Vibrational Study Research Articles

Mathematical model and the solution of the capillary vibration in a nanoscale deformable

The capillary effect acts a key role in our daily life, and its vibration can significantly affect its mass transmission. Here, we aim to study the vibration of the capillary in a nanoscale deformable tube. First, we present the mathematical model, and then we give a detailed study on its vibration characteristics by means of the Hamiltonian‐based method, which is based on the variational principle and Hamiltonian. In the view of the energy conservation, the residual equations are introduced to determine the frequency‐amplitude formulation. We finally verify the effectiveness and reliability of the proposed method by comparing with existing method through the numerical results. The finding in this work is expected to be helpful for the study of the nonlinear vibration.

Charge transfer induced phase transition in Li2MnO3 at high pressure

Efficient and better energy storage materials are of utmost technological importance to reduce energy dependence on the fossil fuels. Li2MnO3is one such material having potential to meet most of the requirements for energy storage. This material has been synthesized using solid state synthesis route. High pressure structural and vibrational studies on this material have been carried out upto ∼22 and 26 GPa respectively. These investigations show occurrence of a hitherto unknown second order phase transition to a new low symmetry phase whose symmetry is constrained to be monoclinic with space group P21/n at pressure of ∼2.3 GPa in Li2MnO3. The bulk modulus and its derivative determined by fitting theP-Vdata with third order Birch-Murnaghan equation of state are 113.3 ± 13.1 GPa and 4.1 ± 1.2 respectively. Mode Grüneisen parameter calculated for all the Raman modes show positive values which indicates the absence of any soft mode in this material. A microscopic mechanism based on bond-charge transfer is invoked and applied to understand the spectroscopic changes occurring in this material which also manifests second order structural phase transition. Enhancement in covalent character of Li-O bonds in the Li-O polyhedra is inferred based on the spectroscopic observation and above mechanism.

Conformation and Bonding of Lanthanide(III) Trihalides LnX3 (Ln = La-Lu; X = F, Cl, Br): A Relativistic Local Vibrational Mode Study.

This study employed relativistic methods to investigate the connection between the conformation and bonding properties of 45 lanthanide trihalides LnX3 (Ln: La-Lu; X:F, Cl, Br). Our findings reveal several insights. The proper symmetry exhibited by open-shell LnX3 requires the inclusion of spin-orbit coupling, achieved with 2-component relativistic Hamiltonians. Fluorines (LnF3) primarily exhibit pyramidal structures, while chlorides and bromides tend to yield planar conformations. For a given halide, the strength of Ln-X bonds increases across the lanthanide series, another outcome of the lanthanide contraction. Both strength and covalency of Ln-X bonds decrease upon the halide, i.e., LnF3 > LnCl3 > LnBr3. We introduced a novel parameter, the local force constant associated with the dihedral β(X-Ln-X-X), ka(β), which quantifies the resistance of these molecules to conformational changes. We observed a correlation between ka(β) and the covalency of the Ln-X bond, with higher ka(β) values indicating a stronger covalent character. Finally, the degree of pyramidalization in the LnX3 structures is connected to (i) the extent of charge donation within the molecule and (ii) the greater covalency of the Ln-X bond. These findings provide valuable insights into the interplay between the electronic structure and molecular geometry in LnX3.

Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation

The present work is devoted to the study of nonlinear vibrations of an electromagnetically actuated cantilever beam subject to harmonic external excitation. The soft actuator that controls the vibratory motion of such components of a robotic structure led to a strongly nonlinear governing differential equation, which was solved in this work by using a highly accurate technique, namely the Optimal Auxiliary Functions Method. Comparisons between the results obtained using our original approach with those of numerical integration show the efficiency and reliability of our procedure, which can be applied to give an explicit analytical approximate solution in two cases: the nonresonant case and the nearly primary resonance. Our technique is effective, simple, easy to use, and very accurate by means of only the first iteration. On the other hand, we present an analysis of the local stability of the model using Routh–Hurwitz criteria and the eigenvalues of the Jacobian matrix. Global stability is analyzed by means of Lyapunov’s direct method and LaSalle’s invariance principle. For the first time, the Lyapunov function depends on the approximate solution obtained using OAFM. Also, Pontryagin’s principle with respect to the control variable is applied in the construction of the Lyapunov function.

