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Electron diffraction using transmission electron microscopy.



Electron diffraction Electron diffraction

The phenomenon associated with interference processes that occur when electrons are scattered by atoms to form diffraction patterns.
 via the transmission electron microscope electron microscope: see 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 (National Institute of Standards & Technology, Washington, DC, www.nist.gov) The standards-defining agency of the U.S. government, formerly the National Bureau of Standards. It is one of three agencies that fall under the Technology Administration (www.technology.  Materials Science and Engineering Materials science and engineering

A multidisciplinary field concerned with the generation and application of knowledge relating to the composition, structure, and processing of materials to their properties and uses.
 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 electron microscopy

Technique that allows examination of samples too small to be seen with a light microscope. Electron beams have much smaller wavelengths than visible light and hence higher resolving power.
.

Key words: crystal structure; crystallography; defects; electron diffraction; phase transitions; quasicrystals; transmission electron microscopy “TEM” redirects here. For other uses, see TEM (disambiguation).

Transmission electron microscopy (TEM) is an imaging technique whereby a beam of electrons is transmitted through a specimen, then an image is formed, magnified and directed to appear either
.

1. Introduction

The use of electron diffraction to solve crystallographic crys·tal·log·ra·phy  
n.
The science of crystal structure and phenomena.



crystal·log
 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 TEM

1. transmission electron microscope.

2. triethylenemelamine.

3. transmissible encephalopathy of mink.
), 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 angstrom (ăng`strəm), abbr. Å, unit of length equal to 10−10 meter (0.0000000001 meter); it is used to measure the wavelengths of visible light and of other forms of electromagnetic radiation, such as ultraviolet ] 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 The plane, perpendicular to the optical axis of the lens, in which images of points in the object field of the lens are focused.  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 diffraction pattern

The interference pattern that results when a wave or a series of waves undergoes diffraction, as when passed through a diffraction grating or the lattices of a crystal.
 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 Fourier transform

In mathematical analysis, an integral transform useful in solving certain types of partial differential equations. A function's Fourier transform is derived by integrating the product of the function and a kernel function (an exponential function raised to
.

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 CBED Convergent-Beam Electron Diffraction
CBED Community-Based Economic Development
CBED Center for Business and Economic Development
CBED Coastal Benthic Exchange Dynamics
CBED Concentration Buffer Exchange and Desalting
CBED Community Based Entrepreneurial Development
) 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 Selected area (electron) diffraction, abbreviated as SAD (SAED), is a crystallographic experimental technique that can be performed inside a transmission electron microscope (TEM).  pattern can be recorded from almost every grain in a polycrystalline Adj. 1. polycrystalline - composed of aggregates of crystals; "polycrystalline metals"
crystalline - consisting of or containing or of the nature of crystals; "granite is crystalline"
 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 Neutron diffraction

The phenomenon associated with the interference processes which occur when neutrons are scattered by the atoms within solids, liquids, and gases.
 are unavailable. Such materials include metastable met·a·sta·ble  
adj.
Of, relating to, or being an unstable and transient but relatively long-lived state of a chemical or physical system, as of a supersaturated solution or an excited atom.
 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 kin·e·mat·ics  
n. (used with a sing. verb)
The branch of mechanics that studies the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it.
 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 HREM High Resolution Electron Microscopy ). 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.

Other major advantages in using electron scattering Electron scattering is the process whereby an electron is deflected from its original trajectory.

Electrons are charged particles and are acted upon by the electromagnetic forces. They are scattered by other charged particles through the electrostatic Coulomb forces.
 for crystallographic studies is that the scattering cross section of matter for electrons is [10.sup.3] to [10.sup.4] larger than for x rays and neutrons, typical wavelengths ([approximately equal to]2 pm) are one hundredth of those for x rays and neutrons, and the electron beam A stream of electrons, or electricity, that is directed towards a receiving object. See electron beam imaging and electron beam lithography.  can be focused to extremely fine probe sizes ([approximately equal to]1 nm) (2). These characteristics mean that much smaller objects can be studied as single crystals with electrons than with other radiation sources. It also means a great sensitivity to small deviations from an average structure caused by ordering, structural distortions, short-range ordering, or presence of defects. Such changes often contribute either very weak superstructure reflections, or diffuse intensity, both of which are very difficult to detect by x-ray or neutron diffraction.

