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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-
Gaithersburg, MD 20899-8554 tron diffraction over other methods, e.g., Key words: crystal structure; crystallog-
x-ray or neutron, arise from the extremely raphy; defects; electron diffraction; phase
short wavelength (2 pm), the strong transitions; quasicrystals; transmission
leonid.bendersky@nist.gov atomic scattering, and the ability to exam- electron microscopy.
frank.gayle@nist.gov ine tiny volumes of matter (10 nm3).
The NIST Materials Science and Engineer- Accepted: August 22, 2001
ing Laboratory has a history of discovery
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- atomicpotential 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.Vainshteinandhiscolleaguesasearlyasthe1940s 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 3 to 5 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 imageofthesamplecanbeobserved.
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 fromthereal 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 Agreatadvantageofthetransmissionelectronmicro-
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-
fromaspecificareaassmallas100nmindiameter.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.
3 2c. This observation mode is called high-resolution elec-
tion (CBED) uses a conical beam ( >10 rad) to pro-
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- menandaberration-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 projectedpotentialofastructure.Forathickerspecimen
single crystal structural information can be obtained for andlessfavorable 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- HREMcanbeusedtodetermineanapproximate struc-
cipitates, nanosize particles etc. tural model, with further refinement of the model using
In order to investigate an electron microscope image, muchhigherresolution 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 (2 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 imagesisattributed to the change of the amplitude probe sizes (1 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
Thustheimagecontrastiscalled 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 manetal.publication, L. Bendersky discovered a differ-
EDS)andZ-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 Al Mn rapidly quenched alloy
80 20
especially when a material consists of multiple phases. showedthat the decagonal phase has a structure of two-
In the following sections, various contributions of dimensionally quasiperiodic layers, which are stacked
NBS/NISTresearchersinthefield 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. novel structure, but also demonstration of the general
principles of quasiperiodicity. Since the discovery of the
first quasiperiodic structures in Al-Mn alloys in 1984,
2. Discovery of New Structures Using enormous progress, both experimental and theoretical,
Selected Area and Convergent Beam has been made. Quasicrystalline phases have been found
Electron Diffraction in more than hundred different metallic systems, and
several quasicrystalline phases have been shown to be
Starting in the early 1980s the Metallurgy Division of thermodynamically more stable than periodic crystals
NBSwasactivelyinvolvedinstudying the fundamentals [9].
of rapid solidification of a melt. In this process, materi- Among other significant discoveries at NIST associ-
als (mostly metallic alloys) crystallize under very rapid ated with the new field of “quasi-crystallography” were:
4
cooling conditions (over 10 C/s). Such extreme condi- • The first conclusive determination of the m35 point
tions very often result in the formation of either new group for the icosahedral phase (for Al-38 %Mn-
metastable or non-equilibrium crystalline or glassy 5%Si (mass fraction) rapidly solidified alloy) [10].
structures. The rapid cooling also causes the formation Here the methods of convergent beam electron dif-
of small-grain polycrystalline microstructures, the con- fraction (CBED) were applied for the first time to a
sequence of a high nucleation rate within the liquid. The quasiperiodic structure. Fig. 4 shows an example of
combination of metastable (and therefore most probably such CBEDpatterns from which the whole (3-dimen-
unknown) structures with very small grain sizes makes sional) pattern symmetries of fivefold [10], threefold
such materials extremely difficult to study by x-ray dif- [111] and twofold [001] orientations were derived (-
fraction, but very suitable for TEM. irrational “golden mean” number).
A study of rapidly solidified Al-Mn alloys by Dan • Polycrystalline aggregates of a cubic phase [-
Shechtmanresultedinoneofthemostimportantdiscov- Al (Mn,Fe) Si ] with an overall icosahedral symme-
9 2 2
eries of modern crystallography—a quasiperiodic struc- try were found in rapidly solidified Al75Mn15xFexSi10
ture with icosahedral symmetry, thus including 5-fold, (x = 5 and 10) alloys [11]. Through a twinning opera-
3-fold, and 2-fold rotation axes of symmetry [7]. Such tion, the cubic axes undergo five-fold rotation about
symmetry was inconsistent with the entire science of irrational <1,,0> axes; however only five orientations
crystallography at that time. The icosahedral symmetry occur among hundreds of crystals (Fig. 5). This is a
of the phase was demonstrated by carefully constructing special orientation relationship without any coinci-
a reciprocal lattice using a series of selected area elec- dence (or twin) lattice, and it is dictated by the non-
tron diffraction. For the first time the existence of a crystallographic symmetry of a motif (in the case of
well-ordered homogeneous (not twinned !) structure the phase—the 54-atom Mackay-icosahedron mo-
having symmetry elements incompatible with transla- tif). The motifs are parallel throughout the entire poly-
tional periodicity was shown. J. W. Cahn and D. Shecht- crystalline aggregate, and the crystal axes change
mandiscussthehistoryofthisremarkablediscoveryand across grain boundaries. Based on this finding, the
its crystallographic aspects in a separate article in this entire concept of twinning and special grain
issue. boundaries was re-examined. A new definition of
999
Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Fig. 3. A series of SAD electron diffraction patterns obtained from the Al Mn rapidly solidified alloy by tilting
78 22
a single grain. Based on these patterns, a unique non-crystallographic 10-fold axis and a one-dimensional
periodicity of the decagonal phase were established.
Fig. 4. CBED patterns taken along (a) fivefold [10], (b) threefold [111] and (c) twofold [001] orientations. The lines indicate the mirror planes
(m).
1000
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