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Figure 21 The geometry of an electron detection system. Electrons which are deflected through an angle greater than 0 after passing through the specimen are not registered by the detector and have thus effectively been 'absorbed' in this experiment. cross-section for scattering through 0 or more is tra then it is possible to describe absorption using the conventional Lambert Beer law. The equation is This describes the fractional intensity, q which remains after absorption in a thickness .v. N...

D dft x il u51

And is obtained from the thin lens formula, equation 1.1. The objective lens of focal length o is used to further demagnify the filament image, producing a probe of diameter d on the surface of the specimen, which is a distance vn below the objective lens. The distance is known as the working distance (WD) of the microscope. The diameter of the final probe on the specimen is then It can be seen that if the strength of the condenser lens is increased, v decreases, and the intermediate beam...

CiSsza514

Now the signal that is detected in the SEM is not a continuous signal, but for each pixel is derived from Ihe number of secondary electrons n arriving at the detector in a lixed time period. Because Uiese events are randomly distributed in lime, simple statistical theory tells us that if Ihe average number of electrons detected from a particular point on the specimen is h then h will vary by an amount up to n about the mean. The noise N is then defined as y n. In a real situation therefore, the...

061x

Equation 1.1 can be differentiated (for constant focal length) to give This shows that di the effective shift in image position, is related to du, the change in position of I he object, via the square of the magnification. The negative sign arises because the shifts are in opposite directions, which does not concern us. Thus if du is set lo be the depth of held, calculated perhaps from equation 1.5, the equivalent depth of focus is a faclor M bigger. At any reasonable magnification the depth of...

Electron microscopy and other techniques

Wc have described in earlier chapters the basic techniques of scanning and transmission microscopy and diffraction. There are now many other techniques available for characterizing materials, each of which has some special advantage. In this final chapter an attempt is made to outline some of the most important techniques which can be used to complement electron microscopy and to point out the areas of overlap between the techniques. We also try to indicate how electron microscopy is...

Specimen

Figure 7.2 A very simplified diagram of a scanning tunneling microscope (STM). As the tip is scanned across the specimen surface the tunnelling current (i) is modified. A feedback system is used to maintain the current, and hence the gap, at the same value, The tiip thus follows the surface contours and its vertical displacement can be used to map the surface topography on a very fine scale. vertical displacement of the tip as the specimen is scanned and is similar in many ways to a...

8

The lKLIvr and 'spdF descriptions of the 16 lowest energy states, together with the number of electrons which each can hold. These stales are not neeessariJy occupied by electrons. A very light element such as helium, which only has two electrons, will have electrons in its K shell only and its L, M and higher shells will be empty. Uranium, with an atomic number of 92 and hence 92 electrons, has electrons in the K, L, M, N O, P and Q shells. This nomenclature is defined and explained...

7172

If higher magnifications are required it is quite straightforward lo add a second projector lens Lo provide a third stage of magnification. Figure 1.3 The ray diagram of a simple two-stage projection microscrope, The object is at O and the final image at C, with an intermediate image at B. Figure 1.3 The ray diagram of a simple two-stage projection microscrope, The object is at O and the final image at C, with an intermediate image at B.

D d x V2U2 d x WDju2

Figure 5.12 Scanning of the electron beam by two sets of coils so that the beam always passes through the optic axis of the objective lens. may be seen from Figure 5.11, not all of Lhe electron beam which passes through the condenser lens can enter Lhe objective lens. If lhe semi-angle of the rays leaving the condenser lens is o q, and Lhe semi-angle of the rays entering the objective lens is ot , then the current in lhe final probe is The current therefore decreases as the condenser lens...

30

Figure 6.2 The depth from which X-rays are produced in a speci men as a function of the electron energy, the nature of the X-rays being detected, and the composition of the matrix. where P is about 10for materials with medium average atomic mass. To illustrate this point, Figure 6.2 shows the depth from which CuK3 and AlK X-rays may be produced by electrons in an Al-Cu alloy in which the major element is either aluminium or copper. If X-ray fluorescence occurs, then the sampling volume may...

