Imaging Strain Fields


As we discussed in Chapter 24, bending of the lattice planes causes a change in the diffraction conditions and therefore a change in the contrast of the image. The presence of a lattice defect in the specimen causes the planes to bend close to the defect. The special feature here is that the bending varies not just laterally, but also through the specimen. Since the details of the bending generally depend on the characteristics of the defect, we can learn about the defect by studying the contrast in the TEM image. This simple principle has led to one of the main applications of TEM, namely, the study of defects in crystalline materials. We can claim that our understanding of the whole field of dislocations and interfaces, for example, has advanced because of TEM. We have even discovered new defects using TEM—like the stacking-fault tetrahedron, the faulted dipole, and the multipole.


Strain Field Burger Vector Screw Dislocation Edge Dislocation Dislocation Loop 


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  1. The text by Hirsch et al. summarizes the early work by the Cambridge group including the derivation of equation 26.10.Google Scholar

Background to Dislocations and Interfaces

  1. Amelinckx, S 1964 The Direct Observation of Dislocations, Academic Press New York. A fascinating summary of the early studies by TEM by the man who influenced many. Source of Figure 26.16.Google Scholar
  2. Amelinckx, S 1979 in Dislocations in Solids 2, (Ed. FRN Nabarro), North-Holland New York. If you’re interested in dislocations, there are many other volumes in this set.Google Scholar
  3. Eshelby, JD, Read WT and Shockley W 1953 Anisotropic Elasticity with Applications to Dislocation Theory Acta Metall. 1, 251–9. An early paper on anisotropic elasticity theory (used by Comis).CrossRefGoogle Scholar
  4. Hirth, JP and Lothe, J 1982 Theory of Dislocations, 2nd Ed., John Wiley & Sons New York. The definitive textbook, but not for the beginner. Source for equation 26.8, buckling of the glide plane, etc. Not a TEM book.Google Scholar
  5. Hull, D. and Bacon, DJ 2001 Introduction to Dislocations, 4th Ed., Pergamon Press New York. A great introductory text.Google Scholar
  6. Matthews, JW, Ed. 1975 Epitaxial Growth, Parts A and B, Academic Press New York. Our hero. Unfortunate grammar in the title.Google Scholar
  7. Nabarro, FRN 1987 Theory of Dislocations, Dover Publications New York.Google Scholar
  8. Porter, DA and Easterling, KE 1992 Phase Transformations in Metals and Alloys, 2nd Ed., Chapman and Hall New York.Google Scholar
  9. Smallman, RE 1985 Modern Physical Metallurgy, 4th Ed., Butterworth-Heinemann Boston.Google Scholar
  10. Steeds, JW 1973 Anisotropic Elastic Theory of Dislocations, Clarendon Press Oxford, UK. As readable as this subject can be: written by a microscopist. See also Eshelby et al.Google Scholar
  11. Sutton, AP and Balluffi, RW 1995 Interfaces in Crystalline Materials, Oxford University Press New York.Google Scholar
  12. Wolf, D and Yip, S, Eds. 1992 Materials Interfaces, Atomic-level Structure and Properties. Chapman and Hall New York. A collection of review articles.Google Scholar

Image Simulation

  1. Head, AK, Humble P, Clarebrough LM, Morton AJ and Forwood, CT 1973 Computed Electron Micrographs and Defect Identification North-Holland New York.Google Scholar
  2. Morton, AJ and Forwood CT 1973 Equilibria of Extended Dislocations Cryst. Lattice Defects 4 165–177. TEM of arrays of interacting dislocations (Section 26.11.C).Google Scholar
  3. Humble, P and Forwood, CT 1975 Identification of Grain Boundary Dislocations I and II Phil. Mag. 31, 1011–23 and 1025–48. Simulating images of interfaces.CrossRefGoogle Scholar
  4. Rasmussen, DR and Carter, CB 1991 A Computer Program for Many-Beam Image Simulation of Amplitude-Contrast Images J. Electron Microsc. Techniques 18, 429. Description of Comis, a great program that died with the advances in operating systems.Thölén, AR 1970a Rapid Method for Obtaining Electron Microscope Contrast Maps of Various Lattice Defects Phil. Mag. 22 175–182. Matrix algorithm for more complex geometries.CrossRefGoogle Scholar
  5. Thölén, AR 1970b On the Ambiguity between Moiré Fringes and the Electron Diffraction Contrast from Closely Spaced dislocations Phys. stat. sol. (a) 2 537–550. Applying the algorithm to a network of orthogonal dislocations (Section 26.11.C).Google Scholar
  6. Thölén, AR and Taftø, J 1993 Periodic Buckling of the Lattice Planes in the Thin Regions of Wedge-Shaped Crystals Ultramicrosc. 48 27–35. TEM of buckled specimens: challenging exercise.CrossRefGoogle Scholar

