Structural Determination of Atomic Substitution Ratio in (K_1−xRb_x)₂SeO₄ Mixed Crystal System

Abstract

In order to explain why Rb₂SeO₄ remains in normal phase down to 0 K while K₂SeO₄ transforms into the modulated phase at finite temperature, crystal structures of the mixed system have been refined at room temperature by X-ray single crystal analysis. Rb ion can be substituted for K ion with keeping the macroscopic symmetry of space group Pnam. Larger size of Rb ion occupies preferentially site 1, while smaller K ion prefers site 2. Here the atomic distance between an alkali ion and oxygen atoms is longer at site 1 than at site 2. The mean substitution ratio coincides with that from chemical analysis, however, the crystallographic structure analysis is only one method to determine the ratios at each site separately. A sublattice model is discussed to interpret the ion replacing effect on the phonon dispersion relation of the mixed crystal system. The hardening of the soft mode branch can be predicted by the change of interactions between the SeO₄ tetrahedrons if the alkali ions are replaced.