Distortion Modes Research Articles

Bend Distortion Effect on Transverse Mode Instability

Transverse mode instability (TMI) limits the power scaling of high-power fiber lasers and amplifiers. One method of mitigating TMI is to strip unwanted modes by bending the fiber. However, the bending-induced mode distortion will change the TMI coefficient and influences the TMI threshold. In this work, we analyzed the bending effects on the mode profiles by inducing different refractive index tilts corresponding to different bending radii. With these mode profiles and with different bending conditions, a modified TMI coefficient was calculated to analyze the bending effects on TMI for different fibers. The simulation results show that tighter bending can lead to a somewhat lower TMI coefficient and slightly improve the TMI threshold.

Neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide

We report the results of a neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide, with a focus on the system of orientational distortions of the framework of PbI6 octahedra. The results are analysed in terms of symmetry-adapted lattice strains and normal mode distortions. The higher-temperature cubic–tetragonal phase transition at 327 K is weakly discontinuous and nearly tricritical. The variations of rotation angles and spontaneous strains with temperature are consistent with a standard Landau theory treatment. The lower-temperature transition to the orthorhombic phase at 165 K is discontinuous, with two systems of octahedral rotations and internal distortions that together can be described by 5 order parameters of different symmetry. In this paper we quantify the various symmetry-breaking distortions and their variation with temperature, together with their relationship to the spontaneous strains, within the formalism of Landau theory. A number of curious results in the low-temperature phase are identified, particularly regarding distortion amplitudes that decrease rather than increase with lowering temperature.

Metal-insulator transition and local-moment collapse in negative charge transfer CaFeO3 under pressure

We compute the electronic structure, spin and charge state of Fe ions, and the structural phase stability of paramagnetic ${\mathrm{CaFeO}}_{3}$ under pressure using a fully self-consistent in charge density $\mathrm{DFT}+$ dynamical mean-field theory method. We show that at ambient pressure ${\mathrm{CaFeO}}_{3}$ is a negative charge transfer insulator characterized by strong localization of the Fe $3d$ electrons. It crystallizes in the monoclinic $P{2}_{1}/n$ crystal structure with a cooperative breathing mode distortion of the lattice. While the Fe $3d$ Wannier occupations and local moments are consistent with robust charge disproportionation of Fe ions in the insulating $P{2}_{1}/n$ phase, the physical charge density difference around the structurally distinct Fe $A$ and Fe $B$ ions with the ``contracted'' and ``expanded'' oxygen octahedra, respectively, is rather weak, of $\ensuremath{\sim}0.04$. This implies the importance of the Fe $3d$ and O $2p$ negative charge transfer and supports the formation of a bond-disproportionated state characterized by the Fe $A 3{d}^{5\ensuremath{-}\ensuremath{\delta}}{\underline{L}}^{2\ensuremath{-}\ensuremath{\delta}}$ and Fe $B 3{d}^{5}$ valence configurations with $\ensuremath{\delta}\ensuremath{\ll}1$, in agreement with strong hybridization between the Fe $3d$ and O $2p$ states. This complex interplay between electronic correlations, strong covalency, and lattice effects, resulting in bond disproportionation, is in many ways reminiscent of the behavior of rare-earth nickelates, $R{\mathrm{NiO}}_{3}$ $(R=\text{rare earth})$. Upon compression, ${\mathrm{CaFeO}}_{3}$ undergoes the metal-to-insulator phase transition (MIT) which is accompanied by a structural transformation into the orthorhombic $Pbnm$ phase. The phase transition is accompanied by suppression of the cooperative breathing mode distortion of the lattice and, hence, results in the melting of bond disproportionation of the Fe ions. Our analysis suggests that the MIT transition is associated with orbital-dependent delocalization of the Fe $3d$ electrons and leads to a remarkable collapse of the local magnetic moments. Our results imply the crucial importance of the interplay of electronic correlations and structural effects to explain the properties of ${\mathrm{CaFeO}}_{3}$.

