Crystal morphology shape calculation

For all three types of anisotropy the coercivity can be calculated (Tab. 7.7). For SD magnetite and maghemite, shape anisotropy, dominates over strain and crystal anisotropy, whereas for hematite and goethite, morphology has little influence on coer-civity. 

The more modern methods of predicting the morphologies of crystals are based on the calculation of the energies of the various faces. The methods are based on the intuitive consideration that the closed polyhedron describing the shape of the crystal is determined by the faces with the lowest surface free energy and that the extension of these faces is inversely proportional to the respective surface free energy. 

As already noted in Section 8, it is practically impossible to measure the shape and size of each cell individually therefore, on uses statistical geometry methods for the calculation of the morphological parameters. Originally, these methods had been developed and used in crystallography, petrography and colloid chemistry for analyzing the macrostructures of crystals, metal alloys, minerals, suspensions, etc. 

Using the BFDH principle and given the unit cell dimensions and space group symmetry conditions, it is possible to identify the most important morphological forms. For molecular systems this approach shows good agreement with experiment and can be used with confidence as an initial prediction of the crystal shape before refinement by further, more sophisticated energy calculations. 

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