In addition, modern transmission electron microscopes provide a number of complementary capabilities known as analytical electron microscopy (6). Different detectors analyze inelasticly scattered electrons (Electron Energy-Loss Spectroscopy, or EELS), excited electromagnetic waves (Energy Dispersion Spectroscopy, or EDS (Electronic Data Systems, Plano, TX, www.eds.com) Founded in 1962 by H. Ross Perot (independent candidate for the President of the U.S. in 1992), EDS is the largest outsourcing and data processing services organization in the country. ) and Z-contrast that provide information on chemical compositions and local atomic environments. Such information, when combined with elastic electron diffraction, 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 presented. The emphasis is on crystallographic aspects of the research. The presented contributions come mainly from the Materials Science and Engineering Laboratory.

2. Discovery of New Structures Using Selected Area and Convergent Beam Electron Diffraction

Starting in the early 1980s the Metallurgy Division of NBS (National Bureau of Standards) See NIST.

NBS - National Bureau of Standards: part of the US Department of Commerce, now NIST.
 was actively involved in studying the fundamentals of rapid solidification of a melt. In this process, materials (mostly metallic alloys) crystallize crys·tal·lize also crys·tal·ize  
v. crys·tal·lized also crys·tal·ized, crys·tal·liz·ing also crys·tal·iz·ing, crys·tal·liz·es also crys·tal·iz·es

v.tr.
1.
 under very rapid cooling conditions (over [10.sup.4] [degrees]C/s). Such extreme conditions 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 consequence of a high nucleation nu·cle·a·tion
n.
1. The beginning of chemical or physical changes at discrete points in a system, such as the formation of crystals in a liquid.

2. The formation of cell nuclei.
 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 diffraction, but very suitable for TEM.

A study of rapidly solidified Al-Mn alloys by Dan Shechtman Dan Shechtman is the Philip Tobias Professor of Materials Science at the Technion - Israel Institute of Technology. In 1982, he discovered the icosahedral phase, which opened the new field of quasiperiodic crystals. Resources
  • D. P. DiVincenzo and P. J.
 resulted in one of the most important discoveries of modern crystallography -- a quasiperiodic structure with icosahedral symmetry A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a total of 120 symmetries including transformations that combine a reflection and a rotation. A regular dodecahedron has the same set of symmetries, since it is the dual of the icosahedron. , 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 electron diffraction. For the first time the existence of a well-ordered homogeneous (not twinned !) structure having symmetry elements incompatible with translational periodicity periodicity /pe·ri·o·dic·i·ty/ (per?e-ah-dis´i-te) recurrence at regular intervals of time.

pe·ri·o·dic·i·ty
n.
1.
 was shown. J. W. Cahn and D. Shechtman discuss the history of this remarkable discovery and its crystallographic aspects in a separate article in this issue.

The discovery of the icosahedral icosahedral

a regular polyhedron with 20 triangular faces, 12 corners and 30 sides, having cubic symmetry with 5:3:2-fold axes. A common structural form for the capsid of many viruses including herpesviruses, adenoviruses, parvoviruses, reoviruses, picornaviruses and retroviruses.
 phase triggered a period of very active research in the new field of quasicrystals. Many NIST researchers contributed actively in the early stages, and TEM played an important role in many aspects of this activity. Shortly after the Shechtman et al. publication, L. Bendersky discovered a different type of quasiperiodic structure -- the decagonal phase with a 10-fold rotation axis, which has an apparent 10/mmm point group (Fig. 3) (8). Electron diffraction analysis of this [Al.sub.80][Mn.sub.20] rapidly quenched quench  
tr.v. quenched, quench·ing, quench·es
1. To put out (a fire, for example); extinguish.

