Forces in covalent crystals

The interplanar force constants defined by eq. (5.3.1) are summarized in Tab. 5.1. As explained in Section 5.4, care was taken to remove from them the anharmonicity of the lowest order allowed by symmetry only the values used for calculation of phonon dispersion are quoted. Translational invariance of the supercell implies that the restoring force on the displaced plane -k is given by ° 

The ab initio determined force constants in Tab. 5.1 or Fig. 5.8.2 leave no doubt as to which of the two potentials mediates the 0-2 interaction they clearly support the idea of angular forces. 

The above arguments and the values of transverse force constants give a great deal of justification to the physical realism 5 Valence Force Field descriptions of covalent crystals - in spite of the disagreement on the actual range of 

The transverse [111] forces show a similar behavior to the transverse [100] ones in particular, the alternation of signs further supports the idea of angular forces we do not plot them because the present picture, stopping at the 4th neighbors, would necessarily be incomplete. 

We have explained in Section 5.2 why the individual interatomic force constants (lx k ) cannot be determined on supercells of reasonable size the force constants fall off with distance rather slowly so that several displaced atoms contribute to forces detected on other sites (Fig. 5.2.1). There is, however, a situation where decoupling of the contributions 

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A feature which might cause surprise in Fig. 5.5.3 is that including one more interaction does not necessarily improve the result two have to be added. This is a remarkable property of the slope at r, the origin of which can be traced back to the nature of transverse forces in covalent crystals. The astic constant c., giving the slope of the TA(A) branch is given, in terms of [lOO]... 

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