Mineralogy: The Ability of an Element to Substitute for Another Mineral

The different notations (either parentheses or brackets) are used as a mechanism for identifying the specific coordinate system employed in the description. For instance, braces are applied to indicate a family of planes whose members are similar in the symmetry of their lattices. On the other hand, brackets are used to identify lattice rows ( Hawthorne, 2012). The lattice parameters describing the shape of a unit cell are a 0, b 0, and c 0. Notably, different angles between crystal boundaries are characteristic of different structural materials. However, despite the variation in the shape of structural species, these angles remain constant. For this reason, fewer unit cell parameters ensure symmetry ( Hawthorne, 2012). When using indices, dividing through by a common factor to obtain the least index ensures that we obtain the smallest integer value. Fewer unit cell parameters are needed for some crystal systems since the variations in the strength of ionic bonds determine the distance between atoms in the crystalline structure ( Hawthorne, 2012). Factors contributing to the ability of an element to substitute for another in a mineral are ionic bonds, for example. In this regard, the specific determinants are the size of the ion in question and the magnitude of the ionic charge. For example, ionic minerals, only are capable of substituting each other. For ionically bonded elements in a mineral, the ionic radius is the most crucial determinant of substitution. Electrically neutral atoms cannot substitute for ions. This substitution may either be limited or unlimited. Whereas unlimited substitution occurs between ions whose radii differ by less than 15%, unlimited substitution occurs when ions differ in size by a range of 15% to 35%. Beyond 35%, no ionic substitution occurs ( Hawthorne, 2012). Polymerization is the process through which molecules expand through the addition of other smaller molecules to the existing structures. Silica can polymerize to form sheets, chains, or networks due to the existence of covalent bonds formed between the silicon and oxygen molecule. The covalent bonds are such that there exist bonding electrons on each of the four oxygen atoms. Therefore, the oxygen atoms can covalently bond with two other silicon atoms. ( Hawthorne, 2012). Silicate minerals are relatively hard because their tetrahedra are isolated, but bonded strongly as a result of the attraction forces of polar ionic charges. Additionally, in chain silicates, each silicon atom is bonded to two other adjacent silicon atoms, or to three oxygen atoms. This bonding results in the formation of tetrahedrons which are strongly linked together by strong covalent bonds. On the other hand, carbonate complexes do not form chains, sheets, or networks because the ionic bonds required to link layers of carbon atoms together are relatively weaker than the stronger covalent bonds between carbon particles. Effectively, this ensures that carbon atoms are strongly linked together, limiting the ability to form sheets ( Hawthorne, 2012). A metope is always black for two reasons. For one, light traveling in the optic axis, either in a uniaxial or biaxial manner, experiences zero birefringence. Secondly, melapotes are always black since isogyre pass through the optic axis ( Hawthorne, 2012). 

References 

Hawthorne, F. C. (2012). A bond-topological approach to theoretical mineralogy: crystal structure, chemical composition, and chemical reactions.  Physics and Chemistry of Minerals,  39 (10), 841-874.