Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Equivalent Bragg spacing

Fig. 12.2. Equivalent Bragg spacing dnpa as calculated from the maxima of the pre-peaks for lower amorphous poly(n-alkyl methacrylates) ( ) as well as amorphous ( ) and semicrystalline ( ) PODMA (cf. Fig. 12.1). The inset shows a schematic picture of the structure of amorphous poly(n-alkyl methacrylates)... Fig. 12.2. Equivalent Bragg spacing dnpa as calculated from the maxima of the pre-peaks for lower amorphous poly(n-alkyl methacrylates) ( ) as well as amorphous ( ) and semicrystalline ( ) PODMA (cf. Fig. 12.1). The inset shows a schematic picture of the structure of amorphous poly(n-alkyl methacrylates)...
Fig. 12.8. Wide angle scattering curves for a P(S—6—ODMA) block copolymer with lamellar morphology (Lam-9 nm) as well as PS and PODMA homopolymers [58]. The curves are shifted vertically. The peak maxima correspond to equivalent Bragg spacings of di = dnps = 3.05 nm (second order peak at 92), ds = 0.85 nm, d4 = 0.46 nm, and ds = dioc = 0.41 nm. Further details are discussed in the text... Fig. 12.8. Wide angle scattering curves for a P(S—6—ODMA) block copolymer with lamellar morphology (Lam-9 nm) as well as PS and PODMA homopolymers [58]. The curves are shifted vertically. The peak maxima correspond to equivalent Bragg spacings of di = dnps = 3.05 nm (second order peak at 92), ds = 0.85 nm, d4 = 0.46 nm, and ds = dioc = 0.41 nm. Further details are discussed in the text...
Fig. 14. Equivalent Bragg spacings as a function of the number of carbon atoms (1) on the alkyl chain. Lines are linear fits to the data. Notice the pronounced Z-dependence oftZi. Fig. 14. Equivalent Bragg spacings as a function of the number of carbon atoms (1) on the alkyl chain. Lines are linear fits to the data. Notice the pronounced Z-dependence oftZi.
Fig. 6. Equivalent Bragg spacings for the peaks of the acrylate and methacrylate polymers as a function of alkyl group size, n. (A) -alkyl acrylates (0) n-alkyl methacrylates ( ) cycloalkyl methaciylates. Linear least-squares lines are shown. From ref. 25. Fig. 6. Equivalent Bragg spacings for the peaks of the acrylate and methacrylate polymers as a function of alkyl group size, n. (A) -alkyl acrylates (0) n-alkyl methacrylates ( ) cycloalkyl methaciylates. Linear least-squares lines are shown. From ref. 25.
Table I. Amorphous peak positions (as equivalent Bragg spacings, d) for the methacrylate and styrene polymers of Figs. 7-9 and 14. [Pg.40]

Gierke also considered that these clusters are interconnected by short, narrow channels in the fluorocarbon backbone network. The diameter of these channels is about 1 mm estimated from hydraulic permeability data. He further considered that the Bragg spacing ( 5nm from SAXS data) can represent the distance between clusters. The cluster-network model is a phenomenological description. Recently, Hsu and Gierke " have derived a semi-phenomenological expression to correlate the variation of cluster diameter with water content, equivalent weight, and cation form of the membrane. They have shown that the short channels are thermodynamically stable. [Pg.448]

Emulsion polymerization produces latexes whose particles are almost perfectly spherical polymer latexes of highly uniform particle size have been knovm since their accidental discovery in 19 7 l y scientists at the Dow Chemical Company. Concentrated monodisperse latexes are frequently iridescent, whereas heterodisperse latexes are white. The iridescence was correctly attributed by Luck, Wesslau and Klier (l) to Bragg reflection of visible light from ordered arrays of particles. Because of the approximate equivalence of their measured Bragg spacing to that expected for a packed array at the same particle diameter (and also beca ase the... [Pg.63]

Notice that the different sets of equivalent parallel planes in the preceding figures have different interplanar spacing d. Among sets of planes (hkl), inter-planar spacing decreases as any index increases. W. L. Bragg showed that a... [Pg.50]

