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
W. Gayle
National Institute of Standards and
Technology,
Gaithersburg, MD 20899-8554
leonid.bendersky@nist.gov
frank.gayle@nist.gov
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 elec-
tron diffraction over other methods, e.g.,
x-ray or neutron, arise from the extremely
short wavelength (
è‰
2 pm), the strong
atomic scattering, and the ability to exam-
ine tiny volumes of matter (
è‰
10 nm
3
).
The NIST Materials Science and Engineer-
ing 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 mi-
croscopy.
Key words:
crystal structure; crystallog-
raphy; defects; electron diffraction; phase
transitions; quasicrystals; transmission
electron microscopy.
Accepted:
August 22, 2001
Available online:
http://www.nist.gov/jres
1.
Introduction
The use of electron diffraction to solve crystallo-
graphic 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
⬚
to 5
⬚
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 capa-
ble of a resolution of 1.65 Ã… for 300 kV (and below 1 Ã…
for 1000 kV) electron energy-loss combined with chem-
ical analysis (through x-ray energy and electron-loss
energy spectroscopy) and a bright coherent field emis-
sion 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 al-
lows diffracted electrons to be focused into a regular
arrangement of diffraction spots that are projected and
recorded as the electron diffraction pattern. If the trans-
mitted 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 mathemat-
ically given by the Fourier transform.
A great advantage of the transmission electron micro-
scope is in the capability to observe, by adjusting the
electron lenses, both electron microscope images (infor-
mation in real space) and diffraction patterns (informa-
tion in reciprocal space) for the same region. By
inserting a selected area aperture and using the parallel
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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.
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 in-
cident 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 diffrac-
tion (CBED) uses a conical beam (
â£
> 10
⫺
3
rad) to pro-
duce diffraction disks, and the intensity distribution in-
side the disks allows unique determination of all the
point groups and most space groups [4]. Because a se-
lected area diffraction pattern can be recorded from
almost every grain in a polycrystalline material, recipro-
cal lattices (
≡
crystal structures) and mutual crystal ori-
entation 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 pre-
cipitates, 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 con-
trast. When only the transmitted beam is used, the ob-
servation mode is called the bright-field method (ac-
cordingly 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-diffrac-
tion, or the amplitude contrast. Amplitude-contrast im-
ages are suitable to study mesoscopic microstructures,
e.g., precipitates, lattice defects, interfaces, and do-
mains. Both kinematic and dynamic scattering theories
are developed to identify crystallographic details of
these heterogeneities [2,3].
Fig. 2.
Three observation modes in electron microscope using an
objective aperture. The center of the objective aperture is on the
optical axis. (a) Bright-field method; (b) dark-field method; (c) high-
resolution electron microscopy (axial illumination).
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 elec-
tron 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 speci-
men and aberration-compensating condition of a micro-
scope, 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 de-
veloped for multislice and Bloch waves methods [5].
HREM can be used to determine an approximate struc-
tural model, with further refinement of the model using
much higher resolution powder x-ray or neutron diffrac-
tion. 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.
Other major advantages in using electron scattering
for crystallographic studies is that the scattering cross
section of matter for electrons is 10
3
to 10
4
larger than
for x rays and neutrons, typical wavelengths (
è‰
2 pm)
are one hundredth of those for x rays and neutrons, and
the electron beam can be focused to extremely fine
probe sizes (
è‰
1 nm) [2]. These characteristics mean
that much smaller objects can be studied as single crys-
tals with electrons than with other radiation sources. It
also means a great sensitivity to small deviations from
an average structure caused by ordering, structural dis-
tortions, short-range ordering, or presence of defects.
Such changes often contribute either very weak super-
structure reflections, or diffuse intensity, both of which
are very difficult to detect by x-ray or neutron diffrac-
tion.
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Journal of Research of the National Institute of Standards and Technology
In addition, modern transmission electron micro-
scopes provide a number of complementary capabilities
known as analytical electron microscopy [6]. Different
detectors analyze inelasticly scattered electrons (Elec-
tron Energy-Loss Spectroscopy, or EELS), excited elec-
tromagnetic waves (Energy Dispersion Spectroscopy, or
EDS) and Z-contrast that provide information on chem-
ical compositions and local atomic environments. Such
information, when combined with elastic electron dif-
fraction, is important in determining structural models,
especially when a material consists of multiple phases.
