On the question of dynamic domains and critical scattering in cubic methylammonium lead triiodide.

We investigate the hypothesis of dynamic tetragonal domains occuring in cubic CH$_3$NH$_3$PbI$_3$ using high-resolution neutron spectroscopy to study a fully deuterated single crystal. The $\textit{R}$-point scattering above the 327.5 K tetragonal-cubic phase transition is always resolution-limited in energy and therefore inconsistent with dynamic domain predictions. This behavior is instead consistent with the central peak phenomenon observed in other perovskites. The scattering may originate from small, static, tetragonal-phase domains nucleating about crystal defects, and the temperature dependence demonstrates the transition is first-order.