2. To suppress; squelch:
 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 th e 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 ther·mo·dy·nam·ic  
adj.
1. Characteristic of or resulting from the conversion of heat into other forms of energy.

2. Of or relating to thermodynamics.
 more stable than periodic crystals (9).

Among other significant discoveries at NIST associated with the new field of "quasi-crystallography" were:

* The first conclusive determination of the m35 point group for the icosahedral phase (for Al-38 %Mn5 %Si (mass fraction) rapidly solidified alloy) (10). Here the methods of convergent beam electron diffraction (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-dimensional) pattern symmetries of fivefold fivefold
Adjective

1. having five times as many or as much

2. composed of five parts

Adverb

by five times as many or as much

Adj. 1.
 [1[tau]0], threefold [111] and twofold [001] orientations were derived ([tau]-irrational "golden mean" number).

* Polycrystalline aggregates of a cubic phase [[alpha]-[Al.sub.9][(Mn,Fe).sub.2][Si.sub.2] with an overall icosahedral symmetry were found in rapidly solidified [Al.sub.75][Mn.sub.15-x][Fe.sub.x][Si.sub.10] (x = 5 and 10) alloys (11). Through a twinning operation, the cubic axes undergo five-fold rotation about irrational <1,[tau],0> axes; however only five orientations occur among hundreds of crystals (Fig. 5). This is a special orientation relationship without any coincidence (or twin) lattice, and it is dictated by the non-crystallographic symmetry of a motif (in the case of the [alpha] phase -- the 54-atom Mackay-icosahedron motif). The motifs are parallel throughout the entire polycrystalline aggregate, and the crystal axes change across grain boundaries Grain boundaries

The internal interfaces that separate neighboring misoriented single crystals in a polycrystalline solid. Most solids such as metals, ceramics, and semiconductors have a crystalline structure, which means that they are made of atoms which are
. Based on this finding, the entire concept of twinning and special grain boundaries was re-examined. A new definition of special orientations, including hypertwins, based on reduction of the number of arithmetically independent lattice vectors was propos ed. This new classification of special orientations within crystalline structures includes 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 dendritic /den·drit·ic/ (den-drit´ik)
1. branched like a tree.

2. pertaining to or possessing dendrites.


den·drit·ic
adj.
Relating to the dendrites of nerve cells.
 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 Al-14 % Mn (atom fraction) produced by electrohydrodynamic atomization Atomization

The process whereby a bulk liquid is transformed into a multiplicity of small drops. This transformation, often called primary atomization, proceeds through the formation of disturbances on the surface of the bulk liquid, followed by their
 (14). The icosahedral phase was found to nucleate nu·cle·ate
adj.
Nucleated.

v.
1. To form into a nucleus.

2. To serve or act as a nucleus for.

3. To provide a nucleus for.

n.
A salt of a nucleic acid.
 very easily; this phenomenon was explained by the possible topological similarities of atomic packing in liquids and icosahedral quasicrystals. Observation of a metallic glass-like structure for the highest cooling rates was explained by the microquasicrystalline structure rather than by a conventional 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 (1) (Digital Signal Controller) A microcontroller and DSP combined on the same chip. It adds the interrupt-driven capabilities normally associated with a microcontroller to a DSP, which typically functions as a continuous process. See microcontroller and DSP.  heating of as-deposited samples (16) proved the concept of microquasicrystalline state.

Taking advantage of the strong scattering of electrons, the presence of incommensurate in·com·men·su·rate  
adj.
1.
a. Not commensurate; disproportionate: a reward incommensurate with their efforts.

b. Inadequate.

2. Incommensurable.
 modulations has been established in several compounds. For example, in [Zr.sub.3][Rh.sub.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.sub.3][([Rh.sub.1-x][Pd.sub.x]).sub.4] alloys has revealed an intriguing correlation between the occurrence of the incommensurate modulation and magnetic and superconducting properties (18).

