Low Symmetry Research Articles

Predictive potential of circular walking in prodromal Parkinson's disease

Background Development of objective, reliable and easy-to-use methods to detect the onset of motor changes in Parkinson's disease (PD) is required to identify the temporal window in which neuromodulatory therapies could be implemented. Turning impairments are present at early stages of PD. However, it is unclear, to date, whether circular walking is also altered in prodromal PD. Objective Explore the predictive potential of circular walking in prodromal PD. Methods We included 102 subjects from a nine-year prospective cohort study (with 712 participants) in the current nested case-control analysis: 16 diagnosed with PD during follow-up (incident PD) and 96 healthy controls, matched in gender, age, and education with a 1:6 ratio. Forty-one gait features were extracted from baseline assessments with accelerometers under single and dual-tasking conditions. A Cox proportional hazards regression analysis was used to test the temporal association of non-correlated gait features to the probability of being diagnosed with PD. Results We identified associations between time from baseline measurement to PD diagnosis for eleven gait features, mostly based on harmonic ratios, step and stride variability, and index of harmonicity, partially in combination with gait speed. Most significant associations indicated that low gait symmetry and low rhythmicity were associated with larger hazard of being diagnosed with PD. Area under the curve ranged 0.63-0.69. Conclusions Despite low sensitivity and specificity, the findings potentially reflect prodromal motor impairments of PD manifested during circular walking, assessed quantitatively with a low-cost and wearable instrument. This will contribute to the characterization of pre-diagnostic PD motor symptoms.

Peak Weight Acceptance, Mid Stance Trough, and Peak Push-Off Force Symmetry Are Decreased in Older Adults Compared With Young Adults.

Gait abnormalities affect an individual's ability to navigate the world independently and occur in 10% of older adults. Examining age-related gait symmetry in nonlaboratory environments is necessary for understanding mobility limitations in older adults. This study examined gait symmetry differences between older and younger adults using in-shoe force sensors. Walking trials were performed at a preferred speed. This is a secondary analysis of data from different studies in which young adults completed 7 trials and older adults completed 3 trials to decrease the impact of fatigue on outcomes in the clinical trial. Peak weight acceptance, mid stance trough, peak push-off, stance time, and impulse were collected during each step within a trial. Symmetry was determined using the absolute symmetry index. A linear mixed effects model showed a significant difference in peak weight acceptance force (P = .039), mid stance trough (P < .001), and peak push-off (P = .007) symmetry between groups. These results indicate that older adults have lower symmetry in peak weight acceptance, mid stance trough, and peak push-off during gait compared with young adults. Understanding how natural loading patterns change throughout life could improve our understanding of how load and load symmetry relate to mobility impairments in older adults.

Debus-Radziszewski Reaction Inspired In Situ "One-Pot" Approach to Construct Luminescent Zirconium-Organic Frameworks.

Metal-organic frameworks have received extensive development in the past three decades, which are generally constructed via the reaction between inorganic building units and commercially available or presynthesized organic linkers. However, the presynthesis of organic linkers is usually time-consuming and unsustainable due to multiple-step separation and purification. Therefore, methodology development of a new strategy is fundamentally important for the construction and further exploration of the applications of MOFs. Herein, we report an in situ "one-pot" strategy inspired by the Debus-Radziszewski reaction, in which the generation of organic linkers from three kinds of simple and commercially available precursors and sequential construction of MOFs are integrated into one solvothermal condition. Based on this method, two zirconium-tetracarboxylate frameworks (HIAM-4028-op and HIAM-4029-op) were successfully prepared, which exhibit bright blue and near-infrared emissions, respectively. Due to the coordinatively unsaturated metal sites and the low symmetry of HIAM-4028-op, the coordination modes in the single crystal can transfer from the pristine 8-connected Zr6 cluster to 8- and 9-connected and to 9- and 12-connected Zr6 cluster coexisting structures via secondary linker installation. To the best of our knowledge, the present work is the first time to construct MOFs using a Debus-Radziszewski reaction-inspired in situ "one-pot" strategy, which opens a new way to design and construct MOFs with specific properties and structures.