Ferroelectric to incommensurate fluctuations crossover in PbHfO3−PbSnO3

Perovskite solid solutions PbHfO3-PbSnO3 offer valuable opportunities for studying the formation mechsnisms of incommensurate phases, owing to the presence of an intermediate (between cubic and incommensurate) phase, which is stabilized in PbHfO3 upon PbSnO3 admixture. Here, x-ray diffuse scattering signal is used to quantify the evolution of susceptibilities related to different modes of distortion (ferroelectric, incommensurate, antiferrodistortive) as a function of temperature and the results are critically compared to the predictions of a minimal symmetry-based Landau-like model with two coupled order parameters (ferroelectric and antiferrodistortive) and incommensurate order parameter being interpreted as inhomogeneous polarization. Experimentally, we observe a Curie-Weiss-like linear dependence of ferroelectric stiffness (inverse of susceptibility related to homogeneous polarization fluctuations) in the cubic phase down to about 50 K above the transition to the intermediate phase, where this dependence nearly saturates. Upon cooling down to the intermediate phase, the maximum of susceptibility shifts gradually to the non-zero wavevector, where another Curie-Weiss-like linear stiffness trend is established, but with respect to the incommensurate order parameter. Symmetry of diffuse scattering distributions indicates an orthorhombic symmetry of the intermediate phase. A notable temperature dependence of the constant that describes the energy of polarization inhomogeneities is observed experimentally, which is in disagreement with the model expectations. Specifics of this dependence suggest the presence of a nearly temperature-independent characteristic length scale for inhomogeneities across several phases. Other differences with the model suggest that the incommensurate order parameter cannot be straightforwardly identified with weakly-inhomogeneous ferroelectric polarization.

The Mn-O bonds Dependence of the Lattice Distortion in LaMnO3

We have investigated the volume collapse occurring in LaMnO3 unit cell using the anisotropic Potts model modified by two types of anisotropic interactions which has been used to study the change of Mn-O bonds lengths as function of temperature. The bond lengths are related to the occupation of the orbits. The lattice parameters and the distortion modes have been investigated as well. We have shown that the collapse is due to the change of Mn-O bonds lengths change as the temperature is raised through the transition. It has been shown that all the parameters studied here decrease with increasing temperature in a narrow temperature range below TJT, and then undergoes a collapse at TJT. These results are in a good agreement with the published experimental results.

Novel Calibration Method for Large-Scale Measuring Camera Based on Distance-Related Distortion Mode

Novel Calibration Method for Large-Scale Measuring Camera Based on Distance-Related Distortion Mode

The Uniaxial Stress-Strain Relationship of Hyperelastic Material Models of Rubber Cracks in the Platens of Papermaking Machines Based on Nonlinear Strain and Stress Measurements with the Finite Element Method.

Finite element analysis is extensively used in the design of rubber products. Rubber products can suffer from large amounts of distortion under working conditions as they are nonlinearly elastic, isotropic, and incompressible materials. Working conditions can vary over a large distortion range, and relate directly to different distortion modes. Hyperelastic material models can describe the observed material behaviour. The goal of this investigation was to understand the stress and relegation fields around the tips of cracks in nearly incompressible, isotropic, hyperelastic accouterments, to directly reveal the uniaxial stress–strain relationship of hyperelastic soft accouterments. Numerical and factual trials showed that measurements of the stress–strain relationship could duly estimate values of nonlinear strain and stress for the neo-Hookean, Yeoh, and Arruda–Boyce hyperelastic material models. Numerical models were constructed using the finite element method. It was found that results concerning strains of 0–20% yielded curvatures that were nearly identical for both the neo-Hookean, and Arruda–Boyce models. We could also see that from the beginning of the test (0–5% strain), the curves produced from our experimental results, alongside those of the neo-Hookean and Arruda–Boyce models were identical. However, the experiment’s curves, alongside those of the Yeoh model, converged at a certain point (30% strain for Pieces No. 1 and 2, and 32% for Piece No. 3). The results showed that these finite element simulations were qualitatively in agreement with the actual experiments. We could also see that the Yeoh models performed better than the neo-Hookean model, and that the neo-Hookean model performed better than the Arruda–Boyce model.

Low hysteresis and enhanced figure-of-merit of pyroelectric energy conversion at compatible phase transformation

The pyroelectricity of polar materials provides great potential for electricity generation from waste heat. The pyroelectric effect of the material can be magnificently enhanced at a first-order phase transformation due to the abrupt jump in spontaneous polarization within a narrow temperature range. Here, we show that the performance of energy conversion by phase transformation is inversely resonant with the hysteresis of thermally driven structural transformations in a (Ba1−xSrx) (Hf0.02Ce0.005Ti0.975)O3 system, corresponding to a singular lattice distortion mode satisfying the crystallographic compatibility condition. Among the finely tuned Sr compositions from 0.04 to 0.10, we discovered that Sr0.07 composition is a promising material candidate in this material system for pyroelectric energy conversion. Our work suggests a rational strategy of material development for pyroelectric energy conversion applications.