In the following sections, various contributions of
NBS/NIST researchers in the field of materials research
with TEM as a central part of investigation are pre-
sented. The emphasis is on crystallographic aspects of
the research. The presented contributions come mainly
from the Materials Science and Engineering Labora-
tory.
2.
Discovery of New Structures Using
Selected Area and Convergent Beam
Electron Diffraction
Starting in the early 1980s the Metallurgy Division of
NBS was actively involved in studying the fundamentals
of rapid solidification of a melt. In this process, materi-
als (mostly metallic alloys) crystallize under very rapid
cooling conditions (over 10
4
⬚
C/s). Such extreme condi-
tions very often result in the formation of either new
metastable or non-equilibrium crystalline or glassy
structures. The rapid cooling also causes the formation
of small-grain polycrystalline microstructures, the con-
sequence of a high nucleation rate within the liquid. The
combination of metastable (and therefore most probably
unknown) structures with very small grain sizes makes
such materials extremely difficult to study by x-ray dif-
fraction, but very suitable for TEM.
A study of rapidly solidified Al-Mn alloys by Dan
Shechtman resulted in one of the most important discov-
eries of modern crystallography—a quasiperiodic struc-
ture with icosahedral symmetry, thus including 5-fold,
3-fold, and 2-fold rotation axes of symmetry [7]. Such
symmetry was inconsistent with the entire science of
crystallography at that time. The icosahedral symmetry
of the phase was demonstrated by carefully constructing
a reciprocal lattice using a series of selected area elec-
tron diffraction. For the first time the existence of a
well-ordered homogeneous (not twinned !) structure
having symmetry elements incompatible with transla-
tional periodicity was shown. J. W. Cahn and D. Shecht-
man discuss the history of this remarkable discovery and
its crystallographic aspects in a separate article in this
issue.
The discovery of the icosahedral phase triggered a
period of very active research in the new field of qua-
sicrystals. Many NIST researchers contributed actively
in the early stages, and TEM played an important role in
many aspects of this activity. Shortly after the Shecht-
man et al. publication, L. Bendersky discovered a differ-
ent type of quasiperiodic structure—the decagonal
phase with a 10-fold rotation axis, which has an appar-
ent 10/mmm point group (Fig. 3) [8]. Electron diffrac-
tion analysis of this Al
80
Mn
20
rapidly quenched alloy
showed that the decagonal phase has a structure of two-
dimensionally quasiperiodic layers, which are stacked
periodically along the ten-fold axis, with a lattice
parameter
c
= 1.24 nm. Shortly thereafter, a similar
decagonal phase but with a different periodicity
(
c
= 1.65 nm) was found in the Al-Pd system [8]. The
importance of the discovery was not only discovery of a
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,
enormous progress, both experimental and theoretical,
has been made. Quasicrystalline phases have been found
in more than hundred different metallic systems, and
several quasicrystalline phases have been shown to be
thermodynamically more stable than periodic crystals
[9].
Among other significant discoveries at NIST associ-
ated with the new field of “quasi-crystallography†were:
• The first conclusive determination of the
m
35 point
group for the icosahedral phase (for Al-38 %Mn-
5 %Si (mass fraction) rapidly solidified alloy) [10].
Here the methods of convergent beam electron dif-
fraction (CBED) were applied for the first time to a
quasiperiodic structure. Fig. 4 shows an example of
such CBED patterns from which the whole (3-dimen-
sional) pattern symmetries of fivefold [1
â¶
0], threefold
[111] and twofold [001] orientations were derived (
â¶
-
irrational “golden mean†number).
• Polycrystalline aggregates of a cubic phase [
â£
-
Al
9
(Mn,Fe)
2
Si
2
] with an overall icosahedral symme-
try were found in rapidly solidified Al
75
Mn
15
⫺
x
Fe
x
Si
10
(
x
= 5 and 10) alloys [11]. Through a twinning opera-
tion, the cubic axes undergo five-fold rotation about
irrational <1,
â¶
,0> axes; however only five orientations
occur among hundreds of crystals (Fig. 5). This is a
special orientation relationship without any coinci-
dence (or twin) lattice, and it is dictated by the non-
crystallographic symmetry of a motif (in the case of
the
â£
phase—the 54-atom Mackay-icosahedron mo-
tif). The motifs are parallel throughout the entire poly-
crystalline aggregate, and the crystal axes change
across grain boundaries. Based on this finding, the
entire concept of twinning and special grain
boundaries was re-examined. A new definition of
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Journal of Research of the National Institute of Standards and Technology
Fig. 3.
