Module structure of doubly periodic arrays over finite fields

Mulan Liu; Lei Hu

doi:10.1007/bf03182359

Dickson polynomials, completely normal polynomials and the cyclic module structure of specific extensions of finite fields

Designs Codes and Cryptography ◽

10.1007/bf00124593 ◽

1996 ◽

Vol 9 (2) ◽

pp. 193-202 ◽

Cited By ~ 1

Author(s):

Alfred Scheerhorn

Keyword(s):

Finite Fields ◽

Module Structure ◽

Cyclic Module ◽

Dickson Polynomials

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High-resolution x-ray analysis of dislocation networks nn tilt boundaries

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100105126 ◽

1988 ◽

Vol 46 ◽

pp. 612-613

Author(s):

J. R. Michael ◽

C. H. Lin ◽

S. L. Sass

Keyword(s):

Grain Boundaries ◽

Analytical Electron Microscopy ◽

Solute Segregation ◽

X Ray ◽

Periodic Arrays ◽

Analytical Electron ◽

Primary Dislocation ◽

Tilt Boundaries ◽

Polycrystalline Solids ◽

Twist Boundaries

The segregation of solute atoms to grain boundaries in polycrystalline solids can be responsible for embrittlement of the grain boundaries. Although Auger electron spectroscopy (AES) and analytical electron microscopy (AEM) have verified the occurrence of solute segregation to grain boundaries, there has been little experimental evidence concerning the distribution of the solute within the plane of the interface. Sickafus and Sass showed that Au segregation causes a change in the primary dislocation structure of small angle [001] twist boundaries in Fe. The bicrystal specimens used in their work, which contain periodic arrays of dislocations to which Au is segregated, provide an excellent opportunity to study the distribution of Au within the boundary by AEM.The thin film Fe-0.8 at% Au bicrystals (composition determined by Rutherford backscattering spectroscopy), ∼60 nm thick, containing [001] twist boundaries were prepared as described previously. The bicrystals were analyzed in a Vacuum Generators HB-501 AEM with a field emission electron source and a Link Analytical windowless x-ray detector.

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Quasiperiodic interfaces: HREM observations of grain and phase boundaries

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100174795 ◽

1990 ◽

Vol 48 (4) ◽

pp. 332-333

Author(s):

K. L. Merkle

Keyword(s):

Atomic Structure ◽

Direct Determination ◽

Lattice Parameter ◽

Atomic Scale ◽

Misfit Dislocations ◽

Oxide Systems ◽

Atomic Structures ◽

Periodic Arrays ◽

Parameter Ratio ◽

Metal Metal

The atomic structures of internal interfaces have recently received considerable attention, not only because of their importance in determining many materials properties, but also because the atomic structure of many interfaces has become accessible to direct atomic-scale observation by modem HREM instruments. In this communication, several interface structures are examined by HREM in terms of their structural periodicities along the interface.It is well known that heterophase boundaries are generally formed by two low-index planes. Often, as is the case in many fcc metal/metal and metal/metal-oxide systems, low energy boundaries form in the cube-on-cube orientation on (111). Since the lattice parameter ratio between the two materials generally is not a rational number, such boundaries are incommensurate. Therefore, even though periodic arrays of misfit dislocations have been observed by TEM techniques for numerous heterophase systems, such interfaces are quasiperiodic on an atomic scale. Interfaces with misfit dislocations are semicoherent, where atomically well-matched regions alternate with regions of misfit. When the misfit is large, misfit localization is often difficult to detect, and direct determination of the atomic structure of the interface from HREM alone, may not be possible.

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Electron Microscope study of commensurate-incommensurate phase transition in BaZnGeO4

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173996 ◽

1990 ◽

Vol 48 (4) ◽

pp. 172-173

Author(s):

Naoki Yamamoto ◽

Makoto Kikuchi ◽

Tooru Atake ◽

Akihiro Hamano ◽

Yasutoshi Saito

Keyword(s):

Phase Transition ◽

Electron Microscope Study ◽

Room Temperature ◽

Hexagonal Lattice ◽

Ferroelectric Materials ◽

Temperature Phase ◽

X Ray Diffraction ◽

X Ray ◽

Periodic Arrays ◽

Modulation Wave Vector

BaZnGeO4 undergoes many phase transitions from I to V phase. The highest temperature phase I has a BaAl2O4 type structure with a hexagonal lattice. Recent X-ray diffraction study showed that the incommensurate (IC) lattice modulation appears along the c axis in the III and IV phases with a period of about 4c, and a commensurate (C) phase with a modulated period of 4c exists between the III and IV phases in the narrow temperature region (—58°C to —47°C on cooling), called the III' phase. The modulations in the IC phases are considered displacive type, but the detailed structures have not been studied. It is also not clear whether the modulation changes into periodic arrays of discommensurations (DC’s) near the III-III' and IV-V phase transition temperature as found in the ferroelectric materials such as Rb2ZnCl4.At room temperature (III phase) satellite reflections were seen around the fundamental reflections in a diffraction pattern (Fig.1) and they aligned along a certain direction deviated from the c* direction, which indicates that the modulation wave vector q tilts from the c* axis. The tilt angle is about 2 degree at room temperature and depends on temperature.

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