Critical Voltage for Non-Centro. Crystals and its Application to the Accurate Measurement of Structure Factor Phases by CBED

1990 ◽  
Vol 48 (2) ◽  
pp. 530-531
Author(s):  
J.C.H. Spence ◽  
J.M. Zuo
Keyword(s):  
Structure Factor ◽  
Dynamical Theory ◽  
Critical Voltage ◽  
Bragg Condition ◽  
Two Phase ◽  
Transmission Electron ◽  
Structure Factors ◽  
Three Phase ◽  
Highly Sensitive ◽  
Image Position

The application of the three-beam dynamical theory of transmission electron diffraction to centrosymmetric and non-centrosymmetric crystals shows that certain regions of three-beam CBED patterns are highly sensitive to the three-phase structure invariant By applying this method to the systematics geometry, a method has been described which allows structure factor phases to be measured with an accuracy of 0.07°. Using the Bethe potentials, we find a degeneracy in eigenvalues at the critical voltage VA for acentric crystals in the systematics orientation whereHere VA is now seen to depend both on the structure factors Vg (in volts) and on the systematics “two=phase” invariant In this paper we consider the application of this method to BeO (wurtzite structure), with g = (004) and h = (002). Then the CBED intensity is most sensitive to Y near the (004) Bragg condition at 46 kV. But since the theory contains only the product KSg, other voltages and orientations are also sensitive.

scholarly journals Non-systematic Three-beam Effects in Dynamical Electron Diffraction and Their Use in Determination of Amplitude and Phase of Structure Factors

1988 ◽  
Vol 41 (3) ◽  
pp. 449 ◽  
Author(s):  
K Marthinsen ◽  
H Matsuhata ◽  
R Hfier ◽  
J Gjfnnes
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Bloch Wave ◽  
Critical Voltage ◽  
Dispersion Surface ◽  
Structure Factors ◽  
Three Phase ◽  
Convergent Beam ◽  
Diffraction Condition

The treatment of non-systematic multiple-beam effects in dynamical diffraction is extended. Expressions for Bloch wave degeneracies are given in the centrosymmetrical four-beam case and for some symmetrical directions. These degeneracies can be determined experimentally either as critical voltages or by locating the exact diffraction condition at a fixed voltage. The accuracy when applied to structure factor determination is comparable with the systematical critical voltage, namely 1% in UfT The three-beam case 0, g, h is treated as well in the non-centrosymmetrical case, where it can be used for determination of phases. It is shown that the contrast features can be represented .by an effective structure factor defined by the gap at the dispersion surface. From the variation in the gap with diffraction condition, a method to determine the three-phase structure invariant I\J = 9 + _ h + h _ 9 is given. The method is based upon the contrast asymmetry in the weaker diffracted beam and can be applied in Kikuchi, convergent beam or channelling patterns. Calculations relating to channelling in backscattering are also presented.

Obtaining the structure factors for an epitaxial film using Cu X-ray radiation

2013 ◽  
Vol 46 (6) ◽  
pp. 1749-1754 ◽  
Author(s):  
P. Wadley ◽  
A. Crespi ◽  
J. Gázquez ◽  
M.A. Roldán ◽  
P. García ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Thin Films ◽  
Structure Factor ◽  
Tetragonal Symmetry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Structure Factors ◽  
Scanning Transmission

Determining atomic positions in thin films by X-ray diffraction is, at present, a task reserved for synchrotron facilities. Here an experimental method is presented which enables the determination of the structure factor amplitudes of thin films using laboratory-based equipment (Cu Kα radiation). This method was tested using an epitaxial 130 nm film of CuMnAs grown on top of a GaAs substrate, which unlike the orthorhombic bulk phase forms a crystal structure with tetragonal symmetry. From the set of structure factor moduli obtained by applying this method, the solution and refinement of the crystal structure of the film has been possible. The results are supported by consistent high-resolution scanning transmission electron microscopy and stoichiometry analyses.

Crystallography of Bcc/T1/T2 Three-Phase Microstructure in the Directionally Solidified Mo-Nb-Si-B Alloy

2015 ◽  
Vol 1760 ◽  
Author(s):  
Naoki Takata ◽  
Nobuaki Sekido ◽  
Masao Takeyama ◽  
John H. Perepezko
Keyword(s):  
Eutectic Reaction ◽  
Directionally Solidified ◽  
Orientation Relationships ◽  
Two Phase ◽  
Constant Growth Rate ◽  
Liquid Phases ◽  
Three Phase ◽  
Ar Gas ◽  
Image Position ◽  
Bcc Phase

ABSTRACTIn the present study, the crystallographic features of bcc/T1/T2 three-phase microstructure in a directionally solidified Mo–32.2Nb–19.5Si–4.7B (at.%) alloy have been examined by electron back-scattering diffraction (EBSD) analysis. The alloy was directionally solidified using an optical floating zone (OFZ) furnace in a flowing Ar gas atmosphere at a constant growth rate of 10 mm/hour. The microstructure of the directionally solidified alloy is characterized by an elongated T2 phase surrounded by inclusions of bcc and T1 phases with an interwoven morphology. The T2 grains are faceted on the (001) planes and elongated along the [110] direction. The T2 phase has an orientation relationship of (001)T2 // (011)bcc and [130]T2 // [2${\rm{\bar 1}}$1]bcc with the bcc phase, whereas any particular orientation relationships of T1 phase with bcc and T2 phases have not been found. These crystallographic features of bcc/T1/T2 three-phase microstructure suggest that the primary T2 phase crystallizes and grows along the [110] direction in liquid phase, followed by nucleation of the bcc phase on the interface between T2 and liquid phases, resulting in bcc/T1 two-phase eutectic reaction surrounding the elongated T2 phase.

