1
824.8
822.2
520.2
118.6
217.3
115.1
113.1
011.2
49.6
08.2
66.1
55.1
43.9
02.8
42.0
9X
e54.0
052.9
250.1
446.6
143.1
139.9
937.2
834.8
832.7
028.8
125.5
022.7
820.6
418.9
617.6
115.4
113.4
511.6
19.9
68.5
76.3
35.2
44.0
02.9
52.1
8
Cs+
154.0
053.0
950.6
447.3
643.9
240.7
337.9
235.4
633.2
729.4
126.1
023.3
321.1
019.3
317.9
215.7
013.7
811.9
810.3
28.9
06.5
15.3
44.0
93.0
52.2
7C
s55.0
053.5
350.6
147.3
143.9
140.7
437.9
335.4
733.2
729.4
126.1
023.3
321.1
019.3
317.9
215.7
013.7
811.9
810.3
28.9
06.5
25.3
44.0
93.0
52.2
7
Ba+
254.0
053.2
151.0
348.0
044.6
741.4
738.5
936.0
733.8
329.9
826.6
923.8
821.5
719.7
218.2
415.9
714.0
912.3
310.6
89.2
36.7
25.4
54.1
93.1
52.3
6B
a56.0
054.3
551.1
347.8
544.6
141.4
838.6
236.0
933.8
429.9
826.6
823.8
821.5
719.7
218.2
515.9
714.0
912.3
310.6
89.2
36.7
25.4
54.1
83.1
62.3
6
La+
354.0
053.3
051.3
448.5
445.3
642.1
939.2
836.6
934.4
130.5
327.2
524.4
322.0
620.1
318.5
816.2
514.3
812.6
611.0
39.5
76.9
35.5
74.2
73.2
62.4
5La
57.0
055.3
551.9
848.5
345.2
342.1
039.2
436.6
934.4
330.5
527.2
624.4
322.0
620.1
318.5
816.2
514.3
812.6
611.0
39.5
76.9
35.5
74.2
73.2
62.4
5
Ce+
454.0
053.3
751.6
049.0
045.9
742.8
839.9
637.3
335.0
031.0
727.7
924.9
722.5
620.5
618. 9
416.5
214.6
612.9
711.3
79.9
07.1
65.6
94.3
63.3
62.5
5C
e58.0
056.3
953.0
549.5
846.2
443.0
640.1
337.5
035.1
731.1
827.8
224.9
322.4
920. 5
118.9
016.5
114.6
512.9
611.3
69.8
97.1
65.6
94.3
53.3
62.5
4
Pr+
356.0
055.3
153.4
050.6
247.4
144.1
641.1
138.3
735.9
431.8
228.3
825.4
422.9
420.8
919. 2
316.7
714.9
113.2
511.6
710.2
07.3
95.8
34.4
43.4
62.6
4P
r59.0
057.4
454.2
950.9
647.6
244.3
341.2
638.5
136.0
531.8
828.3
825.4
022.8
920.8
519.2
116.7
714.9
113.2
411.6
510.1
97.3
85.8
34.4
43.4
62.6
3
Nd+
357.0
056.3
254.4
351.6
748.4
545.1
742.0
739.2
536.7
532.5
128.9
825.9
623.4
021.2
819. 5
617.0
315.1
613.5
211.9
710.5
17.6
35.9
74.5
23.5
52.7
3N
d60.0
058.4
755.3
452.0
248.6
645.3
442.2
139.3
836.8
632.5
628.9
825.9
223.3
521.2
419.5
417.0
215.1
613.5
211.9
610.4
97.6
25.9
74.5
23.5
52.7
3
Sm
+3
59.0
058.3
456.5
053.7
750.5
647.2
344.0
341.0
938.4
533.9
530.2
227.0
524.3
522.1
020. 2
617.5
515.6
314.0
312.5
311.1
08.1
26.2
84.6
83.7
32.9
2Sm
62.0
060.5
357.4
654.1
550.7
747.3
944.1
641.2
038.5
534.0
030.2
327.0
224.3
122.0
620.2
317.5
515.6
314.0
312.5
211.0
98.1
16.2
84.6
73.7
42.9
1
Eu+
360.0
059.3
557.5
354.8
351.6
348.2
845.0
342.0
439.3
334.7
030.8
727.6
224.8
422.5
220. 6
217.8
215.8
614.2
712.7
911.3
88.3
86.4
54.7
63.8
23.0
1E
u63.0
061.5
558.5
255.2
251.8
348.4
345.1
642.1
439.4
234.7
630.8
827.5
924.8
122.4
920.5
917.8
115.8
614.2
712.7
911.3
78.3
76.4
54.7
53.8
23.0
1
Gd+
361.0
060.3
658.5
655.8
852.6
949.3
346.0
542.9
940.2
235.4
831.5
428.2
025.3
522.9
620. 9
918.0
916.0
914.5
013.0
411.6
58.6
36.6
24.8
43.9
03.1
0G
d64.0
062.5
559.4
155.9
852.5
749.2
045. 9
642.9
540.2
135.4
831.5
528.2
125.3
622.9
621.0
018.0
916.0
914.5
013.0
411.6
58.6
36.6
34.8
33.9
13.1
0T
b65.0
063.6
060.6
457.3
753.9
850.5
447.2
044.0
841.2
436.3
332.2
528.7
925.8
423.3
821.3
518.3
616.3
214.7
213.2
811.9
18.8
86.8
14.9
23.9
93.1
9D
y66.0
064.6
361.6
958.4
455.0
651.6
148.2
445.0
842.1
737.1
532.9
729.4
126.3
923.8
521.7
518.6
516.5
414.9
313.5
112.1
69. 1
47.0
05.0
04.0
73.2
8H
o67.0
065.6
562.7
559.5
156.1
452.6
949.2
946.0
843.1
337.9
933.7
030.0
626.9
524.3
322.1
618.9
416.7
715.1
413.7
412.4
19.3
97.1
95.0
94.1
53.3
7E
r68.0
066.6
863.8
160.5
957.2
353.7
750.3
547.1
044.0
938.8
434.4
530.7
227.5
324.8
322.5
819.2
517.0
015.3
513.9
512.6
49. 6
57.3
95.1
84.2
23.4
5T
m69.0
067.7
064.8
661.6
658.3
154.8
551.4
148.1
345.0
739.7
235.2
231.3
928.1
225.3
423.0
319.5
617.2
415.5
514.1
612.8
79.9
07.6
05.2
74.3
03.5
4Y
b70.0
068.7
265.9
162.7
359.3
955.9
352. 4
849.1
646.0
740.6
036.0
032.0
828.7
325.8
723.4
819.8
917.4
815.7
514.3
613.0
810.1
47.8
15.3
74.3
73.6
2Lu
71.0
069.7
066.7
863.4
760.1
156.7
053. 3
150.0
446.9
541.4
436.7
732.7
929.3
726.4
523.9
820.2
517.7
315.9
614.5
513.2
910.3
98.0
35.4
74.4
43.7
0H
f72.0
070.7
267.7
464.3
060.8
657.4
454. 0
850.8
347.7
642.2
437.5
433.5
130.0
327.0
524.5
120.6
318.0
016.1
714.7
513.5
010.6
48.2
55.5
84.5
13.7
8Ta
73.0
071.7
468.7
365.1
961.6
458.1
754.8
151.5
848.5
243.0
138.2
934.2
230.7
027.6
525.0
521.0
318.2
816.3
814.9
413.7
010.8
88.4
75.6
94.5
83.8
5W
74.0
072.7
669.7
466.1
162.4
658.9
255. 5
352.2
949.2
443.7
539.0
234.9
331.3
728.2
825.6
121.4
518.5
816.6
015.1
213.8
911.1
18.7
05.8
14.6
53.9
3R
e75.0
073.7
870.7
667.0
663.3
159.7
056.2
552.9
949.9
444.4
539.7
235.6
232.0
428.9
026.1
821.8
918.8
916.8
215.3
114.0
811. 3
48.9
35.9
44.7
34.0
0
696 A. Appendix
Table
A.2
.(c
ontinued
)
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
6.0
Os
76.0
074.8
071.7
968.0
464.2
060.4
956.9
853.6
950.6
245.1
240.4
036.3
032.7
029.5
426.7
722.3
419.2
217.0
615.5
014.2
611.5
69.1
66.0
74.8
04.0
7Ir
77.0
075.8
372.8
569.0
765.1
461.3
457.7
554.4
051.2
945.7
741.0
536.9
533.3
530.1
727.3
622.8
219.5
717.3
115.7
014.4
411.7
89.3
96.2
14.8
74.1
4P
t78.0
076.9
174.0
870.3
466.3
262.3
558.6
055.1
251.9
346.3
541.6
537.5
834.0
030.8
127.9
723.3
219.9
317.5
715.9
014.6
111.9
99.6
26.3
54.9
44.2
1A
u79.0
077.9
475.1
571.4
067.3
263.2
759.4
355.8
752.6
246.9
742.2
538.1
934.6
231.4
328.5
723.8
320.3
217.8
516.1
014.7
912.1
99.8
56.5
05.0
24.2
8H
g80.0
078.9
076.0
372.2
268.1
164.0
660.2
156.6
453.3
647.6
442.8
738.7
935.2
232.0
229.1
524.3
420.7
218.1
416.3
214.9
712.3
810.0
76.6
65.1
04.3
4T
l81.0
079.7
576.6
972.8
868.8
664.8
661.0
257.4
354.1
248.3
143.4
839.3
835.8
032.6
029.7
324.8
621.1
418.4
516.5
515.1
512.5
710.2
96.8
25.1
94.4
1P
b82.0
080.6
777.4
673.5
469.5
265.5
761.7
958.2
154.8
849.0
144.1
039.9
536.3
633.1
730.3
025.3
921.5
818.7
816.7
915.3
412.7
410.5
06.9
85.2
74.4
7B
i83.0
081.6
378.2
874.2
370.1
666.2
362.4
958.9
555.6
349.7
144.7
340.5
336.9
233.7
230.8
525.9
222.0
319.1
217.0
415.5
312.9
210.7
17.1
65.3
74.5
4Po
84.0
082.6
179.1
674.9
670.7
966.8
563.1
559.6
556.3
650.4
245.3
741.1
137.4
634.2
631.3
926.4
422.4
819.4
817.3
115.7
313.0
810.9
17.3
35.4
64.6
0A
t85.0
083.6
380.1
675.8
471.5
167.4
963.7
660.2
957.0
351.1
246.0
441.7
138.0
234.7
931.9
226.9
622.9
519.8
617.5
915.9
413.2
511.1
17.5
25.5
64.6
7R
n86.0
084.6
581.1
876.7
672.2
968.1
464.3
760.9
057.6
751.8
146.7
042.3
238.5
835.3
232.4
327.4
723.4
220.2
517.8
916.1
713.4
011.3
07.7
05.6
64.7
3Fr
87.0
085.2
981.6
877.4
573.0
668.8
765.0
361.5
358.2
952.4
647.3
642.9
439.1
435.8
532.9
427.9
723.8
920.6
518.2
016.4
013.5
611.4
97.8
95.7
74.8
0R
a88.0
086.1
182.2
278.0
173.7
669.6
165.7
362.1
858.9
253.0
947.9
943.5
539.7
136.3
833.4
528.4
624.3
521.0
518.5
216.6
513.7
211.6
68.0
85.8
94.8
7A
c89.0
087.0
782.9
878.6
174.3
570.2
466.3
962.8
359.5
653.7
348.6
244.1
640.2
736.9
133.9
628.9
524.8
221.4
718.8
616.9
113.8
811.8
48.2
76.0
14.9
5T
h90.0
088.0
783.8
479.2
774.9
370.8
367.0
063.4
660.1
954.3
649.2
544.7
640.8
437.4
434.4
629.4
325.2
921.8
819.2
017.1
814.0
412.0
08.4
66.1
45.0
2Pa
91.0
089.1
385.0
480.5
476.1
171.8
467.8
464.1
560.7
954.8
749.7
645.2
941.3
837.9
834.9
929.9
425.7
622.3
119.5
517.4
514.2
012.1
68.6
56.2
65.1
0U
92.0
090.1
686.0
881.5
477.0
472.7
068.6
164.8
561.4
355.4
450.3
145.8
341.9
238. 5
035.5
030.4
326.2
322.7
319.9
217.7
414.3
612.3
18.8
46.4
05.1
8
Thi
sta
ble
ofx-
ray
atom
icfo
rmfa
ctor
s,f x
(s),
for
elem
ents
and
som
eio
nsw
asob
tain
edfr
omca
lcul
atio
nsw
ith
aD
irac
-Foc
km
etho
dby
D.
Rez
,P.
Rez
and
I.G
rant
:A
cta
Cry
st.A
50,48
1(1
994)
.T
heco
lum
nhe
adin
gsar
es≡
sinθ
/λ,
inun
its
ofA
−1.T
his
diffr
acti
onve
ctor
, s,is
conv
erte
dto
the
Δk
used
inth
ete
xtby
mul
tipl
icat
ion
by4π
.T
heta
bula
ted
valu
esof
f x(s
)ar
ein
elec
tron
unit
s.C
onve
rsio
nto
unit
sof
cmis
perf
orm
edby
mul
tipl
ying
them
byth
e“c
lass
ical
elec
tron
radi
us,”
e2m
−1c−
2=
2.81
794×
10−
13cm
.
A.4 X-Ray Dispersion Corrections for Anomalous Scattering 697
A.4 X-Ray Dispersion Corrections for AnomalousScattering
698 A. Appendix
A.5 Atomic Form Factors for 200 keV Electronsand Procedure for Conversion to Other Voltages
Electron form factors can be obtained from the x-ray atomic form factors,fx(s), with the Mott formula (3.113) as:
fel0(s) =1s2
(Z − fx(s)) ,
where the fx(s) are the values listed in the preceding table. Conversion offel0(s) to units of A requires multiplication by the factor given in (3.113):
2me2
(4π�)2= 2.3933× 10−2 ,
where the extra factor of (4π)−2 originates with the definition s ≡ sinθ/λ (sis converted to the Δk used in the text by multiplication by 4π).
For an incident electron with velocity, v, it is necessary to multiply fel0(s)by the relativistic mass correction factor, γ:
γ ≡ 1√(1 − (v/c)2
,
so that:
fel(s) =(2.3933× 10−2
)γfel0(s) .
For high-energy electrons of known energy E, the following expression isusually more convenient:
γ = 1 +E
mec2� 1 +
E[keV]511
Form factors for 200 keV electrons are given in the following table. They werederived from the previous table of x-ray atomic form factors, fx(s), calculatedwith a Dirac-Fock method by D. Rez, P. Rez and I. Grant: Acta Cryst. A50,481 (1994). Form factors at other electron energies can be obtained fromx-ray form factors by the procedure above.
More conveniently, electron form factors for other accelerating voltagescan be obtained from the values in the following table for 200 keV electronsby multiplying by the ratio of relativistic factors. For example, for 100 keVelectrons the values in the table should be multiplied by the constant factor:
γ100
γ200=
1 + 100/5111 + 200/511
= 0.859 ,
so the values for 100 keV electrons are smaller than those in the table.The column headings in the table are s ≡ sinθ/λ, in units of A−1, Δk ≡
4πs.