Distortion mode anomalies at T MIT = T N in bulk PrNiO3

Distortion mode anomalies at <i>T</i> _MIT = <i>T</i> _N in bulk PrNiO₃

Interplay between breathing-mode distortions and magnetic order in rare-earth nickelates from ab initio magnetic models

We use density-functional theory calculations to explore the magnetic properties of perovskite rare-earth nickelates, $\mathcal{R}$NiO$_3$, by constructing microscopic magnetic models containing all relevant exchange interactions via Wannierization and Green's function techniques. These models elucidate the mechanism behind the formation of antiferromagnetic order with the experimentally observed propagation vector, and explain the reason previous DFT plus Hubbard $U$ calculations favored ferromagnetic order. We perform calculations of magnetic moments and exchange-coupling parameters for different amplitudes of the $R_1^+$ breathing mode distortion, which results in expanded and compressed NiO$_6$ octahedra. We find that the magnetic moment vanishes for the "short bond" nickels, i.e., the ones in the compressed octahedra. The inclusion of spin-orbit coupling demonstrates that the magnetic anisotropy is very small, while the magnetic moment of the short bond nickel atoms tend to zero even for the noncollinear case. Our results provide a clear picture of the trends of the magnetic order across the nickelate series and give insights into the coupling between magnetic order and structural distortions.

3-Phonon Scattering Pathways for Vibrational Energy Transfer in Crystalline RDX.

A long-held belief is that shock energy induces initiation of an energetic material through an energy up-pumping mechanism involving phonon scattering through doorway modes. In this paper, a Fermi's golden rule-based 3-phonon theoretical analysis of energy up-pumping in RDX is presented that considers possible doorway pathways through which energy transfer occurs. On average, modes with frequencies up to 102 cm-1 scatter quickly and transfer over 99% of the vibrational energy to other low-frequency modes up to 102 cm-1 within 0.16 ps. These low-frequency modes scatter less than 0.5% of the vibrational energy directly to modes with significant nitrogen-nitrogen (NN) activity. The midfrequency modes from 102 to 1331 cm-1 further up-pump the energy to these modes within 5.6 ps. The highest-frequency modes scatter and redistribute a small fraction of the vibrational energy to all other modes, which last over 2000 ps. The midfrequency modes between 457 and 462 cm-1 and between 831 and 1331 cm-1 are the most critical for vibrational heating of the NN modes and phenomena, leading to initiation in energetics. In contrast, modes stimulated by the shock with frequencies up to 102 cm-1 dominate vibrational cooling of the NN modes.

Compressed Jahn-Teller octahedra and spin quintet-triplet switching in coordinatively elastic manganese(III) complexes

Complex assembly preferences and resultant spin state choice and Jahn-Teller distortion mode in twelve Mn(III) complexes of varying nuclearity with Schiff base chelate ligands of different sizes are compared. Mononuclear complexes Mn(5-F-Sal2323)]OTf (1), [Mn(5-F-Sal2323)]ClO4 (2) and [Mn(5-F-Sal2323)]NO3, (3) with the 8-carbon R-Sal2323 chelate type show rare axial compression at room temperature and complexes (2) and (3) also show reversible thermal spin state switching from spin quintet to triplet states on cooling. The prevalence of atypical axial compression is further probed by single crystal diffraction studies on high spin mononuclear complexes (4)-(7) with the longer 9-carbon R-Sal2333 chelate series using [Mn(3-OEt-Sal2333)]BF4, (4) [Mn(3,5-diOMe-Sal2333)]BF4·0.5PrOH, (5), [Mn(5-F-Sal2333)]BPh4, (6) and Mn(5-NO2-Sal2333)]BPh4, (7) as examples. Ring closure of both the 8-carbon R-Sal2323 and longer 9-carbon R-Sal2333 ligands was also observed yielding a ligand with a 6-membered ring in the mononuclear complex [Mn(3-OMe,5-NO2-Sal23336R)]·0.07MeOH·0.93MeCN (8) in contrast to a protonated 5-membered ring in the dimeric complex [Mn2(5-Cl-Sal2323H5R)2](ClO4)2·1.85EtOH·0.33MeCN, (9) with the R-Sal2323 chelate type. Finally comparison of the assembly modes of Mn(III) complexes of the 8-carbon R-Sal2323 and 9-carbon R-Sal2333 series with those of the shorter 7-carbon R-Sal2322 ligand series reveal that the mononuclear assembly mode is not favoured with the smaller chelate. Instead three dimeric or cluster complexes with rearranged ligands were recovered in low yield. The structures of these complexes [Mn2(5-NO2-Sal23225R)2]·2BuOH, (10), [Mn2(3,5-diBr-Sal23225R)(3,5-diBr-Sal)3]·0.7EtOH·2.61MeCN, (11) and [Mn2Na(3-NO2,5-OMe-Sal23225R)]ClO4·0.5MeCN (12) are reported and compared with examples with the longer chain R-Sal2323 and R-Sal2333 chelate ligands.

