Vibrational Modes Research Articles

Characterization of Heavy Minerals and Their Possible Sources in Quaternary Alluvial and Beach Sediments by an Integration of Microanalytical Data and Spectroscopy (FTIR, Raman and UV-Vis)

Quaternary stream sediments and beach black sand in north-western Saudi Arabia (namely Wadi Thalbah, Wadi Haramil and Wadi Al Miyah) are characterized by the enrichment of heavy minerals. Concentrates of the heavy minerals in two size fractions (63–125 μm and 125–250 μm) are considered as potential sources of “strategic” accessory minerals. A combination of mineralogical, geochemical and spectroscopic data of opaque and non-opaque minerals is utilized as clues for provenance. ThO2 (up to 17.46 wt%) is correlated with UO2 (up to 7.18 wt%), indicating a possible uranothorite solid solution in zircon. Hafnoan zircon (3.6–5.75 wt% HfO2) is a provenance indicator that indicates a granitic source, mostly highly fractionated granite. In addition, monazite characterizes the same felsic provenance with rare-earth element oxides (La, Ce, Nd and Sm amounting) up to 67.88 wt%. These contents of radionuclides and rare-earth elements assigned the investigated zircon and monazite as “strategic” minerals. In the bulk black sand, V2O5 (up to 0.36 wt%) and ZrO2 (0.57 wt%) are correlated with percentages of magnetite and zircon. Skeletal or star-shaped Ti-magnetite is derived from the basaltic flows. Mn-bearing ilmenite, with up to 5.5 wt% MnO, is derived from the metasediments. The Fourier-transform infrared transmittance (FTIR) spectra indicate lattice vibrational modes of non-opaque silicate heavy minerals, e.g., amphiboles. In addition, the FTIR spectra show O-H vibrational stretching that is related to magnetite and Fe-oxyhydroxides, particularly in the magnetic fraction. Raman data indicate a Verwey transition in the spectrum of magnetite, which is partially replaced by possible ferrite/wüstite during the measurements. The Raman shifts at 223 cm−1 and 460 cm−1 indicate O-Ti-O symmetric stretching vibration and asymmetric stretching vibration of Fe-O bonding in the FeO6 octahedra, respectively. The ultraviolet-visible-near infrared (UV-Vis-NIR) spectra confirm the dominance of ferric iron (Fe3+) as well as some Si4+ transitions of magnetite (226 and 280 nm) in the opaque-rich fractions. Non-opaque heavy silicates such as hornblende and ferrohornblende are responsible for the 192 nm intensity band.

Tailoring the Structural and Optical Properties of Oxychloride Magnesium Tellurite Glass with the Addition of Samarium Ions

In this study, samarium-doped oxychloride magnesium tellurite glass with composition (79−x)TeO2−xMgO−20Li2O−1Sm2O3 (Series 1) and (79−x)TeO2xMgCl2−20Li2O−1Sm2O3 (Series 2) with 0 ≤ x ≤ 15 mol% was prepared by the melt-quenching technique. The structural and optical properties of synthesized samples were investigated, and the XRD results dictated an amorphous nature for both samples. The glass density of both Series 1 and 2 decreased with increasing MgO and MgCl2 content. However, the molar volume behaves in a completely opposite manner to an increase in MgO or MgCl2 content. FTIR spectra revealed from the vibrational wavenumber shift of TeO4 and TeO3 structural units showed a significant rise in HOH vibration mode, which implies its usefulness in boosting water and light absorption. Four absorbance bands were observed via UV-Vis NIR, while the indirect optical band gap around (3.42–3.36) eV and (3.42−3.30) eV for Series 1 and Series 2 were observed from UV-Vis spectroscopy. The emission spectra from the photoluminescence study revealed four distinct bands centered at 562.54, 599.14, 645.63 and 708.40 nm which are attributed to the transition from 4G5/2 – 6HJ/2 (J = 5,7,9,11) of states of Sm3+. The optimum glass with a composition of TeO-MgO 15% demonstrates a high potential for optical device development.

