Electron Diffraction in the Transmission Electron Microscope

Electron Diffraction in the Transmission Electron Microscope

P.E. Champness

• Publisher: Garland Science
• Year: 2020
• ISBN:
  9781000144642
• Edition: 1
• Topic: Ciencias biológicas
• Subtopic: Bioquímica

This book is a practical guide to electron diffraction in the transmission electron microscope (TEM). Case studies and examples are used to provide an invaluable introduction to the subject for those new to the technique. The book explains the basic methods used to obtain diffraction patterns with the TEM. The numerous illustrations aid the understanding of the conclusions reached.

1 Diffraction and the electron microscope

When we look at a distant street light through a finely woven net curtain or an umbrella we see a pattern of bright spots. This pattern is not an image, it is a diffraction pattern. We see a regular array of spots because the fabric of the curtain or the umbrella also has a regular, periodic weave. The pattern that we see is telling us about the periodicity of the weave and its orientation; if you rotate the fabric about a direction perpendicular to its surface, the pattern of spots will also rotate. We will look at this phenomenon in more detail at the end of the next section.

1.1 How a lens forms a diffraction pattern

We are most familiar with the use of lenses to form a (usually) magnified image of an object; for instance, with a magnifying glass or an optical microscope. However, any converging lens used in this way is also forming a diffraction pattern. What happens can be understood by reference to Figure 1.1. Here we have a periodic object (it could be a piece of net curtaining) placed in front of a converging lens which is illuminated by a parallel beam of monochromatic (single wavelength) light. Some of the light is transmitted undeviated through the object and some is ‘scattered’ (some will also be absorbed). The undeviated light travels parallel to the optic axis of the lens and is focused by the lens so that it passes through the principal focal point F₀ at a distance from the lens equal to the focal length, f. A plane drawn through F₀ perpendicular to the axis is the back focal-plane of the lens (note that there is a conjugate, i.e. optically equivalent, front focal-plane at a distance f from the lens on the object side of the lens). Light scattered at angles ± α by the object will form parallel beams which are focused to points F₁ and F₁’ in the back focal-plane, at a distance from the axis proportional to the angle α. This pattern of spots formed when the transmitted and scattered beams are focused into the back focal-plane is the diffraction pattern. In fact, for an infinite, periodic object such as our net curtain the spots are only formed for rays that are scattered in specific directions (we will learn the rule that governs these directions later). The rays that form the diffraction spots in the back focal-plane go on to form an inverted image in the image plane. If you follow the three rays shown in Figure 1.1 that are emerging from any of the three apertures O₁, O₂ or O₃ of the object, you will find that they end up at the same point in the image (rays from O₁ end up at I₁ for example, as you would expect), each having passed through a different diffraction spot. In other words, information about the object is contained in each diffraction spot. A direct consequence of this effect is that, in order for the lens to form an image of the object (i.e. in order to resolve the weave of the curtain material), at least two diffracted beams should enter the objective lens and be allowed to recombine in the image plane. This principle was first described by Ernst Abbe in the 19th century and is known as the Abbe criterion.

Figure 1.1. Formation of an image and diffraction pattern by a lens from an infinite periodic object. For parallel, monochromatic illumination, the transmitted and diffracted beams are focused into spots, F₀, F₁, F₁’ etc., which form the diffraction pattern in the back focal-plane of the lens at a distance f, the focal length, from the lens. Only three diffraction spots are shown for clarity. The diffracted beams recombine to form a magnified image in the image plane. Note that the image is inverted with respect to the object, but the diffraction pattern is not. In effect, the screen of the electron microscope is in the plane l₁−l₃ in the imaging mode and in the plane F₁−F₁’ in the diffraction mode.

If we explore a little further, we find that there is a definite relationship between the periodicity and orientation of the object and the spacing and orientation of the spots in a diffraction pattern. You can easily see what this relationship is if you hold a set of meshes, net-curtain materials or diffraction gratings of varying periodicity in front of a laser pointer (do NOT look directly into the laser beam) or other small torch and view the diffraction pattern produced on the wall on the opposite side of the room. You will find that the spacing of the diffraction spots is inversely proportional to the object’s periodicity (for instance, if you halve the spacing of the grating or mesh, the spacing of the diffraction spots doubles) and that the separation of the spots produced by the grating or by the weave of the net is perpendicular to the lines of the grating (Figure 1.2). (If you do not have a set of such objects, you can see the size effect by rotating a mesh about the direction of one of the threads, thus effectively shortening the mesh periodicity perpendicular to the direction of rotation. The spacing of the corresponding diffraction spots will increase). What we have been looking at in the diffraction pattern is also known as the reciprocal lattice because of the inverse (reciprocal) relationship it bears to the direct lattice — the object.

Figure 1.2. Optical diffraction patterns taken with a laser and recorded under the same conditions. (a) Pattern from a diffraction grating with spacing 0.126 mm. The lines of the grating were parallel to the length of the page; notice that the row of diffraction spots is perpendicular to this direction. (b) Pattern from a 100-mesh electron-microscope grid, grid spacing 0.25 mm. (c) Pattern from a 200-mesh electron-microscope grid, grid spacing 0.125 mm. (d) Pattern from a 400-mesh electron-microscope grid, grid spacing 0.0625 mm. (e) Diffraction pattern from the rectangular two-dimensional ‘crystal’ shown in (f). Note the reciprocal relationship between the spacings in the objects and the spacing of the corresponding row of diffraction spots. Note also that the row of spots is perpendicular to the grating from which it is diffracted.

1.2 Introduction to diffraction in the TEM

A transmission electron microscope (TEM) consists of a source of electrons (the electron gun) and a series of electromagnetic lenses, as shown in Figure 1.3 (see also Table 1.1). The most critical components of a magnetic lens are the soft-iron pole-pieces which produce an axially symmetric magnetic field for focusing the electrons. The rest of the lens is a magnetic yoke containing the windings for energizing the lens with a d.c. current. By varying this current, the magnetic field, and hence the focal length of the lens, is changed. This ability to change the focal length is one of the most important ways in which magnetic lenses differ from glass ones. Another difference is that, unlike the glass lenses in a light microscope, magnetic lenses in an electron microscope, because of their construction, size and weight, cannot be moved physically with respect to one another in order to focus the image, although the specimen can be moved up or down in the holder to achieve a certain amount of focusing. We will see some other differences between the two types of microscope later.

Figure 1.3. Schematic diagram of the lenses and apertures in a modern TEM. The nomenclature shown for the imaging lenses follows that adopted for FEI/Philips instruments. The nomenclature used by other manufacturers is given in Table 1.1. Note: the scan coils will only be present if the instrument is designed for scanning transmission electron microscopy.

Table 1.1. Nomenclature used by different manufacturers for the imaging lenses in a TEM

FEI/Philips	JEOL	Hitachi
Objective	Objective	Objective
Diffraction	First intermediate	First intermediate
Intermediate	Second intermediate	Second intermediate
Projector 1	Third intermediate	First projector
Projector 2	Projector	Second projector

The specimen is placed in a holder in the front focal-plane of the objective lens (Figure 1.3), i.e. at a distance f in front of the lens. Figure 1.4 shows schematically the ray paths for the imaging system of a TEM that employs three stages of magnification. The magnified image produced by the objective in its image plane serves as an object for t...