Photooxidation of Nonanoic Acid by Molecular and Complex Environmental Photosensitizers.

Photochemical aging and photooxidation of atmospheric particles play a crucial role in both the chemical and physical processes occurring in the troposphere. In particular, the presence of organic chromophores within atmospheric aerosols can trigger photosensitized oxidation that drives the atmospheric processes in these interfaces. However, the light-induced oxidation of the surface of atmospheric aerosols, especially those enriched with organic components, remains poorly understood. Herein, we present a gravimetric and vibrational spectroscopy study aimed to investigate the photosensitized oxidation of nonanoic acid (NA), a model system of fatty acids within organic aerosols, in the presence of complex organic photosensitizers and molecular proxies. Specifically, this study shows a comparative analysis of the photosensitized reactions of thin films containing nonanoic acid and four different organic photosensitizers, namely marine dissolved organic matter (m-DOM) and humic acids (HA) as environmental photosensitizers, and 4-imidazolecarboxaldehyde (4IC) and 4-benzoylbenzoic acid (4BBA) as molecular proxies. All reactions show predominant photooxidation of nonanoic acid, with important differences in the rate and yield of product formation depending on the photosensitizer. Limited changes were observed in the organic photosensitizer itself. Results show that, among the photosensitizers examined, 4BBA is the most effective in photooxidizing nonanoic acid. Overall, this work underscores the role of chromophores in the photooxidation of organic thin films and the relevance of such reactions on the surface of aerosols in the marine environment.

Chaotic vibration control of an axially moving string of multidimensional nonlinear dynamic system with an improved FSMC

A new control approach based on fuzzy sliding mode control (FSMC) is proposed to regulate the chaotic vibration of an axial string. Hamilton’s principle is used to formulate the nonlinear equation of motion of the axial translation string, and the von Kármán equations are used to analyse the geometric nonlinearity. The governing equations are nondimensionalized as partial differential equations and transformed into a nonlinear 3-dimensional system via the third-order Galerkin approach. An active control technique based on the FSMC approach is suggested for the derived dynamic system. By using a recurrent neural network model, we can accurately predict and effectively apply a control strategy to suppress chaotic movements. The necessity of the suggested active control method in the regulation of the nonlinear axial translation string system is proven using different chaotic vibrations. The results show that the study of the chaotic vibrations of axially translating strings requires nonlinear multidimensional dynamic systems of axially moving strings; the validity of the proposed control strategy in controlling the chaotic vibration of axially moving strings in a multidimensional form is demonstrated.

Vibrational, theoretical characterisation and In Silico investigation of Norcinnamolaurine: a natural lead for inhibiting AURKA and overcoming immune evasion in Triple-Negative Breast Cancer

ABSTRACT Alkaloids represent a diverse category of natural compounds with noteworthy pharmacological and therapeutic applications. Benzylisoquinoline alkaloids (BIAs) are distinguished by their varied structures and potential medicinal properties. This study specifically investigates Norcinnamolaurine, a BIA found in multiple species and acknowledged for its therapeutic advantages. In the current investigation, we comprehensively analyzed Norcinnamolaurine, encompassing Frontier Molecular Orbital studies, vibrational spectroscopy, nonlinear optical properties, natural bond orbital evaluations, and Fukui's analysis. Additionally, we executed an E-pharmacophore-based screening utilizing the AURKA-Norcinnamolaurine complex. The generated hypothesis underwent database screening; lead compounds from the Natural Product and Drug Bank databases exhibited enhanced binding affinities ranging from −8.602 to −7.148 kcal/mol, demonstrating improved interactions within the AURKA binding pocket. Subsequently, the identified lead compounds were subjected to further analysis via MMGBSA, DFT, and Molecular Dynamics Simulations (MDS). Our findings indicate that Norcinnamolaurine exhibits a superior binding affinity towards the target protein. Significant outcomes were also observed in the vibrational and FMO studies. Moreover, MDS analysis revealed that the resultant complexes maintained relative stability, exhibiting minimal deviation and fluctuations. This stability was corroborated through additional assessments using MMPBSA and PCA/FEL methodologies.