A.5 Atomic Form Factors for 200 keV Electrons 699
Table
A.3
.A
tom
icfo
rmfa
ctors
for
200
keV
elec
trons
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
6.0
He
0.5
81
0.5
69
0.5
40
0.4
98
0.4
48
0.3
97
0.3
47
0.3
02
0.2
62
0.1
98
0.1
52
0.1
19
0.0
95
0.0
77
0.0
63
0.0
45
0.0
33
0.0
26
0.0
20
0.0
17
0.0
11
0.0
07
0.0
04
0.0
02
Li+
1–
13.5
43.5
42
1.6
86
1.0
30
0.7
20
0.5
46
0.4
36
0.3
61
0.2
63
0.2
02
0.1
60
0.1
30
0.1
07
0.0
89
0.0
65
0.0
49
0.0
38
0.0
30
0.0
25
0.0
16
0.0
11
0.0
06
0.0
03
Li
4.5
30
3.8
85
2.6
09
1.6
21
1.0
47
0.7
32
0.5
50
0.4
36
0.3
60
0.2
62
0.2
01
0.1
60
0.1
29
0.1
07
0.0
89
0.0
65
0.0
49
0.0
38
0.0
30
0.0
25
0.0
16
0.0
11
0.0
06
0.0
03
Be+
2–
26.7
56.7
72
3.0
70
1.7
73
1.1
70
0.8
41
0.6
41
0.5
09
0.3
51
0.2
61
0.2
03
0.1
64
0.1
35
0.1
13
0.0
83
0.0
63
0.0
49
0.0
39
0.0
32
0.0
21
0.0
15
0.0
08
0.0
04
Be
4.2
27
3.8
95
3.1
06
2.2
72
1.6
14
1.1
57
0.8
53
0.6
52
0.5
16
0.3
51
0.2
59
0.2
02
0.1
62
0.1
34
0.1
12
0.0
82
0.0
63
0.0
49
0.0
39
0.0
32
0.0
21
0.0
15
0.0
08
0.0
04
B3.8
75
3.6
60
3.1
23
2.4
88
1.9
13
1.4
57
1.1
17
0.8
70
0.6
91
0.4
63
0.3
33
0.2
53
0.2
00
0.1
64
0.1
36
0.1
00
0.0
76
0.0
60
0.0
48
0.0
40
0.0
26
0.0
18
0.0
10
0.0
05
C3.4
38
3.2
98
2.9
40
2.4
79
2.0
20
1.6
20
1.2
95
1.0
40
0.8
43
0.5
75
0.4
13
0.3
11
0.2
43
0.1
97
0.1
63
0.1
18
0.0
89
0.0
70
0.0
57
0.0
47
0.0
31
0.0
22
0.0
12
0.0
06
N3.0
66
2.9
70
2.7
21
2.3
83
2.0
24
1.6
88
1.3
97
1.1
55
0.9
58
0.6
73
0.4
90
0.3
70
0.2
89
0.2
32
0.1
91
0.1
37
0.1
03
0.0
81
0.0
65
0.0
54
0.0
36
0.0
25
0.0
14
0.0
06
O2.7
60
2.6
92
2.5
12
2.2
59
1.9
77
1.6
99
1.4
46
1.2
25
1.0
39
0.7
54
0.5
60
0.4
27
0.3
35
0.2
69
0.2
21
0.1
57
0.1
18
0.0
92
0.0
74
0.0
61
0.0
40
0.0
29
0.0
16
0.0
07
O−
1–
-9.3
91
0.2
50
1.6
36
1.8
00
1.6
59
1.4
44
1.2
33
1.0
46
0.7
57
0.5
61
0.4
27
0.3
35
0.2
69
0.2
21
0.1
57
0.1
18
0.0
92
0.0
74
0.0
61
0.0
40
0.0
29
0.0
16
0.0
07
O−
2–
-21.1
7-1
.790
1.1
49
1.6
97
1.6
52
1.4
57
1.2
44
1.0
53
0.7
59
0.5
62
0.4
27
0.3
35
0.2
69
0.2
21
0.1
57
0.1
18
0.0
92
0.0
74
0.0
61
0.0
40
0.0
29
0.0
16
0.0
07
F2.5
07
2.4
55
2.3
22
2.1
28
1.9
05
1.6
76
1.4
58
1.2
62
1.0
90
0.8
15
0.6
19
0.4
79
0.3
78
0.3
05
0.2
50
0.1
77
0.1
33
0.1
03
0.0
83
0.0
68
0.0
45
0.0
32
0.0
18
0.0
08
F−
1–
-9.7
84
-0.0
60
1.4
26
1.6
82
1.6
11
1.4
45
1.2
64
1.0
95
0.8
19
0.6
20
0.4
79
0.3
78
0.3
05
0.2
50
0.1
77
0.1
33
0.1
03
0.0
83
0.0
68
0.0
45
0.0
32
0.0
18
0.0
08
Ne
2.2
95
2.2
55
2.1
53
2.0
02
1.8
23
1.6
33
1.4
48
1.2
75
1.1
19
0.8
60
0.6
66
0.5
23
0.4
18
0.3
39
0.2
79
0.1
98
0.1
48
0.1
15
0.0
92
0.0
76
0.0
50
0.0
35
0.0
20
0.0
09
Na+
1–
14.8
74.8
37
2.9
18
2.1
83
1.7
84
1.5
16
1.3
14
1.1
49
0.8
93
0.7
03
0.5
60
0.4
52
0.3
70
0.3
07
0.2
19
0.1
64
0.1
27
0.1
01
0.0
83
0.0
54
0.0
39
0.0
22
0.0
10
Na
6.5
93
5.7
42
4.1
20
2.9
16
2.2
15
1.7
99
1.5
21
1.3
15
1.1
49
0.8
92
0.7
03
0.5
60
0.4
52
0.3
70
0.3
07
0.2
19
0.1
64
0.1
27
0.1
01
0.0
83
0.0
54
0.0
39
0.0
22
0.0
10
Mg+
2–
27.7
87.7
81
4.0
44
2.7
01
2.0
45
1.6
58
1.3
96
1.2
03
0.9
28
0.7
35
0.5
92
0.4
82
0.3
98
0. 3
32
0.2
39
0.1
79
0.1
39
0.1
11
0.0
91
0.0
59
0.0
42
0.0
24
0.0
11
Mg
7.2
04
6.5
44
5.0
76
3.6
91
2.7
14
2.0
87
1.6
83
1.4
07
1.2
07
0.9
27
0.7
34
0.5
91
0.4
82
0.3
98
0.3
32
0.2
39
0.1
79
0.1
39
0.1
11
0.0
91
0.0
59
0.0
42
0.0
24
0.0
11
Al+
3–
40.8
410.8
65.2
88
3.3
17
2.3
83
1.8
56
1.5
19
1.2
85
0.9
73
0.7
68
0.6
21
0.5
09
0.4
23
0. 3
55
0.2
58
0.1
94
0.1
51
0.1
20
0.0
98
0.0
64
0.0
45
0.0
26
0.0
12
Al
8.1
62
7.4
61
5.8
87
4.3
47
3.1
95
2.4
14
1.8
95
1.5
43
1.2
96
0.9
72
0.7
66
0.6
19
0.5
08
0.4
23
0.3
55
0.2
58
0.1
94
0.1
51
0.1
20
0.0
98
0.0
64
0.0
45
0.0
26
0.0
12
Si
8.0
05
7.4
67
6.1
77
4.7
67
3.5
97
2.7
37
2.1
33
1.7
12
1.4
13
1.0
33
0.8
03
0.6
47
0.5
33
0.4
45
0.3
76
0.2
76
0.2
09
0.1
63
0.1
30
0.1
06
0. 0
69
0.0
49
0.0
28
0.0
13
P7.6
16
7.2
09
6.1
91
4.9
83
3.8
87
3.0
16
2.3
66
1.8
93
1.5
50
1.1
08
0.8
47
0.6
78
0. 5
57
0.4
66
0.3
95
0.2
92
0.2
22
0.1
74
0.1
39
0.1
14
0.0
74
0.0
52
0.0
30
0.0
14
S7.1
85
6.8
72
6.0
70
5.0
56
4.0
70
3.2
34
2.5
74
2.0
71
1.6
94
1.1
96
0.9
01
0.7
13
0.5
83
0.4
87
0.4
14
0.3
07
0.2
36
0.1
85
0.1
48
0.1
21
0.0
79
0. 0
55
0.0
32
0.0
15
Cl
6.7
57
6.5
12
5.8
75
5.0
32
4.1
66
3.3
89
2.7
44
2.2
32
1.8
34
1.2
91
0.9
62
0.7
53
0. 6
11
0.5
09
0.4
32
0.3
22
0.2
48
0.1
95
0.1
57
0.1
29
0.0
84
0.0
59
0.0
34
0.0
15
Cl−
1–
-4.8
33
4.1
42
4.7
21
4.1
45
3.4
14
2.7
65
2.2
43
1.8
39
1.2
91
0.9
61
0.7
52
0.6
11
0.5
09
0. 4
32
0.3
22
0.2
48
0.1
95
0.1
57
0.1
29
0.0
84
0.0
59
0.0
34
0.0
15
Ar
6.3
60
6.1
65
5.6
52
4.9
50
4.1
96
3.4
89
2.8
76
2.3
70
1.9
64
1.3
88
1.0
29
0.7
98
0.6
43
0.5
33
0.4
51
0.3
36
0.2
60
0.2
06
0.1
66
0.1
36
0.0
89
0.0
62
0.0
36
0.0
16
K+
1–
17.9
97.7
22
5.4
70
4.3
54
3.5
77
2.9
66
2.4
71
2.0
68
1.4
79
1.0
98
0.8
47
0.6
78
0.5
59
0. 4
71
0.3
50
0.2
71
0.2
15
0.1
74
0.1
44
0.0
94
0.0
66
0.0
38
0.0
17
K12.3
810.5
77.5
33
5.5
50
4.3
81
3.5
81
2.9
65
2.4
69
2.0
67
1.4
79
1.0
98
0.8
48
0.6
78
0.5
59
0.4
71
0.3
50
0.2
71
0.2
15
0.1
74
0.1
44
0.0
94
0.0
66
0.0
38
0.0
17
Ca+
2–
30.3
410.2
06.2
45
4.6
44
3.7
15
3.0
62
2.5
59
2.1
56
1.5
62
1.1
66
0.8
99
0.7
16
0.5
87
0. 4
92
0.3
64
0.2
82
0.2
25
0.1
82
0.1
51
0.0
99
0.0
69
0.0
40
0.0
18
Ca
13.6
912.0
88.8
70
6.3
19
4.7
34
3.7
45
3.0
65
2.5
55
2.1
52
1.5
61
1.1
66
0.8
99
0.7
16
0.5
87
0.4
92
0.3
64
0.2
82
0.2
25
0.1
82
0.1
51
0.0
99
0.0
69
0.0
40
0.0
18
Sc
12.8
711.5
58.7
95
6.4
42
4.8
80
3.8
69
3.1
70
2.6
49
2.2
40
1.6
39
1.2
31
0.9
51
0.7
56
0.6
17
0.5
16
0.3
80
0.2
93
0.2
34
0.1
90
0.1
57
0. 1
04
0.0
73
0.0
42
0.0
19
Ti+
4–
55.8
115.7
88.2
64
5.5
26
4.1
58
3.3
26
2.7
51
2.3
20
1.7
06
1.2
91
1.0
01
0.7
96
0.6
49
0. 5
40
0.3
95
0.3
05
0.2
43
0.1
98
0.1
64
0.1
08
0.0
76
0.0
44
0.0
20
Ti
12.1
411.0
28.6
17
6.4
59
4.9
57
3.9
56
3.2
54
2.7
30
2.3
18
1.7
11
1.2
94
1.0
03
0.7
97
0.6
49
0.5
41
0.3
96
0.3
05
0.2
43
0.1
98
0.1
64
0.1
08
0. 0
76
0.0
44
0.0
20
V+
5–
68.7
618.7
59.4
21
6.0
75
4.4
51
3.4
99
2.8
67
2.4
07
1.7
71
1.3
47
1.0
50
0.8
37
0.6
81
0. 5
66
0.4
12
0.3
16
0.2
52
0.2
05
0.1
70
0.1
13
0.0
80
0.0
46
0.0
21
V11.5
010.5
38.4
04
6.4
23
4.9
93
4.0
14
3.3
19
2.7
97
2.3
85
1.7
76
1.3
52
1.0
52
0.8
38
0.6
82
0.5
67
0.4
13
0.3
17
0.2
52
0.2
06
0.1
71
0.1
13
0. 0
80
0.0
46
0.0
21
Cr+
4–
55.9
215.8
88.3
73
5.6
39
4.2
75
3.4
47
2.8
75
2.4
46
1.8
28
1.4
03
1.0
99
0.8
77
0.7
15
0. 5
93
0.4
30
0.3
29
0.2
61
0.2
13
0.1
77
0.1
18
0.0
83
0.0
48
0.0
22
700 A. Appendix
Table
A.3
.(c
ontinued
)
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
6.0
Cr
9.6
76
8.9
46
7.3
73
5.8
96
4.7
83
3.9
65
3.3
42
2.8
49
2.4
49
1.8
39
1.4
09
1.1
01
0.8
78
0.7
15
0.5
93
0.4
31
0.3
29
0.2
62
0.2
13
0.1
77
0.1
18
0.0
83
0.0
48
0.0
22
Mn+
2–
30.5
510.4
16.4
71
4.8
91
3.9
86
3.3
58
2.8
75
2.4
85
1.8
87
1.4
58
1.1
46
0.9
17
0.7
48
0.6
20
0.4
49
0.3
42
0.2
71
0.2
21
0.1
83
0.1
22
0.0
87
0.0
50
0.0
22
Mn
10.4
09.6
49
7.9
50
6.2
70
4.9
86
4.0
69
3.4
01
2.8
93
2.4
90
1.8
85
1.4
57
1.1
45
0.9
17
0.7
48
0.6
21
0.4
49
0.3
42
0.2
71
0.2
21
0.1
83
0.1
22
0.0
87
0.0
50
0.0
22
Fe+
2–
30.4
910.3
66.4
42
4.8
79
3.9
91
3.3
77
2.9
04
2.5
21
1.9
31
1.5
04
1.1
89
0.9
55
0.7
80
0.6
48
0.4
68
0.3
55
0.2
81
0.2
29
0.1
90
0.1
27
0.0
90
0.0
52
0.0
23
Fe
9.9
34
9.2
61
7.7
26
6.1
72
4.9
58
4.0
74
3.4
24
2.9
26
2.5
29
1.9
30
1.5
02
1.1
88
0.9
55
0.7
80
0.6
48
0.4
68
0.3
55
0.2
81
0.2
29
0.1
90
0.1
27
0.0
90
0.0
52
0.0
23
Co+
2–
30.4
210.3
16.4
03
4.8
57
3.9
86
3.3
85
2.9
24
2.5
49
1.9
69
1.5
44
1.2
28
0.9
91
0.8
11
0.6
74
0.4
87
0.3
69
0.2
91
0.2
36
0.1
96
0.1
31
0.0
93
0.0
54
0.0
24
Co
9.5
03
8.8
99
7.5
05
6.0
64
4.9
16
4.0
67
3.4
36
2.9
49
2.5
59
1.9
69
1.5
43
1.2
27
0.9
91
0.8
11
0.6
74
0.4
87
0.3
69
0.2
91
0.2
36
0.1
96
0.1
31
0.0
93
0.0
54
0.0
24
Ni+
2–
30.3
510.2
56.3
57
4.8
29
3.9
73
3.3
87
2.9
37
2.5
71
2.0
01
1.5
81
1.2
65
1.0
25
0.8
42
0.7
01
0.5
06
0.3
83
0.3
01
0.2
44
0.2
03
0.1
36
0.0
97
0.0
56
0.0
25
Ni
9.1
08
8.5
62
7.2
90
5.9
53
4.8
66
4.0
51
3.4
40
2.9
65
2.5
83
2.0
02
1.5
80
1.2
64
1.0
24
0.8
42
0.7
01
0.5
06
0.3
83
0.3
01
0.2
44
0.2
03
0.1
36
0.0
97
0.0
56
0.0
25
Cu+
2–
30.2
810.1
86.3
08
4.7
95
3.9
55
3.3
82
2.9
43
2.5
86
2.0
29
1.6
14
1.2
98
1.0
57
0.8
71
0.7
27
0.5
25
0.3
97
0.3
12
0.2
53
0.2
09
0.1
40
0.1
00
0.0
58
0.0
26
Cu
8.7
44
8.2
48
7.0
84
5.8
39
4.8
10
4.0
29
3.4
36
2.9
74
2.6
01
2.0
30
1.6
13
1.2
97
1.0
56
0.8
71
0.7
27
0.5
25
0.3
97
0.3
12
0.2
53
0.2
09
0.1
40
0.1
00
0.0
58
0.0
26
Zn+
2–
30.2
110.1
26.2
56
4.7
58
3.9
32
3.3
72
2.9
45
2.5
97
2.0
51
1.6
42
1.3
29
1.0
87
0.8
99
0.7
52
0.5
44
0.4
11
0.3
23
0.2
61
0.2
16
0.1
44
0.1
03
0.0
59
0.0
27
Zn
8.4
08
7.9
55
6.8
86
5.7
24
4.7
49
4.0
00
3.4
27
2.9
78
2.6
14
2.0
54
1.6
42
1.3
28
1.0
86
0.8
99
0.7
52
0.5
44
0.4
11
0.3
23
0.2
61
0.2
16
0.1
44
0.1
03
0.0
59
0.0
27
Ga
9.9
36
9.2
63
7.7
54
6.2
38
5.0
42
4.1
62
3.5
16
3.0
27
2.6
43
2.0
74
1.6
63
1.3
53
1.1
12
0.9
24
0.7
75
0.5
63
0.4
26
0.3
34
0.2
69
0.2
23
0.1
49
0.1
06
0.0
61
0.0
28
Ge
10.2
69.6
54
8.2
17
6.6
58
5.3
54
4.3
69
3.6
44
3.1
04
2.6
91
2.0
98
1.6
84
1.3
75
1.1
36
0.9
48
0.7
98
0.5
82
0.4
40
0.3
45
0.2
78
0.2
29
0.1
53
0.1
09
0.0
63
0.0
29
As
10.2
59.7
32
8.4
50
6.9
61
5.6
34
4.5
87
3.7
97
3.2
07
2.7
58
2.1
30
1.7
06
1.3
96
1.1
57
0.9
69
0.8
19
0.6
00
0.4
55
0.3
56
0.2
86
0.2
36
0.1
57
0.1
13
0.0
65
0.0
30
Se
10.1
19.6
64
8.5
41
7.1
63
5.8
67
4.7
94
3.9
60
3.3
25
2.8
41
2.1
70
1.7
30
1.4
16
1.1
77
0.9
89
0.8
38
0.6
17
0.4
69
0.3
67
0.2
95
0.2
43
0.1
62
0.1
16
0.0
67
0.0
30
Br
9.8
51
9.4
73
8.5
05
7.2
64
6.0
36
4.9
75
4.1
19
3.4
51
2.9
36
2.2
21
1.7
59
1.4
37
1.1
96
1.0
07
0.8
57
0.6
34
0.4
83
0.3
78
0.3
04
0.2
50
0. 1
66
0.1
19
0.0
69
0.0
31
Br−
1–
-1.5
54
6.9
72
7.0
49
6.0
49
5.0
05
4.1
37
3.4
59
2.9
39
2.2
20
1.7
59
1.4
36
1.1
95
1.0
07
0. 8
57
0.6
34
0.4
83
0.3
78
0.3
04
0.2
50
0.1
66
0.1
19
0.0
69
0.0
31
Kr
9.5
74
9.2
51
8.4
13
7.3
01
6.1
56
5.1
26
4.2
66
3.5
78
3.0
38
2.2
79
1.7
93
1.4
59
1.2
14
1.0
25
0.8
73
0.6
50
0.4
96
0.3
89
0.3
13
0.2
57
0.1
70
0.1
22
0.0
71
0.0
32
Rb+
1–
20.8
310.3
37.7
68
6.3
21
5.2
41
4.3
78
3.6
86
3.1
33
2.3
43
1.8
32
1.4
85
1.2
33
1.0
42
0. 8
89
0.6
64
0.5
10
0.4
00
0.3
22
0.2
65
0.1
75
0.1
25
0.0
73
0.0
33
Rb
16.2
413.9
810.2
87.8
56
6.3
41
5.2
40
4. 3
75
3.6
83
3.1
32
2.3
43
1.8
33
1.4
85
1.2
33
1.0
42
0.8
89
0.6
64
0.5
10
0.4
00
0.3
22
0.2
65
0.1
75
0. 1
25
0.0
73
0.0
33
Sr+
2–
32.9
612.6
48.4
50
6.5
74
5.3
77
4.4
85
3.7
83
3.2
22
2.4
09
1.8
76
1.5
14
1.2
54
1.0
59
0. 9
05
0.6
79
0.5
22
0.4
11
0.3
31
0.2
72
0.1
79
0.1
28
0.0
75
0.0
34
Sr
18.0
915.9
211.7
78.6
11
6.6
59
5.3
92
4.4
80
3.7
76
3.2
17
2.4
08
1.8
76
1.5
14
1.2
54
1.0
59
0.9
05
0.6
79
0.5
22
0.4
11
0.3
31
0.2
72
0.1
79
0.1
28
0.0
75
0.0
34
Y+
3–
45.4
015.2
09.2
89
6.9
11
5.5
46
4.5
98
3.8
77
3.3
06
2.4
74
1.9
22
1.5
45
1.2
76
1.0
76
0. 9
20
0.6
92
0.5
34
0.4
22
0.3
40
0.2
79
0.1
84
0.1
31
0.0
77
0.0
35
Y17.5
215.7
412.0
99.0
09
6.9
55
5.5
92
4.6
23
3.8
88
3.3
10
2.4
74
1.9
21
1.5
44
1.2
76
1.0
76
0.9
20
0.6
92
0.5
34
0.4
22
0.3
40
0.2
79
0.1
84
0.1
31
0.0
77
0.0
35
Zr+
4–
58.0
517.9
110.2
47.3
19
5.7
51
4.7
25
3.9
73
3.3
87
2.5
38
1.9
70
1.5
79
1.3
01
1.0
94
0. 9
36
0.7
05
0.5
46
0.4
32
0.3
49
0.2
87
0.1
89
0.1
34
0.0
78
0.0
36
Zr
16.8
515.3
412.1
39.2
33
7.1
84
5.7
78
4.7
68
4.0
05
3.4
06
2.5
42
1.9
68
1.5
77
1.2
99
1.0
94
0.9
35
0.7
05
0.5
46
0.4
32
0.3
49
0.2
87
0. 1
89
0.1
34
0.0
78
0.0
36
Nb+
5–
70.8
320.7
411.2
87.7
85
5.9
91
4.8
68
4.0
74
3.4
69
2.6
01
2.0
18
1.6
14
1.3
26
1.1
14
0. 9
51
0.7
18
0.5
57
0.4
42
0.3
57
0.2
94
0.1
93
0.1
37
0.0
80
0.0
