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Using a valence force field model based on that introduced by Martin, wepresent three related methods through which we analytically determine valenceforce field parameters. The methods introduced allow easy derivation of valenceforce field parameters in terms of the Kleinman parameter $\zeta$ and bulkproperties of zincblende and diamond crystals. We start with a model suited forcovalent and weakly ionic materials, where the valence force field parametersare derived in terms of $\zeta$ and the bulk elastic constants $C_{11}$,$C_{12}$, and $C_{44}$. We show that this model breaks down as the materialbecomes more ionic and specifically when the elastic anisotropy factor $A =2C_{44}/(C_{11}-C_{12}) > 2$. The analytic model can be stabilised for ionicmaterials by including Martin's electrostatic terms with effective cation andanion charges in the valence force field model. Inclusion of effective chargesdetermined via the optical phonon mode splitting provides a stable model forall but two of the materials considered (zincblende GaN and AlN). A stablemodel is obtained for all materials considered by also utilising the innerelastic constant $E_{11}$ to determine the magnitude of the effective chargesused in the Coulomb interaction. Test calculations show that the modelsdescribe well structural relaxation in superlattices and alloys, and reproducekey phonon band structure features.

Fully analytic valence force field model for the elastic and inner elastic properties of diamond and zincblende crystals