Robust temperature coefficient of resistance of polycrystalline La0.6Ca0.4MnO3 under magnetic fields at room temperature

In the presence of magnetic field, reducing the loss in temperature coefficient of resistance (TCR) and increasing metal−insulator transition point (TMI) to room temperature are the most important concerns for the application of perovskite manganites in high−precision thermistors. Based on emerging evidence, relevant factor to address these problems lies in the interaction between Jahn−Teller (JT) distortion and magnetic field, which results in spin−orbital coupling (SOC) effect and significantly influences TCR and TMI. In this work, we studied the magnetic field induced SOC effect in polycrystalline La1−xCaxMnO3 (x = 0.225–0.45) materials synthesized via sol−gel technique. Compounds undergo the JT distortions with increasing Ca dopant content, and the most pronounced distortion of 0.0144 at x = 0.40 is correlated with a basal−plane distortion mode. All samples exhibit TMI values between 262 K and 288 K, indicating the enhancement of doping−induced double−exchange interaction. In the magnetic field of 1 T, SOC effect sufficiently suppresses the deterioration of TCR caused by deficient magnetization in La0.6Ca0.4MnO3 to a value of 2.9%·K−1 at room temperature (287 K).

PorphyStruct - A Digital Tool for the Quantitative Assignment of Non-Planar Distortion Modes in Four-Membered Porphyrinoids.

Invited for the cover of this issue are Jens Krumsieck and Martin Bröring from the TU Braunschweig, Germany. The cover image allows a glance into a futuristic lab with an innovative imaging device analyzing structural details of a metal corrole. Read the full text of the article at 10.1002/chem.202101243.

Front Cover: PorphyStruct: A Digital Tool for the Quantitative Assignment of Non‐Planar Distortion Modes in Four‐Membered Porphyrinoids (Chem. Eur. J. 45/2021)

Front Cover: <i>PorphyStruct</i>: A Digital Tool for the Quantitative Assignment of Non‐Planar Distortion Modes in Four‐Membered Porphyrinoids (Chem. Eur. J. 45/2021)

PorphyStruct: A Digital Tool for the Quantitative Assignment of Non-Planar Distortion Modes in Four-Membered Porphyrinoids.

PorphyStruct, a new digital tool for the analysis of non‐planar distortion modes of different porphyrinoids, and its application to corrole structures is reported. The program makes use of the normal‐coordinate structure decomposition technique (NSD) and employs sets of normal modes equivalent to those established for porphyrins in order to describe the out‐of‐plane dislocation pattern of perimeter atoms from corroles, norcorroles, porphycenes and other porphyrinoids quantitatively and in analogy to the established terminology. A comparative study of 17 porphyrin structures shows very similar results to the original NSD analysis and no systematic error. Application to corroles is successful and reveals the necessity to implement an extended basis of normal modes for a large share of experimental structures. The results frequently show the concomitant occurence of several modes but remain interpretable. For group XI metal corroles the phenomenon of supersaddling was unravelled, allowing for more in‐depths discussions of structure‐function correlations.