Electrons and their interaction with the specimen

When thinking about light microscopy we tend to ignore most of the interactions between the Jight and I he specimen. It is sufficient that enough light is transmitted through or reflected from the specimen that the image can easily be seen. The assumption is generally made that the specimen is unchanged by the fact that it has been observed and for most specimens this is a reasonable assumption. However, the interaction of electrons with the material through which they pass may have more...

264

Distances and large active detector areas, cither scintillator or solid state, are desirable. Although we may be able lo detect two phases in a specimen, we may not he able to do so with very good spatial resolution, because, as we saw in section 5,5, and Figure 5,16, the ultimate resolution of the instrument is dependent on the contrast. Having calculated the atomic number contrast from equation 5,23, we can insert this value into equations 5.13 and 5.20, and hence calculate the spatial...

Ww

Planes with d 0 08934 nm and election wavelength 0 00164nm (accelerating voltage 400 kV). 3 What do you expect to happen to an electron diffraction pattern as the accelerating voltage is increased 4 What are the five lowest-index diffracting planes for (a) a primitive cubic crystal (atom position 0 0 0 ), and (b) a body centred cubic crystal (atom positions 0 0 0H0-5 0-5 0-5 . 5 The sum of the indices of the spots in a diffraction pattern taken with the incident electron beam parallel to 111...

Tem

Williams, LI B. and Carter, C B. (1996) Transmission Electron Microscopy A Textbook for Materials Science. New York Plenum Press, Chescoe, D. and Good hew, P. J. (1990) The operation of transmission and scanning microscopes', Royal Microscopical Society Handbook 20. Oxford BIOS. Goodhew, P. J. (1985) Thin foil preparation for electron microscopy', in A. M. Glauert (ed.) Practical Methods in Electron Microscopy, Vol. II, Amsterdam Elsevier. Keyse, R. J., Garratt-Reed, A. J., Goodhew. P, J. and...

B

Figure i.12 Ray diagram illustrating the introduction of chromatic aberration by a single lens. Light of shorter wavelength (blue) is brought to a focus nearer the lens than the longer wavelength (red) light. The smallest 'focused' spot is the disc of least confusion at C. formed. With the screen at lhe compromise position C lhe smallest image is formed, but it is not a point but a disc of cast confusion. All aberration corrections are designed to reduce in size this disc of confusion. In the...

The transmission electron microscope

In Chapter 2 most of the essential parts of a TE M were described. The illumination is provided by an electron gun while the lenses are all electromagnetic and work as described in section 2.4. The remaining necessary components are a viewing screen - usually a simple layer of electron-fluor scent material, viewed through a lead glass window and a camera, which must work in the vacuum within the microscope. These components are assembled into a vertical 'microscope column' of which a typical...

Small Crystalline Particles

These may differ from the matrix in which they are embedded in atomic mass, lattice parameter, crystal structure or orientation. They may also strain the matrix in rather the same way as a dislocation, bending lattice planes. Any one of these effects could be used to form an image of the particles and their Figure 43i Braiding of a 440 extinction contour in a large-angle CBED pattern as it crosses a i 2 IIO dislocation (arrowed) in a diamond specimen. The number of fringes gives g-fo I....

W

Figure 3.17 (a) Ray diagram showing the geometry of Kikuchi lines (see text for details). ( > )The intensity of inelastic scattering when Kikuchi lines are produced. increases, and, as discussed above, the intensity of the diffraction spots decreases as the specimen thickness increases. Figure 3.18 ) shows an example of Kikuchi lines and diffraction spots. It may be seen from Figure 3.17 that the Kikuchi lines are symmetrically astride the diffracting pJanes, and if the specimen is tilted,...

