A topology optimisation for periodic structures of 2D hexagonal lattice

2016 ◽  
Vol 2016.26 (0) ◽  
pp. 2313
Author(s):  
Mizuki KAMAHORI ◽  
Hiroshi ISAKARI ◽  
Toru TAKAHASHI ◽  
Toshiro MATSUMOTO
2018 ◽  
Vol 2018.13 (0) ◽  
pp. 103
Author(s):  
Kei MATSUSHIMA ◽  
Hiroshi ISAKARI ◽  
Toru TAKAHASHI ◽  
Toshiro MATSUMOTO

Author(s):  
Robert E. Vines ◽  
James P. Wolfe

AbstractWe have examined the propagation of surface acoustic waves across structures with periodically varying elastic properties. These so-called phononic lattices include a) alternating layers of aluminum and polymer in a multilayer structure, b) a 2-d hexagonal lattice of holes drilled in an aluminum substrate and filled with polymer, and c) a 2-d hexagonal array of Al posts surrounded by polymer. A simple method is employed for probing the elastic properties of these periodic structures with ultrasound in the 0.5–5 MHz range. Ultrasonic surface waves are introduced and detected by water-immersion transducers, cylindrically focused to a line on the sample surface. Transmission and reflection patterns are observed by continuously scanning the wavevector angle with respect to the symmetry axes of the lattice. By Fourier transforming the transmitted signals using a broadband source, we obtain the frequency responses of the lattices as a function of propagation angle. Phononic band gaps, waveguide channeling and Scholte-like interface modes are observed. The results are compared to models of the propagation of transverse waves through analogous bulk structures, for which theories are available. These preliminary models explain the basic features of the experimental results, such as frequency gaps and wave channeling. A number of observations, however, remain to be explained. The angle-scanning technique provides a powerful probe of these modulated structures.


Author(s):  
H. Engelhardt ◽  
R. Guckenberger ◽  
W. Baumeister

Bacterial photosynthetic membranes contain, apart from lipids and electron transport components, reaction centre (RC) and light harvesting (LH) polypeptides as the main components. The RC-LH complexes in Rhodopseudomonas viridis membranes are known since quite seme time to form a hexagonal lattice structure in vivo; hence this membrane attracted the particular attention of electron microscopists. Contrary to previous claims in the literature we found, however, that 2-D periodically organized photosynthetic membranes are not a unique feature of Rhodopseudomonas viridis. At least five bacterial species, all bacteriophyll b - containing, possess membranes with the RC-LH complexes regularly arrayed. All these membranes appear to have a similar lattice structure and fine-morphology. The lattice spacings of the Ectothiorhodospira haloohloris, Ectothiorhodospira abdelmalekii and Rhodopseudomonas viridis membranes are close to 13 nm, those of Thiocapsa pfennigii and Rhodopseudomonas sulfoviridis are slightly smaller (∼12.5 nm).


Author(s):  
Naoki Yamamoto ◽  
Makoto Kikuchi ◽  
Tooru Atake ◽  
Akihiro Hamano ◽  
Yasutoshi Saito

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.


Author(s):  
Xiao-Wei Guo

Voltage-dependent, anion-selective channels (VDAC) are formed in the mitochondrial outer membrane (mitOM) by a 30-kDa polypeptide. These channels form ordered 2D arrays when mitOMs from Neurospora crassa are treated with soluble phospholipase A2. We obtain low-dose electron microscopic images of unstained specimens of VDAC crystals preserved in vitreous ice, using a Philips EM420 equipped with a Gatan cryo-transfer stage. We then use correlation analysis to compute average projections of the channel crystals. The procedure involves Fourier-filtration of a region within a crystal field to obtain a preliminary average that is subsequently cross-correlated with the entire crystal. Subregions are windowed from the crystal image at coordinates of peaks in the cross-correlation function (CCF, see Figures 1 and 2) and summed to form averages (Figure 3).The VDAC channel forms several different types of crystalline arrays in mitOMs. The polymorph first observed during phospholipase treatment is a parallelogram array (a=13 run, b=11.5 run, θ==109°) containing 6 water-filled pores per unit cell. Figure 1 shows the CCF of a sub-field of such an “oblique” array used to compute the correlation average of Figure 3A. With increased phospholipase treatment, other polymorphs are observed, often co-existing within the same crystal. For example, two distinct (but closely related) types of lattices occur in the field corresponding to the CCF of Figure 2: a “contracted” version of the parallelogram lattice (a=13 run, b=10 run, θ=99°), and a near-rectangular lattice (a=8.5 run, b=5 nm). The pattern of maxima in this CCF suggests that a third, near-hexagonal lattice (a=4.5 nm) may also be present. The correlation averages of Figures 3B-D were computed from polycrystalline fields, using peak coordinates in regions of CCFs corresponding to each of the three lattice types.


Author(s):  
B.C. Muddle ◽  
G.R. Hugo

Electron microdiffraction has been used to determine the crystallography of precipitation in Al-Cu-Mg-Ag and Al-Ge alloys for individual precipitates with dimensions down to 10 nm. The crystallography has been related to the morphology of the precipitates using an analysis based on the intersection point symmetry. This analysis requires that the precipitate form be consistent with the intersection point group, defined as those point symmetry elements common to precipitate and matrix crystals when the precipitate crystal is in its observed orientation relationship with the matrix.In Al-Cu-Mg-Ag alloys with high Cu:Mg ratios and containing trace amounts of silver, a phase designated Ω readily precipitates as thin, hexagonal-shaped plates on matrix {111}α planes. Examples of these precipitates are shown in Fig. 1. The structure of this phase has been the subject of some controversy. An SAED pattern, Fig. 2, recorded from matrix and precipitates parallel to a <11l>α axis is suggestive of hexagonal symmetry and a hexagonal lattice has been proposed on the basis of such patterns.


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