Modulated Atomic Displacement Description and Easy Structural Factor Computing

1982 ◽  
Vol 21 ◽  
Author(s):  
P. Wolfers
Keyword(s):  
Wave Vector ◽  
Atomic Displacement ◽  
Crystallographic Structure ◽  
General Description ◽  
Single Wave ◽  
Scattering Center ◽  
Displacement Vectors ◽  
Vector Approximation ◽  
Vector Case ◽  
Modulated Phase

ABSTRACTThe displacement of a particular atom in a modulated crystallographic structure can be described in terms of a Fourier Series. In the harmonic single wave vector approximation, the structure factor can be written as a function of the atomic displacement vectors. Such expressions are however not valid in the multi-wave-vector case. We propose a general description for the modulation of displacement where each scattering center (atom) is distributed on several sites whose population is modulated. In the paper, we will show that approach is well suited for computing. We have developed a general least squares program which has been applied to the modulated phase of αU(T < 43 K) [2].

scholarly journals Orientation Dependent Mechanical Responses and Plastic Deformation Mechanisms of ZnSe Nano Films under Nanoindentation

Nanomaterials ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 3014
Author(s):  
Chao Xu ◽  
Futi Liu ◽  
Chunmei Liu ◽  
Pei Wang ◽  
Huaping Liu
Keyword(s):  
Plastic Deformation ◽  
Elastic Recovery ◽  
Structural Evolution ◽  
Atomic Displacement ◽  
Deformation Mechanisms ◽  
Formation Mechanisms ◽  
Plastic Deformations ◽  
Mechanical Responses ◽  
Displacement Vectors ◽  
Dynamics Simulations

Although ZnSe has been widely studied due to its attractive electronic and optoelectronic properties, limited data on its plastic deformations are available. Through molecular dynamics simulations, we have investigated the indentations on the (001), (110), and (111) planes of ZnSe nano films. Our results indicate that the elastic modulus, incipient plasticity, elastic recovery ratio, and the structural evolutions during the indenting process of ZnSe nano films show obvious anisotropy. To analyze the correlation of structural evolution and mechanical responses, the atomic displacement vectors, atomic arrangements, and the dislocations of the indented samples are analyzed. Our simulations revealed that the plastic deformations of the indented ZnSe nano films are dominated by the nucleation and propagation of 1/2<110> type dislocations, and the symmetrically distributed prismatic loops emitted during the indenting process are closely related with the mechanical properties. By studying the evolutions of microstructures, the formation process of the dislocations, as well as the formation mechanisms of the emitted prismatic loops under the indented crystalline planes are discussed. The results presented in this work not only provide an answer for the questions about indentation responses of ZnSe nano films, but also offer insight into its plastic deformation mechanisms.

A Computer Method for Facilitating Rapid Quantitative Use of the Philips 300 Goniometer Stage

1973 ◽  
Vol 31 ◽  
pp. 100-101
Author(s):  
Wen-Shian Tzeng ◽  
P. R. Strutt
Keyword(s):  
Stacking Faults ◽  
Thin Foil ◽  
Atomic Displacement ◽  
Computer Method ◽  
Crystallographic Structure ◽  
Polycrystalline Specimen ◽  
Planar Defects ◽  
Precise Characterization ◽  
Actual Computer

A computer method has been developed which facilitates the rapid use of the Philips 300 goniometer stage for quantitative diffraction contrast analyses of lattice imperfections in thin-foil specimens. Using this method it is a straightforward matter to obtain 20 (or even more) different two beam conditions on a single randomly oriented grain in a polycrystalline specimen. Furthermore, the method avoids ambiguity in determining the sense of the atomic displacement of planar defects. Thus it is particularly useful for the precise characterization of stacking faults and anti-phase boundaries. The generality of the method enables it to be used for thin-foil specimens with any crystallographic structure. Basic steps involved in the actual computer program are briefly summarized.

Phase Transition in K3Na(MoO4)2 and Determination of the Twinned Structures of K3Na(MoO4)2 and K2.5Na1.5(MoO4)2 at Room Temperature

1997 ◽  
Vol 53 (4) ◽  
pp. 596-603 ◽  
Author(s):  
J. Fábry ◽  
V. Petrícek ◽  
P. Vanek ◽  
I. Císarová
Keyword(s):  
Phase Transition ◽  
Room Temperature ◽  
Domain Switching ◽  
Point Group ◽  
Atomic Displacement ◽  
Scanning Calorimetry ◽  
Sodium Potassium ◽  
Displacement Vectors ◽  
Reversible Phase Transition