On the determination of enanttomorphs from non-systematic many-beam effects in CBED patterns

1989 ◽  
Vol 47 ◽  
pp. 484-485
Author(s):  
K. Marthinsen ◽  
R. Høier
Keyword(s):  
Structure Factor ◽  
High Accuracy ◽  
Convergent Beam Electron Diffraction ◽  
Bragg Condition ◽  
Sign Problem ◽  
Three Phase ◽  
Convergent Beam ◽  
Diffraction Effects ◽  
Beam Diffraction

A convergent beam electron diffraction (CBED) method which makes it possible to determine structure factor magnitudes and phases with high accuracy has recently been suggested. It is based on detailed simulations of non-systematic many-beam diffraction effects in the disks. Basis for the phase determination is an asymmetry which may appear in a line h with respect to the Bragg condition of the coupled reflection g near a three-beam condition. Approximate analytical three-beam solutions show that the sign and size of this asymmetry depends on the structure factor phases Θh of the reflections h involved through a term cos(Φ) where Φ is the three phase structure invariant, Φ = Θh + Θg + Θh-g. The magnitude of the phase invariant is thus in principle available, but not the sign. The aim of the present work has been to discuss the origin of the sign problem and the possibilities of distinguishing +/−Φ.

Measurement of small structure factors by the critical-voltage effect in HEED: The superlattice reflections in β'nial, β'CoAl and γtial

1992 ◽  
Vol 50 (2) ◽  
pp. 1174-1175
Author(s):  
Alan G. Fox ◽  
Mark A. Tabbernor
Keyword(s):  
Structure Factor ◽  
High Energy ◽  
Critical Voltage ◽  
Intermetallic Alloys ◽  
Rocking Curve ◽  
X Ray ◽  
Structure Factors ◽  
Factor Measurement ◽  
Small Structure ◽  
Convergent Beam

The systematic critical voltage effect, Vc, in high energy electron diffraction has been used for some time to accurately measure low-angle x-ray structure factor structure factor amplitudes (see e.g. 1). It has a significant advantage over other methods for accurate structure factor measurement, such as systematic convergent beam rocking curve or x-ray Pendellösung techniques, in that it is capable of measuring very small structure factors such as the 222 ‘forbidden’ reflections in Si and Ge (see e.g. 2). In the present work the potential of the systematic Vc method for measuring small structure factor amplitudes and average Debye-Waller factors in the intermetallic alloys NiAl, CoAl and TiAl will be demonstrated.The structure factors, F, for ordered stoichiometric B2 alloys comprising A and B atoms such as Ni (Co)Al are given by

How do specimen preparation and crystal perfection affect structure factor measurements by quantitative convergent-beam electron diffraction?

2017 ◽  
Vol 50 (2) ◽  
pp. 602-611 ◽  
Author(s):  
Ding Peng ◽  
Philip N. H. Nakashima
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Convergent Beam Electron Diffraction ◽  
Specimen Preparation ◽  
Crystalline Materials ◽  
Beam Electron ◽  
Crystal Perfection ◽  
Transmission Electron ◽  
Structure Factors ◽  
Convergent Beam

The effectiveness of tripod polishing and crushing as methods of mechanically preparing transmission electron microscopy specimens of hard brittle inorganic crystalline materials is investigated via the example of cerium hexaboride (CeB6). It is shown that tripod polishing produces very large electron-transparent regions of very high crystal perfection compared to the more rapid technique of crushing, which produces crystallites with a high density of imperfections and significant mosaicity in the case studied here where the main crystallite facets are not along the natural {001} cleavage planes of CeB6. The role of specimen quality in limiting the accuracy of structure factor measurements by quantitative convergent-beam electron diffraction (QCBED) is investigated. It is found that the bonding component of structure factors refined from CBED patterns obtained from crushed and tripod-polished specimens varies very significantly. It is shown that tripod-polished specimens yield CBED patterns of much greater integrity than crushed specimens and that the mismatch error that remains in QCBED pattern matching of data from tripod-polished specimens is essentially nonsystematic in nature. This stands in contrast to QCBED using crushed specimens and lends much greater confidence to the accuracy and precision of bonding measurements by QCBED from tripod-polished specimens.