A series of SAD electron diffraction patterns obtained from the Al
78
Mn
22
rapidly solidified alloy by tilting
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 [1
â¶
0], (b) threefold [111] and (c) twofold [001] orientations. The lines indicate the mirror planes
(m).
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Journal of Research of the National Institute of Standards and Technology
Fig. 5.
Polycrystalline aggregates of a cubic phase (
â£
-Al
9
(Mn,Fe)
2
Si
2
) with their overall icosahedral symmetry were found in rapidly solidified
Al
75
Mn
15
⫺
x
Fe
x
Si
10
. A, B, and C are high-resolution images of five orientational variants and corresponding SAD patterns in five-, three-, and
two-fold orientation, respectively.
special orientations, including hypertwins, based on
reduction of the number of arithmetically independent
lattice vectors was proposed. This new classification
of special orientations within crystalline structures in-
cludes both old and new special orientations and can
be easily interpreted in terms of quasilattices.
• The nucleation and growth properties of icosahedral
and decagonal phases were examined. The study
showed that dendritic Al-Mn icosahedral crystals
grow along three-fold axes, and the decagonal phase
nucleates epitaxially on the icosahedral phase, with
coinciding five- and ten-fold axes [12]. F. Gayle gave
beautiful images of the faceted icosahedral crystals in
his study of an Al-Li-Cu alloy [13], which showed
growth of icosahedral phase dendrites along 5-fold
axes.
• TEM was used to study nucleation behavior of the
icosahedral phase in submicron size droplets of
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Al-14 % Mn (atom fraction) produced by electrohy-
drodynamic atomization [14]. The icosahedral phase
was found to nucleate very easily; this phenomenon
was explained by the possible topological similarities
of atomic packing in liquids and icosahedral quasi-
crystals. Observation of a metallic glass-like structure
for the highest cooling rates was explained by the
microquasicrystalline structure rather than by a con-
ventional structure of frozen melt. Modeling of a x-ray
diffraction spectra (obtained from a similar but vapor
deposited structure of Al-Mn) [15] and analysis of
heat evolution during DSC heating of as-deposited
samples [16] proved the concept of microquasicrys-
talline state.
Taking advantage of the strong scattering of elec-
trons, the presence of incommensurate modulations
has been established in several compounds. For exam-
ple, in Zr
3
Rh
4
(with a basic rhombohedral structure)
one-dimensional modulations of atomic distortions was
found. In this structure the modulation vector is normal
to the
c
-axis and incommensurate both in its
k
-value
and direction (Fig. 6) [17]. Further study of the
Zr
3
(Rh
1
⫺
x
Pd
x
)
4
alloys has revealed an intriguing correla-
tion between the occurrence of the incommensurate
modulation and magnetic and superconducting proper-
ties [18].
Fig. 6.
(a) Electron diffraction and (b) corresponding high-resolution image of the Zr
3
Rh
4
compound having a basic
rhombohedral structure and one-dimensional incommensurate modulation
k
i
. (c) Optical image showing a regular array of
triangular domains forming a macrolattice with defects. The domains are related to crystallographic variants (different
directions of a
k
-vector) of the incommensurate phase.
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Incommensurate modulations were also found in a
series of the layered Sr
n
(Nb,Ti)
n
O
3
n
+2
compounds [19].
These structures are composed of pseudo-two-dimen-
sional slabs of a distorted perovskite structure. The slabs
are
n
-octahedra thick and extend parallel to the {110}
perovskite plane. The compounds with
n
= 4, 5, 6, and
7 were observed to undergo a commensurate-incom-
mensurate phase transition in the temperature range
150
⬚
C to 250
⬚
C. The wave-vector of the incommensu-
rate modulation is parallel to [100] direction of the basic
orthorhombic lattice. The incommensurate phase tran-
sition observed in several Sr
n
(Nb,Ti)
n
O
3
n
+2
compounds
were attributed to the structural distortion approximated
by the alternating tilting of the (Ti,Nb)O
6
octahedra,
with amplitudes varying in the direction of the modula-
tion.