Tunable Imaging Distance Focusing Module Directly Driven by a Thin‐plate Piezoelectric Actuator

AbstractWith the advancement of imaging technology, the performance of optical focusing modules becomes crucial for determining imaging quality. Conventional focusing modules frequently face challenges of excessive bulk and weight, complicating the integrated design and limiting application fields. Herein, this study presents a piezo‐actuated optical focusing module (POFM) and the construction strategy to alleviate these issues. A novel radial‐bending resonant‐type piezoelectric actuator (RB‐RPA) is developed to directly drive the POFM. The RB‐RPA, which features a hollow structure (27 × 27 × 7 mm3), utilizes both radial and bending vibration modes of a thin metal plate. It achieves a speed of 122.93 mm s−1, a thrust force of 0.14 N, and a displacement resolution of 0.52 µm. Employing the proposed construction strategy, RB‐RPA is integrated with imaging components to fabricate a POFM prototype. Furthermore, the micrometer‐level displacement resolution of POFM facilitates optical focusing on imaging targets, allowing the acquisition of sharp images within 70 ms. It achieves an image resolution of 119.57 lp mm−1 within a 42 mm segment of the captured image. Finally, a QT‐based interface for the POFM, enables real‐time image capture and sharpness evaluation, thereby enhancing imaging efficiency and integration. This work provides a potential candidate for next‐generation imaging devices.

Contribution of Torsional Vibration Modes and the Influence on Period Ratios in the Seismic Response of Elastic Plate Bent Frame Structures

The structural characteristics of large-span structures inherently differ from those of conventional multistorey structures, making it challenging to accurately describe the contribution of various vibration modes to the overall response using traditional dynamic response analysis methods. Based on the response spectrum method, this paper investigates the influence of the first torsional mode on the overall effects of large-span structures. It proposes a new metric, called the torsional mode contribution factor, to characterize the contribution of torsional modes. Focusing primarily on single-span frames, the study explores the impact of factors such as eccentricity ratio, aspect ratio, and roof stiffness on the torsional mode contribution factor. Additionally, the relationship between the period ratio and the torsional mode contribution factor is examined to assess the necessity of controlling the period ratio. The findings reveal that the contribution of torsional modes to the overall seismic response varies significantly under different conditions, such as eccentricity ratio, aspect ratio, roof stiffness, and torsional stiffness. The torsional mode’s contribution is minimal for small eccentricity ratios, with the response primarily driven by translational modes. As eccentricity increases, translational-torsional coupling becomes more pronounced, amplifying the influence of torsional modes on the overall dynamic response. The study also highlights that increasing roof stiffness and aspect ratios can mitigate torsional effects to a certain extent. Still, excessive eccentricity ratios and stiffness may result in higher torsional contributions. Additionally, it is found that increasing torsional stiffness reduces the influence of torsional modes but does not eliminate the overall torsional deformation. The proposed torsional mode contribution factor offers an effective way to quantify these effects, demonstrating that traditional control methods, such as period ratio control, may not fully capture the torsional contributions.

Exploring Nonlinear Correlations Among Transition Metal Nanocluster Properties Using Deep Learning: A Comparative Analysis with LOO-CV Method and Cosine Similarity.

A novel approach is introduced for the rapid and accurate correlation analysis of nonlinear properties in Transition Metal (TM) clusters utilizing the Deep Leave-One-Out Cross-Validation (LOO-CV) echnique.This investigation demonstrates that the Deep Neural Network (DNN)-based approach offers a more efficient predictive method for various properties of fourth-row TM nanoclusters compared to conventional Density Functional Theory (DFT) methods, which are computationally intensive and time-consuming.The feature space, also known as descriptors, is established based on a broad spectrum of electronic and physical characteristics. Leveraging the similarities among these clusters, the DNN-based model is employed to explore the correlations among TM cluster properties.The proposed method, in conjunction with cosine similarity, achieves remarkable accuracy up to 10-9 for predicting total energy, lowest vibrational mode, binding energy, and HOMO-LUMO energy gap of TM2, TM3, and TM4 nanoclusters. By analyzing corre lation errors, the most closely coupled TM clusters are identified. Notably, Mn and Ni clusters exhibit the highest and lowest levels of energy coupling with other transition metals, respectively. Generally, energy prediction for TM2, TM3, and TM4 clusters exhibit similar trends, while an alternating behavior is observed for vibrational modes and binding energies. Furthermore, Ti, V, and Co demonstrate the highest binding energy correlations with TM2, TM3, and TM4 sets, respectively. Regarding energy gap predictions, Ni ex hibits the strongest correlation in the smallest TM2 clusters, while Cr shows the highest dependence in TM3 and TM4 sets. Lastly, Zn displays the largest error in HOMO-LUMO energy gap across all sets, indicating distinctive independent energy gap characteristics.