The room-temperature phases of sodium potassium molybdates K3Na(MoO4)2 and K2.5Na1.5(MoO4)2 are isostructural with the monoclinic low-temperature phases of KaNa(SeO4)2 and K3Na(CrO4)2, which are twinned distorted glaserite structures. In the molybdates there are two crystallographically independent potassiums and their environment slightly differs from those in K3Na(SeO4)2 and K3Na(CrO4)2. The excessive Na in K2.5Na1.5(MoO4)2 occupies the position of the more firmly bound potassium. A reversible phase transition at 513 K was discovered in KaNa(MoO4)2 by DSC (differential scanning calorimetry), but no such transition in K2.5Na1.5(MoO4)2 was detected. Both samples used in the diffractometer experiment were found to be composed of six domains being related by twinning operations of the point group 6. The twinning may be considered as a combination of a merohedral and a pseudo-merohedral twinning with two- and threefold rotations as twinning operations, respectively. However, a reversible domain switching, which is observable in the related ferroelastic crystals of KaNa(SeO4)2 and K3Na(CrO4)2, was not observed either in K3Na(MoO4)2 or in K2.5Na1.5(MoO4)2, either due to semitransparency of the samples or high ferroelastic distortion. This distortion is manifested by the values of the atomic displacement vectors which are about twice as large as those in the selenate or the chromate.

Electron-diffraction studies in synthetic polymer materials

1983 ◽  
Vol 41 ◽  
pp. 362-365
Author(s):  
D.T. Grubb
Keyword(s):  
Electron Diffraction ◽  
Synthetic Polymer ◽  
Polymer Materials ◽  
Crystallographic Structure ◽  
High Dose ◽  
Electron Dose ◽  
Dose Rates ◽  
First Case ◽  
Diffraction Patterns ◽  
The Many

Diffraction studies in polymeric and other beam sensitive materials may bring to mind the many experiments where diffracted intensity has been used as a measure of the electron dose required to destroy fine structure in the TEM. But this paper is concerned with a range of cases where the diffraction pattern itself contains the important information.In the first case, electron diffraction from paraffins, degraded polyethylene and polyethylene single crystals, all the samples are highly ordered, and their crystallographic structure is well known. The diffraction patterns fade on irradiation and may also change considerably in a-spacing, increasing the unit cell volume on irradiation. The effect is large and continuous far C94H190 paraffin and for PE, while for shorter chains to C 28H58 the change is less, levelling off at high dose, Fig.l. It is also found that the change in a-spacing increases at higher dose rates and at higher irradiation temperatures.

Microstructural characterization of CoPtCr/Cr thin film disks by cross-section TEM and elongated probe micro-diffraction

1991 ◽  
Vol 49 ◽  
pp. 762-763
Author(s):  
M.A. Parker ◽  
K.E. Johnson ◽  
C. Hwang ◽  
A. Bermea
Keyword(s):  
Magnetic Recording ◽  
Electron Probe ◽  
Microstructural Characterization ◽  
Crystallographic Structure ◽  
Recording Media ◽  
Layer By Layer ◽  
Cross Sectional ◽  
New Techniques ◽  
Polished Side

We have reported the dependence of the magnetic and recording properties of CoPtCr recording media on the thickness of the Cr underlayer. It was inferred from XRD data that grain-to-grain epitaxy of the Cr with the CoPtCr was responsible for the interaction observed between these layers. However, no cross-sectional TEM (XTEM) work was performed to confirm this inference. In this paper, we report the application of new techniques for preparing XTEM specimens from actual magnetic recording disks, and for layer-by-layer micro-diffraction with an electron probe elongated parallel to the surface of the deposited structure which elucidate the effect of the crystallographic structure of the Cr on that of the CoPtCr.XTEM specimens were prepared from magnetic recording disks by modifying a technique used to prepare semiconductor specimens. After 3mm disks were prepared per the standard XTEM procedure, these disks were then lapped using a tripod polishing device. A grid with a single 1mmx2mm hole was then glued with M-bond 610 to the polished side of the disk.

Dynamical Scattering in Crystalline Biological Specimens. I. Criteria of Validity for Scattering Approximations

1975 ◽  
Vol 33 ◽  
pp. 192-193
Author(s):  
Robert M. Glaeser ◽  
Bing K. Jap
Keyword(s):  
Biological Sciences ◽  
Electron Microscopy ◽  
Electron Microscope ◽  
Electron Diffraction ◽  
Born Approximation ◽  
Materials Science ◽  
Image Data ◽  
Dynamical Effect ◽  
Crystallographic Structure ◽  
Electron Microscope Image

The dynamical scattering effect, which can be described as the failure of the first Born approximation, is perhaps the most important factor that has prevented the widespread use of electron diffraction intensities for crystallographic structure determination. It would seem to be quite certain that dynamical effects will also interfere with structure analysis based upon electron microscope image data, whenever the dynamical effect seriously perturbs the diffracted wave. While it is normally taken for granted that the dynamical effect must be taken into consideration in materials science applications of electron microscopy, very little attention has been given to this problem in the biological sciences.

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