Structural response of concrete segmental linings in transverse interaction with the TBM. Part 2: Non-axisymmetric conditions

In the second part of this paper, the behaviour of the last assembled ring when loaded simultaneously by the tail seal pressures and the jack forces is investigated in detail for eccentric scenarios of tail seal passage such as those encountered in the Crossrail’s Thames tunnel (CTT). In these non-axisymmetric scenarios, the sealing pressures grow linearly with depth and the ram pad restraints against the tunnel uplift are unevenly distributed over the ring circumference. The parametric study targeted the effect of uneven pad boundaries, tunnel unsupported length, Lu, and lining features on the numerical outputs of selected ten-ring finite element (FE) models. The numerical outputs of interest were ring deformations, internal forces, segment interactions and stress concentrations within the segment bodies. It was found that ring distortions can develop within Lu. The distortion mode is determined by the ram pad boundary. The ring deformations increase with the advance of the sealing pressures and decay with distance from the TBM pads. For a given pad boundary, Lu governs the magnitude of distortion, which, in the cases studied, raised up to 0.30% the tunnel diameter D by the end of the first advance. The tangential component of the jacks’ downward reaction can induce hoop tension at the ring front. The radial reaction forces result in significant hoop and torsional moments, differential radial rotations at transitional longitudinal joints and longitudinal moments in constrained segments. The total angularities of longitudinal joints can exceed recommended tolerances. The lower joints are at a higher risk of developing permanent angularities. Gasket offsets in joints undergoing differential radial rotations are sensitive to Lu. Temporary spear bolts can trim extreme offsets, e.g. 12 mm, down to moderate values. The transverse action of the pads increases the magnitude of peak tensile stresses in constrained segments: hoop spalling stresses at pad interspaces plus radial bursting stresses and ‘longitudinal’ spalling stresses near the rear corner of the longitudinal joints. Torsional shear stresses combined with hoop tension can cause excessive extrados surface tension near the front of constrained segments. Shear failure was identified in convex-convex transitional joints with considerable joint imperfections.

740-watt level optical tap coupler using side-polished large-mode-area double clad fibers for a high power fiber laser.

We fabricated a fiber-optic directional coupler based on evanescent field coupling between side-polished large mode area (LMA) double clad fibers (DCFs) for a high power fiber laser. The tapping ratio of the fabricated coupler was measured to be - 32 dB. The fundamental mode coupled in a core of the lower side-polished fiber (SPF) was transferred to the upper SPF without clad-mode coupling. Two SPFs were directly faced to increase an optical handling power up to 740 W. The tapping ratio of the coupler was constantly maintained at the applied laser output. The beam quality of the laser including the fabricated coupler was maintained to be 1.22, without mode distortion by the coupler.

Intrinsic geometry and director reconstruction for three-dimensional liquid crystals

We give a description of the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals and establish necessary and sufficient conditions for a set of functions to represent these distortions by describing how they couple to the curvature tensor. We demonstrate that, in contrast to the situation in two dimensions, the first-order gradients of the director alone are not sufficient for full reconstruction of the director field from its intrinsic geometry: it is necessary to provide additional information about the second-order director gradients. We describe several different methods by which the director field may be reconstructed from its intrinsic geometry. Finally, we discuss the coupling between individual distortions and curvature from the perspective of Lie algebras and groups and describe homogeneous spaces on which pure modes of distortion can be realised.

A gauge-fixing procedure for spherical fluid membranes and application to computations

A distinguishing feature of lipid (bilayer) membranes is their in-plane fluidity caused by free-flowing lipid molecules on the membrane surface. In continuum models for lipid membranes (e.g., the Helfrich–Canham model), fluidity manifests as invariance of the free energy to change in parametrization of the reference surface; a property termed reparametrization invariance. Two different parametric equations of the surface, related through a reparametrization, have identical equilibrium and stability properties. They can therefore be considered equivalent representations of the same surface. Since there are infinitely many ways to parametrize a surface, there are infinitely many equivalent representations for the surface. This highly redundant representation for a surface poses significant challenges to computations. For example, in computational studies using finite element analysis, extreme mesh distortion and spurious zero-energy modes are reported (Feng and Klug, 2006; Ma and Klug, 2008). In this work, by viewing reparametrization invariance as a form of gauge symmetry, we propose a gauge-fixing procedure for the case of topologically spherical membranes. We show that this procedure breaks gauge symmetry and tames the extreme redundancy of the system. We also demonstrate that this procedure is suitable for efficient numerical computations. We obtain accurate equilibrium configurations for the Helfrich–Canham model while circumventing computational issues noted above.