Satellite reflection

In X-ray diffraction, modulated structures reveal themselves by the appearance of satellite reflections. In between the intense main reflections which correspond to the structure of the approximant, weaker reflections appear they do not fit into the regular pattern of the main reflections. 

After publication of the X-ray study, the charge transfer was obtained from the reciprocal-space position of the satellite reflections, which occur in the diffraction pattern at temperatures below the Peierls-type metal-insulator transition at 53 K (Pouget et al. 1976). Assuming that the gap in the band structure occurs at twice the Fermi wavevector, that is, at 2kF, the position of the satellite reflections corresponds to a charge transfer of 0.59 e, in excellent agreement with the direct integration. The agreement confirms the assumption that the gap in the band structure occurs at 2kF. 

Fig. 8 Part of the 2D diffraction pattern obtained from a twinned single-crystal of Te-III at 7.4 GPa. The main body-centred monoclinic reflections from the two twin components are shown, indexed hk[) and (hkl)2- The satellite reflections are marked with asterisks, and a powder line from the tungsten gasket is marked G . D marks a reflection from one of the diamond anvils...

Fig. 9 Rietveld refinement of incommensurate Te-III at 8.5 GPa. The upper and lower tick marks below the profile mark the peak positions of the main and first order satellite reflections, respectively. The reflections shown in Fig. 8 are identified by their (hklm) indices, where the main reflections are indexed (M/O)...

Figure 4.21 Portion of the (010) plane in the reciprocal lattice of K2Se04. On the left is the lattice for the high-temperature phase and on the right that for the ferroelastic phase. In the high-temperature phase, a softening occurs at a point displaced by 5 from q = (j, 0, 0), shown by a cross. In the incommensurate phase a satellite reflection develops at X.

Experimentally the PD may be studied by diffuse X-ray scattering (DXS) experiments in which the ID distortion of the chains gives rise to weak continuous lines on either side of the layer lines of strong Bragg spots.10 The periodicity of the PD may be determined from the position of the diffuse line. In contrast, 3D superstructures give rise to real satellite reflections associated with the Bragg spots. 

In CoOP above 300 K the compound exists in the Cccm space group, but with characteristic diffuse X-ray lines indicative of the Peierls modulation and no evidence of superstructure formation. Below 300 K a superstructure develops as shown by the appearance of satellite reflections on the X-ray diffraction photographs. At 280 K a phase transition to the Pccn space group occurs and associated with this are changes in the satellite pattern.78 74 Superstructure development which is commensurate with the Peierls modulation is completed about 250 K. 

NiOP already exists in the Pccn group at room temperature and weak diffuse X-ray scattering and kF and 2kF satellite reflections are observed.79 The 2kF spots disappear above 305 K and the conductivity is similar to that observed for CoOP and ZnOP.79,72... 

Figure 12. Simulation of the temperature dependence of the neutron intensities of the first and third harmonics of the incommensurate satellite reflection of copper metaborate at zero magnetic field.

Satellite reflections have been encountered previously in alloy structures and reference is given to articles by Preston (22), Daniel and Lipson (23), and Hargreaves (24). 

The number of low-temperature, high-pressure (LT + HP) structure determinations of organic conductors is not yet very large, but a number of other crystallographic studies under constraint have also been reported. To limit the field of the discussion below, we consider only the case of techniques allowing for the measurement of full crystal structures, since collecting a three-dimensional diffraction data set is more demanding than simple observation of a few main or satellite reflections. 

Up to now we have seen how lattice distortions are detected and characterized. This does not provide a direct observation of the molecular translations, rotations, and deformations associated with the distortion. However, for a few compounds it has been possible to measure a large enough number of satellite or superstructure reflections so that the distorted structure can be parametrized and refined (rigid-body or full structural study). We consider below four examples, taken from materials selected in Section IV. A, which show that such studies are not easy and that the data collection requires special attention. Indeed, it is generally difficult to measure enough satellite reflections, especially if several kinds of the latter coexist (e.g., 2kp and 4kF satellites, high-order satellites, etc.). 

As discussed in Section X, irradiation effects are the main enemy in the case of electron microdiffraction. Granier et al. [31,190] found that not only does the irradiation rapidly destroy the sample, but long before, satellite reflections vanish (Fig. 23). In fact, the coherence between charge density waves is much more sensitive than the material itself. 

Figure 24 Integrated intensity behavior of three satellite reflections versus exposure time in TTF-TCNQ at 13 K. With a rotating copper anode generator (12-kW Rigaku 200) an 0.5% intensity decrease per irradiation hour is observed. (From Ref. 40.)...

Diffuse X-ray and elastic neutron scattering studies revealed the presence of a structural change accompanying the metal-insulator transition In the insulating state below 53 K a set of satellite reflections was discovered with the superlattice... 

Figure 15 Temperature dependence of the intensity and the transverse wave number of the 2 p and the X-ray satellite reflections in TTF-TCNQ. (Reproduced from S. Kagoshima et ah, J. Phys. Soc. Jpn., 41 (1976) 2061, Fig. 9)...

Surface compositions of icy satellites can be observed by reflection spectroscopy (UV to near-IR 0.2-5 pm) [5J. The physical properties and surlace compositions of icy bodies are summarized in Table 9.4. Major satelhtes of Jupiter (except for lo), Saturn, and Uranus show clear evidence of H2O ice (ice I) on Oieir surfaces. Altliough physical properties, such as density, radius, albedo, and surface structure of tlrese satellites differ greatly, they share basic compositional similarity. It is thus assumed that the ice of these satellites is pure H2O when we discuss Oieir internal structiue. The large spectral differences among satellites reflect surface modification histories by impact, volcanism, tectonics, and solar radiation. It is noted that SO2, O2, and O3 are trace components and contaminants. No NH3 or CH) ices, predicted by the equilibrium condensation theory, have yet been detected on these satellites. 

Let us consider the simplest case. Suppose that we have a pure sinusoidal (Cq = 0) wave modulation with a single modulation vector q. The expression of the structure factor for the satellite reflection h = H + mq is reduced to ... 

As the relative humidity is increased it is possible to see satellite reflections developing in the vicinity of spots I and II. Two of these have been identified in the diagrams with the labels III and IV. The satellite reflections arise from an intermediate conformation which, in the early stages of the experiment, co-exists with the D-form. Once again, the intensities of these reflections are a measure of the number of molecules in this intermediate conformation. However, it can be seen that as the relative humidity increases the positions and relative intensity of these reflections vary in a smooth and continuous fashion. 

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