Highly Polarization‐Sensitive Solar‐Blind Ultraviolet Photodetection Based on 1D Rb2CuCl3 Microwires

AbstractPolarization‐sensitive solar‐blind ultraviolet (UV) photodetectors are essential in both civilian and military applications. 1D perovskites derivative Rb2CuCl3 holds promise for polarization‐sensitive solar‐blind UV photodetectors due to its wide direct bandgap, anisotropic crystal structure, and long carrier lifetime. However, no studies on the polarization properties of Rb2CuCl3 are reported. Here, the electronic structural anisotropy of Rb2CuCl3 is confirmed by calculating the partial charge density distribution in the ac‐plane and bc‐plane. Then, the Raman‐active modes and corresponding atomic vibration modes are explored within the bc‐plane through joint experimental and theoretical Raman spectroscopy. Besides, angle‐resolved Raman, photoluminescence, and absorption spectroscopy reveal the intriguing anisotropic photoelectric characteristics of Rb2CuCl3 microwires (MWs). By using single Rb2CuCl3 MW as the photoactive layer, a polarization‐sensitive solar‐blind UV photodetector is fabricated, showing high photoresponsivity of 78 mA W−1 and photocurrent anisotropy ratio of ≈1.7 at 265 nm. Importantly, the proposed photodetectors without encapsulation exhibit excellent stability in ambient air, retaining the original photocurrent after two months, showcasing practical applicability. This study underscores the promise of Rb2CuCl3 for high‐performance polarization‐sensitive solar‐blind UV photodetectors, contributing valuable insights into its electronic structure, photoelectric properties, and practical applicability.

Atomic-scale visualization of defect-induced localized vibrations in GaN.

Phonon engineering is crucial for thermal management in GaN-based power devices, where phonon-defect interactions limit performance. However, detecting nanoscale phonon transport constrained by III-nitride defects is challenging due to limited spatial resolution. Here, we used advanced scanning transmission electron microscopy and electron energy loss spectroscopy to examine vibrational modes in a prismatic stacking fault in GaN. By comparing experimental results with ab initio calculations, we identified three types of defect-derived modes: localized defect modes, a confined bulk mode, and a fully extended mode. Additionally, the PSF exhibits a smaller phonon energy gap and lower acoustic sound speeds than defect-free GaN, suggesting reduced thermal conductivity. Our study elucidates the vibrational behavior of a GaN defect via advanced characterization methods and highlights properties that may affect thermal behavior.

Analysing Spatio-temporal Dynamics of Urban Sprawl, Evolving Pattern of Urban Landscape and Driving Forces of Urban Growth: A Case of Varanasi Planning Region, India

Urban sprawl is at the centre of contemporary urban debates and is very often criticised for its negative social and environmental externalities. Building on geo-spatial methodology and field observations, this study sets out to develop a holistic approach to understanding urban sprawl through a particular focus on a rapidly growing metropolitan urban agglomeration of northern India, that is, Varanasi. Following an analysis of principal urban growth modes through landscape expansion index and changing patterns of urban landscape through landscape metrics, this research refers to a geo-spatially grounded logistic regression model in order to shed light on the dynamic impact of multiple growth factors on the trajectory of urban sprawl in the study area. Moreover, in order to address the evolving nature of urban sprawl in Varanasi and its immediate surroundings this study focuses on a temporal span of 20 years, encompassing two consecutive decades of the 21st century (2001–2011 and 2011–2021). The research concludes by paving a platform for an amalgamation of the findings from different geo-spatial metrics as well as by corroborating the principal findings with the propositions of a number of contemporary hypotheses concerning the spatial growth of urbanised territories.