Vibrational Spectra and Computational Study of Amyl Acetate: MEP, AIM, RDG, NCI, ELF and LOL Analysis

This work is focused on biologically active neat amyl acetate and its solutions in ethanol/heptane. According to the experimental results, when the concentration of amyl acetate in the amyl acetate-ethanol solution decreases, the additional band appears on the low-frequency side. The primary reason for the formation of such additional band is the intermolecular hydrogen bonding between amyl acetate and ethanol. In the amyl acetate-heptane solution, as the concentration of amyl acetate in the solution decreases, the band corresponding to the C=O stretching vibrations shifted to a higher frequency. This is explained by the fact that heptane breaks intermolecular interactions in solution, resulting in a simpler spectral band corresponding to the C=O stretching vibrations. Calculations are also used to study interactions in amyl acetateethanol complexes and their spectral manifestations. When the complex formation energies are calculated, this energy increases with the number of molecules, but the average hydrogen bond energy per one bond remains unchanged. The density functional theory (DFT) method is used to analyze molecular structural parameters: Mulliken atomic charge distribution; thermodynamic parameters; molecular electrostatic potential (MEP) surface; atoms in molecules (AIM) analysis; quantum chemical parameters such as reduced density gradient (RDG) and noncovalent interaction (NCI) analysis; electron localization functions (ELF) analysis; and localized orbital locator (LOL) analysis.

Evaluation of 2D Tantalum Carbide MXene for Room to Mid‐temperature Thermoelectric Applications

AbstractTantalum carbide MXene (Ta4C3Tx) were synthesized via HF etching of the Al intermediate layer from the parental tantalum aluminium carbide MAX phase (Ta4AlC3). The structural and vibrational studies confirm the formation of MXene from the MAX phase without disturbing the hexagonal crystal structure. The synthesized samples were analysed using XRD to understand the phase structure. In and out of plane vibrational properties were examined by Raman spectrometer. XPS confirms the successful HF etching of Al in MXene phase and all other elemental configurations. HR‐SEM and HR‐TEM revile the exfoliated layered structure of the MXene and hexagon diffraction pattern of the tantalum carbide MXene sample with increased d‐spacing. The TGA analysis demonstrated the thermal stability of the as‐synthesized post measured compounds. The synthesized tantalum carbide MXene shows stable thermoelectric properties over six thermal cycles. The temperature dependent transport properties were measured from 303 K to 803 K. Ta4C3Tx MXene shows a maximum Seebeck coefficient of 13.8 μV/K and a power factor of 1.88 μW/mK2 with the low lattice thermal conductivity of 5.42 W/mK at 803 K. In this present investigation, Tantalum carbide MXene demonstrated a decent thermoelectric property with high thermal cycling stability.

Quadratic Frequency Dispersion in the Oscillations of Intermediate-mass Stars

Asteroseismology, the study of stellar vibration, has met with great success, shedding light on stellar interior structure, rotation, and magnetism. Prominently known as δ Scutis, the intermediate-mass main-sequence oscillators that often exhibit rapid rotation and possess complex internal stratification are important targets of asteroseismic study. δ Scuti pulsations are driven by the κ (opacity) mechanism, resulting in a set of acoustic modes that can be challenging to interpret. Here, we apply machine learning to identify new patterns in the pulsation frequencies of δ Scuti stars, discovering resonances spaced according to quadratic functions of integer mode indices. This unusual connection between mode frequencies and indices suggests that rotational influence may play an important role in determining the frequencies of these acoustic oscillations.

Air-stable palladium N[sbnd]Heterocyclic carbene based CCC[sbnd]NHC pincer complexes: Synthesis, characterization, photophysical and Raman vibrational studies, and DFT studies, plus observation of an abnormal carbene pincer

A series of CCCNHC pincer Pd(II)X complexes, where X = Cl, Br, or I, were synthesized by a metalation/transmetalation reaction sequence and characterized by NMR and Raman spectroscopy, photophysical studies, X-ray crystallography, and DFT computational studies. This is the first detailed report of the CCCNHC pincer Pd complexes analogous to the previously reported Pt analogs. Photophysical measurements show that by varying the X ligand, the emission wavelength can be tuned. The chloride complex is a water and air stable blue emitter with a quantum yield of 46 % and all three complexes have photostabilities >90 %. A combined DFT and TD-DFT study has been carried out to investigate ground state and excited state geometries as well as absorption and emission processes of CCCNHC Pd complexes. Theoretical results were compared with the corresponding experimental results and showed good agreement. Raman spectroscopy (computational and experimental) was used to examine Pd-X vibrations which have been rarely reported in the literature. Several by-products of the metalation/transmetalation procedure were identified. A rare mixed normal/abnormal carbene pincer Pd(II)Cl complex was isolated and crystallographically characterized.

