Essential differences between TE and TM band gaps in periodic films at the first Bragg condition

In the Study of small metal particles the shape is a very Important parameter. Using electron microscopy Ino and Owaga(l) have studied the shape of twinned particles of gold. In that work electron diffraction and contrast (dark field) experiments were used to produce models of a crystal particle. In this work we report a method which can give direct information about the shape of an small metal particle in the amstrong- size range with high resolution. The diffraction pattern of a sample containing small metal particles contains in general several systematic and non- systematic reflections and a two-beam condition can not be used in practice. However a N-beam condition produces a reduced extinction distance. On the other hand if a beam is out of the bragg condition the effective extinction distance is even more reduced.

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Spacings and Intensities of Weak-Beam Dark Field Thickness Fringes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100097685 ◽

1981 ◽

Vol 39 ◽

pp. 222-223

Author(s):

M. Avalos-Borja ◽

K. Heinemann

Keyword(s):

Selection Criterion ◽

Dark Field ◽

Dynamical Theory ◽

Bragg Condition ◽

Weak Beam ◽

Kinematical Theory ◽

Equal Thickness

Weak-beam dark field (WBDF) TEM produces narrowly spaced equal-thickness fringes in wedge-shaped crystals. Using non-systematic diffraction conditions, we have shown elsewhere that simple 2-beam kinematical theory (KT) calculations yield average fringe spacings that are for most practical purposes as satisfactorily accurate as the average spacings obtained from optimized multibeam dynamical theory (DT) calculations, As Fig. 1 shows, this result holds for deviations from the Bragg condition as low as 2x10-1 nm-1, and the differences between the results from the two calculational methods become increasingly insignificant for larger excitation errors. (Unless otherwise noted, all results reported here are for gold crystals, using the 200 beam at 100 KV; the DT calculations were made for 74 beams, using the selection criterion D as discussed in ref. [3]).

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Multislice calculations of RHEED patterns from vicinal Si (001)

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100150836 ◽

1993 ◽

Vol 51 ◽

pp. 1000-1001

Author(s):

Scott Lordi

Keyword(s):

Misorientation Angle ◽

Incident Angle ◽

Incident Beam ◽

Experimental Results ◽

Bragg Condition ◽

Vicinal Surfaces ◽

Kinematic Theory ◽

Step Edges

Vicinal Si (001) surfaces are interesting because they are good substrates for the growth of III-V semiconductors. Spots in RHEED patterns from vicinal surfaces are split due to scattering from ordered step arrays and this splitting can be used to determine the misorientation angle, using kinematic arguments. Kinematic theory is generally regarded to be inadequate for the calculation of RHEED intensities; however, only a few dynamical RHEED simulations have been attempted for vicinal surfaces. The multislice formulation of Cowley and Moodie with a recently developed edge patching method was used to calculate RHEED patterns from vicinal Si (001) surfaces. The calculated patterns are qualitatively similar to published experimental results and the positions of the split spots quantitatively agree with kinematic calculations.RHEED patterns were calculated for unreconstructed (bulk terminated) Si (001) surfaces misoriented towards [110] ,with an energy of 15 keV, at an incident angle of 36.63 mrad ([004] bragg condition), and a beam azimuth of [110] (perpendicular to the step edges) and the incident beam pointed down the step staircase.

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Phonon Band Gaps

Journal de Physique I ◽

10.1051/jp1:1997172 ◽

1997 ◽

Vol 7 (3) ◽

pp. 509-519 ◽

Cited By ~ 5

Author(s):

R. M. Hornreich ◽

M. Kugler ◽

S. Shtrikman ◽

C. Sommers

Keyword(s):

Band Gaps ◽

Phonon Band

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Dibenzochrysene Enables Tightly Controlled Docking and Stabilizes Photoexcited States in Dual-Pore Covalent Organic Frameworks

10.26434/chemrxiv.9638633.v1 ◽

2019 ◽

Author(s):

Torben Sick ◽

Niklas Keller ◽

Nicolai Bach ◽

Andreas Koszalkowski ◽

Julian Rotter ◽

...

Keyword(s):

Molecular Docking ◽

Photophysical Properties ◽

Visible Spectrum ◽

Large Family ◽

Building Blocks ◽

Band Gaps ◽

Docking Site ◽

Covalent Organic Frameworks ◽

Connected Node ◽

Optoelectronic Applications

Covalent organic frameworks (COFs), consisting of covalently connected organic building units, combine attractive features such as crystallinity, open porosity and widely tunable physical properties. For optoelectronic applications, the incorporation of heteroatoms into a 2D COF has the potential to yield desired photophysical properties such as lower band gaps, but can also cause lateral offsets of adjacent layers. Here, we introduce dibenzo[g,p]chrysene (DBC) as a novel building block for the synthesis of highly crystalline and porous 2D dual-pore COFs showing interesting properties for optoelectronic applications. The newly synthesized terephthalaldehyde (TA), biphenyl (Biph), and thienothiophene (TT) DBC-COFs combine conjugation in the a,b-plane with a tight packing of adjacent layers guided through the molecular DBC node serving a specific docking site for successive layers. The resulting DBC-COFs exhibit a hexagonal dual-pore kagome geometry, which is comparable to COFs containing another molecular docking site, namely 4,4′,4″,4‴-(ethylene-1,1,2,2-tetrayl)-tetraaniline (ETTA). In this context, the respective interlayer distances decrease from about 4.60 Å in ETTA-COFs to about 3.6 Å in DBC-COFs, leading to well-defined hexagonally faceted single crystals sized about 50-100 nm. The TT DBC-COFs feature broad light absorption covering large parts of the visible spectrum, while Biph DBC-COF shows extraordinary excited state lifetimes exceeding 10 ns. In combination with the large number of recently developed linear conjugated building blocks, the new DBC tetra-connected node is expected to enable the synthesis of a large family of strongly p-stacked, highly ordered 2D COFs with promising optoelectronic properties.

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