Incommensurate modulations were also found in a series of the layered [Sr.sub.n][(Nb,Ti).sub.n] [O.sub.3n+2] compounds (19). These structures are composed of pseudo-two-dimensional slabs of a distorted perovskite Perovskite (calcium titanium oxide, CaTiO3) is a relatively rare mineral on the Earth's crust. Perovskite crystallizes in the orthorhombic (pseudocubic) crystal system.  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-incommensurate phase transition in the temperature range 150 [degrees]C to 250 [degrees]C. The wave-vector of the incommensurate modulation is parallel to [100] direction of the basic orthorhombic or·tho·rhom·bic  
adj.
Of or relating to a crystalline structure of three mutually perpendicular axes of different length.



orthorhombic  
 lattice. The incommensurate phase transition observed in several [Sr.sub.n][(Nb,Ti).sub.n][O.sub.3n+2] compounds were attributed to the structural distortion approximated by the alternating tilting of the (Ti,Nb)[O.sub.6] octahedra, with amplitudes varying in the direction of the modulation.

Very different types of incommensurate modulation were recently found in Ruddlesden-Popper (n = 2) [La.sub.2-2x][Ca.sub.1+2x][Mn.sub.2][O.sub.7] compounds (20). For the composition range 0.6 [less than or equal to] x [less than or equal to] 0.8, two sets of near-orthogonal incommensurate k-vectors normal to the tetragonal tet·ra·gon  
n.
A four-sided polygon; a quadrilateral.



[Late Latin tetrag
 c-axis were identified by electron diffraction. High-resolution imaging confirmed the presence of the incommensurate two-dimensional lattice. The lattice can be approximated with [a.sub.2D] = 5[a.sub.p] ([a.sub.p]--perovskite unit cell). A model based on the previously unobserved type of 4:1 charge/orbital ordering between the [Mn.sup.4+] and [Mn.sup.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 electron microscopes with rather limited resolution, and the approach was mainly to identify one-dimensional structural sequences. Robert S. Roth was the first at NBS to realize the opportunities of using TEM structural imaging to study structures of complex oxides, and in particular "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 Australia and S. lijima from Japan (at that time with Arizona State University Arizona State University, at Tempe; coeducational; opened 1886 as a normal school, became 1925 Tempe State Teachers College, renamed 1945 Arizona State College at Tempe. Its present name was adopted in 1958. ). 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 resulted in the publication of one of the first high-resolution two-dimensional images where the intergrowth in·ter·growth  
n.
1. The growing of one thing with or into another.

2. Mineralogy The growing together of crystals from two or more minerals.
 of 4 X 4, 4 X 3, and 3 X 3 blocks in [TiO.sub.2]*7[Nb.sub.2][O.sub.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.sub.2]:12[Nb.sub.2][O.sub.5] (22), off-stoichiometric x[Nb.sub.2][O.sub.5]*y[WO.sub.3] compounds (23) and mixed-block structures of [Rb.sub.2]O-[Ta.sub.2][O.sub.5], [Rb.sub.2]O-[Nb.sub.2][O.sub.5], and [K.sub.2]O-[Ta.sub.2][O.sub.5] (24).

In the 1980s there was an increased interest in high-quality microwave dielectrics with a high dielectric constant dielectric constant
n.
See permittivity.
 (>30), low losses and near-zero temperature coefficient The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 K.

In the following formula, let R be the physical property to be measured, let T be the temperature of at which the property is measured.
 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 variations of these compounds by using the newly installed at NIST Philips 430 microscope (#) with 0.23 nm point-to-point resolution (25). Using structural imaging, they ascertained the mechanisms of intergrowth defect formation in two important compounds, [Ba.sub.2][Ti.sub.9][O.sub.20] and Ba[Ti.sub.5][O.sub.11]. They found that the most prevalent defect was formation of a new triclinic polytype Pol´y`type

n. 1. (Print.) A cast, or facsimile copy, of an engraved block, matter in type, etc.; as, a polytype in relief s>
, with an ionic arrangement closely related to that in the accepted structure. Stoichiometric stoi·chi·om·e·try  
n.
1. Calculation of the quantities of reactants and products in a chemical reaction.

