Tetrahedra vertex-sharing

Take the network of vertex-sharing tetrahedra of the Cu atoms in MgCu2 (Fig. 15.4) and assume that there is an additional atom inside of every tetrahedron. What structure type would this be ... 

A chain of vertex-sharing tetrahedra results when every tetrahedron has two terminal and two bridging atoms the composition is MX274X2A2 or MX3. The chain can be closed to form a ring as in [SOj], [PO3 Ij, ISiO I3 or [SiOf jg. Endless chains have different shapes depending on the mutual conformation of the tetrahedra (Fig. 16.19). They occur especially among silicates, where the chain shape is also determined by the interactions... 

Some of the simplest of this large family of structures are set out in Table 5.7 the structures are described in later chapters. The table shows the number of octahedra (o) with which each tetrahedron (t) shares vertices, the relative numbers of tetrahedra and octahedra, the contributions to the chemical formula made by each (a shared vertex counting as X and an unshared vertex as X), the formula, and examples of compounds with the structure. 

In a tetrahedron all vertices are equivalent. For the M4O2 block there are two distinct metal sites the metal sites in the edge shared by the two component triangles, which will be called body sites, and the two wing-tip sites. Quite distinct structures result depending on the type of vertex shared. Below I have attempted to... 

Phosphate tetrahedra, P04 , can link up via oxygen-sharing to give polyphosphates in the form of chains and rings. The phosphates, unlike the silicates, contain a central atom with a valency of five. Thus, the maximum number of oxygen atoms that each tetrahedron can share is three, since there must always be one vertex of the tetrahedron that is a terminal oxygen, bound as P=0. 

Structures of heteropolytungstate and isopolytungstate compounds have been determined by x-ray diffraction. The anion stmctures are represented by polyhedra that share corners and edges with one another. Each W is at the center of an octahedron, and an O atom is located in each vertex of the octahedron. The central atom is similarly located at the center of an XO tetrahedron or XO octahedron. Each such polyhedron containing the central atom is generally surrounded by octahedra, which share corners, edges, or both with it and with one another. Thus, the correct total number of... 

If six equilateral triangles share a common vertex, the sum of the angles around the vertex is 6 x 60 = 360°. The array is planar and cannot form part of a regular polyhedron. It is clear that the three possibilities listed give rise to the tetrahedron, the octahedron, and the icosahedron, as shown in Table 3.2. 

Soddyite [21] and the isostructural compound [(U02)2(Ge04)(H20)] [66] contain uranyl pentagonal bipyramids that share equatorial edges, forming chains (Fig. 21). Each of the bipyramids also shares an edge with a tetrahedron. One of the equatorial vertices of each bipyramid in occupied by H2O, and this vertex is not shared with another polyhedron. Each tetrahedron shares two of its edges with bipyramids on either side, and this links the chains of bipyramids into a fiamework. Additional linkages are provided by H bonds. 

---