11

Figure 4.20 Schematic diagram showing the two extreme types of planar defect, (a) In a displacement fault the orientation of the crystal is identical on both sides of the fault and thus s is unchanged, (fa) in an orientation fault s changes across the fault since the imaging planes are slightly tilted. In both cases the lattice may be displaced at the fault and thus in general R changes from zero to some finite value, interference between the beams diffracted in the upper part of the crystal...

A

1 Under focus smallest convergence angle), in focus, over foe us (largest convergence angle) 3 Decreasing the focal length of CI increases the convergence angle and demagnification of the electron source, i.e. il decreases the spol size a I the specimen. If C2 is not adjusted, it also increases the convergence at the specimen 4 From equation 3.4, the Bragg angle of the 002 beam is 10-28 mrad. For a parallel beam of electrons, this diffracted beam will be 10-28 jam away from the undeflected beam...

Microscope Used By Civil Engineers

Figure 5.32 Secondary electron micrographs of a nylon fabric, (o) Uncoated specimen showing image degradation due to microdischarges. (b) A similar specimen after coating with 10 nm of gold in a sputter unit. thus increases and the beam energy moves towards EV There is therefore a self-compensating effect which stabilizes the beam energy close to Because the scattering coefficients are strong functions of the surface till, it may not be easy to eliminate charging from all regions of the sample...

Vj

Figure 4.33 Two images of the same region of an aluminium specimen containing small helium bubbles, (o) in dynamical conditions the cavities appear bright against dark regions of the extinction contour and dark against bright regions, (b) In kinematic conditions the cavities are very slightly brighter than the background but are more visible when, as here, the image is very slightly out of focus and each bubble is surrounded by a dark fringe, the width of a dislocation image obtained with v...

200 300 400 500 600 700

Figure 6.20 Part of an EEL spectrum from boron nitride (BN)h showing the boron and nitrogen K edges. Figure 6.21 A schematic EELS edge showing the energy window A over which the integrated edge intensity is measured. The background is fitted to the region B and then extrapolated as shown by the dashed line. Figure 6.21 A schematic EELS edge showing the energy window A over which the integrated edge intensity is measured. The background is fitted to the region B and then extrapolated as shown by...

Apfim 226

Astigmatism 16, 76 atom columns 78, 107 atom imaging 217, 220, 222 atomic force microscopy (AFM) 216,21719 contrast 78, 100, 148 effect (Z) 201-2 scattering factor 30 atom milling 114-16 atom probe (APFIM) 226 Auger electron 35, 37, 125 emission 35 microscopy 230 spectroscopy 36, 230-1 yield 37 autobias 25 back focal plane 71, 72, 76 background 199, 209, 211 backscatter 32, 33, 34, 37, 126, 189, 196 coefficient 128, 141, 146 detector 130 images 132, 147, 150, 171 signal 127 barrel distortion 16...

M

Figure 4.25 o The case of a boundary between dissimilar materials iin the plane of the specimen. The displacement vector R increases away from the origin O. b The formation of moir fringes when the operating planes in the two crystals are parallel, c An image showing moir fringes in a specimen of Pd Si on silicon. N. A. McAuley Figure 4.25 o The case of a boundary between dissimilar materials iin the plane of the specimen. The displacement vector R increases away from the origin O. b The...

Stem

Figure 2.12 The family of electron microscopes. The two basic imaging systems SEM and TEM are shown in tlie centre. The addition of further detectors or lenses can give each microscope a range of analytical capabilities. X X-ray detector E electron detector. Lhe TEM needs objective and projector lenses and a viewing screen. From these two basic arrangements all the other microscopes to be described in this book have developed. The SEM becomes a microprobe analyser EPMA when an X-ray detector is...

06r

Which implies a resolution of about 0 02 nm, using reasonable values of A 0-0037 nm the wavelength of 100 kV electrons and a 0.1 radians about 5 degrees . This is much smaller than the size of a single atom. Unfortunately, however, in the transmission electron microscope TEM this sort of resolution cannot be obtained because of the lens aberrations. Whereas in a light microscope it is possible Lo correct both chromatic and achromatic aberrations by using subLle combinations of lenses, this is...