Probability density analyses of guest ions in hollandite A(x)Mg(x/2)Ti(8 - x/2)O(16) (A = K, Rb)

Probability density functions (PDFs) of mobile ions in one-dimensional ionic conductors of hollandite A(x)Mg(x/2)Ti(8 - x/2)O(16) (A = K, Rb) were examined by single-crystal X-ray diffraction. A conventional structure model was modified by imposing an additional constraint condition, which is based on microscopic description for the possible displacement of mobile ions adjacent to a vacancy in the tunnel. Joint PDFs and one-particle potentials for mobile ions were obtained from the structure models applying harmonic and anharmonic atomic displacement parameters (ADPs). Potential curves of the ion hopping between neighboring cavities were calculated from the joint PDF of the specific ions of the process. Energy barriers of the ion hopping were estimated at 52-60 meV from anharmonic ADP models of K-hollandite, while the values varied from 140 to 250 meV for Rb-hollandite.