Role of Intermolecular Interactions in Deep Eutectic Solvents for CO2 Capture: Vibrational Spectroscopy and Quantum Chemical Studies.

Recent research and reviews on CO2 capture methods, along with advancements in industry, have highlighted high costs and energy-intensive nature as the primary limitations of conventional direct air capture and storage (DACS) methods. In response to these challenges, deep eutectic solvents (DESs) have emerged as promising absorbents due to their scalability, selectivity, and lower environmental impact compared to other absorbents. However, the molecular origins of their enhanced thermal stability and selectivity for DAC applications have not been explored before. Therefore, the current study focuses on a comprehensive investigation into the molecular interactions within an alkaline DES composed of potassium hydroxide (KOH) and ethylene glycol (EG). Combining Fourier transform infrared (FT-IR) and quantum chemical calculations, the study reports structural changes and intermolecular interactions induced in EG upon addition of KOH and its implications on CO2 capture. Experimental and computational spectroscopic studies confirm the presence of noncovalent interactions (hydrogen bonds) within both EG and the KOH-EG system and point to the aggregation of ions at higher KOH concentrations. Additionally, molecular electrostatic potential (MESP) surface analysis, natural bond orbital (NBO) analysis, quantum theory of atoms-in-molecules (QTAIM) analysis, and reduced density gradient-noncovalent interaction (RDG-NCI) plot analysis elucidate changes in polarizability, charge distribution, hydrogen bond types, noncovalent interactions, and interaction strengths, respectively. Evaluation of explicit and hybrid models assesses their effectiveness in representing intermolecular interactions. This research enhances our understanding of molecular interactions in the KOH-EG system, which are essential for both the absorption and desorption of CO2. The study also aids in predicting and selecting DES components, optimizing their ratios with salts, and fine-tuning the properties of similar solvents and salts for enhanced CO2 capture efficiency.

A Novel Application of Computational Contact Tools on Nonlinear Finite Element Analysis to Predict Ground-Borne Vibrations Generated by Trains in Ballasted Tracks

Predictive numerical models in the study of ground-borne vibrations generated by railway systems have traditionally relied on the subsystem partition approach (segmented). In such a method, loads are individually applied, and the cumulative effect of the rolling stock is obtained through superposition. While this method serves to mitigate computational costs, it may not fully capture the complex interactions involved in ground-borne vibrations—especially in the frequency domain. Recent advancements in computation and software have enabled the development of more sophisticated vibrational contamination prediction models that encompass the entire dynamics of the system, from the rolling stock to the terrain, allowing continuous simulations with a defined time step. Furthermore, the incorporation of computational contact mechanics tools between various elements not only ensures accuracy in the time domain but also extends the analysis into the frequency domain. In this novel approach, the segmented models are shifted to continuous simulations where the nonlinear problem of a rigid–flexible multibody system is fully considered. The model can predict the impact of a high-speed rail (HSR) vehicle passing, capturing the key intricacies of ground-borne vibrations and their impact on the surrounding environment due to a deeper comprehension of the occurrences in the frequency domain.

Solution and Surface Solvation of Nitrate Anions with Iron(III) and Aluminum(III) in Aqueous Environments: A Raman and Vibrational Sum Frequency Generation Study.