Modal analysis and seismic optimization of multi-storey gymnasium frame

In order to improve the seismic resistance capacity of the multi-storey gymnasium frame, based on the finite element analysis method, the dynamic response characteristics were analyzed, and the natural frequencies and vibration modes were obtained. Based on the results of the modal analysis, different reinforcement methods were proposed for verification. Under the excitation conditions of Borego waves, the vibration responses of different nodes in initial model were obtained. Modal verification was carried out by using two methods of shear strengthening and support rod strengthening respectively. The analysis results show that the bearing capacity of the single-span frame is insufficient, the lateral stiffness is small, and it is prone to cause severe torsional vibration damage. It can also be known that the seismic resistance capacity of the support rods reinforcement is more balanced in different directions. It can not only effectively improve the lateral stiffness and bearing capacity of the structure, but also improve the seismic performance of the main structure through the energy dissipation of component yield, which is more suitable for multi-story buildings.

Catalytic behavior, electronic structure and spectroscopic (FT-IR, Raman, UV–vis) properties for the new ionic liquid imidazolium hydrogen sulfate

Catalytic performance, chemical reactivity, vibrational modes and electronic transitions of the ion pair [H–Im]+[HSO4]– were investigated in the current paper. Hence, a combined experimental (Hammett acidity function, infrared, Raman and ultraviolet-visible spectroscopies) and theoretical (molecular electrostatic potential surface, reduced density gradient, frontier molecular orbital analysis, quantum theory of atoms in molecules, net atomic charges, global and local reactivity descriptors) study was conducted. In terms of the catalytic performance, the acetic acid esterification with butanol was evaluated. Important kinetic (rate constant, activation energy, pre-exponential factor) and thermodynamic (enthalpy, entropy, Gibbs free energy barrier) factors for ester production as a function of the temperature and catalyst loading have been determined. Results revealed intensive electron density distribution in [H–Im]+[HSO4]– due to chemical interactions between the cationic and anionic moieties. These bonds were established as electrostatic in nature. The pronounced charge transfers within [H–Im]+[HSO4]– managed the title compound acidity (H0) and its catalytic behavior towards butyl acetate synthesis. Using the thermodynamic and kinetic measurements, a mechanism for acetic acid esterification with butanol in the presence of imidazolium hydrogen sulfate ionic liquid was offered.

An Energy Approach to the Modal Identification of a Variable Thickness Quartz Crystal Plate

The primary objective of modal identification for variable thickness quartz plates is to ascertain their dominant operating mode, which is essential for examining the vibration of beveled quartz resonators. These beveled resonators are plate structures with varying thicknesses. While the beveling process mitigates some spurious modes, it still presents challenges for modal identification. In this work, we introduce a modal identification technique based on the energy method. When a plate with variable thickness is in a resonant state of thickness–shear vibration, the proportions of strain energy and kinetic energy associated with the thickness–shear mode in the total energy reach their peak values. Near this frequency, their proportions are the highest, aiding in identifying the dominant mode. Our research was based on the Mindlin plate theory, and appropriate modal truncation were conducted by retaining three modes for the coupled vibration analysis. The governing equation of the coupled vibration was solved for eigenvalue problem, and the modal energy proportions were calculated based on the determined modal displacement and frequency. Finally, we computed the eigenvalue problems at different beveling time, as well as the modal energies associated with each mode. By calculating the energy proportions, we could clearly identify the dominant mode at each frequency. Our proposed method can effectively assist engineers in identifying vibration modes, facilitating the design and optimization of variable thickness quartz resonators for sensing applications.

A Cluster-Based Deep Learning Model Perceiving Series Correlation for Accurate Prediction of Phonon Spectrum.

