Crystal symmetries geometrical model

Chain Pair Modeling. In the following analysis, we assume that the chains are regular helices, i.e. that they have screw symmetry, with a repeat distance, t. In a perfect crystal, such chains must either be parallel or antiparallel. Four interhelical parameters are required to define the geometric orientation of chain A relative to chain B (see Figure 2). The parameters and their ranges are ... 

In addition to reciprocal and direct space techniques considered in the previous sections, a large variety of approaches may be employed to create a model of the crystal structure in direct space. One of these, i.e. the geometrical method, has been implicitly employed in section 6.9, where the location of a single La atom in the unit cell was established from a simple analysis of the unit cell dimensions and from the availability of low multiplicity sites in the space group symmetry P6/mmm. Here we consider a more complex example, i.e. the solution of several crystal structures occurring in the series of Gd5(SixGei x)4 alloys. These examples illustrate the power of the powder diffraction method in detecting subtle details of the... 

Until now it has been done only for the case of chromium(III) doped in the mineral beryl (50). Here the chromium(III) ion is surrounded by six oxygen ions with a site symmetry Ug for which there are two independent geometrical parameters which are approximately known from the crystal structure. The non-additivity model here tells us that there are three independent one-electron parameters (75) and these can, using AOM, be expressed in terms of the two parameters e g and e n- From polarized crystal spectra the positions of four transitions are approximately known, allowing the determination of three one-electron parameters, plus the Racah parameter B. 

---