Abstract
The Huygens principle of physical optics is developed qualitatively, and then quantitatively with Green’s functions. The relationship between phase and potential is developed. Phase shifts of materials and lenses are described, and combined with propagators in the Cowley–Moodie method for high resolution TEM (HRTEM) image simulation. Experimental effects of lens aberrations, specimens, and beam conditions are discussed. The chapter explains how these effects are incorporated into simulations of images, and shows examples of these effects on HRTEM images. Although direct simulations of images are an important part of the work, the chapter also presents methods for working with images directly, and discusses the risks of some types of interpretations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
At distances much greater than the width of the row of scatterers, however, the outgoing waves no longer resemble a plane wave. This distant region is called the “Fraunhofer region.” Independent mathematical treatments of optics have been developed for the Fresnel and Fraunhofer regions, and the intermediate distances from the scatterer are treated only in special cases. Most of this chapter is concerned with the wavefront in the Fresnel region near the scatterer.
- 2.
To ensure the waves remain as plane waves, our diamond crystal is large compared to the wavelength of light, and the regions of scattering are small compared to the wavelength.
- 3.
- 4.
The precise value of R max will later prove unimportant.
- 5.
Fortunately it is not necessary to know the exact functional form of A(2θ) to perform the integration, or the exact value of R max.
- 6.
The fringe contrast also depends on the curvature of the incident wavefront on the specimen, but the effects of focus are easier to see.
- 7.
Note that exp(ikz 2/R)≃exp(ikR), which has no effect on the intensity because \(\exp(\mathrm{i}k R) \*\exp(- \mathrm{i}k R) = 1\).
- 8.
Note the alternative k-space formulation of (11.48): Ψ i+1(Δk)=Ψ i (Δk)∗Q lens(Δk)P f (Δk).
- 9.
Note the alternative k-space formulation of (11.52): \(\varPsi _{i+1} ( \varDelta k ) =\varPsi _{i} ( \varDelta k ) P_{d_{2}} ( \varDelta k ) \ast Q_{\mathrm{lens}} ( \varDelta k )\* P_{d_{1}} ( \varDelta k ) \). For our point source, Ψ i (Δk)=1.
- 10.
In this case, exp(−iW(Δk)) is a constant of modulus 1, so its Fourier transform is a δ-function. The convolution in (11.58) of this δ-function with the ideal lens function, exp{−ik[(x 2+y 2)/f]}, returns the ideal lens function.
- 11.
- 12.
When the scattering is incoherent or inelastic (both can be parameterized as “absorption”), some image contrast is expected when W=0, however.
- 13.
Note that \(\delta ( \varDelta k_{x},\varDelta k_{y} ) \mathrm{e}^{- \mathrm{i}W ( \varDelta k_{x},\varDelta k_{y} ) }= \delta ( \varDelta k_{x},\varDelta k_{y} ) \mathrm{e}^{- \mathrm{i}W ( 0,0 ) }=\delta ( \varDelta k_{x},\varDelta k_{y} ) \).
- 14.
So although bright-field and dark-field images have resolution limitations owing to the finite size of the objective aperture, these conventional methods are a good choice for making images of features larger than those on the atomic scale.
- 15.
This does not occur when astigmatism is present. Seeking this null contrast condition is an excellent way to stigmate the microscope (Sect. 2.7.4).
- 16.
Other aberrations become important as C s→0, however, as discussed in Sect. 12.6.2.
- 17.
There are different horizontal axes in Fig. 11.20—the first crossover is constant at about 0.6 A−1.
- 18.
This is the reciprocal lattice for the unit cell of the simulation. When atom displacements around defects are of interest, this calculational cell is very large, allowing it to include many k-points to approximate the diffuse scattering between the reciprocal lattice points of the perfect crystal.
- 19.
These damping functions have effective apertures in k-space, so an objective aperture can therefore be used to improve image contrast by eliminating some background noise caused by high-order incoherent scattering.
- 20.
It is clearly necessary to know the objective lens defocus and have some idea of the sample thickness, or it may be impossible to know if the atom columns are bright or dark!
- 21.
For STEM operation, a natural alternative to HRTEM is “HAADF imaging,” discussed in Chap. 12.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fultz, B., Howe, J. (2013). High-Resolution TEM Imaging. In: Transmission Electron Microscopy and Diffractometry of Materials. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29761-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-29761-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29760-1
Online ISBN: 978-3-642-29761-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)