Two-dimensional nanoscale correlations in the strong negative thermal expansion material ScF3

Abstract

We present diffuse x-ray scattering data on the strong negative thermal expansion (NTE) material ${\mathrm{ScF}}_{3}$ and find that two-dimensional nanoscale correlations exist at momentum-space regions associated with possibly rigid rotations of the perovskite octahedra. We address the extent to which rigid octahedral motion describes the dynamical fluctuations behind NTE by generalizing a simple model supporting a single floppy mode that is often used to heuristically describe instances of NTE. We find this model has tendencies toward dynamic inhomogeneities and its application to recent and existing experimental data suggest an intricate link between the nanometer correlation length scale, the energy scale for octahedral tilt fluctuations, and the coefficient of thermal expansion in ${\mathrm{ScF}}_{3}$. We then investigate the breakdown of the rigid limit and propose a resolution to an outstanding debate concerning the role of molecular rigidity in strong NTE materials.