Raman Signature of Stripe Domains in Monolayer WxMo1-xS2 Alloys.

We study the Raman signature of stripe domains in monolayer WxMo1-xS2 alloys, characterized using experimental techniques and density functional theory (DFT) calculations. These stripe domains were found in star-shaped monolayer WS2 exhibiting a high concentration of molybdenum (Mo) atoms in its central region, and unique Raman peaks that were not previously reported. We attribute these peaks to the splitting of the original doubly degenerate E2g modes, arising from the lower symmetry of the W-Mo stripe domains. We confirm the stripe presence and location using high-resolution scanning transmission electron microscopy (STEM) imaging and use DFT to elucidate the structural, electronic, and vibrational properties of the stripes when the stoichiometry corresponds to W0.5Mo0.5S2. The findings provide insight into the evolution of the Raman spectra as stripe domains arise in TMD alloys, thus contributing to a broader understanding of the influence of atomic-level structural modifications on material properties.

Neural structural alterations correlates of quadriceps muscle strength deficits in patients after anterior cruciate ligament reconstruction.

Persistent maladaptive changes of corticospinal tract (CST) and quadriceps strength deficits exist in patients with anterior cruciate ligament reconstruction (ACLR). This study aimed to investigate the relationships between the structural alterations of CST and quadriceps muscle strength deficits in patients with ACLR. Twenty-nine participants who had undergone unilateral ACLR (29 males; age=32.61±6.72 years) were enrolled in a cross-sectional investigation. We chose CST as a region of interest and performed diffusion tensor imaging (DTI) that measured the microstructure of white matter tracts. Maximal voluntary isometric quadriceps muscle strength was assessed using a hand-held dynamometer. Simple and partial correlation analyses were performed between the DTI outcomes and quadriceps muscle strength deficits in patients with ACLR before and after controlling for age, sex, BMI, Tegner activity score, and graft type. Sub-group analyses were also performed to investigate the relationships between the DTI outcomes of CST structure and quadriceps muscle strength deficits according to the graft type before and after controlling for age, sex, BMI, and Tegner activity score. Lower limb symmetry index (LSI) of quadriceps muscle strength was associated with a higher ratio of radial diffusivity (RD, r=-0.379, p=0.042) in corticospinal tracts of the injured hemisphere to those of the non-injured hemisphere in ACLR patients after controlling for age, BMI, Tegner activity score and graft type. In subgroup analyses of ACLR patients with hamstring autografts, we found that higher injured quadriceps muscle strength was associated with higher axial diffusivity (AD, r=0.616, p=0.033) of CST structure and lower LSI of quadriceps muscle strength was associated with higher ratio of mean diffusivity (MD, r=-0.682, p=0.014) and RD (r=-0.759, p=0.004) in corticospinal tracts of the injured hemisphere to those of the non-injured hemisphere in ACLR patients after controlling for age, BMI, Tegner activity score. Decreased integrity (higher ratio of RD) of CST microstructure in ACLR patients was significantly associated with lower quadriceps limb symmetry index, which hinted that quadriceps muscle strength deficits of injured side may be a demyelinating process of CST microstructure in ACLR.

Temperature-induced mobility in octacalcium phosphate impacts crystal symmetry: water dynamics studied by NMR crystallography.

Octacalcium phosphate (OCP, Ca8(PO4)4(HPO4)2·5H2O) is a notable calcium phosphate due to its biocompatibility, making it a widely studied material for bone substitution. It is known to be a precursor of bone mineral, but its role in biomineralisation remains unclear. While the structure of OCP has been the subject of thorough investigations (including using Rietveld refinements of X-ray diffraction data, and NMR crystallography studies), important questions regarding the symmetry and H-bonding network in the material remain. In this study, it is shown that OCP undergoes a lowering of symmetry below 200 K, evidenced by 1H, 17O, 31P and 43Ca solid-state NMR experiments. Using ab initio molecular-dynamics (MD) simulations and gauge including projected augmented wave (GIPAW) DFT calculations of NMR parameters, the presence of rapid motions of the water molecules in the crystal cell at room temperature is proved. This information leads to an improved description of the OCP structure at both low and ambient temperatures, and helps explain long-standing issues of symmetry. Remaining challenges related to the understanding of the structure of OCP are then discussed.

