SOME SIMPLE AX STRUCTURES

We described in Chapter 3 a number of A X structures in which the A atoms form three or four bonds. We now consider four simple 3D structures in which A has six or eight nearest neighbours and, as in the case of the diamond structure, we shall show how these structures can be adapted to suit the bonding requirements of various kinds of A and X atoms. The structures are  

---

After the derivatives of simple binary halides, we will discuss the formation and structures of ternary halides in the systems AX/RXz (with z = 2, 3 and with A an alkali metal, lithium through cesium, or an pseudo-alkali cation such as In, Tr, NHJ) and BX2/RXz (with B a divalent cation) and some mixed systems. Complex rare-earth halides have been reviewed eighteen years ago (Meyer 1982), so that we will focus on generalities and recent developments. 

The above considerations have also been used to construct a simple method for the iterative solution of the linear block system (2.9). Let A denote the Jacobian approximation in (2.9) and A the associated matrix with Qy replaced by 0. Then the system Ax = h can be solved easily because of its nearly upper triangular block structure. On this basis, we constructed a fixed point iteration which is known to converge with contraction rate not greater than the spectral radius p(I — A A), Obviously, since y = 0 in the starting point xo, we will have p < 1 in some neighborhood, which can be monitored. 

---