Atomic displacements in the "charge-ice" pyrochlore Bi2Ti2O7 studied by neutron total scattering

The oxide pyrochlore Bi$_2$Ti$_2$O$_6$O$^\prime$ is known to be associated with large displacements of Bi and O$^\prime$ atoms from their ideal crystallographic positions. Neutron total scattering, analyzed in both reciprocal and real space, is employed here to understand the nature of these displacements. Rietveld analysis and maximum entropy methods are used to produce an average picture of the structural non-ideality. Local structure is modeled via large-box reverse Monte Carlo simulations constrained simultaneously by the Bragg profile and real-space pair distribution function. Direct visualization and statistical analyses of these models show the precise nature of the static Bi and O$^\prime$ displacements. Correlations between neighboring Bi displacements are analyzed using coordinates from the large-box simulations. The framework of continuous symmetry measures has been applied to distributions of O$^\prime$Bi$_4$ tetrahedra to examine deviations from ideality. Bi displacements from ideal positions appear correlated over local length scales. The results are consistent with the idea that these nonmagnetic lone-pair containing pyrochlore compounds can be regarded as highly structurally frustrated systems.