Breathing Transition and Effective Iodine Adsorption in a Temperature-Responsive Zn-Based Flexible Metal-Organic Framework.

A porous and flexible Zn-MOF was synthesized under solvothermal conditions by using the ligand 2,5-furandicarboxylic acid (2,5-FDA). This flexible Zn-MOF demonstrates a temperature-triggered breathing effect. At low temperature (100 K), we obtained the high-symmetry MOF denoted as SM-A with a unit cell volume of 1958 Å3, characterized by triangular narrow pore (np) channels. Upon increasing the temperature from 100 K to 298 K, the lower symmetry referred to as SM-B was obtained, featuring rhombic large pore (lp) channels, along with an expanded unit cell volume of 7823 Å3. This temperature-induced phase transition involves distortion of the channels and a change in the dimensionality of the framework from 3D (SM-A) to 2D (SM-B). The flexible behavior and phase transition were thoroughly justified with the help of single-crystal X-ray diffraction and differential scanning calorimetry. Additionally, BET analysis revealed a surface area of 85.504 m2/g, with mesopores of 3.05 nm. Leveraging the large-pore channels, SM-B at room temperature was employed as an adsorbent for the removal of hazardous iodine in both the vapor and the solution phases. The discovery of such dynamic MOFs holds potential and may pave the way for novel strategies in advanced applications.

Triazolide Complexes of Sodium and Potassium in the Gas Phase.

Aromatic organometallic complexes, such as ferrocene and the "inverse sandwich complex" [Na2Cp]+, are stabilized via charge-transfer (C-T) interactions and cation-π interactions (i.e., charge-induced dipole and charge-quadrupole interactions). Much effort has gone into investigating systems that contain organic moieties, such as benzene or cyclopentadienyl ligands, but less attention has been paid to aromatic systems that contain heteroatoms (e.g., N), possibly owing to the complexity arising from a lowering of symmetry and the introduction of electron lone pair density and dipole moments. Here we investigate sodiated and potassiated clusters of 1,2,3-triazolide, [Mx (123T)x-1]+ (x = 3, 4; M = Na, K), and 1,2,4-triazolide, [Mx (124T)x-1]+ (x = 3, 4; M = Na, K), using a combination of infrared ion spectroscopy (IRIS) and DFT calculations. Cluster structures are strongly influenced by charge-dipole interactions and C-T interactions from N lone pairs to the metal cations. IRIS spectra indicated that the geometries of the triazolide moieties are essentially unperturbed by the interaction with the metal ions. Additional spectral features, not predicted by DFT calculations, that are observed in the 1500-1800 cm-1 region seem to be associated with combination bands involving C-H wagging and ring torsion motions.

Uniformity, Linearity, and Symmetry Enhancement in TiOx/MoS2-xOx Based Analog RRAM via S-Vacancy Confined Nanofilament.

Due to the stochastic formation of conductive filaments (CFs), analog resistive random-access memory (RRAM) struggles to simultaneously achieve low variability, high linearity, and symmetry in conductance tuning, thus complicating on-chip training and limiting versatility of RRAM based computing-in-memory (CIM) chips. In this study, we present a simple and effective approach using monolayer (ML) MoS2 as interlayer to control the CFs formation in TiOx switching layer. The limited S-vacancies (Sv) in MoS2-xOx interlayer can further confine the position, size, and quantity of CFs, resulting in a highly uniform and symmetrical switching behavior. The set and reset voltages (Vset and Vreset) in TiOx/MoS2-xOx based RRAM are symmetric, with cycle-to-cycle variations of 1.28% and 1.7%, respectively. Moreover, high conductance tuning linearity and 64-level switching capabilities are achieved, which facilitate high accuracy (93.02%) on-chip training. This method mitigates the device nonidealities of analog RRAM through Sv confined CFs, accelerating the development of RRAM based CIM chips.