2. The quantitative relationship between reactants and products in a chemical reaction.
 defects with considerable microtwinning and formation of face-sharing octahedra were also observed, while nonstoichiometric defect formation was minimal. TEM structural investigations of microwave dielectr ics continued in 1990s, in conjunction with the phase diagram phase diagram, graph that shows the relation between the solid, liquid, and gaseous states of a substance (see states of matter) as a function of the temperature and pressure.  studies of these materials in the Ceramics Division of NIST by T. Vanderah and R. Roth.

With the acquisition of the ultra-high resolution JEOL JEOL Japan Electron Optics Laboratory 3010 microscope by the Materials Science and Engineering Laboratory (MSEL MSEL Materials Science and Engineering Laboratory
MSEL Milton S. Eisenhower Library (Johns Hopkins University)
MSEL Master Scenario Events List
MSEL Master of Studies in Environmental Law
) of NIST in the 1990s, investigation of structures and defects by high-resolution imaging became routine. In the study of newly discovered structures, often the approach was to develop an approximate model based on experimental high-resolution 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 Powder diffraction is a scientific technique using X-Ray or neutron diffraction on powder or microcrystalline samples for structural characterization of materials.

Ideally, every possible crystalline orientation is represented equally in a powdered sample.
.

A very intriguing and new structural architecture has been recently discovered with the help of high-resolution imaging for a group of six new ferrimagnetic phases in the BaO:[TiO.sub.2]:[Fe.sub.2][O.sub.3] system (26). The compounds were proven to belong to a class of well-ordered intergrowth structures. While in general the structures exhibit 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 hex·ag·o·nal  
adj.
1. Having six sides.

2. Containing a hexagon or shaped like one.

3. Mineralogy
 h-[BaTiO.sub.3] and the second--an Fe-rich, spinel-like structure. Fig. 8a gives an example of high-solution 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 distribution of Fe suggests that all six phases can be considered as self-assembled magnetic multilayer structures, with potentially intrigui ng physical properties. One-dimensional 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.sub.3] blocks (Fig. 8d). The disorder was responsible for the difficulty of determining the structures using x-ray diffraction, even with the use of a single crystal.

A structural study of the microwave dielectric calcium tantalate, [Ca.sub.2][Ta.sub.2][O.sub.7], showed diffraction patterns displaying strong subcell characteristics of the fluorite fluorite (fl`ərīt) or fluorspar (fl  structure. The complex distributions of superlattice A superlattice is a material with periodically alternating layers of several substances. Such structures possess periodicity both on the scale of each layer's crystal lattice and on the scale of the alternating layers.  reflections depend on the nature and concentration of the dopant dopant

Any impurity added to a semiconductor to modify its electrical conductivity. The most common semiconductors, silicon and germanium, form crystalline lattices in which each atom shares electrons with four neighbours (see bonding).
 and on the reaction temperature. Polytypes with n = 3, 4, 5, 6, and 7 were prepared as single crystals by the flux method Flux method is a method of crystal growth where the components of the desired substance are dissolved in a solvent (flux) and growth takes place at relatively low temperatures.  (28). High-resolution electron microscope images were used to determine a characteristic structural feature of the polytypes (Fig. 9). The major feature was a fluorite-type cation cation (kăt'ī`ən), atom or group of atoms carrying a positive charge. The charge results because there are more protons than electrons in the cation.  array, which is periodically twinned on [(111).sub.fluorite] to give mixed cubic-hexagonal stacking of the cation layers. The basic repeating units are slabs of different thicknesses comprising a [Ca.sub.3]Ta layer and a [Ta.sub.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 structure is the 3-block trigonal trigonal /tri·go·nal/ (tri´go-nal)
1. triangular.