37
Nb
14.8
913.7
711.3
49.0
26
7.2
44
5.9
21
4.9
17
4.1
36
3.5
16
2.6
15
2.0
18
1.6
11
1.3
24
1.1
12
0.9
50
0.7
17
0.5
57
0.4
42
0.3
57
0.2
94
0.1
93
0.1
37
0.0
80
0.0
37
Mo+
6–
83.7
023.6
612.4
08.3
01
6.2
62
5.0
29
4.1
83
3.5
53
2.6
62
2.0
66
1.6
51
1.3
53
1.1
34
0. 9
68
0.7
30
0.5
68
0.4
52
0.3
66
0.3
01
0.1
98
0.1
41
0.0
82
0.0
38
Mo
14.3
113.3
311.1
89.0
44
7.3
42
6.0
41
5.0
37
4.2
46
3.6
13
2.6
88
2.0
70
1.6
48
1.3
50
1.1
32
0.9
66
0.7
30
0.5
68
0.4
52
0.3
66
0.3
01
0. 1
98
0.1
41
0.0
82
0.0
38
Ru
13.2
912.5
210.7
68.9
47
7.4
21
6.2
01
5.2
25
4.4
36
3.7
94
2.8
34
2.1
80
1.7
27
1.4
07
1.1
74
0.9
99
0.7
53
0.5
89
0.4
70
0.3
82
0.3
15
0. 2
08
0.1
47
0.0
86
0.0
39
Rh
12.8
312.1
310.5
48.8
54
7.4
16
6.2
45
5.2
94
4.5
15
3.8
73
2.9
04
2.2
36
1.7
70
1.4
38
1.1
97
1.0
17
0.7
65
0.5
98
0.4
79
0.3
90
0.3
22
0.2
12
0.1
50
0.0
87
0.0
40
Pd+
2–
33.8
913.5
79.3
66
7.4
75
6.2
51
5.3
19
4.5
62
3.9
34
2.9
70
2.2
92
1.8
13
1.4
71
1.2
22
1. 0
35
0.7
78
0.6
08
0.4
88
0.3
98
0.3
29
0.2
17
0.1
54
0.0
89
0.0
41
Pd
10.5
210.2
09.3
88
8.3
27
7.2
35
6.2
27
5.3
45
4.5
91
3.9
56
2.9
77
2.2
93
1.8
13
1.4
70
1. 2
21
1.0
35
0.7
78
0.6
08
0.4
88
0.3
98
0.3
29
0.2
17
0.1
54
0.0
89
0.0
41
Ag+
2–
33.7
813.4
99.3
20
7.4
65
6.2
72
5.3
61
4.6
19
3.9
98
3.0
33
2.3
47
1.8
57
1.5
05
1.2
47
1. 0
54
0.7
90
0.6
18
0.4
96
0.4
05
0.3
36
0.2
22
0.1
57
0.0
91
0.0
42
Ag
12.0
211.4
310.0
88.6
26
7.3
48
6.2
79
5.3
87
4.6
39
4.0
10
3.0
36
2.3
47
1.8
57
1.5
04
1.2
47
1.0
54
0.7
90
0.6
18
0.4
96
0.4
05
0.3
36
0. 2
22
0.1
57
0.0
91
0.0
42
A.5 Atomic Form Factors for 200 keV Electrons 701
Table
A.3
.(c
ontinued
)
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
6.0
Cd+
2–
33.6
713.4
09.2
63
7.4
43
6.2
79
5.3
92
4.6
65
4.0
53
3.0
93
2.4
00
1.9
01
1.5
39
1.2
73
1.0
75
0.8
03
0.6
27
0.5
04
0.4
12
0.3
42
0.2
27
0.1
60
0.0
93
0.0
43
Cd
12.8
012.1
610.6
48.9
77.5
35
6.3
78
5.4
48
4.6
89
4.0
60
3.0
89
2.3
97
1.9
00
1.5
39
1.2
74
1.0
75
0.8
03
0.6
27
0.5
04
0.4
12
0.3
42
0.2
27
0.1
60
0.0
93
0.0
43
In14.7
413.7
611.6
09.4
77.7
79
6.5
00
5.5
17
4.7
39
4.1
05
3.1
37
2.4
44
1.9
42
1.5
74
1.3
01
1.0
96
0.8
17
0.6
37
0.5
12
0.4
19
0.3
49
0.2
31
0.1
64
0.0
95
0.0
44
Sn
15.3
614.4
112.2
29.9
38.0
71
6.6
68
5.6
14
4.8
01
4.1
53
3.1
80
2.4
88
1.9
82
1.6
08
1.3
29
1.1
19
0.8
31
0.6
47
0.5
20
0.4
26
0.3
55
0.2
36
0.1
67
0.0
97
0.0
45
Sb
15.5
514.6
912.6
210.3
38.3
69
6.8
64
5.7
36
4.8
79
4.2
08
3.2
22
2.5
28
2.0
20
1.6
42
1.3
58
1.1
42
0.8
45
0.6
57
0.5
27
0.4
33
0.3
61
0.2
41
0.1
70
0.0
98
0.0
45
Te
15.5
514.7
712.8
610.6
48.6
49
7.0
73
5.8
78
4.9
72
4.2
72
3.2
63
2.5
66
2.0
56
1.6
75
1.3
86
1.1
65
0.8
60
0.6
67
0.5
35
0.4
40
0.3
67
0.2
45
0.1
74
0.1
00
0.0
46
I15.2
814.6
012.9
010.8
28.8
78
7.2
76
6.0
32
5.0
81
4.3
48
3.3
07
2.6
01
2.0
90
1.7
06
1.4
13
1.1
88
0.8
76
0.6
78
0.5
43
0.4
46
0.3
72
0.2
50
0.1
77
0.1
02
0.0
47
I−1
–4.0
611.6
610.7
38.9
21
7.3
07
6.0
44
5.0
84
4.3
48
3.3
06
2.6
01
2.0
90
1.7
06
1.4
13
1.1
88
0.8
76
0.6
78
0.5
43
0.4
46
0.3
72
0.2
50
0.1
77
0.1
02
0.0
47
Xe
14.9
814.3
812.8
710.9
49.0
67
7.4
65
6.1
88
5.1
99
4.4
34
3.3
55
2.6
36
2.1
21
1.7
36
1.4
40
1.2
12
0.8
92
0.6
89
0.5
51
0.4
53
0.3
78
0.2
54
0.1
80
0.1
04
0.0
48
Cs+
1–
25.4
814.5
011.3
09.2
26
7.6
05
6.3
20
5.3
12
4.5
23
3.4
08
2.6
73
2.1
52
1.7
64
1.4
66
1.2
35
0.9
09
0.7
00
0.5
60
0.4
59
0.3
84
0.2
58
0.1
84
0.1
06
0.0
49
Cs
22.7
519.5
714.6
111.3
99.2
33
7.6
00
6.3
17
5.3
10
4.5
23
3.4
09
2.6
73
2.1
52
1.7
64
1.4
66
1.2
35
0.9
09
0.7
00
0.5
60
0.4
59
0.3
84
0.2
58
0.1
84
0.1
06
0.0
49
Ba+
2–
37.2
216.5
411.8
49.4
31
7.7
42
6.4
41
5.4
19
4.6
13
3.4
65
2.7
11
2.1
83
1.7
91
1.4
91
1.2
57
0.9
26
0.7
12
0.5
68
0.4
66
0.3
89
0.2
63
0.1
87
0.1
08
0.0
50
Ba
25.2
022.0
016.2
112.0
69.4
85
7.7
37
6.4
30
5.4
12
4.6
11
3.4
66
2.7
12
2.1
83
1.7
91
1.4
91
1.2
57
0.9
26
0.7
12
0.5
68
0.4
66
0.3
89
0.2
63
0.1
87
0.1
08
0.0
50
La+
3–
49.3
418.8
412.5
39.6
94
7.8
89
6.5
57
5.5
21
4.7
01
3.5
25
2.7
52
2.2
14
1.8
18
1.5
16
1.2
79
0.9
42
0.7
24
0.5
77
0.4
72
0.3
95
0.2
67
0.1
90
0.1
10
0.0
50
La
24.6
321.9
416.7
012.5
49.8
02
7.9
39
6.5
72
5.5
22
4.6
98
3.5
23
2.7
51
2.2
14
1.8
18
1.5
16
1.2
79
0.9
42
0.7
24
0.5
77
0.4
72
0.3
95
0.2
67
0.1
90
0.1
10
0.0
50
Ce+
4–
61.6
921.3
313.3
210.0
18.0
55
6.6
74
5.6
19
4.7
87
3.5
87
2.7
94
2.2
45
1.8
44
1.5
39
1.3
01
0.9
59
0.7
36
0.5
86
0.4
79
0.4
00
0.2
71
0.1
94
0.1
12
0.0
51
Ce
24.0
621.5
116.5
012.4
69.7
87
7.9
58
6.6
12
5.5
72
4.7
52
3.5
72
2.7
92
2.2
48
1.8
47
1.5
41
1.3
02
0.9
59
0.7
36
0.5
86
0.4
79
0.4
01
0.2
71
0.1
94
0.1
12
0.0
51
Pr+
3–
49.0
918.6
512.4
19.6
49
7.9
07
6.6
18
5.6
08
4.7
99
3.6
20
2.8
32
2.2
81
1.8
76
1.5
67
1.3
24
0.9
77
0.7
49
0.5
95
0.4
86
0.4
06
0.2
75
0.1
97
0.1
14
0.0
52
Pr
23.4
620.7
615.7
011.9
09.4
78
7.8
16
6.5
62
5.5
71
4.7
75
3.6
12
2.8
32
2.2
84
1.8
79
1.5
68
1.3
25
0.9
77
0.7
49
0.5
95
0.4
87
0.4
06
0. 2
75
0.1
97
0.1
14
0.0
52
Nd+
3–
48.9
618.5
412.3
39.6
11
7.9
00
6.6
35
5.6
39
4.8
39
3.6
62
2.8
70
2.3
13
1.9
04
1.5
92
1.3
47
0.9
94
0.7
62
0.6
05
0.4
94
0.4
12
0.2
79
0.2
00
0.1
15
0.0
53
Nd
22.9
420.3
615.5
011.8
19.4
41
7.8
13
6.5
82
5.6
05
4.8
16
3.6
54
2.8
69
2.3
16
1.9
07
1.5
93
1.3
47
0.9
94
0.7
62
0.6
05
0.4
94
0.4
12
0. 2
79
0.2
00
0.1
15
0.0
53
Sm
+3
–48.6
918.3
212.1
89.5
20
7.8
68
6.6
49
5.6
84
4.9
02
3.7
36
2.9
39
2.3
75
1.9
59
1.6
41
1.3
90
1.0
28
0.7
88
0.6
24
0.5
08
0.4
24
0.2
87
0.2
06
0.1
19
0.0
55
Sm
21.9
819.6
215.1
111.6
19.3
47
7.7
85
6.6
00
5.6
53
4.8
82
3.7
29
2.9
39
2.3
77
1.9
61
1.6
42
1.3
91
1.0
28
0.7
88
0.6
24
0.5
09
0.4
24
0. 2
87
0.2
06
0.1
19
0.0
55
Eu+
3–
48.5
618.2
112.0
99.4
69
7.8
45
6.6
48
5.6
99
4.9
27
3.7
69
2.9
72
2.4
05
1.9
85
1.6
64
1.4
11
1.0
45
0.8
01
0.6
34
0.5
16
0.4
30
0.2
91
0.2
09
0.1
21
0.0
55
Eu
21.5
219.2
714.9
211.5
29.2
97
7.7
65
6.6
02
5.6
70
4.9
08
3.7
62
2.9
71
2.4
06
1.9
87
1.6
66
1.4
12
1.0
45
0.8
01
0.6
34
0.5
16
0.4
30
0. 2
91
0.2
09
0.1
21
0.0
55
Gd+
3–
48.4
418.1
112.0
19.4
17
7.8
19
6.6
43
5.7
10
4.9
48
3.7
99
3.0
02
2.4
33
2.0
11
1.6
87
1.4
32
1.0
62
0.8
14
0.6
44
0.5
24
0.4
36
0.2
95
0.2
12
0.1
23
0.0
56
Gd
21.2
319.2
815.2
911.8
79.5
17
7.8
86
6. 6
74
5.7
22
4.9
52
3.7
99
3.0
02
2.4
32
2.0
11
1.6
87
1.4
32
1.0
62
0.8
14
0.6
44
0.5
24
0.4
36
0.2
95
0.2
12
0.1
23
0.0
56
Tb
20.6
618.5
914.5
311.3
09.1
72
7.7
02
6.5
85
5.6
86
4.9
46
3.8
19
3.0
29
2.4
61
2.0
37
1.7
11
1.4
54
1.0
79
0.8
27
0.6
54
0.5
32
0.4
42
0.2
99
0.2
15
0.1
25
0.0
57
Dy
20.2
518.2
614.3
411.1
99.1
06
7.6
65
6.5
70
5.6
88
4.9
59
3.8
43
3.0
56
2.4
86
2.0
61
1.7
33
1.4
74
1.0
95
0.8
40
0.6
64
0.5
39
0.4
48
0.3
03
0.2
18
0.1
27
0.0
58
Ho
19.8
617.9
414.1
511.0
89.0
38
7.6
26
6.5
52
5.6
86
4.9
68
3.8
64
3.0
80
2.5
11
2.0
84
1.7
54
1.4
93
1.1
11
0.8
53
0.6
75
0.5
47
0.4
55
0. 3
07
0.2
21
0.1
29
0.0
59
Er
19.4
817.6
313.9
710.9
78.9
70
7.5
84
6.5
32
5.6
82
4.9
75
3.8
84
3.1
03
2.5
34
2.1
06
1.7
75
1.5
12
1.1
27
0.8
66
0.6
85
0.5
56
0.4
61
0. 3
11
0.2
24
0.1
31
0.0
60
Tm
19.1
017.3
313.7
910.8
68.9
01
7.5
41
6.5
09
5.6
74
4.9
79
3.9
01
3.1
25
2.5
56
2.1
27
1.7
95
1.5
31
1.1
43
0.8
79
0.6
95
0.5
64
0.4
67
0. 3
15
0.2
27
0.1
33
0.0
61
Yb
18.7
517.0
413.6
110.7
58.8
31
7.4
96
6.4
84
5.6
65
4.9
81
3.9
16
3.1
45
2.5
77
2.1
47
1.8
14
1.5
49
1.1
59
0.8
92
0.7
06
0.5
72
0.4
74
0.3
19
0.2
30
0.1
35
0.0
61
Lu
18.7
617.2
514.0
411.1
49.0
66
7.6
18
6. 5
45
5.6
99
5.0
06
3.9
37
3.1
66
2.5
97
2.1
66
1.8
31
1.5
66
1.1
74
0.9
05
0.7
16
0.5
80
0.4
80
0.3
23
0. 2
33
0.1
36
0.0
62
Hf
18.3
917.0
914.1
911.3
99.2
77
7.7
58
6. 6
32
5.7
54
5.0
45
3.9
63
3.1
88
2.6
16
2.1
84
1.8
48
1.5
81
1.1
88
0.9
17
0.7
26
0.5
88
0.4
87
0.3
27
0.2
36
0.1
38
0.0
63
Ta
17.9
916.8
414.2
311.5
69.4
58
7.8
99
6.7
31
5.8
23
5.0
95
3.9
94
3.2
11
2.6
35
2.2
01
1.8
64
1.5
97
1.2
02
0.9
30
0.7
37
0.5
97
0.4
94
0.3
31
0.2
39
0.1
40
0.0
64
W17.5
916.5
714.1
911.6
89.6
08
8.0
32
6. 8
34
5.9
00
5.1
52
4.0
30
3.2
36
2.6
55
2.2
18
1.8
80
1.6
11
1.2
15
0.9
42
0.7
47
0.6
05
0.5
00
0.3
35
0. 2
42
0.1
42
0.0
65
Re
17.2
016.2
814.1
111.7
49.7
29
8.1
54
6.9
37
5.9
82
5.2
16
4.0
69
3.2
64
2.6
76
2.2
35
1.8
95
1.6
26
1.2
28
0.9
53
0.7
57
0.6
13
0.5
07
0. 3
39
0.2
44
0.1
44
0.0
66
702 A. Appendix
Table
A.3
.(c
ontinued
)
s0.0
0.0
50.1
0.1
50.2
0.2
50.3
0.3
50.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
6.0
Os
16.8
215.9
914.0
011.7
79.8
24
8.2
63
7.0
36
6.0
65
5.2
83
4.1
13
3.2
93
2.6
98
2.2
53
1.9
10
1.6
39
1.2
41
0.9
65
0.7
67
0.6
22
0.5
14
0.3
43
0.2
47
0.1
46
0.0
67
Ir16.3
915.6
413.8
211.7
49.8
71
8.3
42
7.1
21
6.1
43
5.3
50
4.1
60
3.3
26
2.7
22
2.2
71
1.9
25
1.6
53
1.2
53
0.9
76
0.7
76
0.6
30
0.5
21
0.3
48
0.2
50
0.1
47
0.0
67
Pt
15.0
614.4
713.0
411.3
49.7
27
8.3
39
7.1
79
6.2
20
5.4
26
4.2
16
3.3
63
2.7
47
2.2
89
1.9
40
1.6
66
1.2
65
0.9
87
0.7
86
0.6
38
0.5
28
0.3
52
0.2
53
0.1
49
0.0
68
Au
14.6
714.1
412.8
311.2
59.7
22
8.3
80
7.2
41
6.2
87
5.4
91
4.2
67
3.4
00
2.7
73
2.3
09
1.9
56
1.6
79
1.2
76
0.9
97
0.7
95
0.6
46
0.5
35
0.3
56
0.2
56
0.1
51
0.0
69
Hg
15.2
114.6
413.2
311.5
29.8
95
8.4
93
7.3
22
6.3
51
5.5
45
4.3
10
3.4
35
2.8
00
2.3
30
1.9
72
1.6
93
1.2
87
1.0
07
0.8
05
0.6
54
0.5
41
0.3
60
0.2
59
0.1
53
0.0
70
Tl
17.8
116.7
114.3
412.0
110.1
18.6
01
7.3
91
6.4
07
5.5
95
4.3
54
3.4
71
2.8
29
2.3
52
1.9
90
1.7
07
1.2
98
1.0
17
0.8
14
0.6
62
0.5
48
0.3
65
0.2
62
0.1
54
0.0
71
Pb
18.8
317.6
915.1
312.5
210.3
98.7
52
7.4
79
6.4
67
5.6
44
4.3
95
3.5
06
2.8
58
2.3
75
2.0
07
1.7
22
1.3
09
1.0
27
0.8
22
0.6
70
0.5
55
0.3
69
0.2
65
0.1
56
0.0
72
Bi
19.3
318.2
415.7
012.9
710.6
98.9
34
7.5
88
6.5
37
5.6
96
4.4
34
3.5
40
2.8
86
2.3
98
2.0
26
1.7
37
1.3
20
1.0
36
0.8
31
0.6
78
0.5
62
0.3
73
0.2
67
0.1
58
0.0
73
Po
19.5
718.5
516.1
213.3
711.0
09.1
36
7.7
15
6.6
19
5.7
53
4.4
73
3.5
73
2.9
15
2.4
21
2.0
45
1.7
52
1.3
31
1.0
45
0.8
39
0.6
85
0.5
68
0.3
78
0.2
70
0.1
60
0.0
73
At
19.1
318.2
616.1
113.5
611.2
39.3
31
7.8
57
6.7
17
5.8
21
4.5
12
3.6
04
2.9
42
2.4
45
2.0
64
1.7
68
1.3
42
1.0
54
0.8
47
0.6
93
0.5
75
0.3
82
0.2
73
0.1
61
0.0
74
Rn
18.7
217.9
616.0
513.6
811.4
29.5
16
8.0
05
6.8
24
5.8
96
4.5
54
3.6
35
2.9
68
2.4
68
2.0
84
1.7
84
1.3
54
1.0
63
0.8
55
0.7
00
0.5
81
0.3
87
0.2
76
0.1
63
0.0
75
Fr
25.8
122.7
617.7
214.1
311.6
09.6
58
8.1
28
6.9
25
5.9
74
4.6
00
3.6
67
2.9
95
2.4
90
2.1
03
1.8
00
1.3
65
1.0
72
0.8
63
0.7
07
0.5
88
0.3
91
0.2
79
0.1
65
0.0
76
Ra
28.3
725.1
819.2
614.7
911.8
69.7
99
8.2
39
7.0
20
6.0
53
4.6
50
3.7
01
3.0
21
2.5
13
2.1
22
1.8
16
1.3
77
1.0
81
0.8
71
0.7
14
0.5
94
0.3
96
0.2
82
0.1
66
0.0
77
Ac
28.4
825.6
720.0
615.3
812.2
09.9
94
8.3
67
7.1
14
6.1
27
4.6
99
3.7
35
3.0
48
2.5
35
2.1
42
1.8
33
1.3
89
1.0
90
0.8
78
0.7
21
0.6
00
0.4
00
0.2
86
0.1
68
0.0
78
Th
28.1
125.6
820.5
315.8
812.5
510.2
18.5
10
7.2
16
6.2
04
4.7
47
3.7
69
3.0
75
2.5
58
2.1
61
1.8
50
1.4
01
1.0
99
0.8
86
0.7
28
0.6
06
0.4
05
0.2
89
0.1
70
0.0
79
Pa
27.3
324.8
819.8
615.4
912.4
010.2
18.5
71
7.2
98
6.2
87
4.8
12
3.8
14
3.1
06
2.5
82
2.1
80
1.8
65
1.4
12
1.1
08
0.8
94
0.7
34
0.6
12
0.4
09
0.2
92
0.1
71
0.0
79
U26.8
424.5
219.7
215.4
812.4
510.2
88.6
54
7.3
79
6.3
62
4.8
69
3.8
56
3.1
37
2.6
06
2. 1
99
1.8
81
1.4
24
1.1
17
0.9
01
0.7
41
0.6
18
0.4
14
0.2
95
0.1
73
0.0
80
Tab
leen
trie
sar
efo
r20
0ke
Vel
ectr
ons.
The
unit
sfo
ral
lent
ries
are
A.T
heco
lum
nhe
adin
gsar
es≡
sin θ
/λ,i
nun
its
ofA
−1.
Thi
sdi
ffrac
tion
vect
or,s
,is
conv
erte
dto
the
Δk
used
inth
ete
xtby
mul
tipl
icat
ion
by4π
.
A.6 Indexed Single Crystal Diffraction Patterns 703
704 A. Appendix