Empty nose syndrome: new insights from a CFD approach.

Empty Nose Syndrome (ENS) is a debilitating condition which usually arises after aggressive turbinate reduction. However, objective tests to help in the diagnosis of this condition are lacking. Accurate diagnosis of ENS patients is critical for effective diagnosis and treatment. The article's objectives are to utilize computational fluid dynamics (CFD) to analyze nasal airflow resistance and symmetry in suspected ENS patients, classify them into distinct groups based on CFD data, and demonstrate the potential of CFD analysis in refining ENS diagnosis and guiding individualized treatment strategies. This study involved 48 patients diagnosed of ENS. However, we only considered those patients with documented prior turbinate surgery (eventually plus septal surgery), CT scan with signs of prior surgery, and a history of ENS with symptoms included in the ENS Q6. We employed computational fluid dynamics (CFD) to analyze nasal airflow resistance and symmetry. Patients were classified into three groups based on their CFD data: low resistance and normal symmetry, evident asymmetry, and normal CFD parameters. Half of patients (24 out of 48) were found in the low resistance and normal symmetry group, indicating 'typical' ENS. A smaller group (8) exhibited evident asymmetry, suggesting unilateral ENS or failure of previous surgery. Finally, 16 patients whose CFD parameters are inside the normal range of flow and resistance were classified in the normal breathing group. Our findings highlight the value of CFD analysis in classifying ENS patients based on airflow characteristics, as CFD analysis seems helpful in refining the diagnosis of ENS. This classification system can potentially aid in tailoring individual treatment strategies and improving patient outcomes. Further research is necessary to validate these results and explore the clinical implications of different ENS subgroups. Level 4 [1].

Ultrasound measurement of abdominal and low back muscle symmetry in adult degenerative lumbar scoliosis: A case-control study

Background Individuals with adult degenerative lumbar scoliosis (ADLS) have underlying biomechanical alterations along the trunk muscles. However, few studies have evaluated trunk muscles in ADLS. Objective To quantify and evaluate the symmetry, thickness, and stiffness (shear modulus) of the abdominal and back muscles in ADLS participants. Methods This was a case-control study with participants aged 60–79 years with ADLS (n = 37) and without ADLS (n = 37). Radiographic examination data were collected from the participants. Ultrasound thickness and shear modulus measurements were performed to compare differences in the rectus abdominis, external oblique, internal oblique, transversus abdominis (TrA), multifidus, erector spinae, and quadratus lumborum muscles in the supine, prone and standing positions in the ADLS (n = 37) and control groups (n = 37). Thicknesses and shear modulus were compared. Results The absolute thickness of the TrA in ADLS group was significantly greater on the convex side than on the concave side in both the supine (2.978 ± 0.552 vs. 2.556 ± 0.513, p = 0.041) and standing positions (2.671 ± 0.475 vs. 2.054 ± 0.401, p = 0.034). The percentage changes in both sides of the shear modulus of the TrA were significantly greater in the ADLS group than in the control group for the supine position ( p = 0.019), and standing position ( p = 0.039). Conclusions Compared with those in the control group, only the absolute muscle thicknesses and percent change in the shear modulus of the TrA in the ADLS participants were more asymmetric.

Limb Symmetry Index in Collegiate Dancers Using the Modified Star Excursion Balance Test and Single Leg Hops.

