Local structure of the lone-pair pyrochlore Bi$_2$Ti$_2$O$_7$ and the search for polar ordering

Pyrochlore oxides of the formula $A_2B_2$O$_7$ contain geometrically frustrated $A$ and $B$ sublattices, leading to a multitude of complex phenomena including high dielectric constants, glassy spin interactions, and low-temperature peaks in heat capacity. In Bi$_2$Ti$_2$O$_7$, large atomic displacements ($\sim 0.4$ \AA) on the diamond-type OBi$_4$ sublattice cannot cooperatively order to accommodate the Bi lone pair. Instead, polar distortions form a charge ice with no long-range order, and powder diffraction finds Bi$_2$Ti$_2$O$_7$ to remain centrosymmetric at 2 K. We move beyond Rietveld analysis to describe the real-space, local structure of this highly disordered oxide. By conducting large-box reverse Monte Carlo (RMC) simulations on neutron total scattering data, we produce a model that contains details invisible to traditional crystallographic techniques. In addition to describing the local structure of Bi$_2$Ti$_2$O$_7$, we present capabilities of the RMC technique and its application to complex disorder in other crystalline materials.