Structure factor determination from critical voltages in electron diffraction

1989 ◽  
Vol 47 ◽  
pp. 490-491
Author(s):  
J. Gjønnes ◽  
H. Matsuhata ◽  
J. Taftø
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Critical Voltage ◽  
Order Structure ◽  
Kikuchi Pattern ◽  
Additional Information ◽  
Selection Of Configurations ◽  
Structure Factors ◽  
Temperature Factors ◽  
Selection Of

The principle of the critical voltage method in electron diffraction is an attractive one: a relation between structure factors can be determined with high precision from measurement of the condition for vanishing contrast of a contrast detail in the Kikuchi pattern or in the CBED pattern. In practice the method meets with some apparent and real limitations. The original, second order critical voltage in the systematic case (Watanabe, Uyeda and Fukuhara) depends on high accelerating voltage and can be applied mainly to strong low order structure factors from simple substances. Accurate additional information about other structure factors and temperature factors must be obtained from other methods. In order to increase the utility of the method a wider selection of configurations suitable for measurement has to be found. Several investigators have focussed on non-systematic cases: Gjønnes and Høier, Steeds.

Germanium supersaturation during the crystallization of amorphous Te–Ge–Sn thin films

1991 ◽  
Vol 6 (12) ◽  
pp. 2666-2676 ◽  
Author(s):  
M. Libera ◽  
M. Chen ◽  
K. Rubin
Keyword(s):  
Thin Films ◽  
Electron Diffraction ◽  
Phase Field ◽  
Optical Recording ◽  
Laser Exposure ◽  
Two Phase ◽  
Storage Media ◽  
Transmission Electron ◽  
Three Phase ◽  
Nonequilibrium Crystallization

The structure and phase relations of Te–Ge–Sn thin films are examined with application to erasable optical storage media. Free energy data from the literature predict that the region of the Te–Ge–Sn phase diagram between Ge, Sn, and the TeGe–TeSn pseudobinary consists of one two-phase field [α–Ge and Te50 (GexSn1−x)50] and one three-phase field (α–Ge, β–Sn, and TeSn). Electron diffraction from five different Te–Ge–Sn films annealed at 623 K experimentally confirms this prediction. One composition from the two-phase field is deposited as a tri-layer film with the structure 150 nm SiO2/75 nm Te36.3Ge47.4Sn16.3/150 nm SiO2 on a grooved disk substrate, and the microstructure resulting from low-power (12 mW) CW and higher-power (∽50 mW) pulsed laser exposure is studied by transmission electron microscopy and electron diffraction. Of particular significance is that laser-induced crystallization produces a single-phase structure consisting of the Te–Ge–Sn compound phase which is supersaturated with respect to the excess Ge. This supersaturation leads to a disordering of the equilibrium NaCl-type structure of this phase. Crystallization of a micron-sized amorphous spot on a ∼200 ns time scale occurs by a diffusionless process. The fast erase times required by a phase-change optical recording application can thus be achieved in off-stoichiometric compound compositions by way of a nonequilibrium crystallization process.

A Magnetic Spectrometer for a Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 436-437
Author(s):  
A. Kosiara ◽  
J. W. Wiggins ◽  
M. Beer
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Magnetic Spectrometer ◽  
Fringe Field ◽  
Curvature Radius ◽  
Magnetic Pole ◽  
Quadrupole Field ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Under Construction ◽  
Image Position

A magnetic spectrometer to be attached to the Johns Hopkins S. T. E. M. is under construction. Its main purpose will be to investigate electron interactions with biological molecules in the energy range of 40 KeV to 100 KeV. The spectrometer is of the type described by Kerwin and by Crewe Its magnetic pole boundary is given by the equationwhere R is the electron curvature radius. In our case, R = 15 cm. The electron beam will be deflected by an angle of 90°. The distance between the electron source and the pole boundary will be 30 cm. A linear fringe field will be generated by a quadrupole field arrangement. This is accomplished by a grounded mirror plate and a 45° taper of the magnetic pole.

Some Applications of the U. S. Steel MVEM

1973 ◽  
Vol 31 ◽  
pp. 4-5
Author(s):  
J. S. Lally ◽  
L. E. Thomas ◽  
R. M. Fisher
Keyword(s):  
Electron Diffraction ◽  
Debye Temperature ◽  
Metals And Alloys ◽  
Critical Voltage ◽  
Dynamical Diffraction ◽  
Phase Structures ◽  
Structure Factors ◽  
Local Bonding ◽  
Diffraction Phenomenon ◽  
Multi Phase

A variety of materials containing many different microstructures have been examined with the USS MVEM. Three topics have been selected to illustrate some of the more recent studies of diffraction phenomena and defect, grain and multi-phase structures of metals and minerals.(1) Critical Voltage Effects in Metals and Alloys - This many-beam dynamical diffraction phenomenon, in which some Bragg resonances vanish at certain accelerating voltages, Vc, depends sensitively on the spacing of diffracting planes, Debye temperature θD and structure factors. Vc values can be measured to ± 0.5% in the HVEM ana used to obtain improved extinction distances and θD values appropriate to electron diffraction, as well as to probe local bonding effects and composition variations in alloys.

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