Columnar shifts as symmetry-breaking degrees of freedom in molecular perovskites

Abstract

We introduce columnar shifts-collective rigid-body translations-as a structural degree of freedom relevant to the phase behaviour of molecular perovskites ABX (X = molecular anion). Like the well-known octahedral tilts of conventional perovskites, shifts also preserve the octahedral coordination geometry of the B-site cation in molecular perovskites, and so are predisposed to influencing the low-energy dynamics and displacive phase transitions of these topical systems. We present a qualitative overview of the interplay between shift activation and crystal symmetry breaking, and introduce a generalised terminology to allow characterisation of simple shift distortions, drawing analogy to the "Glazer notation" for octahedral tilts. We apply our approach to the interpretation of a representative selection of azide and formate perovskite structures, and discuss the implications for functional exploitation of shift degrees of freedom in negative thermal expansion materials and hybrid ferroelectrics.

An Unusual Phase Transition Driven by Vibrational Entropy Changes in a Hybrid Organic–Inorganic Perovskite

“…To better understand the distortions in these structures, the [Mn(N 3 ) 3 ] − frameworks have been compared with the framework of a notional cubic parent framework in space group Pm m (Supporting Information, Figure S5), using the computer program ISODISTORT . A very significant distortion in each structure is associated with irreducible representation (irrep) M 3 − (at k = , ,0); this distortion has been described elsewhere as a “columnar shift” . In the HT structure there is also significant distortion associated with irrep R 4 + , which is well known in perovskites to give out‐of‐phase octahedral tilting and in this case the tilt system a − b − b − .…”

Molecular perovskite high-energetic materials

“…The presented materials belong to the so-called molecular perovskites [28] with a general formula of ABX 3 , which topologically mimic the cubic structure of the very well-known inorganic perovskites, the simplest high-symmetry structure for ternary compounds, but have at least one organic molecular component (usually A component). Recently, molecular perovskites have attracted growing attention, as illustrated by the extensive studies on methyl-ammonium lead iodide for high performance solar cells [29][30][31][32], and the phase transitions together with the relevant switching physical properties [33][34][35].…”

Strongly Coloured Thiocyanate Frameworks with Perovskite-Analogue Structures

“…Instead, the size of the tilts is largely driven by the general tendency towards higher density structures and the geometry of 6 ], which has Ni(NCS) 6 octahedra, has tilts which belong to the conventional a + b À b À tilt system whereas CsCd(SCN) 3 , which has more exible Cd(NCS) 6 octahedra with bent Cd-N-C bond angles (as small as 116.5 ), has more complex cooperative distortions, including unconventional tilts. 5 The shapes of the molecular orbitals of the thiocyanate ligand also explain the magnitude of the observed tilts in these frameworks. There is no unique way of decomposing the total tilts into separate rotations around each of the three axes, as the octahedral rotations do not commute.…”