Contrast Theory

  1. Amelinckx, S 1992 in Electron Microscopy in Materials Science, (Eds PG Merli and MV Antisari), World Scientific River Edge NJ. Includes discussion of dislocation strain field relaxing at the surface.Google Scholar
  2. Amelinckx, S and Van Dyck, D 1992 in Electron Diffraction Techniques 2 (Ed. J.M. Cowley), p. 1, Oxford University Press New York.Google Scholar
  3. Ashby, MF and Brown, LM 1963 Diffraction Contrast from Spherically Symmetrical Coherency Strain Phil. Mag. 8 1083–1103 and On Diffraction Contrast from Inclusions Phil. Mag. 8 1649-1676. Ashby-Brown contrast.Google Scholar
  4. de Graef, M and Clarke, DR 1993 Strain Contrast at Crack Tips for in-situ Transmission Electron Microscopy Straining Experiments Ultramicrosc. 49, 354–365. TEM of crack tips: challenging exercise.CrossRefGoogle Scholar
  5. Goringe, MJ 1975 in Electron Microscopy in Materials Science (Eds. U Valdré and E Ruedl), p. 555, Commission of the European Communities Luxembourg. Further discussion of equation 26.10 and much more.Google Scholar
  6. Hirsch, PB, Howie, A and Whelan, MJ 1960 Kinematical Theory of Diffraction Contrast of Electron Transmission Microscope Images of Dislocations and Other Defects Phil Trans Roy Soc. A252 499–529. Early paper you should read, with more on the column approximation.Google Scholar
  7. The original series of papers by H Hashimoto, PB Hirsch, A Howie, MJ Whelan in Proc. Roy. Soc. London A 252 499 (1960), 263 217 (1960), 267 206 (1962), and 268 80 (1962) are strongly recommended.Google Scholar

On the Non-Column Approximation

  1. Howie, A and Basinski ZS 1968 Approximations of the Dynamical Theory of Diffraction Contrast Phil. Mag. 17 1039–1063.Google Scholar
  2. Howie, A and Sworn H 1970 Column Approximation Effects in High Resolution Electron Microscopy using Weak Diffracted Beams Phil. Mag. 31 861–864.Google Scholar


  1. Hughes, DA and Hansen, N 1995 High Angle Boundaries and Orientation Distributions at Large Strains Scripta Met. Mater. 33 315–321. Particularly clear illustration of the value of producing a large specimen area.CrossRefGoogle Scholar
  2. Karth, S, Krumhansl, JA, Sethna, JP and Wickham, LK 1995 Disorder-Driven Pretransitional Tweed Pattern in Martensitic Transformations Phys. Rev. B 52 803–822. Early work considering statistical structural fluctuations on image contrast (in Section 26.10).CrossRefGoogle Scholar
  3. Takayanagi, K, Tanishiro, Y, Yagi, K, Kobayashi, K and Honjo, G 1988 UHV-TEM Study on the Reconstructed Surface of Au(111): Metastable p× pand Stable p × 1 Surface Structure Surf. Sci. 205 637–651. They showed surface dislocations by TEM before they were discovered by STM.CrossRefGoogle Scholar
  4. Tunstall, WJ, Hirsch, PB and Steeds, JW 1964 Effects of Surface Stress Relaxation on Electron Microscope Images of Dislocations Normal to Thin Metal Foils Phil. Mag. 9 99–119. Classic paper on the contrast seen when a screw dislocation intersects a surface.CrossRefGoogle Scholar
  5. Wilkens, M 1978 in Diffraction and Imaging Techniques in Materials Science, 2nd Ed. (Eds S Amelinckx, R Gevers and J Van Landuyt) p.185 North-Holland New York. A detailed analysis of butterflies, lozenges and peanuts (Figure 26.12).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.The University of Alabama in HuntsvilleHuntsvilleUSA
  2. 2.University of ConnecticutStorrsUSA

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