A.6 Indexed Single Crystal Diffraction Patterns 705
706 A. Appendix
A.6 Indexed Single Crystal Diffraction Patterns 707
708 A. Appendix
A.6 Indexed Single Crystal Diffraction Patterns 709
710 A. Appendix
A.6 Indexed Single Crystal Diffraction Patterns 711
712 A. Appendix
A.7 Stereographic Projections 713
714 A. Appendix
A.7 Stereographic Projections 715
716 A. Appendix
A.8 Examples of Fourier Transforms 717
718 A. Appendix
A.8 Examples of Fourier Transforms 719
720 A. Appendix
A.9 Debye–Waller Factor from Wave Amplitude
Another approach to calculating the Debye–Waller factor, perhaps simplerthan that of Chapter 9, makes use of the phase relationships in the diffractedwave. The instantaneous positions of the atom centers are {ri + δi}, and theintensity, I(Δk), is written as ψ∗ψ :
I(Δk) =∑
i
f∗i e+iΔk·(ri+δi)
∑j
fje−iΔk·(rj+δj) , (A.1)
I(Δk) =∑
i
∑j
f∗i fje+iΔk·(ri−rj)e+iΔk·(δi−δj) . (A.2)
We confine our attention to Bragg peaks where Δk · (ri − rj) = 2πinteger,so the first exponential in (A.2) is 1:
I(Δk) =∑
i
∑j
f∗i fjeiΔk·(δi−δj) . (A.3)
We assume the displacements are small, and expand the exponential in (A.3):
I(Δk) =∑
i
∑j
f∗i fj
(1 + iΔk · (δi − δj) − 1
2[Δk · (δi − δj)
]2). (A.4)
We simplify further by assuming that the differences, δi −δj , average to zerowhen summed over all pairs separated by ri − rj :
I(Δk) = |f |2∑
i
∑j
(1 − 1
2[Δk · (δi − δj)
]2). (A.5)
From (9.162) the isotropic average of [Δk · (δi − δj)]2 is 1/3Δk2(δi − δj)2
so:
I(Δk) = N2|f |2(1 − 1
6Δk2(δi − δj)2
). (A.6)
Following Sect. 9.2.2, we assume that the displacements of the atom centers,δi and δj , are isotropic random variables with a Gaussian distribution and acharacteristic range, δ. The difference, δi −δj , will therefore have an averagerange of
√2 δ, allowing us to simplify (A.6) as:
I(Δk) = N2|f |2(1 − 1
3Δk2δ2
). (A.7)
Approximately, the third factor in (A.7) is the exponential function:
I(Δk) = N2|f |2e−1/3Δk2δ2. (A.8)
The exponential factor in (A.8) is the Debye–Waller factor. It is essentiallythe same as (9.59), but with an additional factor of 1/3 in the exponent. Thederivation of (9.59) was performed in one dimension, so the
⟨x2⟩
in (9.59)corresponds to the average value of x2 along the direction Δk. Equation (A.8)refers to the average of the mean-squared displacement over all directions inspace, δ2. It can be important to specify which average is being reported.
A.10 Review of Dislocations 721
A.10 Review of Dislocations
Structure of a Dislocation
A dislocation is the only line defect in a solid. A large body of knowledgehas formed around dislocations because their movement is the elementarymechanism of plastic deformation of many crystalline materials. In addition,dislocations in semiconducting crystals are sinks for charge carriers. Morethan any other experimental technique, TEM has revealed the structuresand interactions of dislocations.
There are two types of “pure” dislocations. An edge dislocation is theeasiest to illustrate. In Fig. A.2, notice how an extra half-plane of atoms hasbeen inserted in the upper half of the simple cubic crystal. This extra half-plane terminates at the “core” of the edge dislocation line. On the figure isdrawn a circuit of 5 × 5 × 5 × 5 atoms. This circuit, known as a “Burgerscircuit,” does not close perfectly when it encloses the dislocation line. (Itdoes close in a perfect simple cubic crystal, of course, and it also closesperfectly when it is drawn in a dislocated crystal around a region that doesnot contain the dislocation core.) The vector from the end to the start of thecircuit is defined as the “Burgers vector” of the dislocation, b. Dislocationsare characterized by their Burgers vector and the direction of their dislocationline. The magnitude of the Burgers vector parameterizes the strength of thedislocation – dislocations with larger Burgers vectors cause larger crystallinedistortions. The “character” of the dislocation is determined by the directionof the Burgers vector with respect to the direction of the dislocation line. InFig. A.2 the Burgers vector is perpendicular to the dislocation line. This isan “edge dislocation.”
The other type of “pure” dislocation has its Burgers vector parallel tothe dislocation line. It is a “screw dislocation,” and is illustrated in Fig. A.3.Around the core of a screw dislocation, the crystal planes form a helix. Whenwe complete a Burgers circuit in the x-y plane in Fig. A.3, the vector fromfinish to start lies along z. For a screw dislocation, b is parallel to the line ofthe dislocation.
In general, dislocations are neither pure edge dislocations nor pure screwdislocations, but rather have their Burgers vectors at some intermediate an-gle to the line of their cores. These are “mixed dislocations.” Whenever adislocation line is curved, part of the dislocation must have mixed character.An example of a curved dislocation line is shown in Fig. A.4, with labels in-dicating the pure edge and screw parts. All other parts of the dislocation areof mixed character. Notice how the dislocation was made. The crystal wascut in the lower right corner, and the top (gray) atoms were pushed to theleft with respect to the lower (black) atoms. The edge of the cut is the dislo-cation line. A Burgers circuit around any part of this dislocation line alwaysgives the same Burgers vector. Since the dislocation line changes direction,however, the character of the dislocation changes along its line.
722 A. Appendix
Fig. A.2. Edge dislocation in a cu-bic crystal. Dislocation line is par-allel to by, b = a〈100〉, and b is per-pendicular to the dislocation line.
Fig. A.3. Screw dislocation in acylinder of cubic crystal. Disloca-tion line is parallel to bz, b =a〈001〉, and b is parallel to the dis-location line.
A dislocation loop, which is mostly of mixed character, is illustrated inFig. A.5. A planar circular cut is made inside a block of material. The atomsacross this cut are sheared as shown in the figure. The edge of the cut isthe dislocation line. On the left and right edges of this dislocation loop wehave edge dislocations (with b of opposite signs). On the front and back, thedislocation loop has pure screw character (again with b of opposite signs).Everywhere else the dislocation has mixed character.
Strain Energy of a Dislocation (Self Energy)
A dislocation generates large elastic strains in the surrounding crystal, as isevident from Figs. A.2-A.4. The strain in the material in the dislocation core
A.10 Review of Dislocations 723
pure edge
purescrew
displacement(and b)
Fig. A.4. Mixed dislocationin a cubic crystal. Quarter-circle of cut plane is in thelower right. All atoms acrossthe cut are displaced to theleft by b.
Fig. A.5. Left: dislocation loop ina cube of crystal. All atoms acrossthe cut are displaced to the left byb. Right: top view of loop.
(usually considered to be cylinder of radius 5b) is so large that its excessenergy cannot be accurately regarded as elastic energy. Sometimes this “coreenergy” is estimated from the heat of fusion of the crystal. Outside the coreregion, however, it is reasonable to calculate the energy by linear elasticitytheory. It turns out that this total elastic energy in the surrounding crystal istypically an order-of-magnitude larger than the energy of the core region. Ap-proximately, therefore, the energy cost of making a unit length of dislocationline is equal to the elastic energy per unit length of the dislocation.
We have seen how dislocations can be created by a cut-and-shear process.The dislocation line is located at the edge of the cut, and the Burgers vector isthe vector of the shear displacement. We seek the energy needed to make thedislocation this way. First note that the cut itself requires no energy, since theatoms across the cut are properly reconnected after the dislocation is made.The energy needed to make the dislocation is the energy required to make theshear across the cut surface. Think of the cut crystal as a spring. An elasticrestoring force opposes the shear, and this restoring force is proportional tothe shear times the shear modulus, G. The distance of displacement acrossthe cut is b. The elastic energy stored in the crystal is obtained by integratingthe force over the distance, x, of shear for 1 cm of dislocation line:
724 A. Appendix
Eelastic ∝1cm∫0
b∫0
Gxdxdz . (A.9)
Eelastic = Gb2K [J/cm] . (A.10)
Here K is a geometrical constant that depends on the size and shape ofthe crystal (and somewhat on the dislocation character). Neglecting the coreenergy (which is often small), the energy cost of creating a unit length ofedge dislocation is the Eelastic of (A.10).
Dislocation Reactions
Because the self-energy of a dislocation increases as b2, dislocations Burgersvectors that are as small as possible. Figure A.6 shows how to accommo-date two extra half-planes with either one dislocation of b = 2a, or twodislocations, each of b = a. The total elastic energy of a crystal with the twoseparate, smaller dislocations is half as large, however. Big dislocations there-fore break into smaller ones, so single dislocations have the smallest possibleBurgers vector. The lower limit to the Burgers vector is set by the require-ment that the atoms must match positions across the cut in the crystal. Thislower limit is typically the distance between nearest-neighbor atoms. SmallerBurgers vectors are usually not possible, but an exception occurs for fcc andhcp crystals.
a
Fig. A.6. Accommodation ofthe same slip by two disloca-tions or by one dislocation.
Stacking Faults in fcc Crystals
A special dislocation reaction occurs for dislocations on {111} planes in fcccrystals. Figure A.7 shows how the stacking of close-packed planes determineswhether the crystal is fcc or hcp.
The “perfect dislocation” in the fcc crystal has a Burgers vector of thenearest-neighbor separation, b = 1/2[110]. The shifts between the adjacentlayers of the fcc structure are smaller than this, however, and we can obtainthese shifts by creating a “stacking fault” in the fcc crystal. Specifically,assume that we interrupt the ABCABCABC stacking of the fcc crystal andmake a small shift of a {111} plane as: ABCAB|ABCABC. Here we have
A.10 Review of Dislocations 725
A
B
C
A
B
A
a b
c d
Fig. A.7. (a) fcc stacking of close-packed (111) planes; perspective view of threelayers, with the cubic face marked with the square. (b) Stacking of the three typesof (111) planes seen from above. The next layer will be an A-layer, and will locatedirectly above the dark A-layer at the bottom. (c) hcp stacking of close-packed(0001) basal planes; perspective view of three layers. (d) Stacking of the two typesof close-packed planes seen from above. The next layer will be an A-layer, and willlocate directly above the dark A-layer at the bottom.
errored in the stacking by placing an A-layer to the immediate right of aB-layer. The structure is still close packed, but there is a narrow region ofhcp crystal (. . . AB|AB. . . ). This region of hcp crystal need not extend to theedge of the crystal, however. At the boundary of the hcp region we can inserta “Shockley partial” dislocation, which has a Burgers vector equal to the shiftbetween an A and a B-layer. This shift is a vector of the type: a/6〈112〉.