The spectral properties are the most prevalent continuous representation for characterizing transport phenomena and excitation responses, yet their accurate predictions remain a challenge due to the inability to perceive series correlations by existing machine learning (ML) models. Herein, a ML model named cluster-based series graph networks (CSGN) is developed based on the dynamical theory of crystal lattices to predict phonon density of states (PDOS) spectrum for crystal materials. The multiple atomic cluster representation is constructed to capture the diverse vibration modes, while the mixture Gaussian process and dynamic time warping mechanism are compiled to project from clusters to PDOS spectrum. Accurate predictions of complicated spectra with multiple or overlapping peaks are achieved. The high performance of CSGN model can be attributed to the pertinent feature extraction and the appropriate similarity evaluation, which enable the natural perception of structure-property relation and intrinsic series correlations as confirmed in the predictive results. The transferable and interpretable CSGN model advances ML predictions of spectral properties and reveals the potential of designing ML methods based on physical mechanisms.

Research on operating characteristics of V-shaped ultrasonic motor based on improved electromechanical coupling model

Abstract As a complex electromechanical coupling system, evaluating the motion characteristics of an ultrasonic motor via an accurate theoretical model is challenging due to the strong coupling between its electrical and mechanical properties. To address this issue, the paper first establishes a complete dynamic model of the V-shaped ultrasonic motor (VUSM). In contrast to the traditional dynamic model, the proposed model incorporates the centroid vibration of the stator and applies the weighted residual method to reduce the computational complexity by simplifying the dynamic model from infinite-dimensional degrees of freedom to two degrees of freedom. Subsequently, the finite element method is employed to determine the vibration mode of the stator structure and derive the two-phase operational mode of the motor. Using these two-phase working modes, the model is then solved to predict the motor's output characteristics under any operational condition. Furthermore, an electrical model accounting for preload nonlinearity was developed based on the dynamic model and compared with the model without considering preload nonlinearity, supported by experimental verification. The findings demonstrate that the established dynamic model and electrical model can accurately simulate the changing laws of the input and output characteristics of the motor, which provides assistance for the subsequent operation status evaluation of the motor and fault diagnosis during operation.

Assessing the Partial Hessian Approximation in QM/MM-Based Vibrational Analysis.

The partial Hessian approximation is often used in vibrational analysis of quantum mechanics/molecular mechanics (QM/MM) systems because calculating the full Hessian matrix is computationally impractical. This approach aligns with the core concept of QM/MM, which focuses on the QM subsystem. Thus, using the partial Hessian approximation implies that the main interest is in the local vibrational modes of the QM subsystem. Here, we investigate the accuracy and applicability of the partial Hessian vibrational analysis (PHVA) approach as it is typically used within QM/MM, i.e., only the Hessian belonging to the QM subsystem is computed. We focus on solute-solvent systems with small, rigid solutes. To separate two of the major sources of errors, we perform two separate analyses. First, we study the effects of the partial Hessian approximation on local normal modes, harmonic frequencies, and harmonic IR and Raman intensities by comparing them to those obtained using full Hessians, where both partial and full Hessians are calculated at the QM level. Then, we quantify the errors introduced by QM/MM used with the PHVA by comparing normal modes, frequencies, and intensities obtained using partial Hessians calculated using a QM/MM-type embedding approach to those obtained using partial Hessians calculated at the QM level. Another aspect of the PHVA is the appearance of normal modes resembling the translation and rotation of the QM subsystem. These pseudotranslational and pseudorotational modes should be removed as they are collective vibrations of the atoms in the QM subsystem relative to a frozen MM subsystem and, thus, not well-described. We show that projecting out translation and rotation, usually done for systems in isolation, can adversely affect other normal modes. Instead, the pseudotranslational and pseudorotational modes can be identified and removed.