2. pertaining to a trigone.


trigonal

1. triangular.

2. pertaining to a trigone.
 weberite [P3.sub.1]21 (3T) (28). In the 7M polytype the h-stacked [Ta.sub.3]Ca layers divide the structure into two blocks of c-stacked layers which contain 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).

4. Study of Phase Transitions

The essential feature of a structural phase transition is the change of symmetry. Most often it is a low temperature (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 domains, 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 contrast), in combination with SAD and CB electron diffraction, is the most suitable technique for this approach. For very small domain structures, high-resolut ion imaging and Fast-Fourier Transform are most appropriate.

In the early 1990s the interest in a new generation of high-temperature materials High-temperature materials

A metal or alloy which serves above about 1000°F (540°C). More specifically, the materials which operate at such temperatures consist principally of some stainless steels, superalloys, refractory metals, and certain ceramic
 for aerospace applications led scientists from the Metallurgy Division of NIST to study intermetallic compounds Intermetallic compounds

Materials composed of two or more types of metal atoms, which exist as homogeneous, composite substances and differ discontinuously in structure from that of the constituent metals. They are also called, preferably, intermetallic phases.
, in particular the Ti-AlNb 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 transition from the high-temperature BCC (Blind Carbon Copy) The field in an e-mail header that names additional recipients for the message. It is similar to carbon copy (cc), but the names do not appear in the recipient's message. Not all e-mail systems support the bcc feature. See fcc.  phase, with formation of a Widmanstatten-type lamellar structure Lamellar structures or microstructures are composed of fine, alternating layers of different materials in the form of lamellae. They are often observed in cases where a phase transformation front moves quickly, leaving behind two solid products, as in rapid cooling of  (an HCP-to-FCC transition plus ordering) and omega-type displacements (32). Study of the [Ti.sub.2]AlNb and [Ti.sub.4][AlNb.sub.3] alloys showed the presence of two phases: the Ti/Nb-rich b.c.c. phase and the ternary (programming) ternary - A description of an operator taking three arguments. The only common example is C's ?: operator which is used in the form "CONDITION ? EXP1 : EXP2" and returns EXP1 if CONDITION is true else EXP2.  orthorhombic [Ti.sub.2]AlNb phase (33). Depending on the alloy composition, one of the phases was observed as a precipitate with plate morphology in the matrix of the other phase. For the [Ti.sub.4][Al.sub.3]Nb alloy, formation of a sequence of metastable [omega]-related ph ases from the B2 (ordered BCC) phase was established and summarized in the form of maximal group-subgroup relationship (Fig. 10) (34). An equilibrium low temperature phase has the [B8.sub.2] structure (and triple-cell [D8.sub.2] structure for the more Nb-rich compositions). The metastable [omega] phase and both [B8.sub.2] and [D8.sub.2] are structurally related to the B2 phase by displacement (collapse) of every two (out of three) (111) planes. The [omega]-type structures were verified by means of transmission electron microscopy and by single crystal x-ray diffraction.

For Ti-25 %Al-12.5 %Nb (atom fraction), the transformation path from high temperatures includes the formation of the intermediate hexagonal [DO.sub.19] phase, and subsequent formation of the low-temperature orthorhombic O ([Ti.sub.2]AlNb) phase. For alloys close to Ti-25 %Al-25 %Nb (atom fraction), the path involves an intermediate B19 structure and subsequent formation of a translational domain structure of the O phase (35). The experimental results were summarized as a sequence of crystallographic structural relationships developed from subgroup symmetry relations (36) (Fig. 11). Symmetry elements lost in each step of the sequence determine the possibilities for variants of the low symmetry phase and domains with characteristic interfaces that can be present in the microstructure mi·cro·struc·ture  
n.
The structure of an organism or object as revealed through microscopic examination.


