Phase contrast and lattice imaging

Phase contrast means that scattered radiation has a phase shift applied to it, and this results in intensity changes that form an image. The basic reason for this can be seen in Fig. 3.7. Normally, scattered radiation is 90° out of phase with the unscattered radiation. The result of recombining them is a phase shift in the transmitted wave but no change in amplitude (Fig. 3.7A). This phase shift is normally described in terms of a refractive index not equal to 1. If the sample is homogenous and all the scatter is in the forward direction, there is no way to affect the phase of one wave and not the other. But if inhomogeneities make the scattered 

In the TEM, the phase shift of scattered waves is a complicated function of defocus and 

The appearance of the image will change in a complicated manner with very small changes in focus. Numerical simulation of the expected image from model structures is a very important part of high resolution electron microscopy (HREM) and this requires accurate determination of all the operating parameters, [40,45,46]. Other factors besides sin( f) that affect image formation and must be taken into account in 

In phase contrast scattered beams are allowed to pass through a large objective aperture and recombine with the unscattered beam to form the image. This would give no contrast if the objective lens was perfect, and perfectly in focus. The lens is not perfect, and often defocused, causing the scattered beams to be phase shifted. 

Mass thickness contrast is generally weak in polymers. Staining, shadowing or decoration methods (Chapter 4) have to be applied to enhance this contrast. Diffraction contrast, produced by the scattering of diffracted beams outside the objective aperture, is limited by radiation damage of crystallinity. This leaves phase contrast, where scattered beams (inside the objective aperture) are phaseshifted and recombined with the unscattered beam. 

The analogous light microscope method uses a phase plate to produce a phaseshift. Defocusing the objective lens is the method used to produce this phaseshift in the electron microscope. The situation is quite complex. The nature of the defocus-phaseshift relation must be well known in order to interpret the resulting images accurately. Phase contrast is always present, but can often be ignored except at high resolution or deliberate defocus [40,49, 63] (Section 3.1.4). 

If the scattered beam is a sharp spot diffracted from a single crystal, the phase contrast image when it is recombined is an image of the crystal lattice. This specialized phase contrast technique is applied to the study of atomic scale structure in crystalline specimens of metals and ceramics. It has only rarely been applied to the study of polymer materials due primarily to their instability in the electron beam. Lattice images have been obtained from radiation stable aromatic molecules, such as the liquid crystalline polymers (Section 5.6). They have shown important information regarding the ordered structure. 

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H(u) is the Fourier Transform of h(r) and is called the contrast transfer function (CTF). u is a reciprocal-lattice vector that can be expressed by image Fourier coefficients. The CTF is the product of an aperture function A(u), a wave attenuation function E(u) and a lens aberration function B(u) = exp(ix(u)). Typically, a mathematical description of the lens aberration function to lowest orders builds on the Weak Phase Approximation and yields the expression ... 

Figure 14.1. Schematic diagram showing the principle of image formation and diffraction in the transmission electron microscope. The incident beam/o illuminates the specimen. Scattered and unscattered electrons are collected by the objective lens and foeused back to form first an electron diffraction pattern and then an image. For a 2D or 3D crystal, the electron-diffraetion pattern would show a lattice of spots, eaeh of whose intensity is a small fraetion of that of the incident beam. In praetiee, an in-focus image has no eontrast, so images are recorded with the objeetive lens slightly defocused to take advantage of the out-of-focus phase-contrast mechanism.

Figure 7 Phase-contrast two-beam STEM lattice image for Au(lOO) crystal using zero-order and 200 reflexions. Lattice spacing is 2.04 A...

A phase difference arises between Woixi) and x ) mainly because of the difference in the path length. As a result, interference fringes (a lattice image) appear in the image. The image contrast is called phase contrast since it owes its origin to the phase difference. For a very thin specimen with an incident beam of unit amplitude, 7q = 1 7g,... 

Figure 2. Transmission electron micrographs of iridium crystallites hosted in NaX (a) and platinum crystallites hosted in ZSM-5 (b). The phase contrast imaging of the zeolite lattices represents an internal scale.

The three commonly encountered contrast mechanisms in TEM imaging are (i) mass-thickness contrast which occurs due to greater absorption or scattering of incident electrons from denser or thicker parts of the specimen (ii) diffraction contrast where crystalline regions of different orientation exhibit different contrast due to the orientational dependence of Bragg diffraction and (iii) phase contrast where phase-shifted waves from the undiffracted and diffracted beams are allowed to interfere and generate lattice fringes. 

Deliberate defocusing enhances phase contrast at lower magnifications but it must be used with caution. If there is only random structure in the specimen, deliberate or accidental defocus may induce clearly visible structure unrelated to the specimen—artifacts. Thomas [59] discussed this in detail for polymer microscopy, quoting several TEM studies of polymers that were dominated by phase contrast artifacts. With care, artifacts can be recognized [63, 64] and phase contrast imaging can be successfully applied to polymer systems (e.g., [65]). Phase contrast at high resolution produces lattice images (see Section 2.4.4 and Section 3.1.5). 

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