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Perovskite photovoltaic ABX$_3$ systems are being studied due to their high energy-conversion efficiencies with current emphasis placed on pure inorganic systems. In this work, synchrotron single-crystal diffraction measurements combined with second harmonic generation measurements reveal the absence of inversion symmetry below room temperature in CsPbBr$_3$. Local structural analysis by pair distribution function and X-ray absorption fine structure methods are performed to ascertain the local ordering, atomic pair correlations, and phase evolution in a broad range of temperatures. The currently accepted space group assignments for CsPbBr$_3$ are found to be incorrect in a manner that profoundly impacts physical properties. New assignments are obtained for the bulk structure: $Im$$\bar{3}$ (above $\sim$ 410 K), $P$2$_1$/$m$ (between $\sim$ 300 K and $\sim$ 410 K), and the polar group $Pm$ (below $\sim$ 300 K), respectively. The newly observed structural distortions exist in the bulk structure consistent with the expectation of previous photoluminescence and Raman measurements. High-pressure measurements reveal multiple low-pressure phases, one of which exists as a metastable phase at ambient pressure. This work should help guide research in the perovskite photovoltaic community to better control the structure under operational conditions and further improve transport and optical properties., Comment: 7 Figures in main text (20 pages), 18 Figure groups and 10 Table groups in supplementary documentation (42 pages)

In hybrid improper ferroelectric systems, polarization arises from the onset of successive nonpolar lattice modes. In this work, measurements and modeling were performed to determine the spatial symmetries of the phases involved in the transitions to these modes. Structural and optical measurements reveal that the tilt and rotation distortions of the MnO6 or TiO6 polyhedra relative to the high symmetry phases driving ferroelectricity in the hybrid improper Ca3X2O7 system (X=Mn and Ti) condense at different temperatures. The tilt angle vanishes abruptly at T$_T$ ~ 400 K for Ca3Mn2O7 (and continuously for X=Ti) and the rotation mode amplitude is suppressed at much higher temperatures T$_R$ ~1060 K. Moreover, Raman measurements in Ca3Mn2O7 under isotropic pressure reveal that the polyhedral tilts can be suppressed by very low pressures (between 1.4 and2.3 GPa) indicating their softness. These results indicate that the Ca3Mn2O7 system provides a new platform for strain engineering of ferroelectric properties in film based systems with substrate induced strain., Comment: Eight figures and one table in main text. Twenty-two figures and eleven tables in supplementary document