Electron diffraction using transmission electron microscopy

Journal of Research of the National Institute of Standards and Technology, Nov, 2001 by Leonid A. Bendersky, Frank W. Gayle

Electron diffraction via the transmission electron microscope is a powerful method for characterizing the structure of materials, including perfect crystals and defect structures. The advantages of electron diffraction over other methods, e.g., x-ray or neutron, arise from the extremely short wavelength ([approximately equal to]2 pm), the strong atomic scattering, and the ability to examine tiny volumes of matter ([approximately equal to]10 [nm.sup.3]). The NIST Materials Science and Engineering Laboratory has a history of discovery and characterization of new structures through electron diffraction, alone or in combination with other diffraction methods. This paper provides a survey of some of this work enabled through electron microscopy.

Key words: crystal structure; crystallography; defects; electron diffraction; phase transitions; quasicrystals; transmission electron microscopy.

1. Introduction

The use of electron diffraction to solve crystallographic problems was pioneered in the Soviet Union by B. K. Vainshtein and his colleagues as early as the 1940s (1). In the elektronograf, magnetic lenses were used to focus 50 keV to 100 keV electrons to obtain diffraction with scattering angles up to 3[degrees] to 5[degrees] and numerous structures of organic and inorganic substances were solved. The elektronograf is very similar to a modern transmission electron microscope (TEM), in which the scattered transmitted beams can be also recombined to form an image. As the result of numerous advances in optics and microscope design, modern TEMs are capable of a resolution of 1.65 [Angstrom] for 300 kV (and below 1 [Angstrom] for 1000 kV) electron energy-loss combined with chemical analysis (through x-ray energy and electron-loss energy spectroscopy) and a bright coherent field emission source of electrons.

The main principles of electron microscopy can be understood by use of optical ray diagrams (2,3), as shown in Fig. 1. Diffracted waves scattered by the atomic potential form diffraction spots on the back focal plane after being focused with the objective lens. The diffracted waves are recombined to form an image on the image plane. The use of electromagnetic lenses allows diffracted electrons to be focused into a regular arrangement of diffraction spots that are projected and recorded as the electron diffraction pattern. If the transmitted and the diffracted beams interfere on the image plane, a magnified image of the sample can be observed. The space where the diffraction pattern forms is called reciprocal space, while the space at the image plane or at a specimen is called real space. The transformation from the real space to the reciprocal space is mathematically given by the Fourier transform.

A great advantage of the transmission electron microscope is in the capability to observe, by adjusting the electron lenses, both electron microscope images (information in real space) and diffraction patterns (information in reciprocal space) for the same region. By inserting a selected area aperture and using the parallel incident beam illumination, we get a diffraction pattern from a specific area as small as 100 nm in diameter. The recently developed microdiffraction methods, where incident electrons are converged on a specimen, can now be used to get a diffraction pattern from an area only a few nm in diameter. Convergent beam electron diffraction (CBED) uses a conical beam ([alpha] > [10.sup.-3] rad) to produce diffraction disks, and the intensity distribution inside the disks allows unique determination of all the point groups and most space groups -(4). Because a selected area diffraction pattern can be recorded from almost every grain in a polycrystalline material, reciprocal lattices ([equivalent to] crystal structures) and mutual crystal orientation relationships can be easily obtained. Therefore single crystal structural information can be obtained for many materials for which single crystals of the sizes suitable for x-ray or neutron diffraction are unavailable. Such materials include metastable or unstable phases, products of low temperature phase transitions, fine precipitates, nanosize particles etc.

In order to investigate an electron microscope image, first the electron diffraction pattern is obtained. Then by passing the transmitted beam or one of the diffracted beams through a small objective aperture (positioned in the back focal plane) and changing lenses to the imaging mode, we can observe the image with enhanced contrast. When only the transmitted beam is used, the observation mode is called the bright-field method (accordingly a bright-field image), Fig. 2a. When one diffracted beam is selected (Fig. 2b), it is called the dark field method (and a dark field image). The contrast in these images is attributed to the change of the amplitude of either the transmitted beam or diffracted beam due to absorption and dynamic scattering in the specimens. Thus the image contrast is called the absorption-diffraction, or the amplitude contrast. Amplitude-contrast images are suitable to study mesoscopic microstructures, e.g., precipitates, lattice defects, interfaces, and domains. Both kinematic and dynamic sc attering theories are developed to identify crystallographic details of these heterogeneities (2,3).

It is also possible to form electron microscope images by selecting more than two beams on the back focal plane using a large objective aperture, as shown in Fig. 2c. This observation mode is called high-resolution electron microscopy (HREM). The image results from the multiple beam interference (because of the differences of phase of the transmitted and diffracted beams) and is called the phase contrast image. For a very thin specimen and aberration-compensating condition of a microscope, the phase contrast corresponds closely to the projected potential of a structure. For a thicker specimen and less favorable conditions the phase contrast has to be compared with calculated images. Theory of dynamic scattering and phase contrast formation is now well developed for multislice and Bloch waves methods (5). HREM can be used to determine an approximate structural model, with further refinement of the model using much higher resolution powder x-ray or neutron diffraction. However, the most powerful use of HREM is in determining disordered or defect structures. Many of the disordered structures are impossible either to detect or determine by other methods.