The Critical Voltage Effect in Zone Axis Patterns. A Theoretical Study

1980 ◽  
Vol 98 (1) ◽  
pp. 349-364
Author(s):  
R. Gevers ◽  
M. David ◽  
W. Herremans
Author(s):  
B. F. Buxton

In cross-grating high energy electron diffraction, the scattering of the incident beam by the atomic string potentials is often so strong that there are many zone axis critical voltages below 1 MV. Steeds et al. (1976, 1977) have therefore explored the possibility of obtaining structural information from these critical voltages. In particular, for simple zone axes of high symmetry with only one string of atoms in each unit cell of the projected potential, they were able to characterize zone axis patterns by the critical voltage Ec and a thickness parameter ξ24 defined as the (2)-(4) extinction length at an orientation approximately midway between the zone axis and the first Brillouin zone boundary. Here a simple model atomic string potential will be used to investigate the information which can be gleaned from these parameters.The atomic string approximation (ASA) developed by Buxton and Tremewan (1977) will be used in order to avoid the large matrices encountered in the conventional many-beam theory.


Author(s):  
Yoshitomo Tanaka ◽  
Takuo Fujimoto ◽  
Yoshitsugu Tomokiyo ◽  
Yoko Suyama

1993 ◽  
Vol 328 ◽  
Author(s):  
D.R.M. Williams ◽  
A. Halperin

ABSTRACTWe present a theoretical study of liquid crystalline polymers in nematic solvents. We focus on the following topics: (i) Rod-like chains confined between plates, (ii) Flexible chains in a slit (iii) Nematic brushes and double-brushes (iv) Anchoring transitions. Confined and grafted chains in nematic solvents can exhibit a variety of interesting effects, including quasi-piezoelectricity and a lowering of the critical voltage for the Fréedericksz transition.


1987 ◽  
Vol 55 (1) ◽  
pp. 17-38 ◽  
Author(s):  
H. Matsuhata ◽  
J. W. Steeds
Keyword(s):  

Author(s):  
M. Saunders ◽  
A. G. Fox ◽  
P. A. Midgley

The zone-axis CBED pattern-matching technique ZAPMATCH [Bird & Saunders (1992). Ultramicroscopy, 45, 241–251] has been applied to low-order structure-factor measurements in nickel and copper. Considerable disagreement exists between previously published results obtained with a variety of solid-state theories and experimental techniques. The nickel ZAPMATCH results confirm previous electron-diffraction critical-voltage measurements and are in excellent agreement with FLAPW (full-potential linearized augmented plane-wave) theory calculations. This is further proof of the accuracy achievable with ZAPMATCH analysis. For copper, however, while the results support the findings of previous experimental measurements, they are consistently higher than those given by a range of solid-state theories, perhaps demonstrating some limitation in the existing theory. Two extensions to the ZAPMATCH technique are also considered. First, rules are developed to determine the number of structure factors that can be refined accurately from a given CBED pattern. Second, the imaginary potential generally introduced to account for the effects of thermal diffuse scattering (TDS) is also refined. It is shown that, while the widely used Einstein model is a useful approximation, the refined values are consistently higher than the model predicts. In addition, the importance of a second-order (real) TDS correction arising from the Einstein model is investigated. Although its effects are limited in this instance, it may prove to be more significant at lower beam energies or for materials of higher atomic number.


Author(s):  
J. S. Lally ◽  
R. J. Lee

In the 50 year period since the discovery of electron diffraction from crystals there has been much theoretical effort devoted to the calculation of diffracted intensities as a function of crystal thickness, orientation, and structure. However, in many applications of electron diffraction what is required is a simple identification of an unknown structure when some of the shape and orientation parameters required for intensity calculations are not known. In these circumstances an automated method is needed to solve diffraction patterns obtained near crystal zone axis directions that includes the effects of systematic absences of reflections due to lattice symmetry effects and additional reflections due to double diffraction processes.Two programs have been developed to enable relatively inexperienced microscopists to identify unknown crystals from diffraction patterns. Before indexing any given electron diffraction pattern, a set of possible crystal structures must be selected for comparison against the unknown.


Author(s):  
J. S. Lally ◽  
L. E. Thomas ◽  
R. M. Fisher

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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