Weak-Beam Dark-Field Microscopy

  • David B. Williams
  • C. Barry Carter


The term ‘weak-beam microscopy’ refers to the formation of a diffraction-contrast image in either BF or DF where the useful information is transferred by weakly excited beams. The DF approach has been more widely used, in part because it can be understood using quite simple physical models. It also gives stronger contrast; we see white lines on a dark gray background. This chapter will be concerned only with the DF approach. Historically, the weak-beam dark-field (WBDF often abbreviated to WB) method became important because under certain special diffraction conditions, dislocations can be imaged as narrow lines which are approximately 1.5nm wide. Equally important is the fact that the positions of these lines are well defined with respect to the dislocation cores; they are also relatively insensitive to both the foil thickness and the position of the dislocations in the specimen. The technique is particularly useful if you are studying dissociated dislocations where pairs of partial dislocations may only be ~4 nm apart and yet this separation greatly affects the properties of the material.


Burger Vector Partial Dislocation Diffract Beam Dislocation Core Bloch Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

The Technique

  1. Cockayne, DJH 1972 A Theoretical Analysis of the Weak-Beam Method of Electron Microscopy [Defectoscopy] Z. Naturf. 27a, 452–460. Derives equation 27.2.Google Scholar
  2. Cockayne, DJH 1981 Weak-Beam Electron Microscopy Ann. Rev. Mater. Sci. 11, 75–95. A review of WB.Google Scholar
  3. Cockayne, DJH, Ray, ILF and Whelan, MJ 1969 Investigations of Dislocation Strain Fields Using Weak Beams Phil. Mag. 20, 1265–1270. The original paper; derives equations 27.10 and 27.15.Google Scholar
  4. Hirsch, PB, Howie, A and Whelan, MJ 1960 A Kinematical Theory of Diffraction Contrast of the Electron Transmission Microscope Images of Dislocations and Other Defects Proc. Roy. Soc. London A 252, 499–529. Always worth another look.Google Scholar
  5. Stobbs, WM 1975 The Weak Beam Technique in Electron Microscopy in Materials Science, vol. II (Eds. U Valdrè and E Ruedl), p. 591–646, CEC Brussels. A masterful review which also compared WB and a Stradivarius.Google Scholar
  6. Stobbs, WM and Sworn, C 1971 The Weak Beam Technique as Applied to the Determination of the Stacking- Fault Energy of Copper Phil. Mag. 24, 1365–1381. WB calculations using anisotropic elasticity.Google Scholar

Some Defects

  1. Carter, CB 1984 What’s New in Dislocation Dissociation? in Dislocations –1984 (Eds. P Veyssière, L Kubin, and J Castaing), p. 227, Editions du CNRS Paris. A 50th birthday review of dissociated dislocations.Google Scholar
  2. Carter, CB and Holmes, SM, 1975 The Study of Faulted Dipoles in Copper Using Weak-Beam Electron Microscopy Phil. Mag. 32 (3), 599–614.Google Scholar
  3. Carter, CB, Mills, MJ, Medlin, DL and Angelo, JE 1995 The 112 Lateral Twin Boundaries in FCC Metals in 7th International Conference Intergranular and Interphase Boundaries in Materials, Lisbon, Portugal. The ‘thickness’ of a plane is important in WB! (Section 27.7.)Google Scholar
  4. Föll, H, Carter, CB and Wilkens, M 1980 Weak-Beam Contrast of Stacking Faults in Transmission Electron Microscopy Phys. stat. sol. (A) 58, 393–407. Discusses the anomalous WB contrast from SFs.Google Scholar
  5. Gerthsen, D and Carter, CB 1993 Stacking-Fault Energies of GaAs Phys. stat. sol. (A) 136, 29–43. An experimentalist’s comparison of WB and HRTEM.Google Scholar
  6. Hazzledine, PM, Karnthaler, HP and Wintner, E 1975 Non-parallel Dissociation of Dislocations in Thin Foils Phil. Mag. 32, 81–97. Used WB to show the unambiguous effect of surfaces on dislocation core splitting: a paper with broad implications for the microscopists.Google Scholar
  7. Wilson, AR and Cockayne, DJH 1985 Calculated Asymmetry for Weak Beam Intrinsic Stacking Fault Images Phil. Mag. A51, 341–354. More on the WB contrast from SFs.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

Personalised recommendations