Approximant crystals

Figure 7. PIXE spectrum of a radioactive inclusion. The relative uranium and lead contents yields an approximate crystal age of 1.5 Ga.

The breadth of the band near 10,100 cm-1 in the a and y spectra of grunerite and the shoulder at 8,500 cm-1 are attributed to absorption by Fe2+ ions in the Ml, M2 and M3 positions. Assuming a lower-level splitting of 500 cm-1 for the t2g orbitals of Fe2+ ions located in these relatively undistorted octahedral sites, an energy level diagram similar to that for the orthopyroxene Ml site (fig. 5.16) may be constructed leading to the approximate crystal field parameters... 

Biissem (B12) determined the approximate crystal structure of C4AF. Subsequent determinations or refinements were reported for preparations with. Y = 0 (C F) (B13,C4,B11),. v = 0.285 and 0..36 (C2) and, v = 0.5 (C3). Fig. 1.8 shows the structure for the compositional range with 0.33 <. Y < 0.7. It is built from layers of corner-sharing octahedra similar to those in perovskite (CaTiOj), alternating with layers composed of chains of tetrahedra, together with Ca " ions. The layers are perpendicular to the h axis and the chains are parallel to c. The composition of an individual octahedral layer in the ac cross-section of the unit cell is MiO. and that of an individual chain is where M and T denote octahedral and... 

Experimentally, for crystals of known structure, any two reflections in the ZOLZ can be used to identify fhe zone axis and fhe approximate crystal orientation using... 

Information on symmetry and (approximate) crystal structure of material... 

Despite these limitations, minimization techniques are straightforward, robust and readily applicable, and can be applied to systems with large and complex unit cells. They are being used increasingly to refine approximate crystal structures and to calculate the relative energies of different polymorphs, as discussed later in this chapter and in Chapters 3 and 5. Highly complex structures may, moreover, now be modelled routinely as will be apparent in the discussion of silicates in Chapter 9 and high temperature superconductors in Chapter 10. 

As a general guide, the data shown in Table 5.1 give the approximate crystal size made for various designs when crystallizing the indicated products. 

Figure 4.7. Approximate crystal structures of chelating biphosphine rhodium complexes (other ligands omitted for clarity).

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