Very different types of incommensurate modulation
were recently found in Ruddlesden-Popper (
n
= 2)
La
2
⫺
2
x
Ca
1+2
x
Mn
2
O
7
compounds [20]. For the composi-
tion range 0.6
ⱕ
x
ⱕ
0.8, two sets of near-orthogonal
incommensurate
k
-vectors normal to the tetragonal
c
-
axis were identified by electron diffraction. High-reso-
lution imaging confirmed the presence of the incom-
mensurate two-dimensional lattice. The lattice can be
approximated with
a
2D
= 5
a
p
(
a
p
—perovskite unit cell).
A model based on the previously unobserved type of 4:1
charge/orbital ordering between the Mn
4+
and Mn
3+
cations was suggested. Investigation of the magnetic and
electric properties of the compounds also indicates the
presence of the charge ordering.
3.
Structural High-Resolution Microscopy
High-resolution electron microscopy techniques were
developed in the early 1970s for imaging structures of
inorganic crystals at the unit cell level and their extended
defects. In these early works the researchers used elec-
tron microscopes with rather limited resolution, and the
approach was mainly to identify one-dimensional struc-
tural sequences. Robert S. Roth was the first at NBS to
realize the opportunities of using TEM structural imag-
ing to study structures of complex oxides, and in partic-
ular “solid solutions,†which in fact occurred by inter-
growth of layers of closely related structures/phases. In
the 70s he actively collaborated with the pioneers in
multi-beam structural imaging, J. Allpress from Aus-
tralia and S. Iijima from Japan (at that time with Ari-
zona State University). In the 5th Materials Research
Symposium sponsored by NBS and organized by R. S.
Roth and S. J. Schneider, Jr., many of the publications
were dedicated to resolving structural issues with the
help of novel multi-beam imaging.
Collaboration between S. Iijima and R. S. Roth re-
sulted in the publication of one of the first high-resolu-
tion two-dimensional images where the intergrowth of
4
â«»
4, 4
â«»
3, and 3
â«»
3 blocks in TiO
2
âˆ
7Nb
2
O
5
was
imaged, thus demonstrating the possibility of solving
complex structures directly (Fig. 7, adapted from [21]).
This and similar efforts were essential in establishing
the important structural principles of crystallographic
shear and Wadsley defects (coherent intergrowth of one
member of the structural family with another). Within
the systems studied by Roth were polymorphs of
ZrO
2
:12Nb
2
O
5
[22], off-stoichiometric
x
Nb
2
O
5
âˆ
y
WO
3
compounds [23] and mixed-block structures of Rb
2
O-
Ta
2
O
5
, Rb
2
O-Nb
2
O
5
, and K
2
O-Ta
2
O
5
[24].
In the 1980s there was an increased interest in high-
quality microwave dielectrics with a high dielectric con-
stant (>30), low losses and near-zero temperature coeffi-
cient of the dielectric constant. At that time, the most
acceptable materials were barium titanates. R. S. Roth
and his post-doc P. K. Davies studied structural varia-
tions of these compounds by using the newly installed at
NIST Philips 430 microscope
1
with 0.23 nm point-to-
point resolution [25]. Using structural imaging, they
ascertained the mechanisms of intergrowth defect for-
mation in two important compounds, Ba
2
Ti
9
O
20
and
BaTi
5
O
11
. They found that the most prevalent defect was
formation of a new triclinic polytype, with an ionic
arrangement closely related to that in the accepted struc-
ture. Stoichiometric defects with considerable mi-
crotwinning and formation of face-sharing octahedra
were also observed, while nonstoichiometric defect for-
mation was minimal. TEM structural investigations of
microwave dielectrics continued in 1990s, in conjunc-
tion with the phase diagram studies of these materials in
the Ceramics Division of NIST by T. Vanderah and R.
Roth.
With the acquisition of the ultra-high resolution
JEOL3010 microscope by the Materials Science and
Engineering Laboratory (MSEL) of NIST in the 1990s,
investigation of structures and defects by high-resolution
imaging became routine. In the study of newly discov-
ered structures, often the approach was to develop an
approximate model based on experimental high-resolu-
tion images and electron diffraction, and then to work
out image simulations compatible with the experimental
images, and finally to refine the model using higher
resolution x-ray or neutron powder diffraction.
1
Certain commercial equipment, instruments, or materials are identi-
fied in this paper to foster understanding. Such identification does not
imply recommendation or endorsement by the National Institute of
Standards and Technology, nor does it imply that the materials or
equipment identified are necessarily the best available for the purpose.
