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Weak-Beam Dark-Field Microscopy

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Transmission Electron Microscopy

Abstract

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.

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The Technique

  • Cockayne, DJH 1972 A Theoretical Analysis of the Weak-Beam Method of Electron Microscopy [Defectoscopy] Z. Naturf. 27a, 452–460. Derives equation 27.2.

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  • Cockayne, DJH 1981 Weak-Beam Electron Microscopy Ann. Rev. Mater. Sci. 11, 75–95. A review of WB.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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Some Defects

  • 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.

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  • Carter, CB and Holmes, SM, 1975 The Study of Faulted Dipoles in Copper Using Weak-Beam Electron Microscopy Phil. Mag. 32 (3), 599–614.

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  • 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.)

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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Correspondence to David B. Williams .

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Williams, D.B., Carter, C.B. (2009). Weak-Beam Dark-Field Microscopy. In: Transmission Electron Microscopy. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76501-3_27

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