Simple superatom model for lattice dynamics of dodecaborides RB12 (RÂ =Â Zr, Yb, Lu)

In this paper lattice dynamics of dodecaborides RB12 (R = Zr, Yb, Lu) is studied using the superatom model. Within this model, a group of strongly bound boron atoms placed at the vertices of cubooctahedron is substituted with a superatom, which possesses the mass equal to the sum of the masses of all atoms in the cluster. Based on this approach, phenomenological models for Yb(Lu)B12 and ZrB12 describing phonon dispersion up to 45 meV for Yb(Lu)B12 and up to 35 meV for ZrB12 are developed. Good agreement between experimental and modeled dispersion curves is found in both acoustic and low-energy optic regions for ZrB12, while in Yb(Lu)B12, description of acoustic phonons can only be regarded as satisfactory. The comparison with Einstein oscillator approximation is presented. Analysis of the interatomic interactions is performed on the basis of the Born von Karman force constants model. It is shown that the model makes it possible to calculate specific heat with a 5% error margin up to approximately 100 K, while a more commonly used Debye model only provides correct values up to 60 K.