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Fig. 7
. (a) High-resolution two-dimensional lattice image from a fragment of TiO
2
:7Nb
2
O
5
, showing
several displacements associated with the presence of isolated 3
â«»
3 blocks (arrowed) in the matrix of
4
â«»
3 blocks. (b) Idealized model of the area outlined in (a). The crystallographic shear (CS) planes
(containing tetrahedral metal atoms) are marked. They suffer a displacement at the points where 3
â«»
3
blocks (arrowed) occur.
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
A very intriguing and new structural architecture has
been recently discovered with the help of high-resolu-
tion imaging for a group of six new ferrimagnetic phases
in the BaO:TiO
2
:Fe
2
O
3
system [26]. The compounds
were proven to belong to a class of well-ordered inter-
growth structures. While in general the structures ex-
hibit a close-packed framework of [O + (Ba/O)] layers
(with stacking sequences different for different phases),
two types of alternating structural two-dimensional
slabs were identified. The first has a structure of the
hexagonal
h
-BaTiO
3
and the second—an Fe-rich,
spinel-like structure. Fig. 8a gives an example of high-
resolution imaging of such structure (observed for the M
phase). Energy-filtered mapping using EELS was used
to establish the compositional distribution of Fe, Ti, and
Ba (Fig. 8b) [27]. The strongly heterogeneous distribu-
tion of Fe suggests that all six phases can be considered
as self-assembled magnetic multilayer structures, with
potentially intriguing physical properties. One-dimen-
sional structural disorder was observed typically for the
phases (Fig. 8c) and identified as resulting from a poor
spatial correlation (translation within a closed-packed
plane) between the h-BaTiO
3
blocks (Fig. 8d). The dis-
order was responsible for the difficulty of determining
the structures using x-ray diffraction, even with the use
of a single crystal.
Fig. 8.
(a) HRTEM images of the M phase taken in orientations corresponding to [1120] (upper micrograph) and [1100] (lower micrograph) zone
axes of the hexagonal Ba(Ti,Fe)O
3
layer. On the background the yellow and pink stripes correspond to P (perovskite) and H-type (magnetite) slabs,
respectively. (b) Composional maps of the M phase (in [1120] zone axis orientaion) obtained with Ti L
2,3
, Ba M
4,5
, and Fe L
2,3
edges. The maps
show the Ti composition is relatively uniform throughout the crystals whereas the Fe elemental distribution reveals an enhancement corresponding
to the H slabs. Similarly, the Ba distribution is decreased in the H slabs relative to the P slabs. (c) A schematic drawing of a reciprocal lattice of
the compounds showing the typical rods of continuous intensity in the
c
-direction. (d) The image obtained by inverse FFT shows only the H slabs.
Rectangles correspond to a characteristic structural element of the H slab and emphasize random shift of the H slabs.
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
A structural study of the microwave dielectric cal-
cium tantalate, Ca
2
Ta
2
O
7
, showed diffraction patterns
displaying strong subcell characteristics of the fluorite
structure. The complex distributions of superlattice re-
flections depend on the nature and concentration of the
dopant and on the reaction temperature. Polytypes with
n
= 3, 4, 5, 6, and 7 were prepared as single crystals by
the flux method [28]. High-resolution electron micro-
scope images were used to determine a characteristic
structural feature of the polytypes (Fig. 9). The major
feature was a fluorite-type cation array, which is period-
ically twinned on (111)
fluorite
to give mixed cubic-hexag-
onal stacking of the cation layers. The basic repeating
units are slabs of different thicknesses comprising a
Ca
3
Ta layer and a Ta
3
Ca layer. Single crystal x-ray and
powder x-ray and neutron data were used to determine
an exact structure of the polytypes. For
n
= 3, the struc-
ture is the 3-block trigonal weberite P3
1
21 (3T) [28]. In
the 7M polytype the
h
-stacked Ta
3
Ca layers divide the
structure into two blocks of
c
-stacked layers which con-
tain 3 and 4 repeating units and can be thus designated
as 3M and 4M blocks. The stacking sequence of metal
atom layers in the 7M polytype is
hccccchccccccch
...
For the 5M polytype, the
h
-stacked layers divide the
structure into two 2M and 3M blocks. The metal atom
layer stacking sequence is then
hccchccccch
... [29].
Fig. 9.