Hydrated trivalent metal nitrate salts, Fe(NO3)3·9H2O and Al(NO3)3·9H2O, in both solid and aqueous phases are investigated. Raman and surface-selective vibrational sum frequency generation (SFG) spectroscopy, are used to shed light on ion-ion interactions and hydration in several spectral regions spanning low frequency (440-550 cm-1) to higher frequency modes of nitrate and water (720, 1050, 1250-1450, and 2800-3750 cm-1). These frequencies span the metal-water mode, nitrate in-plane deformation, nitrate symmetric and asymmetric modes, and the OH stretch of condensed phase water molecules. Comparison to NaNO3, and in some cases KNO3, is also shown, providing insight. Splitting and frequency shifts are observed and discussed for both the solid state and solution phase. The Lewis acidity of Fe3+ and Al3+ ions plays a significant role in the observed spectra, in particular for the nitrate asymmetric band splitting and frequency shift. The spectral response from water solvation for iron and aluminum nitrates is nonlinear as compared to linear for sodium nitrate, suggesting significantly different solvation environments that are limited by water hydration capacity at higher concentrations. Moreover, a non-hydrogen bonded OH, dangling OH, from hydrating water molecules is observed spectroscopically for Al and Fe nitrate solutions. Furthermore, aluminum nitrate perturbs the surface water structure more than iron nitrate despite aluminum being a weaker Lewis acid. The surface water structure is thus found to be unique for the Al(NO3)3 solutions as compared to both Fe(NO3)3 and NaNO3, such that surface solvation is more pronounced. This observation exemplifies the nature of the Fe(III) and Al(III) ions and their substantial influence on the surface water structure.

A Novel Approach of the Viscoelasticity of Axially Functional Graded Bar and Application of Harmonic Vibration Analysis of an Isotropic Beam as Support

The use of smart materials and passive controllers in modern technologies has stimulated the study of vibration in elastic systems with viscoelastic damping. It is also possible to create components with precise material distribution coefficients and distinct properties, such as Functionally Graded Materials. This work investigates the resonant frequency characteristics of a beam supported at its ends by Axially Functionally Graded (AFG) viscoelastic bars using the finite element method. The set of equations governing motion is obtained by assuming Euler–Bernoulli beam theory for the beam and bar theory for the bars using Lagrange’s equations. The material properties of the functionally graded bar is assumed to vary through the length according to the power law distribution. The longitudinal loss factor values are used to define the internal damping coefficient, which is also dependent on the Young’s modulus value varying along the bar. The effects of the length-varying material properties and internal damping of the FG support bars on the force transmission TR and frequency parameters λ are examined in detail. No study has been found in the literature on the vibration of viscoelastic FG bar-supported beams subjected to a harmonic force at the centre point. It is shown that using bars formed with combinations of different materials considering material damping will be useful to keep the vibration level and force transmission at a certain value and control the frequency parameters.

Synthesis, vibrational, thermal, topological, electronic, electrochemical stability and DFT studies of new DABCO based ionic liquids

The design of new ILs with different anions could provide interesting physico-chemical properties and for these reasons, the knowledge about the synthesis, the thermal, vibrational, topological, electronic, electrochemical properties and interaction between the selected cation-anion in these ILs are important subjects. Therefore, the understanding about these properties of these compounds is an important subject of study. In this work, we studied three ionic liquids based on the 1-decyl-1,4-diazabicyclo[2.2.2]octane, DABCO-cation, where the corresponding anions were [Br]-, [PF6]-, and [N(SO₂CF₃)₂]-. The syntheses of these bicyclic DABCO ionic liquids are based on an alkylation reaction of 1,4-diazabicyclo[2.2.2] octane and 1-bromodecanefollowed by anion exchange. The obtained ILs are characterized by 1H, 13C, 19F and 31P-NMR spectroscopy. Vibrational spectroscopy studies are conducted by infrared (FTIR/ATR) and Raman spectroscopy in the wavenumber range 600–4000 cm-1 and 45–3500 cm-1, respectively. Furthermore, the thermal stabilities were investigated using the thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) methods. Results indicate that the thermal stability follow the order [C10DABCO][Br]<[C10DABCO][PF6]<[C10DABCO][N(SO₂CF₃)₂]. Additionally, the structural parameters, electrostatic potential (ESP) maps, interaction energies, non-covalent interaction (NCI), atoms in molecule (AIM) analysis, natural bond orbital (NBO), frontier molecular orbital (FMO) analysis and Electrochemical window (ECW) are studied and analyzed by means of DFT calculations at the M06–2X-GD3/AUG–cc–pVDZ level of theory.