Consider a specific dislocation reaction for which the total Burgers vectorsacross the arrow are equal1:
a/2[110] → a/6[121] + a/6[211] . (A.11)
The energy, proportional to the square of the Burgers vector, is smaller forthe two Shockley partials on the right than the single perfect dislocation onthe left, as we verify by calculating the energies (A.10):
Eperfect
E2partials=
KGa2/4(12 + 12 + 0
)2KGa2/36
(12 + 22 + 12
) =32
. (A.12)
Equation (A.12) shows that it is energetically favorable for a perfect dislo-cation in an fcc crystal to split into two Shockley partial dislocations, whichthen repel each other elastically (as discussed in the next subsection). Thereis, however, a thin region of hcp crystal between these two Shockley partials(the stacking fault), and the stacking fault energy tends to keep the partials
1 The conservation of Burgers vector is equivalent to the fact that a dislocationline cannot terminate in the middle of a crystal, but must extend to the surfaceor form a loop.
726 A. Appendix
from getting too far apart. Equilibrium separations of Shockley partial dis-locations, measured by TEM, are a means of determining the stacking faultenergy of fcc crystals. This stacking fault energy is qualitatively related tothe free energy difference between the fcc and hcp crystal structures.
Stable Arrays of Dislocations
Look again at the atom positions around the dislocation core in Fig. A.2.Inserting an extra half-plane of atoms in the top half of the crystal causescompressive stresses above, and tensile stresses below the dislocation line. Anedge dislocation line, seen on end in Fig. A.8, is marked with a “⊥” symbol.The circles are lines of constant strain.
Fig. A.8. Compression and tension fieldsaround an edge dislocation.
Dislocations interact with each other through their elastic fields, so groupsof dislocations are frequently found in special arrangements. For example, twoedge dislocations with the same Burgers vector repel each other when theyare situated on the same glide plane. When they are close together, theircompression and tensile strains add. The elastic energy increases quadrati-cally with the strain field. It is therefore favorable for the dislocations to moveapart as in Fig. A.9 (cf., Fig. A.6), so there is an elastic repulsion betweenthese two edge dislocations.
repulsion Fig. A.9. Elastic repulsion of two edge disloca-tions on the same glide plane.
The six dislocations on the left of Fig. A.10 are in a stable configuration,however, since the compressive stress above each dislocation cancels partiallythe tensile stress below its neighboring dislocation. Perturbing the disloca-tions out of this linear array increases the elastic energy. The right side ofFig. A.10 shows in more detail the extra half-planes of the six edge disloca-tions in a simple cubic crystal. This dislocation array creates a low-angle tiltboundary between two perfect crystals. This particular example is a sym-metric tilt boundary. Other types of tilt boundaries are possible, as are twistboundaries comprising arrays of screw dislocations. Arrays of (1-dimensional)dislocations are common at 2-dimensional interfaces between different phasesin a material.
A.10 Review of Dislocations 727
Fig. A.10. Stable dislocation structure constitut-ing a small angle tilt boundary.
728 A. Appendix
A.11 TEM Laboratory Exercises
This appendix presents the content of a university laboratory course de-signed to familiarize the new user with the practice of microscope calibra-tion, conventional diffraction and imaging techniques, and energy-dispersivex-ray spectroscopy. In such a course, students have access to the instrumentin three hour sessions. Each laboratory requires 3–4 sessions to complete. Ad-ditional time is required for developing photographic plates, data analysis,report writing, and perhaps specimen preparation.
The alignment, Au, and MoO3 exercises in Laboratory 1 require 2–3 ses-sions. Sample tilting is needed in Laboratory 2 on DF imaging of θ′ precipi-tates, and tilting requires some practice. Laboratory 3 on EDS of θ′ precipi-tates is straightforward, and could perhaps be performed before Laboratory2. Laboratory 4 on dislocations and stacking faults in stainless steel is typicalof physical metallurgy research with conventional TEM. The instructor mayconsider substituting another laboratory on a material more relevant to theresearch interests of the student.
The authors often modify the laboratories – some variations are givenin the Specimen or Procedures sections. Similarly, the alignment proceduresmust be adapted for a particular microscope. The format of these alignmentprocedures, condensed versions of instructions usually found in the micro-scope manufacturers’ manuals, are handy references in the laboratory. Pleaseread the manufacturer’s manuals, however – they are generally well writtenand rich in information.
A.11.1 Preliminary – JEOL 2000FX Daily Operation
Beginning the Session1. Be sure the column vacuum is 1 × 10−4 Pa (blue scale) on the ion gaugebehind the microscope. Alternatively, the “PEG” gauge setting for the vac-uum meter in the lower left panel should be in the green range. If any redlights to the right of the vacuum meter are on, please get help. The “AccelVoltage” and “Filament Ready” lights (left panel) should both be green.2. Adjust the brightness and contrast knobs to the right of the CRT to viewthe CRT. Remove objective and intermediate apertures from the column.3. Before inserting a sample into the column, make sure the goniometer islocked in the zero position and the X and Y translates (page 2 on the CRTscreen) are on zero. Now insert the specimen into the goniometer. The redlight will come on and then turn off. Let this light cycle repeat at least sixtimes before inserting the specimen into the column.4. If necessary, fill the cold-trap with liquid nitrogen using the small plasticfunnel and a styrofoam cup. It holds about two cupfuls of LN. Do not attemptto lift the LN dewar up to the cold-trap. It is usually necessary to use theLN dewar only during the summer when the humidity is high.
A.11 TEM Laboratory Exercises 729
Obtaining a Beam
1. Set accelerating voltage to 200 kV using the white toggle switch on leftpanel (page 1 on CRT screen) and depress “HT ON”. The HT will step upto 200 kV and the “Beam Current” should read approximately 100 μA (darkcurrent). If you need to adjust the high tension, use the <HTS> <RET>command to set the high tension step and use the white toggle switch to setthe value.2. Increase filament heating to “3”; wait 3 minutes. Reach filament saturationby increasing heating at 0.5 step/minute. The filament bias should be about56 as of 8/26/99. Adjust the fine “Bias” for a beam current ≈115 μA with ajust-saturated filament (about 15 μA above dark current).Alignment of the Illumination System1. Use the “Mag 1” button and white toggle “Selector” switch on the rightpanel to select a convenient magnification, maybe 15 kX. Use the “Brightness”knob on the left panel to adjust the beam intensity and the “Shift” knobs onthe left and right panels to center the beam on the screen. Focus the imageusing the “Obj Focus” control. The step switch adjusts the strength of thefocus; 1 is the smallest increment.2. Establish the eucentric position as follows. Set the objective lens currenton page 4 of the CRT to 7.00 (for AHP20L pole piece). Use the small knob (Zcontrol) knob under the rod on the goniometer to focus the specimen. Thisshould be very close to the eucentric position. To further converge on theeucentric position: 1) release the lock on the goniometer and set it to zero,2) tilt the specimen a few degrees and bring the image back to the centerwith the small knob, and 3) return to zero and adjust the focus. Repeat steps1)-3) until the image does not move with tilt in either direction.3. Align filament at about 60 kX with a slightly undersaturated filamentimage using “Gun” button and “Def” knobs (tilt) in right drawer under “De-flector” row of buttons and center the filament image on the screen with the“Shift” knobs (translate) in drawer. The filament image should be symmet-rical. Saturate the filament after aligning.4. Align illumination down the optic axis of the condenser lens system byswitching between “Spot Size 5” and “Spot Size 1” at about 50 kX and cen-tering the beam. Use the “Brightness Shift” knobs to center the beam with“Spot Size 5,” and the “Gun” button and “Shift” knobs in the right drawerfor “Spot Size 1”. Return to spot size 2 when aligned and use “Spot” buttonand “Shift” knobs in right drawer for final adjustment at spot size 2. Thespot size is shown on page 1 of the screen and can be changed by the toggleswitch “Spot Size” on the left panel.5. Using “Spot Size 2” and condenser aperture 2 or 3, center condenser aper-ture and correct condenser astigmatism. Use “Con Stigmator” button and“Def” knobs in right drawer. Use the detail in a slightly undersaturated fila-ment image at >60 kX, and return to saturation after astigmatism correction.
730 A. Appendix
6. Wobble beam tilts by depressing “Image X, Y Wobbler” buttons (eithersingly or together) on right panel. Center beam by depressing “Tilt” buttonin right drawer (under Cond/Def/Adj) and using “Shift” and “Def” buttonsto make the filament image stationary.Alignment of the Imaging System1. Find an area of interest and focus the specimen.2. Establish the voltage center by depressing the “Brit Tilt” button on theleft panel, pushing “HT Wobbler” on the right panel, and adjusting the “Def”knobs on the left and right panels to obtain a stationary image with the beamcentered on the optic axis. Use the highest magnification possible, at least250 kX. Turn off the “Brit Tilt” button after adjustment to save the setting.3. If desired, turn on the TV and the Gatan CCD camera control. To use theTV, flip the “Camera In” button on the CCD camera control unit and focusthe image. Use “Auto Contrast” except for unusual cases. If the TV is white,spread the beam to reduce the electron intensity on the TV camera. TheTV is useful for correcting the objective lens astigmatism. NOTE: Becausefocusing accuracy is better on the large or small phosphorus screens, youmust use them for your negatives to be in focus.4. Correct the objective lens astigmatism by depressing the “Obj Stig” buttonon the left panel and adjusting the “Def” knobs. The X and Y stigmatorsettings can be read on page 6 of the screen. Typical settings for the X andY stigmators are about 0.1 and −0.25, respectively. It is convenient to usethe TV at >500 kX. Adjust objective astigmatism by: 1) focussing the image,2) using one “Obj Stig” knob to make the image as sharp as possible, and3) using the other “Obj Stig” knob to make the image as sharp as possible.Repeat 1–3 until the image is as sharp as possible and goes in and out offocus symmetrically as the objective lens is over and underfocused. You maythen correct astigmatism by seeking the minimum contrast condition usingthe amorphous region near the edge of a hole (using the same steps 1–3 whenthe objective aperture is out).5. Make final adjustments to the specimen tilt, alignment, insert objectiveaperture, touch up astigmatism, etc.Alignment of Diffraction System1. Adjust the beam to fill the screen and insert the selected area aperture(bottom aperture drive) at about 30 kX. Go to diffraction mode by pushing“Diff” button on right panel. Adjust camera length to a reasonable value(≈100 cm) using white toggle “Selector” switch on right panel. Center theillumination and adjust the intensity. Remove the objective aperture.2. Focus the diffraction pattern by inserting the objective aperture and usethe “Diff Focus” knob (right panel) to focus the aperture edge.3. Depress the “Proj” button in the right drawer and use the “Shift” knobsto center the transmitted beam onto the optic axis.
A.11 TEM Laboratory Exercises 731
Taking Photographs
1. Select automatic or manual exposure time on Page 1 of screen. The fullscreen or the small screen can be used to estimate the exposure time. Insertthe small screen by pulling the lever located on the right side of the viewingchamber.3. For automatic plate advance, press “Auto” on the right panel. For manualplate advance, press “Photo” on the right panel after each picture to advancethe next negative.4. The “Photo” light will illuminate when a plate has advanced. When theplate is in position press “Photo” to start the exposure. The film will dropinto the receiving chamber after the exposure.Finishing the Session
1. Return magnification to a relatively low setting (maybe 1 kX), slightlydefocus beam and remove objective and intermediate apertures.2. Turn off the TV and the Gatan CCD camera control.3. Turn down the filament slowly (about one step every 10 sec) until “3,”then turn down continuously to “Off”. Release the HT button.4. If you have adjusted the filament bias, reset it to its original value, slightlylower than at the end of the session.5. Reset X and Y goniometers to zero and center the specimen. The specimenposition (X and Y in 0.001 mm up to 1.0 mm) is shown on page 2 of the CRT.Remove the specimen from the column.6. Exchange film cassettes. It takes about 20 minutes for the vacuum torecover after the plates are exchanged, provided the new cassettes have beenthoroughly evacuated. Please allow time for this in your session.7. Reset number of unexposed plates by typing <FUN 50> <RET>.8. Sign the log book and note any problems, etc.9. Turn down the CRT intensity (right panel), panel light (left panel) andkeyboard light (right drawer).Other Useful InformationThe binoculars are helpful for focussing, correcting the objective lens astig-matism, focussing the objective aperture edge, etc.1. First insert the small screen using the lever to the right of the viewingchamber.2. Adjust the distance between the eyepieces to form a single image.3. Close your right eye and focus your left eye on the screen (focus on thepointer or dirt on the screen) by rotating the ring at the base of the eyepiece.4. Look through both eyes and focus the right eye on the screen by rotatingthe ring at the base of the eyepiece.Aperture Drives
732 A. Appendix
All the aperture drives work the same. An aperture drive is inserted by switch-ing the lever to the left. There are three apertures in a drive (six for thecondenser aperture). A particular aperture is selected by turning the largestouter sleeve CW for smaller apertures and CCW for larger ones. The smallknob on the right and the inner sleeve are the X-Y translates for the aper-tures.If You Get LostIf you are in the image (or diffraction) mode and get lost (i.e., everything goesblack), reduce the magnification (to 2–10 kX), remove the objective and SADapertures, spread out the illumination and look for the beam. (Translate thespecimen if it has grid bars.) If you still can’t find the beam, please get help.
A.11.2 Laboratory 1 – Microscope Proceduresand Calibration with Au and MoO3
The principles of operation and alignment of the transmission electron micro-scope should be learned as soon as possible. This laboratory exercise coversbasic imaging and diffraction, and provides calibration information neededin the later laboratories. The Au and MoO3 exercises are often the first re-warding experiences with a TEM.
A. Camera Constant Determination
Specimen. Polycrystalline Au film evaporated onto a holey carbon film sup-ported on a 200 mesh copper grid. (Such Au samples are available from ven-dors of microscope supplies.)
Measurements. (a) With the microscope at 200 kV and the specimen inthe eucentric position, obtain two focused bright-field (BF) images of thesame specimen area at a medium magnification (∼ 60 kX) using the largestand smallest objective lens apertures. Photograph the corresponding electrondiffraction patterns (with a camera length of ∼ 100 cm) using the double-exposure technique with the objective aperture in to record also the sizesand positions of the two different objective apertures.Explain why the size and position of the objective aperture affects the con-trast in the image.(b) Photograph two selected-area diffraction (SAD) patterns (with a cameralength of ∼ 100 cm) from the same specimen area using the largest and small-est intermediate apertures. Photograph the corresponding BF images, againusing a double exposure with the intermediate aperture in and the objectiveaperture out (and an appropriate magnification) to record the sizes and po-sitions of the intermediate apertures. Also record the objective, intermediateand projector lens currents.Calculate the microscope camera constant (λL) from these results.
A.11 Laboratory 1 – Au and MoO3 733
Explain why the size of the intermediate aperture affects the appearance ofthe diffraction pattern.Procedures for taking images and SAD patterns.(written for the JEOL 2000FX)Starting with a properly aligned TEM in the magnification (Mag) mode, andthe specimen in the eucentric position:
• Focus the image using the objective lens (focus) controls.• Insert the desired SAD aperture and center it.• Go to the SAD diffraction mode (Diff).• Remove the objective aperture (if it was in).• Center the illumination and spread the beam to obtain sharp diffraction
spots.• Focus the spot pattern using the diffraction focus knob. (You can insert
the objective aperture and focus the aperture edge to confirm that the spotpattern is in focus.)
• Center the diffraction pattern on the screen using the projector alignmentknobs in the right drawer.
• Set the exposure to approximately 1/3–1/4 of the full-screen meter reading,and photograph the diffraction pattern. (Alternatively, you may use about3/4 of the small screen reading as an exposure estimate).
• Insert and center the desired objective lens aperture.• Return to the magnification (Mag) mode.• Focus and stigmate the image using the objective lens stigmator controls
(stigmation is required only on the first image). Using the meter reading,photograph the image.
• (Repeat for all magnifications and diffraction patterns.)
Taking Double Exposures. For double exposures, press the photo buttonto start the exposure process, and then press it a second time while the screenis raising. This prevents the film from advancing after the first exposure.When the first exposure is complete, the photo button light comes back on.Press the button again for the second exposure (after setting the desiredexposure time).
B. Astigmatism Correction
Specimen. Same evaporated Au as above.
Procedures. Find a small hole in the holey carbon film that is not coveredwith gold, i.e., the carbon is exposed around the edge of the hole. Go to ahigh magnification (∼ 500 kX) so the granular features in the carbon film arevisible. (You may want to insert a medium-size objective aperture to increasethe contrast from the amorphous carbon. Make sure the aperture is centered!)
View the image on the TV rate camera and correct the astigmatism usingthe stigmator knobs on the microscope. Remove the TV-rate camera, and use
734 A. Appendix
the CCD camera with a simultaneous live FFT display to perform a final cor-rection of the astigmatism. When the astigmatism is corrected, record threeimages on the CCD in overfocused, minimum contrast, and underfocusedconditions. Print these images and their corresponding FFTs, and discusstheir features.
C. Rotation Calibration(written for the Philips EM400T)
Specimen. Molybdenum trioxide on carbon substrates. (MoO3 is formed byheating a Mo wire with an oxygen-acetylene torch in air. Carbon substratessupported on 200 mesh copper grids are passed through the smoke to collectthe MoO3 crystals.)
