Bragg stacks

While not the optimal layer thickness for the Bragg stack, which would have dielectric layer thicknesses that are one-quarter of the wavelength of light that is to be filtered, it makes good use of the available layers in the... 

Figure 4.21 Solid models of the long-wavelength tunable Fabry-Perot interferometer (left) and the short-wavelength interferometer (right). The short-wavelength interferometer has a Bragg stack consisting of Oxide2 trapped between Polyl and Poly2 for the top reflector. (Courtesy of Kevin Louchis and Benjamin Hemphill, Team Ninja Star in the Eye, EEl 15-Winter 2008, Final Report.)...

Tailored refractive index of inorganic mesoporous mixed-oxide Bragg stacks with bio-inspired hygrochromic optical properties. /. Mater. Chem. C, 1 (39), 6202-6209. 

Pavlichenko, I., Exner, A.T., Guehl, M Lugli, P Scarpa, G and Lotsch, B.V. (2012) Humidity-enhanced thermally tunable Ti02/Si02 Bragg stacks. J, Phys, Chem, C, 116, 298-305. 

Hie color effects are created by scattering as a consequence of the morphology, which approximates a ID Bragg stack composed of alternating layers of materials with contrast in refractive index, n. For a two-component A-B multilayer stack, the first-order wavelength of peak reflectivity at normal incidence, XpR, is a function of the optical thickness of each layer according to the following equation ... 

Powder X-ray diffraction and SAXS were employed here to explore the microstructure of hard carbon samples with high capacities. Powder X-ray diffraction measurements were made on all the samples listed in Table 4. We concentrate here on sample BrlOOO, shown in Fig. 27. A weak and broad (002) Bragg peak (near 22°) is observed. Well formed (100) (at about 43.3°) and (110) (near 80°) peaks are also seen. The sample is predominantly made up of graphene sheets with a lateral extension of about 20-30A (referring to Table 2, applying the Scherrer equation to the (100) peaks). These layers are not stacked in a parallel fashion, and therefore, there must be small pores or voids between them. We used SAXS to probe these pores. 

It is well known that the stacked lamellae of semi-crystalline polymers result in the long period which usually gives two (or three) diffuse Bragg reflections. We will focus on the first reflection (named LI) and the secondary reflection (named L2) at two (/-ranges, denoted as qu and qu, respectively [30,31]. 

Figure 113 Schematic crystal structure of one layer of talc. Such layers are stacked to make the complete structure. The large and medium open circles represent oxygen atoms.The cross-hatched large circles represent hydroxyls (OH).The small open circles represent magnesium atoms (Mg) and the cross-hatched small circles represent silicon (Si) atoms. Figure is reproduced from Bragg, Claringbull and Taylor (1965).

Bragg mirrors on periodic stacks of layers Periodic stacks of metal nanoparticles or dielectric layers with alternating high and low refractive index produce a desired reflectance of the mirror that depends on the thickness and the refractive index of the layers in the stack 16,17... 

For the evaluation of the response of the sensor, we selected several vapors of different polarity. The vapors included water (H20), acetonitrile (ACN), toluene, and dichloromethane (DCM). Solvent polarity and refractive index of tested vapors are listed in Table 4.346 47. The spectral range for the evaluation of the vapor responses of the colloidal crystal film was selected as 700 995 nm, which covered only the fundamental Bragg diffraction peak on the (111) planes of the colloidal crystal film to further reduce effects from possible stacking defects in the film as suggested in the literature44. 

Fig. 9. X-ray intensity distributions (arbitrary scale) from aggregates formed by different polyglutamine peptides (Q , for n = 8,15, 28, 45) polyGln45 (dried), polyGln28 (vapor hydrated), polyGln15 (vapor hydrated), and polyGlng (lyophilized). The vertical bars indicate the positions of the Bragg reflections. The first interference peak for slab stacking of Q8 is indicated by. See Sharma et al. (2005) for further details.

Water on Smectites. Compared to vermiculites, smectites present a more difficult experimental system because of the lack of stacking order of the layers. For these materials, the traditional technique of X-ray diffraction, either using the Bragg or non-Bragg intensities, is of little use. Spectroscopic techniques, especially nuclear magnetic resonance and infrared, as well as neutron and X-ray scattering have provided detailed information about the position of the water molecules, the dynamics of the water molecule motions, and the coordination about the interlayer cations. 

It is evident from physical considerations that the Bragg conditions for diffraction will be of exactly the same kind as for X-rays. However, quantitative results require the solution of the optical problem of diffraction by a finite stack of dielectric sheets having a periodic variation of dielectric constant. This problem is best handled by numerical means and the question is discussed by Hayter et al. [53J, who also give references to earlier papers in which the numerical methods are fully discussed. Similar methods have also been made use of by Nicklow et al. [541. Further studies were made by Highfield et al. [55]. 

A characteristic feature of these partially oxidized bis(oxalato)platinate salts of divalent cations is the coexistence of two modulations of the lattice over a wide temperature range (a) a one-dimensional modulation, as detected by the appearance of diffuse lines on X-ray films, perpendicular to the [Pt(C204)2] anion stacking direction and surrounding the even Bragg reflection layer lines of non-zero order (b) a three-dimensional modulation which gives rise to a complicated pattern of fine satellite spots in the neighbourhood of every reciprocal layer line. 

Iodine oxidation of Ni(OEP) and Cu(OEP) yields polycrystalline materials with a range of stoichiometries.108 Resonance Raman studies indicate the presence of I5- in contrast to the I3 observed for larger ring macrocycles. Single crystal studies of Ni(TMP)I indicate a metal-over-metal stack arrangement but with the Ni(TMP) unit puckered. The iodine superlattice is incommensurate with the Bragg lattice.107 The room temperature conductivity is 10 Q-1 cm-1 and increases on lowering the temperature to reach a rounded maximum at 115 K. The spin susceptibility is temperature independent down to a transition temperature of 28 K, well below the conductivity maximum. Below 28 K the susceptibility decreases in an activated fashion with Ajk 60 K.108... 

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