Thermal-biomechanical manikin applied in turbulent airflow and vibration systems in transient conditions

This paper applied a thermal-biomechanical manikin in turbulent airflow and vibration systems in transient conditions. This numerical model evaluated the thermal and biomechanical components to which the human body is subjected. The first one considers the first-order equations systems based on the thermal numerical model, while the second one considers the second-order equations systems based on the vibration numerical model. This second-order equations system is converted into a first-order equation system. The resolution of the thermal and biomechanical numerical models is made through the Runge-Kutta-Fehlberg method with error control. The thermal numerical model is used in the study of the steady-state and transient conditions when the skin is subjected to mean and turbulent airflow. The biomechanical numerical model is used in the study of the human body vibrations applied to the feet, that a standing person is subjected, using periodical and random vibration signals of the floor. The thermal analysis shows that with an air fluctuation velocity, the skin temperature reduces slightly. The amplitude of the vibration in the lower body section is higher than in the upper body section. The introduction of the randomised vibration, in the periodical vibration, the human body vibration increases the fluctuation level.

Numerical study of the vortex-induced vibrations of a cantilevered pipe with a concentrated mass end using a wake oscillator model

In this paper, a numerical study based on a wake oscillator model has been carried out to determine the vortex-induced vibration (VIV) response characteristics of a flexible cantilevered pipe with a concentrated mass at the free end. First, a coupled model consisting of a cantilevered pipe and a wake oscillator is established, followed by discretization of the model and an iterative solution using the second-order central difference method. The displacement response and frequency response characteristics for different flow velocities and concentrated end masses have been compared. The numerical results reveal that the maximum value of the structural vibration displacement occurs at the bottom; i.e., free boundary end, for the cantilevered pipe with a concentrated mass at the free end. The dominant vibration mode typically shows a stepwise increase for an increase of the maximum flow velocity. As the vibration mode is transmitted from a lower order to a higher one, the vibration displacement of the structural end decreases fast. As the concentrated end mass increases, the dominant vibration mode shows a stepwise decrease, and as the vibration mode is transmitted from a higher order to a lower one, the vibration displacement of the structural end experiences a sharp increase.

A new organic–inorganic chloride (H3N–(CH2)6–NH3)[SnCl6]: Crystal structure, thermal analysis, vibrational study, and electrical properties

In this work, a new Organic-Inorganic chloride (H3N–(CH2)6-NH3)[SnCl6] (1) has been synthesized and characterized by single crystal X-ray diffraction (XRD), IR, Raman and impedance spectroscopies. The crystallographic study displays that the title compound crystallizes in the triclinic system with the P−1 space group. The vibrational study (IR, Raman) at room temperature confirmed the existence of the organic and inorganic functional groups. Differential scanning calorimetry (DSC) analysis reveals the existence of three reversible phase transitions at T1 = 345/325 K, T2 = 483/443 K, and T3 = 496/465 K (Heating/Cooling). Furthermore, the conductivity analysis and the dielectric properties confirm the presence of these phase transitions. AC-conductivity measurement of (1) has been investigated using complex impedance spectroscopy in frequency and temperature range 10 Hz–5 MHz and 313–523 K, respectively. The study of Nyquist plots showed the contribution of grains and grain boundaries in the electrical study, confirming the existence of a non-Debye type relaxation. The AC conductivity shows that the material has the potential of impedance sensors.

Structural, vibrational, and electrical study of the topological insulator PbBi2Te4 at high pressure

We report a joint experimental and theoretical study of the structural, vibrational, and electric properties of the topological insulator PbBi2Te4 under compression through X-ray diffraction, Raman scattering, and electrical measurements at high pressure, which are complemented with theoretical calculations that include the analysis of the topological electron density. The internal polyhedral compressibility of the rhombohedral phase, the behavior of its Raman-active modes, the electrical behavior, and the nature of its different bonds under compression are discussed and compared with their parent binary compounds and with related ternary materials. Interestingly, PbBi2Te4 retains its topological insulating properties as far as the rhombohedral tetradymite-like phase is retained under compression, unlike other tetradymite-like compounds. In addition, PbBi2Te4 undergoes an unconventional reversible pressure-induced decomposition into the high-pressure phases of its parent binary compounds (PbTe and Bi2Te3) above 8 GPa. Finally, we discuss that the intralayer bonds in the tetradymite-like structure of PbBi2Te4 are electron-deficient multicenter bonds; i.e. bonds of the same kind as those present in its parent binary compounds, in related chalcogenides, such as SnSb2Te4, and in general in chalcogenide-based phase change materials. These unconventional bonds are intermediate between covalent and metallic bonds and provide exceptional properties to the materials.