Introduction to lattice dynamics by Martin T. Dove

By Martin T. Dove

This can be a fabulous creation to lattice dynamics. it's hugely readable yet very sizeable. it is a great spot to begin studying this subject, and for plenty of it could have all that one must learn about the sphere.

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The phase difference would then have been transfered to the amplitude, and we would end up with the same final equations. We perform the same analysis as we used in the previous chapter for the monatomic chain. 3). 6) \ k = -(G + g)uk +(G + g exp(ika))Uk We can write these simultaneous equations in the matrix form: (Mco2k-{G For this equation to have a solution, the determinant of the matrix must equal zero. 8) This equation can easily be solved, although the general solution is somewhat cumbersome.

The basic model has been developed by adding constraints between the parameters; for example, the dispersive interaction -Ar"6 Some fundamentals 13 is usually subject to the constraint that ACH = (ACCAHH)1/2, which follows from the fact that the dispersive interaction is proportional to the product of the polarisabilities of the two interacting atoms. The model has also been developed to allow for the existence of small charges on the atoms, and it has been extended to include N, O, F and Cl atoms (Williams 1973; Williams and Cox 1984; Williams and Houpt 1986; Hsu and Williams 1980; Cox et al.

10) Clearly the first frequency is large and varies only weakly with k, whilst the second frequency has the same behaviour as the acoustic mode we met in the model for the monatomic chain. The first branch (flat at k = 0) is called the optic mode,2 partly because it has a frequency that is in the vicinity of the optical region of the electromagnetic spectrum3 (whereas the acoustic mode has an acoustic frequency), but also because the atomic motions associated with this branch are the same as the response to an oscillating electromagnetic field.

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