A Closure Contact Model of Self-Affine Rough Surfaces Considering Small-, Meso-, and Large-Scale Stage Without Adhesive

Contact interface is essential for the dynamic response of the bolted structures. To accurately predict the dynamic characteristics of bolted joint structures, a fractal extension of the segmented scale model, i.e., the JK model, is proposed in this paper to comprehensively analyze the dynamic contact performance of engineering surfaces and revisit the multi-scale model based on the concept of asperities. The influence of asperity geometry, dimensionless material properties, and the elastic, elastoplastic, and full plastic mechanical models of a single asperity is established considering the asperity–substrate interaction. Then, a segmented scale contact model of rough surfaces is proposed based on the island distribution function in a strict sense. The mechanical contact process of determining rough surfaces is divided into small-scale, medium-scale, and large-scale stages. Moreover, cross-scale boundary conditions, i.e., al1′, al2′, and al3′, are provided through strict mathematical deduction. The results show that the real contact area and contact stiffness are positively correlated with fractal dimension and negatively correlated with fractal roughness. On a small scale, the contact damping decreases with an increase in load. In meso-scale and large-scale stages, the contact damping increases with the load. Finally, the reliability of the proposed model is verified by setting up three groups of modal vibration experiments.

Legal Regime of the Settlement of Disputes Arising from a Contract of Multimodal Carriage of Goods within CEMAC Land lock Countries

CEMAC landlocked countries (specifically Chad and Central African Republic) depend solely on Cameroon who serves as a transit state for the transportation of goods to and from these landlocked countries. Thus, the entering into bilateral conventions helped to facilitate and create transit corridors for the transportation of goods amongst these countries. Meanwhile Cameroon which serves as a transit state to these landlocked countries has four modes of transport (road, rail, water and air), while Chad and Central African Republic have just two or three principal mode of transportation namely road, rail and air. However, these modes of transportation pose unique challenges, particularly in countries with limited infrastructure. Through doctrinal analysis of both primary and secondary sources of data, this article seeks to examine the legal framework in resolving disputes arising from contracts of multimodal carriage of goods available to landlocked countries of the Central African Economic and Monetary Community (CEMAC). Our findings revealed that, the legal framework in resolving disputes arising from contracts of multimodal carriage of goods available to landlocked countries are not effectively implemented. As a result, some salient recommendations have been made to bridge the gap between theory and practice amongst these countries in general and Cameroon in particular.

Non-Invasive Detection of Nitrogen Deficiency in Cannabis sativa Using Hand-Held Raman Spectroscopy

Proper crop management requires rapid detection methods for abiotic and biotic stresses to ensure plant health and yield. Hemp (Cannabis sativa L.) is an emerging economically and environmentally sustainable crop capable of yielding high biomass. Nitrogen deficiency significantly reduces hemp plant growth, affecting photosynthetic capacity and ultimately decreasing yield. When symptoms of nitrogen deficiency are visible to humans, there is often already lost yield. A real-time, non-destructive detection method, such as Raman spectroscopy, is therefore critical to identify nitrogen deficiency in living hemp plant tissue for fast, precise crop remediation. A two-part experiment was conducted to investigate portable Raman spectroscopy as a viable hemp nitrogen deficiency detection method and to compare the technique’s predictive ability against a handheld SPAD (chlorophyll index) meter. Raman spectra and SPAD readings were used to train separate nitrogen deficiency discrimination models. Raman scans displayed characteristic spectral markers indicative of nitrogen deficiency corresponding to vibrational modes of carotenoids, essential pigments for photosynthesis. The Raman-based model consistently predicted nitrogen deficiency in hemp prior to the onset of visible stress symptoms across both experiments, while SPAD only differentiated nitrogen deficiency in the second experiment when the stress was more pronounced. Our findings add to the repertoire of plant stresses that hand-held Raman spectroscopy can detect by demonstrating the ability to provide assessments of nitrogen deficiency. This method can be implemented at the point of cultivation, allowing for timely interventions and efficient resource use.

Multimode vibrational coupling across the insulator-to-metal transition in 1T-TaS2 in THz cavities.

The use of optical cavities on resonance with material excitations allows controlling light-matter interaction in both the regimes of weak and strong coupling. We study here the multimode vibrational coupling of low energy phonons in the charge-density-wave material 1T-TaS2 across its insulator-to-metal phase transition. For this purpose, we embed 1T-TaS2 into THz Fabry-Pérot cryogenic cavities tunable in frequency within the spectral range of the vibrational modes of the insulating phase and track the linear response of the coupled phonons across the insulator-to-metal transition. In the low temperature dielectric state, we reveal the signatures of a multimode vibrational strong collective coupling. The observed polariton modes inherit character from all the vibrational resonances as a consequence of the cavity-mediated hybridization. We reveal that the vibrational strong collective coupling is suppressed across the insulator-to-metal transition as a consequence of the phonon-screening induced by the free charges. Our findings emphasize how the response of cavity-coupled vibrations can be modified by the presence of free charges, uncovering a new direction toward the tuning of coherent light-matter interaction in cavity-confined correlated materials.