microstructure
Noun

a structure on a microscopic scale, such as that of a metal or a cell
. Fig. 11 gives three examples of such domain: (A) [Ti.sub.2]AlNb alloy, rotational domains of the O phase accommodated in the form of a hierarchical twin structure; (B) [Ti.sub.2]AlNb alloy, interfaces between translational domains formed in the course of the Pm 3m (B2)-to-Pmm a(B19) transition; (C) a two-phase mixture of [DO.sub.19] (a matrix) and three-variants 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 relationship was also applied to phase transformations in other systems, and in particular to transformations between ordered polymorphs of the microwave dielectric Ca([Ca.sub.1/3][Nb.sub.2/3])[O.sub.3] (38) and Ca([Ca.sub.1/3][Nb.sub.2/3])[O.sub.3]-[CaTiO.sub.3] (39). Four [Ca.sub.4][Nb.sub.2][O.sub.9] polymorphs with perovskite-related structures and different arrangements of B-site cations were identified. Ordering of the B-cations ([Ca.sup.2+] and [Nb.sup.5+]) in this system is combined with displacement of oxygen ions by octahedral oc·ta·he·dral  
adj.
Having eight plane surfaces.



octa·hedral·ly adv.
 tilting. Three of the polymorphs have 1:1 (monoclinic mon·o·clin·ic  
adj.
Of or relating to three unequal crystal axes, two of which intersect obliquely and are perpendicular to the third.


monoclinic
Adjective

Crystallog
 [P2.sub.1]/c), 2:1 (monoclinic [P2.sub.1]/c) and 3:1 (triclinic P1) ordering. The 1:1 ordered structure features alternating [{111}.sub.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 polymorph /poly·morph/ (pol´i-morf) colloquial term for polymorphonuclear leukocyte.

polymorph

a colloquial term for a polymorphonuclear leukocyte.
 exhibits {CaNbNb...} sequence of the [{111}.sub.c] B-cation planes. The metastable 3:1 structure is de rived from the 1:1 ordered structure by a partial ordering partial ordering - A relation R is a partial ordering if it is a pre-order (i.e. it is reflexive (x R x) and transitive (x R y R z => x R z)) and it is also antisymmetric (x R y R x => x = y).  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 and neutron powder diffraction data (40). The relationship 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.sub.4][Nb.sub.2][O.sub.9] polymorphs (deduced from electron diffraction data) do not exhibit group/subgroup relations, and, therefore, phase transitions between them must be first-order transitions.

Different problems related to the microstructural formation were solved using conventional TEM. For example, in the study of Diffusion-Induced Grain Boundary Migration (DIGM DIGM Diffusion Induced Grain Boundary Migration ) phenomena, the effect of diffusion of [Cr.sub.2][O.sub.3] into polycrystalline [Al.sub.2][O.sub.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 migration and the generation of misfit mis·fit  
n.
1. Something of the wrong size or shape for its purpose.

2. One who is unable to adjust to one's environment or circumstances or is considered to be disturbingly different from others.
 dislocations. When these dislocations were observed using bright and dark field transmission electron microscopy, a good correlation was found between the dislocation spacing and the chromium concentration in the alloyed regions. Another problem related to the plastic deformation plastic deformation,
n any irreversible deformation of tissues.
 of [Al.sub.2][O.sub.3] by slip and twinning was investigated by examining the regions surrounding a microhardness indentation in·den·ta·tion
n.
A notch, a pit, or a depression.
 using TEM (42). The results establish: (1) the occurrence of pyramidal slip on {1123} <1100>, 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 discontinuous /dis·con·tin·u·ous/ (dis?kon-tin´u-us)
1. interrupted; intermittent; marked by breaks.

2. discrete; separate.

3. lacking logical order or coherence.
 coarsening in the [Ti.sub.3]Al ([[alpha].sub.2]) / TiAl ([gamma]) fully lamellar structure was examined (43). Three morphologies were observed in discontinuously coarsened coars·en  
tr. & intr.v. coars·ened, coars·en·ing, coars·ens
To make or become coarse.

