Empirical methods of solving crystal structures

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 

This simple visual analysis of powder diffraction patterns is usually a good indicator that there are detectable changes in the atomic structures of the materials in question but the overall structural motif remains closely related. Based on this conclusion and assuming that at least one of the materials belongs to the SmsGe4 type, it should be possible to establish details of atomic distributions in these three lattices, provided the quality of diffraction data is sufficient.  

Examples considered in this section are also similar to the case of hydrated and anhydrous FeP04 discussed in the previous section. The major difference is in the better crystallinity of the Gd5(SixGei x)4 materials and in the resulting higher quality of powder diffraction data, which facilitate a straightforward Rietveld refinement of individual atomic and profile parameters without the need for a preliminary quantum mechanical and/or geometrical optimizations. 

Johnson, Rare earth - germanium and -silicon compounds at 5 4 and 5 3 compositions, Acta Cryst. 22, 940 (1967). 

Johnson, and A.G. Tharp, Crystal structure of Sm5Ge4, Acta Cryst. 22, 269 (1967). 

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