Experimental Measurements. (a) Find a small crystallite of MoO3 withwell-defined facets. With the magnification (M) and diffraction (D) modes,use the double exposure method to record superimposed BF images of thespecimen and its corresponding SAD diffraction pattern. Repeat this proce-dure on the same crystallite for each magnification (intermediate lens current)in the M mode – magnifications of 10, 13, 17, 22, 28, 36, 46, 60, 80 and 100 kX(10 total). (Note: The most common camera lengths are typically 575 and800 mm.)(b) Record the currents of the objective, diffraction, intermediate and pro-jector lenses (P1 and P2) for each magnification in the M mode, and for thediffraction patterns in the D mode, using the display selector knob in theback panel.
Data Analysis. (a) Using the superimposed BF/SAD images, graph themagnitude and direction of the image rotation as a function of magnification.Comment on the important features of this plot. The crystallography of theMoO3 crystal and its relationship to the diffraction pattern are illustrated inFig. A.11 for a JEOL 100CX microscope. There are errors in these featuresin all four references below, so be careful!(b) Measure the width of the MoO3 crystal and plot the crystal width as afunction of the dial magnification. (A small crystal is required if its edges areto remain in the field of view at high magnification.)(c) On two separate graphs, plot the objective, diffraction, intermediate andprojector lens currents for the magnification (M) and diffraction (D) modes asa function of the dial magnification. Discuss the significance of these graphsfor image magnification and accuracy in SAD.References for Laboratory 1
1. J. W. Edington: Practical Transmission Electron Microscopy in MaterialsScience - 1. Operation and Calibration of the TEM (Philips Technical Library,Eindhoven, Netherlands 1974).
A.11 Laboratory 2 – Diffraction of θ′ Precipitates 735
Fig. A.11. Image rota-tion calibration of JEOL120CX microscope oper-ated at 120 kV. Note abruptchange in image rotation at40 kX.
2. J. W. Edington: Practical Transmission Electron Microscopy in MaterialsScience - 2. Electron Diffraction in the Electron Microscope, (Philips Tech-nical Library, Eindhoven, Netherlands 1974) pp. 11-16.3. G. Thomas and M. J. Goringe: Transmission Electron Microscopy of Ma-terials (John Wiley and Sons, NY 1979) pp. 28-33.4. D. B. Williams: Practical Analytical Electron Microscopy in Materials Sci-ence (Philips Electron Instruments, Inc. Mahwah, NJ 1984) pp. 26-30.
A.11.3 Laboratory 2 – Diffraction Analysis of θ′ Precipitates
This experiment introduces the important methods of electron diffraction anddark-field imaging to determine the identity and orientation relationship ofprecipitates in a matrix. For an introductory laboratory, θ′ precipitates haveproved convenient in size and contrast against the Al matrix. This exercisealso provides experience with sample tilt, which may require a prior session ofpractice. Laboratory 2 couples well with the energy-dispersive x-ray analysisin Laboratory 3, but the two can be performed independently.
Background. The θ′ phase is a metastable precipitate that often formsduring aging of Al-Cu base alloys. It has a tetragonal crystal structure withspace group symmetry I4/mmm and a = 0.404 nm and c = 0.58 nm. Aperspective drawing of the unit cell of the θ′ phase is shown in Fig. A.12. The
736 A. Appendix
unit cell contains four atoms of Al and two atoms of Cu. The θ′ precipitatesform as thin plates on the 100 planes in the Al matrix with the orientationrelationship (001)θ′ ‖ (001)Al and [100]θ′ ‖ [100]Al.
Fig. A.12. Left: Labeled crystal structure of θ′ precipitate. Right: Orientations ofthree variants of θ′ plates in the fcc Al matrix.
The θ′ phase forms as thin plates on all three {001}Al matrix planes.When a thin foil is viewed along a 〈001〉Al orientation, one variant of θ′
phase is face-on, while the other two variants are edge-on and perpendicu-lar to each another (see Fig. A.12). The Al matrix and each variant of θ′
phase each produce a different diffraction pattern. When all three variantsare present within the selected area aperture, all of these diffraction patternsare superimposed. If a small selected area aperture is used, however, it maybe possible to obtain diffraction patterns from only one or two variants ofprecipitate. Figure A.13 shows diffraction patterns for the Al matrix in a〈001〉 orientation, and two variants of the θ′ phase, one face-on along [001]θ′and the other edge-on along [100]θ′. (The diffraction pattern for the thirdvariant of θ′ can be obtained by rotating the [100]θ′ pattern on the lowerright by 90◦.) All three of these patterns can then be superimposed to obtainthe composite diffraction pattern in Fig. A.14. An experimental 〈001〉Al SADpattern containing all three precipitate variants (and also double-diffractionspots) is also shown in Fig. A.14.
The different variants of precipitate can be identified by bringing each ofthe precipitate diffractions labeled 1, 2 and 3 in the composite pattern ontothe optic axis within a small objective aperture, and making a dark-field (DF)image.
Specimen. Electropolished thin foils of Al–4.0 wt%Cu alloy. A sheet of poly-crystalline alloy about 150 μm thick was solution treated for 1 h at 550◦C,quenched into water and aged for 12 h at 300◦C to produce well-developedθ′ precipitate plates. Disks 3 mm in diameter were punched from the sheetand electropolished in a twin-jet Fischione apparatus using a 25 %HNO3–methanol solution at about –40◦C and 15 V.
A.11 Laboratory 2 – Diffraction of θ′ Precipitates 737
Fig. A.13. Indexed 〈001〉 diffraction patterns from fcc Al matrix (left), and twovariants of θ′ precipitates within the Al matrix (right).
Fig. A.14. Composite diffraction pattern from all three variants of θ′ precipitatein Al matrix in [100] zone axis. Left: schematic, Right: experimental SAD.
738 A. Appendix
(Alternative samples: carbon extraction replicas from a medium carbon steel,or pieces of aluminum beverage cans.)
Procedures
(a) Before going to the microscope, photocopy and enlarge the low indexfcc diffraction patterns in the Appendix of this book. On a second set ofdiffraction patterns you should prepare a set of Kikuchi line patterns. To doso, draw straight lines through the low index spots. The line through thespot g should be oriented perpendicularly to the direction g (the direction ofthe spot from the origin). You may want to plot other low-index diffractionpatterns for the θ′ phase using a computer program, if available. Please readsome of the four references below. They contain information about the crystalstructure, morphology, interfacial structure, and growth kinetics of the θ′
phase.(b) Obtain SAD patterns of the matrix and precipitates by tilting the speci-men to low-index orientations such as 〈001〉Al, 〈011〉Al or 〈112〉Al. Use Kikuchiline patterns and indexed diffraction patterns to help you. The 〈001〉Al zoneaxis is the easiest to interpret, so you should try to obtain this orientation.Orient the specimen so that the pattern is exactly on the zone axis. Spreadthe illumination and take long exposures when photographing diffraction pat-terns so the faint precipitate spots will be sharp and visible. You might tryseveral different exposures until you get a feel for the best exposure (typi-cally about 1/4 of the automatic exposure reading). Don’t forget to focus thediffraction pattern!(c) To identify the precipitates in the intermediate aperture that contributedto the SAD pattern, photograph the corresponding BF images using thedouble-exposure technique. You may want to experiment with different sizeapertures, using a large aperture to obtain a pattern from all three θ′ variants,using a smaller aperture to obtain diffraction patterns from only one or twovariants.(d) Photograph DF images of each of the θ′ variants on the three {100}Al
planes. Do this by tilting the incident beam into the position of the pre-cipitate diffraction spot, so the −g diffraction appears on the optic axis.(Avoid the “amateur mistake.”) Also photograph the corresponding diffrac-tion patterns. Record the precipitate diffraction that was used to form theDF image. This can be done by either photographing the beam-stop, or us-ing the double-exposure technique with the objective aperture superimposedon the diffraction pattern for one of the exposures. This record is needed topositively identify each precipitate variant.(e) Identify the θ′ precipitates by fully indexing the diffraction patterns andcorrelating them to the particle morphologies and orientations in the BF andDF images. Your rotation calibration from the previous lab will be usefulhere. Also determine the lattice spacings for the θ′ phase by using the Al
A.11 Laboratory 3 – EDS of θ′ Precipitates 739
diffraction pattern as a standard, with crystallographic data for this phaseprovided in the references.(f) On a 〈001〉 stereographic projection, show the orientation relationshipbetween the θ′ precipitate and matrix. Mark most of the low-index polesfor the precipitate and matrix phases. Diffraction programs that also plotstereographic projections are very useful for this.
References for Laboratory 21. J. M. Silcock and T.J. Heal: Acta Cryst. 9, 680 (1956).2. G. C. Weatherly and R. B. Nicholson: Philos. Mag. A 17, 801 (1968).3. U. Dahmen and K. H. Westmacott: Phys. Stat. Sol. (a) 80, 248 (1983).4. G. W. Lorimer: in Precipitation Processes in Solids (TMS-AIME, Warren-dale, PA 1978) p. 87.
A.11.4 Laboratory 3 – Chemical Analysis of θ′ Precipitates
This laboratory could be performed simultaneously with laboratory 2, since ituses the same specimens of θ′ precipitates in Al–Cu. The present laboratorydemonstrates microbeam chemical analysis with EDS spectroscopy.
Specimen. Same electropolished thin foils of Al–4.0 wt% Cu alloy used inLaboratory 2.
Procedures. (a) Using the same basic probe conditions as in b below, butwith the beam spread over a large area near the edge of the foil, acquire anEDS spectrum with at least 100,000 counts in the Al Kα peak. Assumingthis spectrum represents the average alloy composition, use this spectrum todetermine the k-factor for Al and Cu.(b) Obtain EDS spectra from about 6 different edge-on θ′ plates using thesame probe and counting conditions. Try a small spot size (say 8) for 60 secand work near the edge of the foil, i.e., thin-film conditions. If you need morecounts, switch to a larger spot size (maybe 6) or a longer counting time. Usethe second or third condenser aperture to obtain a well-defined probe.(c) Take bright-field images of each θ′ plate. Use the double exposure tech-nique to show the size and position of the probe on the plate. Use a magni-fication of around 100 kX.(d) Find three edge-on θ′ plates in about the same area (same specimenthickness) but with different plate thicknesses. How do their EDS spectracompare?(e) Choose three plates, one very near the edge of the foil, one slightly furtherin, and the third even further in. How do their spectra compare and why?(f) If you have time, obtain three more spectra on the same precipitate in arelatively thin area with spot sizes of 2, 4, 6 and 8. How does the spot sizeaffect the spectra and why?
740 A. Appendix
(g) If you have time, obtain three spectra along the length of the same pre-cipitate using the same spot size as in b above. What causes the variationamong the spectra?(h) If you still have time, use a spot size of 8 and take a composition profileacross the precipitate/matrix interface. You will need a high magnificationto do this.
References for Laboratory 3same as for Laboratory 2
A.11.5 Laboratory 4 – Contrast Analysis of Defects
This experiment gives experience in defect identification using contrast anal-ysis. The defect type, plane and displacement vector as well as the Burgersvectors of isolated perfect dislocations partial dislocations bounding stackingfaults will be determined. It is more challenging to attempt a full stackingfault analysis as in Sect. 7.12.5.
Specimen. Electropolished thin foils of AISI Type 302 (or 309) fcc stainlesssteel, annealed and lightly cold-rolled. Disks 3 mm in diameter were punchedfrom the rolled sheet and electropolished in a twin-jet Fischione apparatususing a 10 % perchloric acid–ethanol solution at about –15◦C and 30 V.(Alternative samples: Cu–7 %Al sample deformed approximately 5 % in ten-sion, interfacial dislocations on the θ′ plates used in Laboratory 3, misfitdislocations in Si-Ge heterostructures, dislocations in NiAl deformed a fewpercent in tension.)
Procedures
(a) Before going to the microscope, prepare contrast analysis (g ·b) tables fordefect visibility, paying particular attention to low-index orientations such as〈110〉, 〈100〉, 〈112〉, and 〈111〉. Examples of contrast tables are presented inSect. 7.8. The 〈110〉 orientation is particularly good for analysis since manydifferent g vectors are available in this orientation. Other microscopists liketo start with a 〈100〉 orientation, since it is also a convenient starting place fortilting into other zone axes. To identify uniquely the dislocation line directionor Burgers vector, you will need at least two zone axes.(b) Locate isolated planar defects in the foil (either singly or in groups) andimage the same area in a strong two-beam, bright-field (BF) and centereddark-field (DF) condition with s = 0. Try to ensure that the deviation pa-rameter s is identical for the BF and DF images by tilting the foil so thatthe relevant extinction contour passes through the defect(s) to be analyzed.Record the corresponding SAD patterns. Check the crystallographic orienta-tion on either side of the planar defect. If it is different, record both patterns.
A.11 Laboratory 4 – Defect Analysis 741
(c) Continue to image the same defect region under other two-beam BFconditions indicated by the contrast tables prepared in a above. Again, payparticular attention to the deviation parameter to ensure that s ≥ 0. Lookfor evidence of bounding partial dislocations. Record the corresponding SADpatterns.(d) Using additional diffraction conditions (as identified in your contrasttable), image isolated slip dislocations or dislocation pile-ups present in thefoil. Record the corresponding SAD pattern.(e) By trace analysis on an appropriate stereographic projection, identify thedefect planes and slip planes. Arrange the data to show the nature of thedefects and determine the Burgers vectors of all dislocations.
References for Laboratory 41. J. W. Edington: Practical Electron Microscopy in Materials Science Vol-ume 3 - Interpretation of Transmission Electron Micrographs (Philips Tech-nical Library, Eindhoven 1975) pp. 10-55.2. G. Thomas and M. J. Goringe: Transmission Electron Microscopy of Ma-terials (John Wiley and Sons, New York 1979) pp. 142-169.3. P. B. Hirsch, et al.: Electron Microscopy of Thin Crystals (R. E. KriegerPub. Co., Malabar, FL 1977) pp. 141-147, 162-193, 222-275, 295-316.4. P. H. Humphrey and K. M. Bowkett: Philos. Mag. 24, 225 (1971).5. J. M. Silcock and W. J. Tunstall: Philos. Mag. A 10, 361 (1965).
742 A. Appendix
A.12 Fundamental and Derived Constants
Fundamental Constants
� = 1.0546 × 10−27 erg·sec = 6.5821× 10−16 eV·seckB = 1.3807× 10−23 J/(atom·K) = 8.6174× 10−5 eV/(atom·K)R = 0.00198 kcal/(mole·K) = 8.3145 J/(mole·K) (gas constant)c = 2.998× 1010 cm/sec (speed of light in vacuum)me = 0.91094× 10−27 g = 0.5110 MeV·c−2 (electron mass)mn = 1.6749× 10−24 g = 939.55 MeV·c−2 (neutron mass)NA = 6.02214× 1023 atoms/mole (Avogadro constant)e = 4.80 × 10−10 esu = 1.6022× 10−19 coulombμ0 = 1.26 × 10−6 henry/mε0 = 8.85 × 10−12 farad/m
a0 = �2/(mee
2) = 5.292× 10−9 cm (Bohr radius)e2/(mec
2) = 2.81794× 10−13 cm (classical electron radius)e2/(2a0) = R (Rydberg) = 13.606 eV (K-shell energy of hydrogen)e�/(2mec) = 0.9274× 10−20 erg/oersted (Bohr magneton)�
2/(2me) = 3.813× 10−16 eV cm2
Definitions
1 becquerel (B) = 1 disintegration/second1 Curie = 3.7 × 1010 disintegrations/second
radiation dose:1 roentgen (R) = 0.000258 coulomb/kilogramGray (Gy) = 1 J/kG
Sievert (Sv) is a unit of “radiation dose equivalent” (meaning that doses ofradiation with equal numbers of Sieverts have similar biological effects, evenwhen the types of radiation are different). It includes a dimensionless qualityfactor, Q (Q∼1 for x-rays, 10 for neutrons, and 20 for α-particles), and energydistribution factor, N. The dose in Sv for an energy deposition of D in Grays[J/kG] is:
Sv = Q×N×D [J/kG]Rad equivalent man (rem) is a unit of radiation dose equivalent approximatelyequal to 0.01 Sv for hard x-rays.