High-resolution TEM image for 7M-Ca
2
Ta
2
O
7
viewed along [110] and the
corresponding simulated phase-contrast image (inset). The simulated image was
obtained for 35 nm thickness,
⫺
50 nm defocus value and the 10 nm
⫺
1
aperture. The
4- and 3-layers structural blocks are emphasized.
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
4.
Study of Phase Transitions
The essential feature of a structural phase transition is
the change of symmetry. Most often it is a low temper-
ature (room temperature) phase that is studied, which
has a lower symmetry than the high temperature
phase(s). Its space group often is a subgroup of that of
the high temperature phase. Therefore, a single crystal
(grain) of the high temperature phase at low temperature
is subdivided into a number of symmetry-related do-
mains, or structural variants. The variants are either
rotational (twins) or translational (anti-phase domains,
or APDs), and separated from each other by specific
interfaces. Knowledge of the crystallographic nature of
the interfaces and the structure of the low temperature
phase will often allow prediction of the structure of high
temperature phases and possible intermediate phases
[30,31]. TEM direct-space imaging (amplitude con-
trast), in combination with SAD and CB electron dif-
fraction, is the most suitable technique for this approach.
For very small domain structures, high-resolution imag-
ing and Fast-Fourier Transform are most appropriate.
In the early 1990s the interest in a new generation of
high-temperature materials for aerospace applications
led scientists from the Metallurgy Division of NIST to
study intermetallic compounds, in particular the Ti-Al-
Nb alloys. The use of TEM was extremely helpful in
understanding the complexity of phase transformations
occurring in these materials. The transformations in the
Ti-Al-Nb system include (1) a martensitic-like transi-
tion from the high-temperature BCC phase, with forma-
tion of a Widmanstatten-type lamellar structure (an
HCP-to-FCC transition plus ordering) and omega-type
displacements [32]. Study of the Ti
2
AlNb and Ti
4
AlNb
3
alloys showed the presence of two phases: the Ti/Nb-
rich b.c.c. phase and the ternary orthorhombic Ti
2
AlNb
phase [33]. Depending on the alloy composition, one of
the phases was observed as a precipitate with plate mor-
phology in the matrix of the other phase. For the
Ti
4
Al
3
Nb alloy, formation of a sequence of metastable
â»
-related phases from the B2 (ordered BCC) phase was
established and summarized in the form of maximal
group-subgroup relationship (Fig. 10) [34]. An equi-
librium low temperature phase has the B8
2
structure
(and triple-cell D8
2
structure for the more Nb-rich com-
positions). The metastable
â»
phase and both B8
2
and
D8
2
are structurally related to the B2 phase by displace-
ment (collapse) of every two (out of three) (111) planes.
The
â»
-type structures were verified by means of trans-
mission electron microscopy and by single crystal x-ray
diffraction.
For Ti-25 %Al-12.5 %Nb (atom fraction), the trans-
formation path from high temperatures includes the for-
mation of the intermediate hexagonal DO
19
phase, and
subsequent formation of the low-temperature or-
thorhombic O (Ti
2
AlNb) phase. For alloys close to Ti-
25 %Al-25 %Nb (atom fraction), the path involves an
intermediate Bl9 structure and subsequent formation of
a translational domain structure of the O phase [35].
The experimental results were summarized as a se-
quence of crystallographic structural relationships de-
veloped from subgroup symmetry relations [36] (Fig.
11). Symmetry elements lost in each step of the se-
quence determine the possibilities for variants of the low
symmetry phase and domains with characteristic inter-
faces that can be present in the microstructure. Fig. 11
gives three examples of such domain: (A) Ti
2
AlNb alloy,
rotational domains of the O phase accommodated in the
form of a hierarchical twin structure; (B) Ti
2
AlNb alloy,
interfaces between translational domains formed in the
course of the
Pm
3
m
(B2)-to-
Pmm
a(B19) transition; (C)
a two-phase mixture of DO
19
(a matrix) and three-vari-
ants of O-phase (precipitates). The orientation of inter-
domain interfaces is determined by the requirement for
a strain-free interface (as in Fig. 11A and C). A structure
of the O-phase (an important ternary phase, currently a
base for new high-temperature composites) was refined
using the preliminary model derived from the TEM
studies and powder neutron diffraction data [37].
