The Adiabatic Bond Charge Model

The phonon dispersion curves of all covalent semiconductors with diamond or sphalerite structure show one characteristic feature from which only diamond itself is an exception the TA phonon branches have very low frequencies and are very flat away from the zone center, although the corresponding shear moduli (slopes of w(q) at q = 0) have rather high values. Examples of dispersion curves for Ge and GaAs are shown in Figs.4.13,14. This behaviour is most easily understood with the bond charge model which has been developed for the lattice dynamics of covalent materials. 

The covalent bond is usually formed from two electrons, one from each atom participating in the bond. These electrons tend to be partially localized in the region between the two atoms and constitute the bond charge (BC). If each ion contributes a charge - Ze/2 to each bond 6f a tetrahe-drally coordinated compound, the magnitude of the BC is -Ze and the ions  

A B semiconductors, the BC is believed to shift toward the group V ion and divides the bond length roughly in the ratio 5 3 [4.50]. 

In the bond charge model, the effect of the metal-like binding is described by central forces between nearest-neighbour ions while the covalent bonding is described by interactions involving the BC s [4.51,52]. In the adiabatic bond charge model of WEBER [4.17,18], the constraint that the BC s are fixed on the midway positions between the atoms is removed. Instead, they are allowed to move adiabatically like the electronic shells in the shell 

Linear chain formed by alternating ions and bond charges. F and f are the force constants of the model 

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The temperature dependence of the spin-lattice relaxation time corresponding to the inelastic scattering of phonons by the Ge quadrupole moment in Ge single crystals is calculated in the framework of the adiabatic bond charge model. The results obtained agree with the experimental data. " ... 

Weber, W. (1977) Adiabatic bond charge model for the phonons in diamond. Phys. Rev. B 15, 4789-803. 

An adiabatic bond charge model for covalent crystals has also been put forward by JOHNSON [4.53] and by JOHNSON and MOORE [4.54] in contrast to WEBER S model, all interactions in Johnsons model are purely electrostatic. Finally, it should be mentioned that bond charge models have also been used to study the vibrations of diatomic and polyatomic molecules [4.55,56]. 

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