The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units

A user-friendly web-based software tool called `ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.

Structural chemistry of layered lead halide perovskites containing single octahedral layers

We present a comprehensive review of the structural chemistry of hybrid lead halides of stoichiometry APbX 4, A 2PbX4 or A A′PbX 4, where A and A′ are organic ammonium cations and X = Cl, Br or I. These compounds may be considered as layered perovskites, containing isolated, infinite layers of corner-sharing PbX 4 octahedra separated by the organic species. First, over 250 crystal structures were extracted from the CCDC and classified in terms of unit-cell metrics and crystal symmetry. Symmetry mode analysis was then used to identify the nature of key structural distortions of the [PbX 4]∞ layers. Two generic types of distortion are prevalent in this family: tilting of the octahedral units and shifts of the inorganic layers relative to each other. Although the octahedral tilting modes are well known in the crystallography of purely inorganic perovskites, the additional layer-shift modes are shown to enormously enrich the structural options available in layered hybrid perovskites. Some examples and trends are discussed in more detail in order to show how the nature of the interlayer organic species can influence the overall structural architecture; although the main aim of the paper is to encourage workers in the field to make use of the systematic crystallographic methods used here to further understand and rationalize their own compounds, and perhaps to be able to design-in particular structural features in future work.

Ruga mechanics of soft-orifice closure under external pressure

Here, we report the closure resistance of a soft-material bilayer orifice increases against external pressure, along with ruga-phase evolution, in contrast to the conventional predictions of the matrix-free cylindrical-shell buckling pressure. Experiments demonstrate that the generic soft-material orifice creases in a threefold symmetry at a limit-load pressure of p / μ ≈ 1.20, where μ is the shear modulus. Once the creasing initiates, the triple crease wings gradually grow as the pressure increases until the orifice completely closes at p / μ ≈ 3.0. By contrast, a stiff-surface bilayer orifice initially wrinkles with a multifold symmetry mode and subsequently develops ruga-phase evolution, progressively reducing the orifice cross-sectional area as pressure increases. The buckling-initiation mode is determined by the layer's thickness and stiffness, and the pressure by two types of the layer's instability modes—the surface-layer-wrinkling mode for a compliant and the ring-buckling mode for a stiff layer. The ring-buckling mode tends to set the twofold symmetry for the entire post-buckling closure process, while the high-frequency surface-layer-wrinkling mode evolves with successive symmetry breaking to a final closure configuration of two- or threefold symmetry. Finally, we found that the threefold symmetry mode for the entire closure process provides the orifice's strongest closure resistance, and human saphenous veins remarkably follow this threefold symmetry ruga evolution pathway.

Recognition of Crack-Rubbing Coupling Fault of Bearing under High Water Pressure Based on Polar Symmetry Mode Decomposition

The precision of current research on fault recognition of marine bearing remains to be improved. Therefore, a recognition method of crack-rubbing coupling fault of bearing under high water pressure based on polar symmetry mode decomposition is proposed in this article. The structure of marine bearing was analyzed, and the system was divided into several subsystems. Then, the nonlinearity relationship among the subsystems was confirmed. One subsystem was used to represent other subsystems, which was imported into the kinetic equation to obtain the equation after dimensionality reduction. According to the results of dimensionality reduction, the features of signal were measured from time domain, energy, and entropy. Meanwhile, the interior features of signal were extracted. Based on the feature extraction, the classifier of probabilistic neural network was introduced. The signal was recognized, and the recognition results were output via the training of signal sample data. Experimental results show that the method has better dimensionality reduction effect and high recognition precision. The method is practical.

Controlling Multiple Orderings in Metal Thiocyanate Molecular Perovskites Ax{Ni[Bi(SCN)6]}

<p>We report four new A-site vacancy ordered thiocyanate double double perovskites,</p><p>A1􀀀xfNi[Bi(SCN)6]1􀀀x3 }, A = K⁺, NH4⁺, CH3(NH3)⁺ (MeNH₃⁺) and C(NH₂)₃⁺ (Gua⁺), including the first examples of thiocyanate perovskites containing organic A-site cations. We show, using a combination of X-ray and neutron diffraction, that the structure of these frameworks depends on the A-site cation, and that these frameworks possess complex vacancy-ordering patterns and cooperative octahedral tilts distinctly different from atomic perovskites. Density functional theory calculations uncover the energetic origin of these complex orders and allow us to propose a simple rule to predict favoured A-site cation orderings for a given tilt sequence. We use these insights, in combination with symmetry mode analyses, to show that these complex orders offer a new route to non-centrosymmetric perovskites which render them as excellent candidates for</p><p>piezo- and ferroelectric applications.</p>

Controlling Multiple Orderings in Metal Thiocyanate Molecular Perovskites Ax{Ni[Bi(SCN)6]}

<p>We report four new A-site vacancy ordered thiocyanate double double perovskites,</p><p>A1􀀀xfNi[Bi(SCN)6]1􀀀x3 }, A = K⁺, NH4⁺, CH3(NH3)⁺ (MeNH₃⁺) and C(NH₂)₃⁺ (Gua⁺), including the first examples of thiocyanate perovskites containing organic A-site cations. We show, using a combination of X-ray and neutron diffraction, that the structure of these frameworks depends on the A-site cation, and that these frameworks possess complex vacancy-ordering patterns and cooperative octahedral tilts distinctly different from atomic perovskites. Density functional theory calculations uncover the energetic origin of these complex orders and allow us to propose a simple rule to predict favoured A-site cation orderings for a given tilt sequence. We use these insights, in combination with symmetry mode analyses, to show that these complex orders offer a new route to non-centrosymmetric perovskites which render them as excellent candidates for</p><p>piezo- and ferroelectric applications.</p>

Switchable Rashba anisotropy in layered hybrid organic–inorganic perovskite by hybrid improper ferroelectricity

Hybrid organic–inorganic perovskites (HOIPs) are introducing exotic directions in the photovoltaic materials landscape. The coexistence of inversion symmetry breaking and spin–orbit interactions play a key role in their optoelectronic properties. We perform a detailed study on a recently synthesized ferroelectric layered HOIP, (AMP)PbI4 (AMP = 4-aminomethyl-piperidinium). The calculated polarization and Rashba parameters are in excellent agreement with experimental values. Moreover, we report a striking effect, i.e., an extraordinarily large Rashba anisotropy that is tunable by ferroelectric polarization: as polarization is reversed, not only the spin texture chirality is inverted, but also the major and minor axes of the Rashba anisotropy ellipse in k-space are interchanged—a pseudo rotation. A k·p model Hamiltonian and symmetry-mode analysis reveal a quadrilinear coupling between the cation-rotation modes responsible for the Rashba ellipse pseudo-rotation, the framework rotation, and the polarization. These findings may provide different avenues for spin-optoelectronic devices such as spin valves or spin FETs.