Chemical grip tetrahedral solids

The same effect can be seen in the zig-zag chain of Fig.. 3-11. It is remarkable that we can compute the angular force constant in that model exactly, as well as in the Bond Orbital Approximation (see Problems 8-1 and 8-2). The results turn out to be identical for the homopolar semiconductors, but for polar semiconductors, the exact solution has a, replaced by . Sokel has shown that the result is not so simple for the tetrahedral solid, but turns out quantitatively to be very close to an dependence. We will also find an ot dependence when we treat tetrahedral solids in terms of the chemical grip in Section I9-F. This suggests the approximation to the full calculation,... 

Before making application of this formula to tlie perovskites, let us make a brief application to ionic crystals- we summarized the results of this application in Chapter 13 -and to simple tetrahedral solids. In the alkali halides, we focus upon the occupied p states in the halogen ion and calculate the chemical grip associated with interaction of the halogen ion with the alkali, v stales. These arc the same couplings that were included in the calculation of ion softening in Section 14-C. The coupling W2 of Eq. (19-29) becomes the matrix element = 1.84 h /(md ), and 2W i, is to be identified with the = 9.1 h l(nul ) used in Table 14-2. Then (Eq. 19-29) becomes... 

By comparison of Eqs. (19-34) and (19-35) we. sec that the calculation based upon the chemical grip corresponds to the form we obtained from consideration of bond orbitals for tetrahedral solids with A equal to 7/12. In particular, we obtain the V2 0c dependence suggested in Eq. (8-15). 

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