The approach of the maximal group-subgroup rela-
tionship was also applied to phase transformations in
other systems, and in particular to transformations be-
tween ordered polymorphs of the microwave dielectric
Ca(Ca
1/3
Nb
2/3
)O
3
[38] and Ca(Ca
1/3
Nb
2/3
)O
3
-CaTiO
3
[39]. Four Ca
4
Nb
2
O
9
polymorphs with perovskite-re-
lated structures and different arrangements of B-site
cations were identified. Ordering of the B-cations (Ca
2+
and Nb
5+
) in this system is combined with displacement
of oxygen ions by octahedral tilting. Three of the poly-
morphs have 1:1 (monoclinic
P
2
1
/
c
), 2:1 (monoclinic
P
2
1
/
c
) and 3:1 (triclinic
P
1) ordering. The 1:1 ordered
structure features alternating {111}
c
planes occupied
exclusively by Nb, and the occupied by a disordered
mixture of Ca and the remaining Nb cations, while the
1:2 ordered polymorph exhibits {CaNbNb...} sequence
of the {111}
c
B-cation planes. The metastable 3:1 struc-
ture is derived from the 1:1 ordered structure by a par-
tial ordering of Ca and Nb cations on those B-sites
which were occupied by a random Ca/Nb mixture in the
1:1 ordered array; the resulting ordered arrangement can
be viewed as 1:3 type. The models were subsequently
validated by Rietveld refinements using combined x-ray
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Fig. 10.
A sequence of
â»
-related phases formed from the high temperature B2 (ordered BCC) phase in the Ti
4
AI
3
Nb alloy is summarized in the
form of maximal group-subgroup relationship. Dark field images A and B show microstructures of (A) metastable
â»
'
phase and (B) a mixture of
â»
"
and B8
2
phases.
and neutron powder diffraction data [40]. The relation-
ship between the polymorphs in the form of maximal
subgroup relationship was derived from the complex
hierarchy of interfaces observed by TEM (Fig. 12). The
space groups of the ordered Ca
4
Nb
2
O
9
polymorphs (de-
duced from electron diffraction data) do not exhibit
group/subgroup relations, and, therefore, phase transi-
tions between them must be first-order transitions.
Different problems related to the microstructural for-
mation were solved using conventional TEM. For exam-
ple, in the study of Diffusion-Induced Grain Boundary
Migration (DIGM) phenomena, the effect of diffusion
of Cr
2
O
3
into polycrystalline Al
2
O
3
down grain
boundaries and concomitant generation of local stresses
due to the change of lattice parameter were studied [41].
Relief of these stresses occurred by grain boundary mi-
gration and the generation of misfit dislocations. When
these dislocations were observed using bright and dark
field transmission electron microscopy, a good correla-
tion was found between the dislocation spacing and the
chromium concentration in the alloyed regions. Another
problem related to the plastic deformation of A1
2
O
3
by
slip and twinning was investigated by examining the
regions surrounding a microhardness indentation using
TEM [42]. The results establish: (1) the occurrence of
pyramidal slip on {1123}
å…·
1100
å…¸
, and (2) the nature of
basal twins in this material. The observations on basal
twins, in particular, have led to a completely different
description for the twinning process. In the study of
important Ti-Al aerospace alloys, the morphology of
discontinuous coarsening in the Ti
3
Al (
â£
2
) / TiAl (
â¥
)
fully lamellar structure was examined [43]. Three mor-
phologies were observed in discontinuously coarsened
lamellar structures (secondary lamellae). Type-(I)
lamellae have the low energy habit plane as their lamel-
lar interfaces, and have the same lamellar direction as
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Fig. 11.
A sequence of phases formed from the high temperature B2 (ordered BCC) Ti-Al-Nb phase is summarized in the form of maximal
group-subgroup relationship. (A) Ti
2
AINb alloy, rotational domains of the O phase accommodated in the form of hierarchical twin structure; (B)
Ti
2
AINb alloy, interfaces between translational domain formed in the
Pm
3
m
(B2)-to-
Pmma
(B19) transition; (C) two-phase mixture of DO
19
(matrix) and O-phase (precipitates).
the original primary lamellae. Type-(II) lamellae have
the same crystallographic orientation of
â£
2
plates as that
in the original primary lamellae, but have a different
lamellar direction from the original primary lamellae,
and have irregular faceted lamellar interfaces. Type-(III)
lamellae have a different lamellar direction and a differ-
ent crystallographic orientation of the
â£
2
plates from that
in the original primary lamellae, but have the low energy
habit plane as their lamellar interfaces. The growth ki-
netics of these three types of lamellae were analyzed by
modifying the Livingston and Cahn treatment in order
to obtain the dependence of the secondary lamellar
morphologies on misorientation between the penetrated
primary lamellae, the advancing secondary lamellae
and the lamellar colony boundaries.
