Bragg peaks, reflections

With the new VME/UNIX control system on the polarised hot-neutron normal-beam diffractometer D3 at ILL, each measurement cycle for both peak and background intensities lasts 2 s, and the (+)/(-) counting-time fractions are defined with a 1 MHz clock. There are two detector scalers and two monitor scalers ((+) and (-) states). In Table 1, we compare the flipping ratio measured for the strong 200 and the weak 600 Bragg peak reflections of a CoFe sample. As expected, the standard deviation cr (if) is improved in the case of the strong reflection (16%). 

Figure 1 Bragg diffraction. A reflected neutron wavefront (D, Dj) making an angle 6 wKh planes of atoms will show constructive interference (a Bragg peak maxima) whan the difference in path length between Df and (2CT) equals an integral number of wavelengths X. From the construction, XB = d sin 6.

Such off-zone-centre, soft-mode systems offer the most favourable conditions for a test of the hypothesis that the central peak is a precursor to a Bragg reflection in the transformation phase. Zone-centre softening, such as occurs in NbaSn, results in the central mode scattering emerging from an existing Bragg peak, which ultimately splits in the lower symmetry transformation structure, which presents a problem with resolution. 

The important information about the properties of smectic layers can be obtained from the relative intensities of the (OOn) Bragg peaks. The electron density profile along the layer normal is described by a spatial distribution function p(z). The function p(z) may be represented as a convolution of the molecular form factor F(z) and the molecular centre of mass distribution f(z) across the layers [43]. The function F(z) may be calculated on the basis of a certain model for layer organization [37, 48]. The distribution function f(z) is usually expanded into a Fourier series f(z) = cos(nqoz), where the coefficients = (cos(nqoz)) are the de Gennes-McMillan translational order parameters of the smectic A phase. According to the convolution theorem, the intensities of the (OOn) reflections from the smectic layers are simply proportional to the square of the translational order parameters t ... 

The used S5mbols are K, scale factor n, number of Bragg peaks A, correction factor for absorption P, polarization factor Jk, multiplicity factor Lk, Lorentz factor Ok, preferred orientation correction Fk squared structure factor for the kth reflection, including the Debye-Waller factor profile function describing the profile of the k h reflection. 

The crystal symmetry changes that accompany order-disorder transitions, discussed in Section 17.1.2, give rise to diffraction phenomena that allow the transitions to be studied quantitatively. In particular, the loss of symmetry is accompanied by the appearance of additional Bragg peaks, called superlattice reflections, and their intensities can be used to measure the evolution of order parameters. 

Molecular orientational order in adsorbed monolayers can be inferred indirectly from elastic neutron diffraction experiments if it results in a structural phase transition which alters the translational symmetry of the 2D lattice. In such cases, Bragg reflections appear which are not present in the orientationally disordered state. Experiments of this type have inferred orientational order in monolayers of oxygen (41) and nitrogen (42) adsorbed on graphite. However, these experiments have not observed a sufficient number of Bragg reflections to determine the molecular orientation by comparing relative Bragg peak intensities with a model structure factor. 

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