1 joule = 1 J = 1 W·s = 1 N·m = 1 kg·m2·s−2
1 joule = 107 erg1 newton = 1 N = 1 kg·m·s−2
1 dyne = 1 g·cm·s−2 = 10−5 N1 erg = 1 dyne·cm = 1 g·cm2·s−2
1 Pascal = 1 Pa = 1 N·m−2
1 coulomb = 1 C = 1 A·s1 ampere = 1 A = 1 C/s
A.12 Fundamental and Derived Constants 743
1 volt = 1 V = 1 W·A−1 = 1 m2·kg·A−1·s−3
1 ohm = 1 Ω = 1 V·A−1 = 1 m2·kg·A−2·s−3
1 farad = 1 F = 1 C·V−1 = 1 m−2·kg−1·A2·s41 henry = 1 H = 1 Wb·A−1 = 1 m2·kg·A−2·s−2
1 tesla = 1 T = 10, 000 gauss = 1 Wb·m−2 = 1 V·s·m−2 = 1 kg·s−2·A−1
Conversion Factors
1 A = 0.1 nm = 10−4 μm = 10−10 m1 b (barn) = 10−24 cm2
1 eV = 1.6045× 10−12 erg1 eV/atom = 23.0605 kcal/mole = 96.4853 kJ/mole1 cal = 4.1840 J1 bar= 105 Pa1 torr = 1 T = 133 Pa1 kG = 5.6096× 1029 MeV·c−2
Useful Facts
energy of 1 A photon = 12.3984 keVhν for 1012 Hz = 4.13567 meV1 meV = 8.0655 cm−1
temperature associated with 1 eV = 11, 600 Klattice parameter of Si (in vacuum at 22.5◦C) = 5.431021 A
Neutron Wavelengths, Energies, Velocities
En = 81.81 λ−2 (energy-wavelength relation for neutrons [meV, A])λn = 3955.4/vn (wavelength-velocity relation for neutrons [A, m/s])En = 5.2276×10−6 v2
n (energy-velocity relation for neutrons [meV, m/s])
Some X-Ray Wavelengths [A]
Element Kα Kα1 Kα2 Kβ1
Cr 2.29092 2.28962 2.29351 2.08480
Co 1.79021 1.78896 1.79278 1.62075
Cu 1.54178 1.54052 1.54433 1.39217
Mo 0.71069 0.70926 0.71354 0.632253
Ag 0.56083 0.55936 0.56377 0.49701
744 A. Appendix
Relativistic Electron Wavelengths
For an electron of energy E [keV] and wavelength λ [A]:
λ = h[2meE
(1 +
E
2mec2
)]−1/2
=0.3877
E1/2 (1 + 0.9788× 10−3E)1/2
kinetic energy≡ T = 12mev
2 = 12E 1+γ
γ2
Table A.4. Parameters of high-energy electrons
E [keV] λ [A] γ v [c] T [keV]
100 0.03700 1.1957 0.5482 76.79
120 0.03348 1.2348 0.5867 87.94
150 0.02956 1.2935 0.6343 102.8
200 0.02507 1.3914 0.6953 123.6
300 0.01968 1.587 0.7765 154.1
400 0.01643 1.7827 0.8279 175.1
500 0.01421 1.9785 0.8628 190.2
1000 0.008715 2.957 0.9411 226.3
Index
aberrations, 102, 195, 197, 602, 603– allowed by symmetry, 599– higher order, 602absorption (electron incoherence), 613,
627, 659absorption and thin-film approximation
(table), 212absorption correction, 43, 211– flat specimen, 43– granularity, 47– validity, 47absorption edge, 167accidental degeneracy, 17Ag-Cu interface, 566Aharonov–Bohm effect, 65Al12Mn, 78Al-4wt.% Cu alloy, 255Al-Cu, 735Al-Cu θ′ phase, 268Al-Ge interface, 566Al-Li alloy, 74α boundary, 405amateur mistake, 261, 266, 378, 738amorphous material, 491– one-dimensional, 491analytical TEM, 62, 164anisotropy, elastic, 377, 411, 429anomalous scattering, 132, 462– partial pair correlations, 501antibonding orbitals, 168antiphase boundary, 404– superlattice diffraction, 405aperture angle, 69, 89, 115, 605– optimum, 111apertureless image, 72artificial rays, 69Ashby-Brown contrast, 409astigmatism, 104, 531, 570, 603– correction procedure, 106, 531– salt and pepper contrast, 107atom, 1
– as point, 458atomic displacement disorder, 469atomic form factor, 225– dependence on Δk, 150– destructive interference at angles,
142– effective Bohr radius, 146– electron, table of, 698– electrons and x-rays, 149– model potentials, 144– Mott formula, 149– physical picture, 141– Rutherford, 146– screened Coulomb potential, 144– sensitivity to bonding electrons, 151– shape of atom, 141, 150– shapes of V (r), 150– Thomas–Fermi, 146– x-ray, table of, 693atomic periodicities, resolution of, 82atomic size effect, 477Auger effect, 13, 221autocorrelation function, 2, 459average potential of solid, 613Avogadro constant, 742axial dark-field imaging, 74, 261, 378axial divergence, 26, 430
B2 structure, 244, 567back focal plane, 68, 71background, 57– subtraction and integration, 48backscattered electron image (BEI),
200backscattered electrons, 200bar, 743barn, 743barrier penetration, 589basis vectors, 235beam propagation, 623beam representation, 612beam tilt
746 Index
– coils, 572– dislocation position, 582– HRTEM, 553, 570beams and Bloch waves, 628– normalization, 630beats– acoustic, 627– mathematical analysis, 632– pattern, 632– physical picture, 627becquerel, 742Beer’s law, 205bend contour, 353, 414– Cu-Co, 357– diffraction patterns, 356bending magnets, 21Bethe asymptotic cross-section, 189Bethe ridge, 179Bethe surface, 186, 187biology, 73biprism, 65black cross, 326Bloch waves, 628– amplitudes and dispersion surface,
654– change across defect, 657– channeled, 591– characteristics, 638– energies, 637– orthogonality, 635– propagator, 660– representation, 612– weighting coefficients, 630block diagram of a TEM, 62Blue Boy, 135blue sky, 129Boersch effect, 103Bohr magneton, 742Bohr radius– dependence on Z, 146– effective, 146Born approximation, 139, 224, 619– first, 139– higher order, 139Bose–Einstein statistics, 476boundary conditions, 644Bragg’s law, 3Bragg–Brentano geometry, 26bremsstrahlung– coherent, 59– intensity, 16, 24bright-field (BF) imaging, 68, 71, 337,
353, 542, 547, 649
brightness, 22, 108– compromises, 167– conservation of, 109– electron gun, 113, 605brilliance, 22broadening of x-ray peaks, 2, 6– complement of TEM, 452– dislocation, 452– meaning of size and strain, 452– stacking faults, 444buckled specimen, 353, 420Burgers circuit, 721– in HRTEM image, 84Burgers vector, 362, 565, 721– conservation of, 725– fcc, 366
calorie, 743camera constant, 78– calibration, 78– determination of, 732camera equation, 78camera-length, 78, 88carrier, 83catalyst, 562, 563Cauchy function, 432CCD cameras, 378, 578CdSe, 606center of gravity, 505center of the goniometer, 50channeling, 586characteristic x-ray, 13, 16, 24chemical bonding, 170chemical disorder, 469, 481chemical map, 63chemical short-range order, 481, 485children’s jacks, 264chromatic aberration, 103, 195, 197,
604– importance of thin specimens, 103classical electron radius, 129, 742Cliff–Lorimer factor, 208– calculation, 211– experimental determination, 210coherence, 122coherent bremsstrahlung, 59coherent elastic scattering, 123coherent imaging, 583coherent scattering, 119– forward direction, 142, 503– inelastic, 123, 155– phases, 128column approximation, 446column lengths
Index 747
– distribution, 448– neighbor pairs in column, 450– random termination, 449coma, 603complementarity of BF and DF, 74Compton scattering, 132– incoherence, 133computer control, 601condenser lens– aperture, 88– convergence (C2), 88– spot size (C1), 88constants, 742constructive interference, 3, 119contrast transfer function, 550– damping of, 554– incoherent vs. coherent, 594conventional modes, 71conventional TEM, 79convergence angle control, 207convergent-beam electron diffraction
(CBED), 79, 304– α-Ti, 321, 328, 329– BF disk symmetry, 316– black cross, 326– DF disk symmetry, 316– diffraction group, 316, 317– disk and crystal symmetry, 317– disk intensity nonuniformity, 81– Ewald sphere, 305– FeS2, 327– Friedel’s law, 315– G disk symmetry, 317– Gjønnes–Moodie lines, 325– glide plane, 325– HOLZ lines and lattice parameter,
312– HOLZ radius Gn, 310– illumination, 80– intensity oscillations in disk, 307– point group, 314– positions of disks, 311– – orthorhombic examples, 312– projection diffraction group, 316– sample thickness determination, 307– screw axis, 325– semi-angle of convergence, 306– space group, 322, 325, 327– special positions, 325– symmetric many-beam, 325– unit cell, 309– whole pattern symmetry, 316conversion factors, 743
convolution– commutative property, 464– defined, 431– delta function, 459, 464– example, 432– Gaussians, 432– Lorentzians, 432– of potential and beams, 618– theorem, 435– Voigt function, 433core excitations, table of energies, 178core hole, 170– decay, 164Cornu spiral, 529, 581correlations, 485– short-range, 486costs, 604Coulombic interaction, 181, 593coupled harmonic oscillators, 624, 626,
674Cowley-Moodie method, 672critical angle, 588crystal potential– inversion symmetry, 619– real, 619crystal symmetry elements, 317crystal system notation, 241crystallite sizes– distribution and TEM, 453– Patterson function, 467– TEM and x-ray, 453Cu2O, 152Cu-Co, 412Curie, 742
d-orbitals (shapes), 152damping function, 560dark-field (DF) imaging, 68, 71, 72,
337, 542, 547, 649dead time, 30Debye model, 475Debye–Scherrer, 10Debye–Waller factor, 171, 472, 585, 720– calculation of, 475– concept, 474– conventions, 475deconvolution, 433– Fourier transform procedure, 433– frequency filter, 439– procedure with noise, 438defects, 338δ boundary, 405delta function, 459density, 44
748 Index
density heterogeneity, 497density of unoccupied states, 169density-density correlations, 510depth of field, 89, 115, 604, 605depth of focus, 89, 115detector– analytic TEM, 34– annular dark-field, 584– beryllium window, 33– calorimetric, 34– charge sensitive preamplifier, 36– count rates, 31– dead layer, 32– energy resolution, 30– escape peak, 32– gas-filled proportional counter, 31– intrinsic semiconductor, 32– position-sensitive, 34– quantum efficiency, 30– scintillation counter, 31– Si[Li], 34– silicon drift, 33– solid state, 32– table of characteristics, 31– x-ray, 30deviation parameter, s, 256, 339, 343– effective, 646– Kikuchi lines, 299deviation vector, s, 256, 339– in dynamical theory, 617differential scattering cross-section, 126– inelastic, 183diffraction– beams across defect, 659– coherence, 229– Δk and θ, 229– effect of apertures, 104– electron, 224– fine structure, 264– forbidden diffractions, 238– Fourier transform of potential, 228– frequency and time, 227– incident wave, 226– line broadening, 423– rel-rods, 252– shape factor, 235– structure factor, 235– structure factor rules, 237– translational invariance in plane, 9– vectors and coordinates, 226– wave, 226– wavevectors, 228diffraction contrast, 62, 72, 337
– dynamical– – dislocation, 656– – interface, 656– – stacking fault, 656– dynamical without absorption, 655– null contrast, 359– strain fields, 358diffraction coupling, 166diffraction lens, 88diffraction mode, 70diffraction pattern– background, 57– bcc, 705, 706– chemical composition, 7– crystallite sizes, 9– dc, 707, 708– fcc, 703, 704– hcp, 709–712– indexed powder, 691– internal strains, 6, 427– internal stresses, 428– peak broadening, 6– silicon, 4– size effect broadening, 7, 425diffraction vector, 81diffuse scattering, 457– chemical disorder, 484, 591– displacement disorder, 477– Huang, 478– short-range order (SRO), 488– thermal, 474, 592dilatation, 427dipole approximation, 191dipole oscillator, 128Dirac δ-function, 218, 459Dirac equation, 17Dirac notation, 180dirty dark-field technique, 74disk of least confusion, 102– resolution, 110dislocation, 337, 360, 721– Burgers vector, 721, 741– charge sinks, 721– contrast tables, 740– core, 723– dipole, 368– double image, 374– dynamical contrast, 376, 658– edge, 362, 721– fcc and hcp, 724– g · b analysis, 740– groups of, 726– image width, 374
Index 749
– interactions, 726– loop, 722– mixed, 721– partial, 725– phase-amplitude diagram, 361– plastic deformation, 721– position of image, 361, 373– reactions, 724– screw, 364, 721– self energy, 722– strain field, 726– superdislocation, 368– tilt boundary, 726– weak-beam dark-field method, 378dispersion corrections, 697dispersion surface, 634, 653displacement disorder– dynamic, 469– static, 469divergence– thick hexapole, 599DO19 structure, 566dopant, 597double diffraction– forbidden diffractions, 302– – tilting experiment, 302double exposures, 733double-differential cross-section, 184double-tilt holder, 274drift of sample, 378Duane–Hunt rule, 14dynamical absences– space group, 327dynamical theory– boundary conditions, 644– eigenvalue problem, 671– extinction distances, 671– intuitive approach, 611– multibeam, 618, 669– multibeam and HRTEM, 669– multislice method, 672– phase grating, 671– propagator, 671– vs. kinematical theory, 619, 623
effective deviation parameter, 343effective extinction distance, 343eigenfunctions for electrons, 612elastic anisotropy, 444, 480elastic cross-section– Rutherford, 147elastic scattering, 123electric dipole radiation, 128
electric dipole selection rule, 19, 59electron– holography, 65electron coherence length, 88electron energy-loss near-edge structure
(ELNES), 169electron energy-loss spectrometry
(EELS), 62, 593, 606– background in spectrum, 167– chemical analysis, 191– energy filter, 577– experimental intensities, 185– fine structure, 169, 170– M4,5 edge, 198– magnetic prism, 194– Ni spectrum, 167– nomenclature for edges, 168– partial cross-section, 189– plasmon peak, 167– spectrometer, 165, 586– – monochromator, 606– – aperture, 188– – diffraction-coupled, 166– – entrance aperture, 166, 186– – image-coupled, 166– – parallel or serial, 165– spectrum– – background, 191– – edge jump, 219– – multiple scattering, 192– thickness gradients, 578– typical spectrum, 167– white lines, 167, 171– zero-loss peak, 167, 607electron form factors, table of, 698electron gun– brightness, 108– filament saturation, 86– self-bias design, 85– thermionic triode, 85electron interaction parameter, 558electron mass, 742electron microprobe, 201, 205electron probe size, 207, 208electron scattering– Born approximation, 136– coherent elastic, 136– Green’s functions, 138electron wave probability, 136electron wavelengths, table of, 743electron-atom interactions, 13electronic transition nomenclature, 168electropolishing, 736
750 Index
elegant collar, 135, 152elemental mapping, 38energy, 123energy transfer, 10energy-dispersive x-ray spectrometry
(EDS), 30, 62, 200, 593– artifacts, 213– background, 208– compositional accuracy, 216– confidence level, 216– detector take-off angle, 206– electron trajectories in materials, 200– escape path, 206– hole count, 214– k-factor determination, 739– microchemical analysis, 204– minimum detectable mass (MDM),
216– minimum mass fraction (MMF), 216– practice, 739– quantification, 206– sensitivity versus Z, 165– spectrometer, 205– spurious x-rays, 214– statistical analyses, 216– Student-t distribution, 216– typical spectrum, 205, 219energy-filtered TEM (EFTEM), 577– chemical mapping, 196– diffraction contrast, 196– energy-filtered TEM imaging, 193– instrumentation, 193– spatial resolution, 198equatorial divergence, 26eucentric tilt, 101Everhart-Thornley detector, 203Ewald sphere– and Bragg’s Law, 259– axial dark-field imaging, 261– construction, 257, 258– curvature, 258– dynamical theory, 651– Laue condition, 258– manipulations, 259excitation error, sg , 616– in dynamical theory, 617extended electron energy-loss fine
structure (EXELFS), 170extended x-ray absorption fine structure
(EXAFS), 173extinction distance, 343, 612, 616– and structure factor, 620– effective, 343
– table of, 344extracted particle, 76
factors of 2π, 233, 458, 646Faraday cage, 207fast Fourier transform, 561– deconvolution, 455Fe3Al, 406Fe-Cu (grain boundaries), 507FeCo, 244field effect transistor, 36field emission gun, 86– cold, 86– Schottky, 86filament lifetime, 85fingerprinting, 5first-order Laue zone (FOLZ), 262, 311fission, 153fluorescence correction, 212fluorescence yield, 203flux (in scattering), 125focused ion-beam milling, 214focusing circle, 27focusing strength, 67forbidden diffractions, 238, 242– double diffraction, 302forbidden transitions, 19form factor– electron, 140– – table of, 698– physical picture, 141– x-ray, 131– – table of, 693forward scattering (coherence), 503Fourier transform– bare Coulomb, 146– complex, 436– cutoff oscillations, 438– decaying exponential, 145– deconvolution, 433– Gaussian, 438– Lorentzian, 145, 438– low-pass filter, 438– scattered wave, 140– table of pairs, 717Frank interstitial loop– HRTEM image of, 84Fraunhofer region, 520Fresnel fringes, 581– astigmatism, 107– at edge, 530– focus, 107, 531, 581– spacing, 531Fresnel integrals, 529
Index 751
Fresnel propagator, 533Fresnel region, 520Fresnel zones, 524Friedel’s law, 448, 461– CBED, 315
g · b rule, 362GaAs, 83gas gain, 31Gaussian damping function, 560Gaussian focus, 547, 569Gaussian function, 451Gaussian image plane, 102Gaussian thermal displacements, 720Geiger, 147generalized oscillator strength (GOS),
185, 186geometrical optics, 66Gjønnes–Moodie (GM) lines, 325glass lens, 91– concave, 95– Fermat’s principle, 96– phase shifts, 95– shape of surface, 94– spherical surface, 95goniometer, 25, 274– Bragg–Brentano, 26– circle, 26– TEM sample, 66grain boundary, 407, 565Gray, 742Green’s function, 138– spherical wavelet, 519– wave equation, 532growth ledges, 415Guinier approximation, 504, 506Guinier radius, 506Guinier–Preston zones, 254
HAADF imaging, 62, 583– defocus, 595– electron channeling, 586, 596– electron scattering, 591– electron tunneling, 589– resolution, 594– sample drift, 586– source of incoherence, 584, 585– vs. HRTEM images, 594half-width-at-half-maximum (HWHM),
424hexagonal close packed– interplanar spacings, 55– structure factor rule, 55
hexapole, 598Hf, 605high-resolution TEM (HRTEM), 81– as interference patterns, 83– compensate aberration with defocus,
