Fractional site occupation of Hf_(5-x)Nb_xGe_4: crystallographic investigation and thermodynamic modeling

摘要

The binary compound Hf_5Ge_4 (structure type Sm_5Ge_4, oP36, Pnma) was found to form an extended ternary solid solution Hf_(5-x)Nb_xGe_4 with 0 ≤ x ≤ 3.8. This solid solution was investigated by X-ray diffraction employing powder- as well as single crystal methods. Structure refinements at several different compositions within the phase revealed strongly preferred site occupation by Nb at the three crystallographically independent metal sites of the Sm_5Ge_4-type structure yielding an almost stepwise substitution mechanism of the two transition metals. Chemical bonding and site occupation are discussed on the basis of extended Huckel calculations performed on Hf_5Ge_4, and site volumes (Dirichlet domains) as well as atomic orbital occupations (site potentials) are correlated with the observed substitution mechanism. A thermodynamic model based on the compound energy formalism was developed in order to link the observed substitution mechanism to thermodynamic properties (Gibbs energies) of the different sublattices formed by the crystallographically independent sites.