Volume 106, Number 6, November–December 2001 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 106, 997–1012 (2001)] Electron Diffraction Using Transmission Electron Microscopy Volume 106 Number 6 November–December 2001 Leonid A. Bendersky and Frank Electron diffraction via the transmission combination with other diffraction methods. W. Gayle electron microscope is a powerful This paper provides a survey of some of method for characterizing the structure of this work enabled through electron mi- National Institute of Standards and materials, including perfect crystals and croscopy. Technology, defect structures. The advantages of elec- tron diffraction over other methods, e.g., Gaithersburg, MD 20899-8554 Key words: crystal structure; crystallog- x-ray or neutron, arise from the extremely raphy; defects; electron diffraction; phase ഠ short wavelength ( 2 pm), the strong transitions; quasicrystals; transmission [email protected] atomic scattering, and the ability to exam- electron microscopy. ഠ 3 [email protected] ine tiny volumes of matter ( 10 nm ). The NIST Materials Science and Engineer- ing Laboratory has a history of discovery Accepted: August 22, 2001 and characterization of new structures through electron diffraction, alone or in Available online: http://www.nist.gov/jres 1. Introduction The use of electron diffraction to solve crystallo- atomic potential form diffraction spots on the back focal graphic problems was pioneered in the Soviet Union by plane after being focused with the objective lens. The B. K. Vainshtein and his colleagues as early as the 1940s diffracted waves are recombined to form an image on [1]. In the elektronograf, magnetic lenses were used to the image plane. The use of electromagnetic lenses al- focus 50 keV to 100 keV electrons to obtain diffraction lows diffracted electrons to be focused into a regular with scattering angles up to 3Њ to 5Њ and numerous arrangement of diffraction spots that are projected and structures of organic and inorganic substances were recorded as the electron diffraction pattern. If the trans- solved. The elektronograf is very similar to a modern mitted and the diffracted beams interfere on the image transmission electron microscope (TEM), in which the plane, a magnified image of the sample can be observed. scattered transmitted beams can be also recombined to The space where the diffraction pattern forms is called form an image. As the result of numerous advances in reciprocal space, while the space at the image plane or optics and microscope design, modern TEMs are capa- at a specimen is called real space. The transformation ble of a resolution of 1.65 Å for 300 kV (and below 1 Å from the real space to the reciprocal space is mathemat- for 1000 kV) electron energy-loss combined with chem- ically given by the Fourier transform. ical analysis (through x-ray energy and electron-loss A great advantage of the transmission electron micro- energy spectroscopy) and a bright coherent field emis- scope is in the capability to observe, by adjusting the sion source of electrons. electron lenses, both electron microscope images (infor- The main principles of electron microscopy can be mation in real space) and diffraction patterns (informa- understood by use of optical ray diagrams [2,3], as tion in reciprocal space) for the same region. By shown in Fig. 1. Diffracted waves scattered by the inserting a selected area aperture and using the parallel 997 Volume 106, Number 6, November–December 2001 Journal of Research of the National Institute of Standards and Technology Fig. 1. Optical ray diagram with an optical objective lens showing the principle of the imaging process in a transmission electron micro- scope. Fig. 2. Three observation modes in electron microscope using an objective aperture. The center of the objective aperture is on the incident beam illumination, we get a diffraction pattern optical axis. (a) Bright-field method; (b) dark-field method; (c) high- from a specific area as small as 100 nm in diameter. The resolution electron microscopy (axial illumination). recently developed microdiffraction methods, where in- cident electrons are converged on a specimen, can now It is also possible to form electron microscope images be used to get a diffraction pattern from an area only a by selecting more than two beams on the back focal few nm in diameter. Convergent beam electron diffrac- plane using a large objective aperture, as shown in Fig. tion (CBED) uses a conical beam (␣ >10Ϫ3 rad) to pro- 2c. This observation mode is called high-resolution elec- duce diffraction disks, and the intensity distribution in- tron microscopy (HREM). The image results from the side the disks allows unique determination of all the multiple beam interference (because of the differences point groups and most space groups [4]. Because a se- of phase of the transmitted and diffracted beams) and is lected area diffraction pattern can be recorded from called the phase contrast image. For a very thin speci- almost every grain in a polycrystalline material, recipro- men and