Bragg lines

The Crystallite Size and the Scherrer Formula. The Scherrer formula is based on a restricted assumption assuming that the peak shape is dominated by size effects. The problem of Bragg line broadening, originating from particle size, was first investigated by Scherrer [30] who derived the well-known and widely used law ... 

The Dark-Field symmetry is observed inside a hkl diffracted disk (often characterized by its diffraction vector g) which is exactly in Bragg orientation. This situation occurs when the hkl Bragg line goes through the center of its hkl diffracted disk. 

On the starting monometallic catalyst (Fig. 5b), the Bragg lines characteristic of Ni particules are present, but the small particle size (about 3 nm) drastically broaden the bands. 

Between the (111) Bragg lines of Pd and Cu, the three samples, which contain the same amount of Pd and a growing amount of Cu, exhibit a broad peak whose... 

The first report of a neutron diffraction study of this series of materials appeared in 1979 (Akimitsu et al. 1979) and clearly manifested a two-dimensional eharacter of the spin system. An experiment on a non-stoichiometric single erystal of YFc204 revealed that there are magnetie Bragg lines, instead of Bragg spots. 

Fig. 73. Neutron diffraction patterns of polycrystals of non-stoichiometric YFc204 at 297 and 82 K. A saw-tooth diffraction profile at low temperature indicates a Bragg line. (Funahashi et al. 1984.)...

As is shown in fig. 74, the saw-tooth form disappears below and several peaks of ordinary shape due to Bragg spots instead of Bragg lines are observed. It is certain that the spins order three-dimensionally below the Verwey transition point. 

Bragg lines parallel to the c -axis in the neutron diffraction and the paramagnetic-like doublet of isolated T layers in the Mossbauer spectra of Lu2Fe307, at temperatures where spins on double T layers order, are a clear manifestation of a two-dimensionality of the spin correlation in these compounds. It is very likely that the rare earth elements in the U blocks couple weakly with transition metal ions on both sides of them and that the chain of the exchange interactions along the c-axis are cut at the U block. 

The eigenvalue of the matrix of eq. (22) takes a maximum aih = k = provided that J is positive, or the exchange interaction is antiferromagnetic. Bragg lines at (1,5,/) prove that this is the case. Sublattices in the (j, 3) structure are also shown in fig. 84. It is to be noted that, besides the repetition of the sublattices along the [1,1] direction by every three atomic lines, a three-fold symmetry exists with a symmetry axis perpendicular to the plane of the cation sites. 

Fig. 7.23 XRD pattern of as-prepared LiFeP04 material lower curve) and positive electrode after 200 cycles lower curves). Bragg lines are indexed in the Pmna S.G. Notice that the olivine framework remains intact after cycling at 60 °C...

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