Introduction: Dance is physically demanding and often involves unilateral movements performed within a small base of support. Prior authors have reported that dancers use one leg preferentially over the other (ie, lower extremity asymmetry). Increased leg asymmetry-quantified using the Limb Symmetry Index (LSI), is associated with increased injury risk. Clinicians often use LSI to make return-to-performance decisions (eg, >85% performance on injured vs non-injured limb). However, limited research has examined leg symmetry in collegiate dancers. Purpose: To examine LSI in collegiate dancers using the modified star excursion balance test (mSEBT) and single-leg hop test (SLH). Methods: 120 healthy collegiate dancers (105 females, 15 males; 18.31 ± 0.80 years; 164.18 ± 7.12 cm; 61.18 ± 8.46 kg) performed the mSEBT (normalized to % leg-length: LL) in the anterior, posteromedial, and posterolateral directions and the SLH test (normalized to % body height: BH) across both legs using previously published guidelines. mSEBT scores were averaged for all three directions per leg. SLH scores were averaged per leg. LSI was calculated as (lower value/higher value) × 100 to obtain a percentage. Results: Mean mSEBT scores were 95.7 ± 14.2%LL (lower score) and 96.6 ± 14.3%LL (higher score). Dancers LSI for mSEBT was 99.1 ± 0.9%. Mean SLH scores were 82.8 ± 13.3%BH (lower score) and 86.4 ± 13.5%BH (higher score). Dancers LSI for SLH was 95.9 ± 3.5%. Conclusions: Dancers' LSI% was greater than 90% for mSEBT and SLH, concurrent with the normal values of LSI > 90% in healthy, physically active adults. Dancers displayed lower leg symmetry. Practitioners can thus use the contralateral leg as a reference for return-to-performance decisions following injury in dancers. LSI should be integrated into a comprehensive screening process to identify large (>85%) asymmetries and guide training programs post-injury to assist educators and practitioners' evidence-based return-to-performance decisions. Future researchers should examine LSI in other dance genres and across levels.Level of Evidence: 2C.

Crystallographic symmetry increasing in the pressure-induced phase transition of the hydrogen-bonded organic crystal 1-methylhydantoin.

In situ high-pressure Raman spectroscopy and synchrotron angular dispersive x-ray diffraction techniques, combined with first-principles calculations, have been performed to investigate the 1-methylhydantoin (C4H6N2O2, 1-MH) molecular crystal. High-pressure experiments have shown that phase I (monoclinic system) begins to transform into phase II (orthorhombic system) at pressures above 4.0GPa, and the transformation range is from 4.0 to 14.2GPa. It is proposed that the mechanism of phase transition is the interlayer contraction and rearrangement of the hydrogen-bonding network due to the enhanced strong hydrogen-bonded interactions at high pressures. This study provides some theoretical basis for this rare pressure-induced phase transition from low symmetry to high symmetry in organic supramolecular polymorphism.

Engineering Corrole and Porphyrin-Based Multivariate Metal-Organic Frameworks for Si-H Bond Insertion.

As a contracted porphyrin analogue, corrole shows a more acidic and trinegative/triprotic nature compared with porphyrin in the field of coordination chemistry. However, the direct introduction of corrole into a metal-organic framework is quite difficult due to its lower C2V symmetry. Herein, we report the one-pot synthesis of a series of corrole and porphyrin-based multivariate porphyrinic metal-organic frameworks M1(TCPC)@M2-PCN-222 (M1 = CuIII, MnIII, FeIVCl; TCPC = 5,10,15-tris(4-carboxyphenyl) corrole; M2 = CoII, CuII, NiII, FeIIICl) and applied them to the insertion of a Si-H bond with α-diazoacetates. The resultant FeCl(TCPC)@Ni-PCN-222 displayed the highest efficiency with a turnover number of 796 based on the amount of Fe, which could be reused at least 5 times without a negligible loss of activity. Mechanistic studies disclosed that the reactivity of FeCl(TCPC)@Ni-PCN-222 came from the synergistic effect between FeCl(TCPC) and Ni-PCN-222, in which FeCl(TCPC) acted as the active site in the formation of metal-carbene, whereas Ni-PCN-222 helped condense the silane molecules for boosting the insertion of the Si-H bond.