Adj. 1. coarsened - made coarse or crude by lack of skill
inferior - of low or inferior quality
 lamellar structures (secondary lamellae lamellae
(lmel´ē),
n the nearly parallel layers of bone tissue found in compact bone.
). Type-(I) lamellae have the low energy habit plane as their lamellar lamellar /la·mel·lar/ (lah-mel´ar)
1. pertaining to or resembling lamellae.

2. lamellated (1).


lamellar

pertaining to or emanating from lamella.
 interfaces, and have the same lamellar direction as the original primary lamellae. Type-(II) lamellae have the same crystallographic orientation of [[alpha].sub.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 different crystallographic orientation of the [[alpha].sub.2] plates from that in the original primary lamellae, but have the low energy habit plane as their lamellar interfaces. The growth kinetics 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 collaborative effort with Martin Marietta Laboratory to determine the origins of the ultra-high strength in Weldalite aluminum alloys, later used to build the Space Shuttle External Tank A Space Shuttle External Tank (ET) is the component of the Space Shuttle launch vehicle that contains the liquid hydrogen fuel and liquid oxygen oxidizer. During lift-off and ascent it supplies the fuel and oxidizer under pressure to the three space shuttle main engines  to reduce launch weight. This novel aluminum 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 recrystallization recrystallization,
n the return of a wrought metal to crystalline form because of excessive cold working or excessive application of heat.


recrystallization
. TEM imaging and diffraction was required to sort out the complex microstructure responsible for the high strength of the alloy. Our microstructural studies established that the Weldalite alloys are strengthened primarily by the equilibrium [T.sub.1]-[Al.sub.2]CuLi phase, in contrast to other commercial aluminum alloys, which are strengthened by metastable precipitate phases. In addition to [T.sub.1], additional strengthening arises from 3 other lath or plate-Like precipitates (S'-[Al.sub.2]CuMg, [eta]'-[Al.sub.2]Cu and an unknown phase), all lying on distinct habit planes in the matrix (Fig. 13) (44). When [alpha]', or [Al.sub.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.

5. Conclusions

The NBS/NIST Materials Science and Engineering Laboratory has a history of discovery of new phases and classes of crystallographic structures through transmission electron microscopy and electron diffraction. The power of electron diffraction has allowed the determination of structural details, both in perfect crystals and in defect structures, which are too subtle for x-ray or neutron 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.

Accepted: August 22, 2001

Available online: http://www.nist.gov/jres

(#.) Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology National Institute of Standards and Technology, governmental agency within the U.S. Dept. of Commerce with the mission of "working with industry to develop and apply technology, measurements, and standards" in the national interest. , nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

6. References

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(2.) Many excellent books are written on the theory and practice of TEM. One of the first and best is by P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley, and M. J. Whelan, Electron Microscopy of Thin Crystals, R. E. Krieger Publishing Co. (1977).

(3.) Electron Diffraction Techniques, J. M. Cowley, ed., International Union of Crystallography The International Union of Crystallography (IUCr) is a member of the International Council for Science (ICSU) and exists to serve the world community of crystallographers. See also
X-ray crystallography

Crystallography External links
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New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
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n. pl. ya·gis
A directional radio and television antenna consisting of a horizontal conductor with several insulated dipoles parallel to and in the plane of the conductor.
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An integration of logic programming into Lisp.

["A Modifiable Representation System", M. Genesereth et al, HPP 80-22, CS Dept Stanford U 1980].
 Special Publ. 547 (1999) p. 127.

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About the authors: Leonid Bendersky is a metallurgist in the Metallurgy Division of the NIST Materials Science and Engineering Laboratory. Frank Gayle is leader of the Materials Structure and Characterization Group in the Metallurgy Division. The National Institute of Standards and Technology is an agency of the Technology Administration, U.S. Department of Commerce.
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