Читать книгу Earth Materials онлайн

78 страница из 155

 Rule 5: The number of different cations and anions in a crystal structure tends to be small. This is called the rule of parsimony.

coordination number (CN)coordination polyhedron

When ions of opposite charge combine to form minerals, each cation attracts as many nearest neighbor anions as can fit around it as approximate “spheres in contact”. In this way, the basic units of crystal structure are formed which grow into crystals as multiples of such units are added to the existing structure. One can visualize crystal structures in terms of different coordinating cations and coordinated anions that together define a simple three‐dimensional polyhedron structure. As detailed in ssss1 and ssss1, complex polyhedral structures develop by linking of multiple coordination polyhedra.

radius ratio (RRRc/Ra)

ssss1 Relationship between radius ratio, coordination number, and coordination polyhedra.

Radius ratio (Rc/Ra) Coordination number Coordination type Coordination polyhedron <0.155 2 Linear Line 0.155–0.225 3 Triangular Triangle 0.225–0.414 4 Tetrahedral Tetrahedron 0.414–0.732 6 Octahedral Octahedron 0.732–1.00 8 Cubic Cube >1.00 12 Cubic or hexagonal closest packed Cubeoctahedron complex

The general relationship between radius ratio, coordination number and the type of coordination polyhedron that results is summarized in ssss1. For radius ratios less than 0.155, the coordination number is 2 and the “polyhedron” is a line. The appearance of these coordination polyhedra is summarized in ssss1.