aberration-compensating condition of a micro- cal lattices (≡crystal structures) and mutual crystal ori- scope, the phase contrast corresponds closely to the entation relationships can be easily obtained. Therefore projected potential of a structure. For a thicker specimen single crystal structural information can be obtained for and less favorable conditions the phase contrast has to be many materials for which single crystals of the sizes compared with calculated images. Theory of dynamic suitable for x-ray or neutron diffraction are unavailable. scattering and phase contrast formation is now well de- Such materials include metastable or unstable phases, veloped for multislice and Bloch waves methods [5]. products of low temperature phase transitions, fine pre- HREM can be used to determine an approximate struc- cipitates, nanosize particles etc. tural model, with further refinement of the model using In order to investigate an electron microscope image, much higher resolution powder x-ray or neutron diffrac- first the electron diffraction pattern is obtained. Then by tion. However, the most powerful use of HREM is in passing the transmitted beam or one of the diffracted determining disordered or defect structures. Many of beams through a small objective aperture (positioned in the disordered structures are impossible either to detect the back focal plane) and changing lenses to the imaging or determine by other methods. mode, we can observe the image with enhanced con- Other major advantages in using electron scattering trast. When only the transmitted beam is used, the ob- for crystallographic studies is that the scattering cross servation mode is called the bright-field method (ac- section of matter for electrons is 103 to 104 larger than cordingly a bright-field image), Fig. 2a. When one for x rays and neutrons, typical wavelengths (ഠ2 pm) diffracted beam is selected (Fig. 2b), it is called the dark are one hundredth of those for x rays and neutrons, and field method (and a dark field image). The contrast in the electron beam can be focused to extremely fine these images is attributed to the change of the amplitude probe sizes (ഠ1 nm) [2]. These characteristics mean of either the transmitted beam or diffracted beam due to that much smaller objects can be studied as single crys- absorption and dynamic scattering in the specimens. tals with electrons than with other radiation sources. It Thus the image contrast is called the absorption-diffrac- also means a great sensitivity to small deviations from tion, or the amplitude contrast. Amplitude-contrast im- an average structure caused by ordering, structural dis- ages are suitable to study mesoscopic microstructures, tortions, short-range ordering, or presence of defects. e.g., precipitates, lattice defects, interfaces, and do- Such changes often contribute either very weak super- mains. Both kinematic and dynamic scattering theories structure reflections, or diffuse intensity, both of which are developed to identify crystallographic details of are very difficult to detect by x-ray or neutron diffrac- these heterogeneities [2,3]. tion. 998 Volume 106, Number 6, November–December 2001 Journal of Research of the National Institute of Standards and Technology In addition, modern transmission electron micro- The discovery of the icosahedral phase triggered a scopes provide a number of complementary capabilities period of very active research in the new field of qua- known as analytical electron microscopy [6]. Different sicrystals. Many NIST researchers contributed actively detectors analyze inelasticly scattered electrons (Elec- in the early stages, and TEM played an important role in tron Energy-Loss Spectroscopy, or EELS), excited elec- many aspects of this activity. Shortly after the Shecht- tromagnetic waves (Energy Dispersion Spectroscopy, or man et al. publication, L. Bendersky discovered a differ- EDS) and Z-contrast that provide information on chem- ent type of quasiperiodic structure—the decagonal ical compositions and local atomic environments. Such phase with a 10-fold rotation axis, which has an appar- information, when combined with elastic electron dif- ent 10/mmm point group (Fig. 3) [8]. Electron diffrac- fraction, is important in determining structural models, tion analysis of this Al80Mn20 rapidly quenched alloy especially when a material consists of multiple phases. showed that the decagonal phase has a structure of two- In the following sections, various contributions of dimensionally quasiperiodic layers, which are stacked NBS/NIST researchers in the field of materials research periodically along the ten-fold axis, with a lattice with TEM as a central part of investigation are pre- parameter c = 1.24 nm. Shortly thereafter, a similar sented. The emphasis is on crystallographic aspects of decagonal phase but with a different periodicity the research. The presented contributions come mainly (c = 1.65 nm) was found in the Al-Pd system [8]. The from the Materials Science and Engineering Labora- importance of the discovery was not only discovery of a tory.