541– effect of defocus, 539– effect of spherical aberration, 540– experimental, 538– image matching, 555– lens characteristics, 546– microscope parameters, 559– simple interpretations, 567– specimen parameters, 556– total error in phase, 541high-resolution TEM practice– anomalous spot intensities, 578– beam tilt effects, 572– defocus, 569– doubling of spot periodicities, 573– FFTs from local regions, 577– minimum contrast condition, 569– sample thickness, 575– surface layers, 578– use of EELS, 576high-resolution TEM simulations– beam convergence, 560– diffuse scattering, 561– measurement of parameters, 561– microscope instabilities, 560– other helpful programs, 576– procedure, 556– quantifying parameters, 560– size of array and unit cell, 561– specimen and microscope, 568higher-order Laue zone (HOLZ), 262,
311– dynamical absences, 328– excess and deficit lines, 313– lines and lattice parameter, 312hole count, 214holography, 65homogeneous medium, plane wave in,
518Honl dispersion corrections, 131Howie–Whelan–Darwin equations, 617Huang scattering, 478Huygens principle, 522– spherical wave analysis, 523hydrogenic atom, 188
ideal gas, 503illumination angle, 88illumination system
752 Index
– convergence (C2), 88– lenses, 85, 87– point source, 87– spot size (C1), 88image coupling, 166image shift, 603imaging lens system, 88– cross-overs, 100– image inversions, 88imaging mode, 70imaging plates, 35, 378in-situ studies, 64incident plane wave, 136incoherence, 119, 122incoherent elastic scattering, 123incoherent imaging, 583incoherent inelastic scattering, 123incoherent scattering, 122, 583index of refraction, 91indexing diffraction patterns– concept, 4, 274– easy way, 276– indexed patterns, 691– row and column checks, 279– start with diffraction spots, 279– start with zone axis, 276inelastic, 123inelastic electron scattering, 593inelastic form factor, 182, 593inelastic scattering, 10, 123information limit, 551, 604– HAADF imaging, 594insertion device, 21instrument function, 435instrumental broadening, 430integral cross-section, 190integral inelastic cross-section, 220interband transition, 606interface– coherent, 565– crystal-liquid, 576– incoherent, 566– semicoherent, 566intermediate aperture, 76intermediate lens, 70, 88internal interfaces– displacement vector, 384– phase shifts, 384– phase-amplitude diagram, 388internal stress, 428International Centre for Diffraction
Data, 5interphase boundaries, 565
interstitial loop, 407ionization, 13– cross-section, 204isomorphous substitutions, 462isotopic substitutions, 462isotropic averages, 488
JEOL 2000FX, 728JEOL 200CX, 570JEOL 2010F, 61JEOL 4000EX, 553, 570Johansson crystals, 27jump-ratio image, 196
K-B mirror, 29Kikuchi lines– deviation parameter, 299– indexing, 294– Kikuchi maps, 299– Kossel cones, 293– measure of s, 340, 379– origin, 291– sign of s, 299– specimen orientation, 296– visibility, 293kinematical theory– disorder, 457– validity, 224, 339, 347– vs. dynamical theory, 619, 623, 673kinematics of inelastic scattering, 178knock-on damage, 218Kossel cones, 293
l’Hospital’s rule, 249L10 structure, 566LaB6 thermionic electron source, 85laboratory exercises, 728lattice fringe imaging, 543lattice parameter measurement, 49lattice translation vectors– primitive, 230Laue condition, 233– and Bragg’s law, 233– Ewald sphere, 258Laue method, 10– backscatter Laue of Si, 11Laue monotonic scattering, 484, 488Laue zones, 262, 311– symmetry and specimen tilt, 262ledges, 565lens, 194, 534– aberrations, 102, 602– as phase shifter, 534– curvature of glass, 93
Index 753
– double convex, 93– glass, 92– ideal phase function, 534– magnetic, 97– performance criteria, 102, 602– phase transfer function, 543– transfer, 600lens and propagator rules, 534lens design– phase shifts, 95– ray tracing, 93lens formula, 68, 116, 535light in transparent medium, 521line of no contrast, 409, 410liquid crystal, 563, 564lobe aberration, 603Lorentz factor, 40, 42Lorentz force, 599Lorentz microscopy, 63Lorentzian function, 448, 451– second moment divergence, 456
magnetic lens– electron trajectory, 98– focusing action, 99– image rotation, 99, 734– Lorentz forces of solenoid, 98– pole pieces, 97– post-field, 99– rotation calibration with MoO3, 100,
734main amplifier, 37manufacturers (TEM), 65, 167, 214Marsden, 147mass attenuation coefficients, 134– x-ray, table of, 692mass-thickness contrast, 73, 338materials, 1– chemical compositions, 1– crystal structure, 1– diffraction pattern, 2– microstructures, 1matrix C or C−1, 631mean inner potential, 152measured intensities, 45metallic glass, 5, 495metals, cold-worked, 452microchemical analysis, 164microstructure, 1, 61, 337Miller index, 3minimum contrast condition, 569modulation, 83moire fringes, 389, 416
– parallel, 389– rotational, 390momentum transfer, 10monochromatic radiation, 10monochromator, 27– asymmetrically-cut crystal, 28– diffracted beam, 29– electron, 166– incident beam, 29Monte Carlo, 200Moseley’s laws, 18, 217Mossbauer diffraction, 158– chemical sensitivity, 160– form factors, 158– interference with x-ray scattering,
160– resonance and phase, 159Mossbauer spectroscopy, 160Mott formula, 149multi-body spatial correlations, 500multi-lens systems, 69multichannel analyzer, 38multiphonon scattering, 585, 592multiplicity, 44multislice method– accuracy, 581– defocus, 559– deviation parameter, 581– in k-space, 558– microscope parameters, 559– phase shifts in, 538– projected potential, 558– slice thickness, 556
nanocrystal– CeO2 and Pd, 562, 563– Fe-Cu, 445– KI, 563, 564– Ni3Fe, 444nanodiffraction, 76nanostructure, 562, 597nanotube– single-wall carbon, 562, 564nearest-neighbor shells, 490Nelson–Riley lattice parameter
determination, 51neutron– chopper, 153– coherent scattering length, 154– magnetic scattering, 154– mass, 742– moderation, 153– polarized, 154– potential or resonance scattering, 154
754 Index
– reactor source, 153– spallation source, 153– time-of-flight monochromator, 153– transmutation of samples, 154– wavelength, 742NIST SRM, 45Nobel prizes, 2nomenclature– EELS edges, 168– electronic transitions, 168– x-ray, 17, 19non-dipole transitions, 191normal stress, 428normalization of vectors, 277nuclear exciton, 158null contrast condition, 359
objective aperture, 68objective lens, 66– construction, 88– pole pieces, 88optical fiber principle, 586ordering, 486orientation for diffraction, 38orientation relationship– crystallographic, 290– image and diffraction pattern, 89orthogonality condition, 434orthogonality relationships, 615osmium staining, 73
pair distribution function, 496– synchrotron source, 500pair probability (conditional), 486partial cross-section, 189partial dislocation, 391, 725– Frank, 391– Shockley, 391partial pair correlations, 500Patterson function, 446, 457– atomic displacement disorder, 470– average crystal, 469– chemical disorder, 483– definition of, 459– deviation crystal, 469– example, 466– graphical construction, 462– homogeneous disorder, 469– infinite δ series, 464– perfect crystal, 463– random displacements, 471– SRO, 488– thermal spread, 474
Pauli principle, 183peak width vs. Δk method, 441Pearson VII function, 53Peltier cooler, 34pendellosung, 624periodic boundary conditions, 561perturbation theory, 590, 637phase– and materials, 536– of electron wavefront, 517– velocity, 120phase contrast, 62, 338phase errors, 83– constructive interference, 548– lens accuracy, 95phase fraction determination, 45– integrated areas, 48– internal standard method, 48– retained austenite, 48phase grating, 558, 621– approximation, 675phase problem, 462– anomalous scattering, 462phase relationships, 83, 119, 447phase transfer function, 536phase-amplitude diagram, 339, 345,
346, 673– bend contour, 353– dislocation, 361– Fresnel zones, 526– in dynamical theory, 623– interfaces, 384– moire fringes, 388– of white noise, 437– screw dislocation, 369, 373– stacking fault, 395– thickness fringes, 348phase-space transform chopper, 272Philips EM400T, 208Philips EM430, 547phonon, 157, 476, 591– multiphonon scattering, 585, 592– scattering, 123, 157photoelectric scattering, 131π boundary, 405Planck’s constant, 10, 116, 742plasmon, 167, 173– data, table of, 177– lifetime, 175– mean free path, 175, 217– specimen thickness, 175, 218point resolution, 548Poisson ratio, 429
Index 755
polar net, 285polarization correction, 43polarized incident radiation, 47pole-zero cancellation, 37poly-DCH polymer, 78polychromatic radiation, 10polycrystalline Au, 732polymer (liquid crystal), 563, 564Porod law, 508, 515Porod plot, 510– fractal particles, 510– surface area, 510position-sensitive detector, 27– area detector, 35– charge-coupled-device, 35, 578– delay line, 35– imaging plates, 35, 578– measured intensities, 45– pixellated diodes, 35– resistive wire, 34powder average for x-ray diffractometry,
46powder method, 12precipitate– coherency, 408– fringe contrast, 403– image of coherent, 412– incoherent, 413– orientation relationship, 739– semi-coherent, 413– variants, 736principal quantum number, 17principal strains, 428projected potential, 558projector lens, 70, 88– distortion, 276propagator, 532, 558pseudo-Voigt function, 53, 433
quadrupole lens, 106quantum dot, 606quantum efficiency, 30quantum electrodynamics, 13quantum mechanics, 10, 17quantum numbers, 17quasi-elastic, 429
radial distribution function, 172, 495,511
– small-angle scattering, 512radio analogy for HRTEM, 83radius of gyration, 506ray diagram, 66
– for TEM, 114ray tracing, 71, 93real image, 66receiving slit, 26reciprocal lattice, 231– dimensionality, 273– primitive translation vectors, 232reciprocal lattice vectors– fcc, bcc, sc, 234– uniqueness, 232reciprocity– in optics, 595reduced diffraction intensity, 498reduced x-ray interference function, 501refinement methods, 52– constraints, 54– parameters, 52– peak shape, 53reflected waves, 520refractive index, 91rel-disk, 265rel-rods, 252relativistic correction, 116, 743relaxation energy, 477representations in quantum mechanics,
612, 633residual contrast, 364, 369resolution, 110– energy, 166– limit in HRTEM, 112– limit in STEM, 584– optimal, 548– point, 548– point-to-point, 550– state-of-the-art in 2007, 84– vertical, 605resonance scattering, 154Richardson’s constant, 113Rietveld refinement, 52right-hand rule, 275– zone-axis convention, 279roentgen, 742Ronchigram, 602rotating anode source, 24Rutherford cross-section, 147Rutherford scattering, 200– in HAADF imaging, 586, 592Rydberg, 17, 742
sample shape for x-ray diffractometry,46
Sb in Si, 597scanning electron microscopy (SEM),
200, 202, 205
756 Index
scanning transmission electronmicroscopy (STEM), 62, 583, 584
scattered wave, 519scattering– complementarity of different
methods, 153– differential cross-section, 126– phase lag, 522– total cross-section, 127scattering factor– electron, 557scattering potential, 224– time-varying, 155Scherrer equation, 426Scherzer defocus, 550, 570, 582Scherzer resolution, 548, 550– in HAADF imaging, 584Schrodinger equation, 16, 518, 614– Green’s function, 138, 519secondary electron imaging (SEI), 202secondary electrons, 202Seemann–Bohlin diffractometer, 27selected-area diffraction (SAD), 76– spherical aberration, 117selection rule, 59semiconductor device, 605shape factor, 339, 446, 466, 502– and s, 257– column of atoms, 446– definition, 236– envelope function, 250– intensity, 341, 466– rectangular prism, 247– rel-rods, 252– sphere, disk, rod, 253shear strain, 428shielding by core electrons, 19Shockley partial dislocation, 725short-range order (SRO), 481, 485– single crystal, 490– Warren–Cowley parameters, 486Si, 4, 83, 597Si dumbbells, 596Si-Ge superlattice, 597side-centered orthorhombic lattice, 270side-entry stage, 101sideband, 83Sievert, 742SIGMAK, SIGMAL, 190sign of s, 299signal-to-noise ratio, 30simultaneous strain and size broaden-
ing, 440
single channel analyzer, 37single crystal methods, 10single-wall carbon nanotube, 562SiO2, 605size broadening, 424, 446, 456, 467skilled microscopist, 62, 106, 215, 539,
572, 586slit width, 39, 430small-angle scattering, 502– concept, 502– from continuum, 503– Guinier radius, 506– neutron (SANS), 512– Porod plot, 510– x-ray (SAXS), 512solid mechanics, 430solid-solid interfaces by HRTEM, 565Soller slits, 26, 430space group (CBED), 327spectral brilliance, 22spectrum image, 193spherical aberration, 102, 598, 599, 602– and defocus in HRTEM, 102, 539– and underfocus for SAD, 76– correction, 578, 598– effect on SAD, 117– negative, 604– phase distortion, 84spin, 17spin wave scattering, 123spin-orbit splitting, 19spot size control (C1), 207stacking fault, 391, 444– analysis example, 400– asymmetry of images, 666– bounding partials, 397, 399– diffraction peak broadening, 444– diffraction peak shifts, 446– dynamical theory, 660, 663– dynamical treatment, 397– energy, 726– extrinsic/intrinsic rule, 399– graphite, 414– HRTEM image of, 84– kinematical treatment, 391, 395– tetrahedra, 407– top of specimen, 399, 400– visibility, 397– widths in images, 402staining, 73star aberration, 603statistical scatter, 30, 52, 58, 436stereographic projection, 713–716
Index 757
– construction, 282– electron diffraction patterns, 284– examples, 286– Kurdjumov-Sachs relationship, 290– polar net, 285– poles, 282– rules for manipulation, 284, 285– twinning, 288– Wulff net, 285, 713, 716stigmation, 105– procedure, 531, 547, 733– stigmator, 106Stokes correction, 433storage ring, 20strain broadening– distribution of strains, 427, 441, 477– heterogeneity of strains, 477– origin, 426strain fields, 340, 358stray fields, 604strip chart recorder, 455structural image, 544structure factor, 339– and s, 257– and extinction distance, 620– bcc, 240– dc, 4, 240– definition, 236– fcc, 240– hcp, 55– lattice, 241– phase factor, 230– sc, 237– simple lattice, 230sum peak, 37supercell, 556superlattice diffractions, 243, 246– B1 structure, 244– B2 table of, 245– L10-ordered structure, 246– L12-ordered structure, 247symmetry elements and diffraction
groups, 318synchrotron radiation, 20, 191– beamlines, 22– pair distribution function, 500– user and safety programs, 23systematic absences– glide planes, 243– screw axes, 243
take-off angle, 25TEM laboratory practice
– alignments, 729– apertures, 731, 738– eucentric height, 729– film plates and vacuum, 731– JEOL 2000FX, 728– laboratory exercises, 728– preparation, 738– procedures, 732– shutdown, 731– startup, 728– stigmation correction, 730– voltage center, 730– wobbler, 730thermal diffuse scattering, 469, 472thermal field emission gun, 86thermal vibrations, 513thermionic electron gun, 85θ′ precipitate, 735thickness contours, 349– effect of absorption, 352– wedge-shaped specimen, 351thin-film approximation, 208Thomas Gainsborough, 135Thompson scattering, 129three dimensional imaging, 605three-window image, 196through-focus series, 562, 570, 573Ti-Al, 366, 565Ti-Al-Mo alloy, 567tilt of beam or crystal, 559torr, 743total internal reflection, 587total scattering cross-section, 127transfer lens, 600transparency broadening, 430tungsten filament, 85tunneling, 589turbulence of air, 604twin, 416– boundary, 407two-beam BF images, 342– antiphase boundary, 406– contrast of dislocation, 376– dislocation, 363, 370, 371– moire fringes, 391– stacking fault, 397, 402– twin boundary, 407two-beam dynamical theory, 625, 630,
640two-lens system, 70
undulator, 21uniform strain, 477unmixing, 486
758 Index
vacancy, 407– loop, 407valence electrons, 151, 170vector ψ or φ, 632Vegard’s law, 478vertical resolution, 605vibrations, 604videorecording for kinetics, 65void, 408– Fresnel effect, 408Voigt function, 433– second moment divergence, 456voltage center alignment, 571
Warren–Cowley SRO parameters, 486wave amplitudes, 122wave crests, 120– match at interface, 92wave equation– Green’s function, 532wavefront modulations, 621wavelengths– electron, table of, 743– x-ray, table of, 743wavelet (defined), 119, 223wavevector of electron in solid, 614weak phase object, 545weak-beam dark-field method, 378– analysis of, 380– deviation parameter, s, 380– dislocations in Si, 384– g-3g, 378– Kikuchi lines, 379– stationary phase, 381Wehnelt electrode, 85white lines, 167, 171white noise, 437Wien filter, 166wiggler, 21window discriminator, 37wobbling, 572Wulff net, 285, 713, 716
x-ray– absorption, 43– absorption coefficients, table of, 692
– anomalous scattering, 132, 161– – chart, 697– bremsstrahlung, 14– characteristic, 13– characteristic depth, 134– classical electrodynamics of scatter-
ing, 128– coherent bremsstrahlung, 59– Compton scattering, 132– detector, 30– dispersion corrections, 131– electric dipole radiation, 128– energy spectrum, 38– energy-wavelength relation, 15– form factors, table of, 693– generation, 13– line broadening, 423– mapping, 38– mass attenuation (absorption), 134– mirror, 29– near-resonance scattering, 130– notation, 19, 20– photoelectric scattering, 131– scattering, 128– scattering dependence on atomic
number, 131– spectrometer, 34– spectroscopy system, 37– spurious, 213– synchrotron radiation, 20– tube, 23– wavelength distribution, 15– wavelengths, table of, 743
Young’s modulus, 429, 444
Z-contrast imaging, see HAADFimaging, 338, 583
ZAF correction, 211Zemlin tableau, 601zero-loss peak, 167, 607zero-order Laue zone, ZOLZ, 262zero-point vibrations– diffuse scattering from, 476zone axis, 275