Spectroscopy and crystal-field analysis of low-symmetry Er[formula omitted] centres in K[formula omitted]YF[formula omitted] microparticles

K2YF5 crystals doped with lanthanide ions have a variety of possible optical applications. Owing to the low symmetry of the system, the crystal structure cannot be unambiguously determined by x-ray diffraction. However, electron-paramagnetic resonance studies have demonstrated that lanthanide ions substitute for yttrium in sites of Cs local symmetry. In this work, we use high-resolution absorption and laser spectroscopy to determine electronic energy levels for Er3+ ions in K2YF5 microparticles. A total of 39 crystal-field energy levels, distributed among 7 multiplets of the Er3+ ion, have been assigned. This optical data is used for crystal-field modelling of the electronic structure of Er3+ in K2YF5. Our model is fitted not only to the electronic energy levels, but also to the ground-state g-tensor. This magnetic-splitting data defines the axis system of the calculation, avoiding ambiguities associated with low-symmetry crystal-field fits.

Measurement of ground reaction forces in cats after total hip replacement.

The aim of this study was to evaluate ground reaction forces (GRFs) in cats after unilateral total hip replacement (THR) and compare them with cats after femoral head and neck ostectomy (FHO). The databases of the Small Animal Clinic of the Veterinary University in Vienna and three referral clinics were searched for cats that had undergone unilateral THR with the BioMedtrix Micro total hip system or FHO more than 6 months previously. Owners were invited to complete a survey and bring their cats for re-examination, inlcuding clinical and orthopaedic examinations, hip radiography and a gait analysis using a pressure-sensitive plate. Nine cats were included in each group. Cats after THR showed larger GRF values (peak vertical force [PFz] and vertical impulse [IFz] normalised to total force [%TF]) on the operated limb. The resulting symmetry indices (SIs) were lower in terms of vertical force in 7/9 (78%) cats and vertical impulse in 6/9 (67%) cats between the hindlimbs in cats after THR compared with FHO - SI (PFz) = 3.31% ± 2.19% (THR) vs 4.84% ± 2.99% (FHO) and SI (IFz) = 5.17% ± 3.66% (THR) vs 8.27% ± 3.12% (FHO). Cats after FHO showed significantly lower muscle circumference and range of motion (ROM) at the operated hindlimb compared with the contralateral side, whereas cats after THR showed no statistically significant differences between their hindlimbs. Owner surveys revealed significant differences in their subjective assessment of activity and change in gait between the two groups, with better values for cats after THR. This was the first study that measured GRFs in cats after THR. PFz (%TF) and IFz (%TF) values were higher in the operated limb of the THR group than in those of the FHO group, resulting in lower symmetry indices (indicating better symmetry) and better loading of the corresponding hindlimb. This finding is clinically relevant and can help in making decisions regarding the treatment of hip joint pathologies in cats.

Electrostatically Dominated Pre-Organization in Cyclodextrin Metal-Organic Frameworks.

Electrostatic interactions between oppositely charged entities play a key role in pre-organizing substrates and stabilizing transition states of reactions in enzymes. The use of electrostatic interactions to pre-organize ions in nanoconfined pores, however, has not been investigated to its full potential. Herein, we describe how carboxylate anions can be pre-organized at the behest of their electrostatic interactions with K+ cations in nanoconfined tunnels present in γ-cyclodextrin metal-organic frameworks, i.e., CD-MOFs. Several carboxylate anions, which are all much smaller than the cavities of the tunnels, were visualized by X-ray crystallography when nanoconfined in CD-MOFs, despite the large voids present in the tunnels. These anions were found to be aligned within a planar array defined by four K+ cations, positioned around the periphery of the tunnels. The strong electrostatic interactions between the carboxylate anions and the K+ cations dictate the orientation of the anions and override the influence of all other possible noncovalent bonding interactions between them and the tunnels. Consequently, the aligned pairs of γ-cyclodextrin rings constituting the tunnels become distorted, resulting in them having lower symmetry and fewer disordered carboxylate anions in the solid state. Our findings offer a transformative strategy for controlling the packing and orientation of ions in nanoconfined environments.

Improving Americium/Curium Separation Factors in the AmSel Process through Symmetry Lowering of the Diglycolamide Extractant.