As the crystal is rotated in the X-ray beam, various reciprocal-lattice points come into contact with this sphere, each producing a beam in the direction of a line from the center of the sphere of reflection through the reciprocal-latticepoint that is in contact with the sphere. The reflection produced when reciprocal-lattice point Pfrki contacts the sphere is called the hkl reflection and, according to Bragg s model, is caused by reflection from the set of equivalent, parallel, real-space planes (hkl). [Pg.58]

The multiplicity factor, m, specifies the number of equivalent lattice planes that may all cause reflection at the same Bragg angle position, that is, the number of equally spaced planes cutting a unit cell in a particular, Qikl), crystalline plane family. In the case of low symmetry systems, the multiplicity factor will be low every time. On the other hand, for high symmetry systems, a single family of... [Pg.36]

In the Bragg formulation of diffraction we thus refer to reflections from lattice planes and can ignore the positions of the atoms. The Laue formulation of diffraction, on the other hand, considers only diffraction from atoms but can be shown to be equivalent to the Bragg formulation. The two formulations are compared in Fig. 2B for planes with Miller indices (110). What is important in diffraction is the difference in path length between x-rays scattered from two atoms. The distance si + s2 in the Laue formulation is the same as the distance 2s shown for the Bragg formulation. The Laue approach is by far the more useful one for complicated problems and leads to the concept of the reciprocal lattice (Blaurock, 1982 Warren, 1969) and the reciprocal lattice vector S = Q 14n that makes it possible to create a representation of the crystal lattice in reciprocal space. [Pg.49]

The standard way to describe the orientation of a plane is by a vector d perpendicular (normal) to it. An equivalent description for Bragg planes is in terms of how many times they intersect each of the three unit cell axes in one lattice repeat (Figure 11). These Miller indices h (for axis a), k (for axis b), and / (for axis c) uniquely define the plane and its X-ray reflection for instance, 1 (1,0,0) plane intersects the x-axis once, a (2,1,0) plane, the x-axis once, and the j-axis twice, and so on. In principle, it is possible to calculate the vector Akki knowing the Miller indices h,k,l and the unit cell vectors a, b, and c. In practice, this may not be easy. As we want to have a simple description of the normal vectors Akki (which determine when Bragg s law will hold) we adopt a different set of basis vectors (a, b, c ), called the reciprocal lattice and the space they define is called reciprocal space. Each plane can be described by a vector ... [Pg.59]

The smearing of reciprocal space in a powder experiment makes the measurement easier but results in a loss of information. Reflections overlap from lattice planes whose vectors lie in different directions but which have the same J-spacing. These cannot be resolved in the measurement. Some of these overlaps are dictated by symmetry (systematic overlaps) and others are accidental. Systematic overlaps are less serious for equivalent reflections [e.g., the six Bragg peaks (100), (- 100), (010),. . . from the faces of a cube] since the multiplicity is known from the symmetry. For highly crystalline samples, accidental overlaps can be reduced by making measurements... [Pg.12]


See other pages where Equivalent Bragg spacing is mentioned: [Pg.501]    [Pg.36]    [Pg.501]    [Pg.36]    [Pg.300]    [Pg.112]    [Pg.196]    [Pg.205]    [Pg.214]    [Pg.297]    [Pg.103]    [Pg.377]    [Pg.154]    [Pg.243]    [Pg.189]    [Pg.210]    [Pg.290]    [Pg.609]    [Pg.291]    [Pg.26]    [Pg.370]    [Pg.45]    [Pg.192]    [Pg.159]    [Pg.97]    [Pg.84]    [Pg.53]    [Pg.36]    [Pg.116]    [Pg.29]    [Pg.33]    [Pg.259]    [Pg.164]    [Pg.93]    [Pg.198]    [Pg.157]    [Pg.158]    [Pg.232]    [Pg.238]   
See also in sourсe #XX -- [ Pg.36 , Pg.38 , Pg.40 ]




SEARCH



Bragg

Bragg spacing

© 2024 chempedia.info