Finite element simulations of quartz crystal microbalances (QCM): from Sauerbrey to fractional viscoelasticity under water

2D finite element simulations are performed on QCM working in the thickness-shear mode and loaded with different homogeneous films. They include a purely elastic film, a viscoelastic Maxwellian liquid, viscoelastic-Voigt solid, and the fractional viscoelastic (power-law) version of each case. Unlike single-relaxation kind models, fractional viscoelasticity considers the relaxation-time spectrum often found in polymeric materials. The films are tested in air or covered with liquids of different viscosities. Two substrate thicknesses are tested: 100 nm and 500 nm, the latter being close to the condition that promotes the resonance of the adsorbed film. In all cases the simulations are compared with small-load approximation theory (SLA). The 100 nm films follow the theory closely, although significant deviations of the SLA are observed as the overtone number n increases, even in purely elastic films. We also show that it is possible to identify the viscoelastic ‘fingerprint’ of the 100 nm films in air using raw data and Sauerbrey’s equivalent thickness obtained with the QCM in the 3 < n < 13 range. These numerical data are validated by experimental measurements of crosslinked polydimethylsiloxane films with thicknesses ∼150 nm. In contrast, the 500 nm films deviate notoriously from the SLA, for all viscoelastic models and overtones, with the largest deviation observed in the elastic film. When a liquid layer covers the QCM without an adsorbed film, the only overtone that numerically reproduces the theoretical value is the fundamental, n = 1. For n > 1, strong coupling between the solid and liquid is detected, and the original vibration modes of the crystal are altered by the presence of the liquid. Finally, the numerical simulations suggest that it is possible to detect whether a viscoelastic film is formed under a liquid layer using only the information from n = 1. In these film/liquid systems we also observe the so-called missing-mass effect, although the theory and simulations exhibit different levels of impact of such effect when the liquid viscosity is high.

Energy band gap tuning of Ba-Ca hexagonal ferrite by Dy3+ ion substitution (0 ≤ x ≤ 0.2) to improve spectral, structural, dielectric and photocatalytic properties

In the present study, Dy3+ substituted M-type Ba0.5Ca0.5DyxFe12-xO19 (0.00 ≤ x ≤ 0.20) hexagonal ferrites were synthesized using sol-gel auto-combustion method with lemon extract as a fuel. The single hexaferrite phase with space group P63/mmc is revealed by the X-ray powder diffraction (XRD) patterns. The Field emission scanning electron microscopy (FESEM) exhibits the agglomeration of nanoplates with vacancies at some places. Energy dispersive X-ray photoelectron spectroscopy (EDAX) mapping confirmed the presence of Ba, Ca, Fe, O, and Dy in the hexaferrite. Fourier Transform Infrared (FTIR) spectroscopy exhibits two characteristic bands at 579 and 429 cm−1 corresponding to tetrahedral and octahedral metal ions-oxygen stretching, revealing the occurrence of the ferrite phase. The optical energy band gap calculated using the Tauc plots was found to increase with the increase in dysprosium substitution to fall within the range of 2.8–3.5 eV. The Raman spectra confirmed the Raman vibration modes and M-type structures of hexagonal ferrites (HFs). The dielectric constant values drop rapidly with increasing frequency up to a few KHz and then gradually for the further higher frequencies. The occurrence of Ba and Ca with 2+, while Dy, and Fe with 3+ oxidation states is confirmed using X-ray photoelectron spectroscopy (XPS). The HFs exhibit remarkable efficiency by degrading the Reactive Brown dye to 99.3 % in just 15 min, equivalent to a high degradation reaction rate constant (k) value of up to 0.0396 min−1. Consequently, the catalyst shows promising potential for environmental remediation.