Partitioning and transmutation are important strategies for closing the nuclear fuel cycle. The diglycolamide extractant TODGA has played a major role in the development of solvent extraction processes for nuclear fuel reprocessing due to its good extraction performance, its hydrolytic and radiolytic stability, and its compliance with the CHON principle. However, due to drawbacks such as the tendency to form a third phase during extraction if no phase modifiers are used, continued research on diglycolamide-type extractants has led to the development of diglycolamides with decreased symmetry. In this study, it is shown that the recently developed diglycolamide, N,N-diisopropyl-N',N'-didodecyldiglycolamide (iPDdDGA), is a potential alternative to TODGA with improved separation between Am and Cm or the Ln. Using the AmSel system as a reference, the extraction kinetics, influence of the acid concentration, influence of the iPDdDGA concentration, and influence of temperature were evaluated. Slope analysis indicates similar average stoichiometries for iPDdDGA and TODGA complexes, but the extraction efficiency of iPDdDGA is orders of magnitude higher. The feasibility of selective americium stripping in combination with the hydrophilic sulfonated bis-triazinyl bipyridine SO3-Ph-BTBP complexant was demonstrated. Selective stripping of americium was found to be possible, and the use of iPDdDGA gave an unexpected improvement in Am/Cm separation, with SFCm/Am values of up to 3.0. This represents a small but significant improvement compared to the 2.5 value typically found for TODGA, and it demonstrates the potential of this solvent extraction system to improve existing processes based on diglycolamide-type extractants.

Direct electron detection for EBSD of low symmetry & beam sensitive ceramics

Electron backscatter diffraction (EBSD) is a powerful tool for determining the orientations of near-surface grains in engineering materials. However, many ceramics present challenges for routine EBSD data collection and indexing due to small grain sizes, high crack densities, beam and charge sensitivities, low crystal symmetries, and pseudo-symmetric pattern variants. Micro-cracked monoclinic hafnia, tetragonal hafnon, and hafnia/hafnon composites exhibit all such features, and are used in the present work to show the efficacy of a novel workflow based on a direct detecting EBSD sensor and a state-of-the-art pattern indexing approach. At 5 and 10 keV primary beam energies (where beam-induced damage and surface charge accumulation are minimal), the direct electron detector produces superior diffraction patterns with 10x lower doses compared to a phosphor-coupled indirect detector. Further, pseudo-symmetric variant-related indexing errors from a Hough-based approach (which account for at least 4%-14% of map areas) are easily resolved by dictionary indexing. In short, the workflow unlocks fundamentally new opportunities to characterize materials historically unsuited for EBSD.

Helical-photon-dressed states determining unidirectional π-electron rotations in aromatic ring molecules.

We theoretically demonstrated that helical-photon-dressed states determine the rotational directions of the π-electrons of aromatic ring molecules formed by a circularly polarized or an elliptically polarized laser. This theory was verified using a minimal three-electronic-state model under the frozen nuclei condition. The model consists of the ground state and either a doubly degenerate electronic excited state or two quasi-degenerate excited states. Three helical-photon-dressed states were derived by solving the time-dependent Schrödinger equation within the semi-classical treatment of light-molecule interactions and rotating wave approximation. The angular momenta of the two helical-photon-dressed states represent the classical rotational direction, and that of the remaining state represents the opposite rotation, that is, non-classical rotation. Classical rotation means that π-electrons have the same rotational direction as that of a given helical electric field vector and obeys the classical equations of motion. Non-classical rotation indicates that the rotational direction is opposite to that of the helical electric field vector. Non-classical rotation is forbidden in an aromatic ring molecule with high symmetry formed by a circularly polarized laser but is allowed in a low symmetric aromatic ring molecule. The sum of the angular momenta of the three dressed states is zero. This is called the sum law for the angular momentum components in this paper. Benzene (D6h) and toluene (CS) were adopted as typical aromatic ring molecules of high and low symmetries, respectively. Finally, considering the effects of nuclear vibrations in the adiabatic approximation, an expression for the π-electron angular momentum was derived and applied to toluene.