Olivines, structural formula

Let the disorder parameter be z. Then the structural Formula of these olivines can be written as ... 

With a known mineral, as determined by electron diffraction or other technique (such as X-ray diffraction), determination of the stoichiometry and structural formula can be a suitable test for analytical precision of thin-film elemental analyses. This simple test follows the practice commonly employed for electron microprobe data in which the accuracy (and completeness) of an analysis is judged by the departure from stoichiometry calculated for a given mineral. Thus, thin-film analyses of olivines, pyroxenes, garnets, feldspars and many other common rock-forming minerals can be examined for internal consistency via a calculation of structural formulae. 

This differential CFSE factor is demonstrated by the formation of hortono-lite, (Mgo5Fe05)2Si04, by the mixing of forsterite and fayalite components. To a close approximation, Mg2+ and Fe2+ ions may be assumed to be randomly distributed in the olivine structure eq., (7.12), so that 0.5 Fe2+ ions per formula unit occupy each of the Ml and M2 positions. The CFSE s of the Fe2+ ion in the Ml and M2 sites of hortonolite are approximately -53.2 and -52.0 kJ/mole, respectively, and in fayalite the corresponding CFSE are -50.9 kJ/mole (Ml site) and -51.2 kJ/mole (M2 site) (eqs (5.2) and (5.3) table 5.16). The formation of hortonolite may be represented as follows ... 

Olivine is a particularly simple case because the chemical variation principally involves a single octahedral site and not the tetrahedral cation, Si. Other silicate minerals are more complex having a number of independent polyhedral sites and cationic substitutions in each. For these, the conversion of a chemical analysis into a structural formula is not a trivial exercise. 

That solids with different compositions can adopt identical crystal shapes was documented in 1819 by Mitscherlich, who called the phenomenon isomorphism (Mitscherlich 1819, Melhado 1980). Isomorphism can describe phases with similar atomic architectures but unlike constituents, such as NaCl and PbS, and it also can refer to members of a continuous solid solution series, such as the olivine group with formula (Mg,Fe)2Si04. Three years later, Mitscherlich documented the complementary property of polymorphism, whereby phases with identical compositions occur as different structures (Mitscherlich 1822). Although mineralogists of the nineteenth century recognized the important inter-relationship between crystal structure and composition, the crystallographic probes available for structure determination did not keep pace with advances in wet chemical analysis. Consequently, understanding the effects that chemical modifications exert on crystal structures could be revealed only by careful measurements of subtle variations in habit. 

The first nomenclature for inorganic structure types has been proposed by Ewald Hermann in 1931. They used letters to designate the kind of chemical compound and numerals to distinguish among compounds with the same general formula. The chemical elements are designated by the letter A, the binary compounds by the letter B, the AB2 compounds by C and so on. Examples are A1 for Cu, A10 for Hg, B1 for NaCI, B3 for ZnS (sphalerite), HI2 for Mg2Si04 (olivine), G1 for CaCOa (calcite). This notation has not received much acceptance, possibly due to its lack of self explanatory structural information. 

---