Precipitation of second phases in aluminum alloys
presents another challenging application for electron
diffraction due to the small dimensions and multiple
variants of the precipitates, which are most often
metastable phases in commercial alloys and tempers. In
the late 1980s the Metallurgy Division had a collabora-
tive effort with Martin Marietta Laboratory to deter-
mine the origins of the ultra-high strength in Weldalite
aluminum alloys, later used to build the Space Shuttle
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
Fig. 12.
Top. Symmetry tree describing group/subgroup relations between the three Ca
4
Nb
2
O
9
polymorphs with distinct (1:1, 1:2, and 1:3)
arrangements of the B-cations; the numbers in brackets indicate the number of crystallographic variants generated by the corresponding
minimal symmetry reductions. Since all three phases feature similar
b
⫺
b
⫺
c
+
octahedral tilting, their space groups are subgroups of
Pbnm
, which
describes a disordered perovskite structure with the same tilting. Bottom: a-Dark-field image of the single grain containing the metastable 1:3
ordered Ca
4
Nb
2
O
9
polymorph. b-Magnified view of the area outlined by rectangular in (a). Twin-type domains
I
and
II
in the area labelled
a are related to the
Pm
3
m
→
Pbnm
octahedral tilting transition. The domains exhibit a substructure consisting of both rotational (1 and 2 in
the area labelled b) and translational (A, B, C, and D) domains. The domains 1 and 2 can be described by the
Pbnm
→
P
1 symmetry reduction,
while the domains A, B, C, and D can be accounted for by the lost of the
c
-glide plane (
P
2
1
/
c
→
P
1) and doubling of the
c
lattice parameter.
Additionally precipitates of the 1:2 ordered polymorph nucleated in the 1:3 ordered matrix are seen in b (indicated by arrows).
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Volume 106, Number 6, November–December 2001
Journal of Research of the National Institute of Standards and Technology
External Tank to reduce launch weight. This novel alu-
minum alloy was primarily strengthened with 1.2 % Li
and 4.0 % Cu (mass fraction). Silver and magnesium
were added, 0.4 % each, to aid precipitation of second
phases, and 0.1 % Zr was added to inhibit recrystalliza-
tion. TEM imaging and diffraction was required to sort
out the complex microstructure responsible for the high
strength of the alloy. Our microstructural studies estab-
lished that the Weldalite alloys are strengthened primar-
ily by the equilibrium T
1
-Al
2
CuLi phase, in contrast to
other commercial aluminum alloys, which are strength-
ened by metastable precipitate phases. In addition to T
1
,
additional strengthening arises from 3 other lath or
plate-like precipitates (S
'
-Al
2
CuMg,
â©
'
-Al
2
Cu and an
unknown phase), all lying on distinct habit planes in the
matrix (Fig. 13) [44]. When
â£
'
, or Al
3
(Zr,X), which
inhibits grain boundary motion, is included, it appears
that this alloy in the highest strength condition may
represent a metastable equilibrium between six phases.
Fig. 13.
This ultra high strength aluminum alloy is strengthened by a
mix of precipitates, including the prominent T1-Al
2
CuLi platelets
lying on matrix {111} planes, and platelike
âª
'
(on {100} planes) and
lath S
'
precipitates (on {210} planes), identified by the diffraction
pattern.
5.
Conclusions
The NBS/NIST Materials Science and Engineering
Laboratory has a history of discovery of new phases and
classes of crystallographic structures through transmis-
sion electron microscopy and electron diffraction. The
power of electron diffraction has allowed the determina-
tion of structural details, both in perfect crystals and in
defect structures, which are too subtle for x-ray or neu-
tron diffraction techniques. Research within MSEL has
lead to discoveries ranging from entirely new classes of
crystallography and crystal defects to advancement of
the understanding of commercial aerospace alloys.
6.
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About the authors:
Leonid Bendersky is a metallurgist
in the Metallurgy Division of the NIST Materials Sci-
ence and Engineering Laboratory. Frank Gayle is
leader of the Materials Structure and Characterization
Group in the Metallurgy Division. The National Insti-
tute of Standards and Technology is an agency of the
Technology Administration, U.S. Department of Com-
merce.
1012