Abstract
Improving coating technology and thin film formation by optimizing the experimental parameters has become essential for various industrial and technological fields. This work aims to study the influence of the precursor materials on the physical and electro-optical properties of Cr2O3 thin films. The solutions were prepared using the sol–gel route and deposited on glass slides using the spin coating technique. The structure and morphology of the films were studied using XRD, FT-infrared (IR), and field-emission scan-electron microscope. The results indicated the formation of a high-purity Cr2O3 (Eskolaite) phase in the form of spherical nanoparticles with sizes of 17–25 nm. Three bands appear at 490, 765, and 889
1 Introduction
Thin film and surface coating technology are applied in various fields, including superconducting technology, semiconductor devices, optical coatings, and energy applications [1,2]. Cr2O3 is one of the best coatings because it is mechanically strong, very hard (its hardness is in the range of 18–29.7 GPa), chemically inert, resistant to oxidation, has a high melting point (∼2,435°C), a large band gap, an n-type semi-conductor, antiferromagnetic, has a linear magneto-electric effect, is cost-effective, and has low toxicity. Additionally, the α-Cr2O3 (Eskolaite) with a rhombohedral (primitive cell) in hexagonal (unit cell) structure is the most thermo-dynamically stable compound among all other chromium oxides: Cr3O, Cr2O, CrO, Cr3O4, Cr5O12, Cr3O8, Cr8O21, CrO2, and CrO3. Moreover, nano-sized α-Cr2O3 demonstrates remarkable characteristics, revealing its superparamagnetic nature as the particle size decreases. These characteristics are motivating the authors to fabricate protective coatings of α-Cr2O3 films for various applications, including modern pigments, photonics, catalysis, drug delivery systems, H2 storage, flexible supercapacitors, insulating layers for magnetic data devices, and hard coatings for molds, tools, and machines for high-temperature applications [3,4,5,6,7,8,9,10,11,12].
These fascinating features, as well as the related technological applications, pique the interest of various research groups to prepare α-Cr2O3 NPs utilizing chemical, physical, and biological synthesis processes. A review of the literature showed that the morphological, physical, and chemical properties of α-Cr2O3 are affected by the starting material (Cr source), the solvent, the surfactant agent, and other factors used in the preparation process. Using chromium nitrate and triethanolamine, Vashistha et al. [4] made 49.96 nm-sized Cr2O3 nanoparticles (NPs) by a microwave-assisted method. Nakazawa et al. [7] prepared Cr2O3 NPs by ball milling and studied their ferromagnetic behavior at room temperature (RT). Pei and Zhang [13] made 50–70 nm-sized Cr2O3 NPs by heating CrO3 and HCHO together in water, without stirring or adding a surfactant. According to Tobia et al. [14], calcination of the chromium nitrate at 1,400°C in air for 24 h yielded (bulk) Cr2O3 (1.5 µm in size). Chromium hydroxide, on the other hand, was heated to between 200 and 1,400°C in air or oxygen to make Cr2O3 NPs (6–70 nm) with interesting magnetic properties [14]. Anandan and Rajendran [15] studied the influence of the solvent (alcoholic and aqueous) on the structure and magnetic properties of Cr2O3 NPs derived from CrO3 via a solvothermal reaction. Moreover, the thermal treatment of chromium nitrate in KOH solution at temperatures >350°C can yield nanocrystalline Cr2O3 green pigments, suitable for NIR (750–2,500 nm) reflection, through co-precipitation or hydrothermal methods [16]. Yıldırım [17] fabricated Cr2O3 NPs by the microemulsion method and improved their energy storage performances by covering them with Ni and Co NPs, applying the microwave-assisted solvothermal route. The aqueous and ethanolic extracts of Cassia fistula leaves, at pH = 7 and 1.2, were used as reducing and capping agents to obtain Cr2O3 NPs of sizes in the range of 15–24 nm [18].
For thin film and coating purposes, Tsegay et al. [3] prepared Cr2O3 quasi- and meso-spherical, nanorod, and nanocoating on Cu substrate by drop casting and spin coating at 600–1,200 rpm. Mehr et al. [5] improved the mechanical properties of atomic layer-deposited (ALD) Cr2O3 films, 70–95 nm thick, by Ti doping. The radio frequency (RF) sputtering technique was used by Saritas to prepare Cr2O3 films for H2 gas sensing (the as-deposited film) and corrosion resistance applications (the annealed films) [6]. Rani et al. [8] developed Pd-Cr2O3 electrode films using reactive DC magnetron co-sputtering for supercapacitor devices. Moreover, Jia et al. [9] fabricated pure and Y-doped Cr2O3 films using multi-arc ion plating technology with improved tribological properties.
El Sayed and Shaban [19,20] suggested that the physicochemical properties (morphology, wettability, and optical constants) of IrO and Cu2O/CuO films can be tuned by adjusting the spin speed, number of coated layers, annealing temperature, and doping process. Arca et al. [21] developed (Mg, N)-doped Cr2O3 (p-type) films by spray pyrolysis using chromium chloride or chromium nitrate, MgCl2 or Mg(CH3CO2)2 as Mg sources, and NH4Cl or NH4(CH3CO2)2 for N doping. They observed that the presence of
The physical routes (PLD, sputtering, ALD, and multi-arc ion plating) are expensive synthetic methods that require expensive precursors and complex equipment. On the other hand, the chemical methods (spray pyrolysis, drop casting, dip coating, and spin coating) are simple and provide high-quality films. Combining sol–gel with spin coating is an advantageous choice as it enables precise control over the films’ composition, simplifies the adjustment of experimental (deposition) parameters, facilitates large-scale substrate deposition, and minimizes precursor waste (material use) [23].
The present work reports, for the first time, the influence of different precursors (chromium acetate and chromium nitrate), 2-methoxyethanol and ethanol as solvents, and monoethanolamine and acetic acid (AA) as stabilizing agents on the structural, morphological, electrical, and optical features of Cr2O3 thin films. The structure and morphology of the films were investigated by XRD, FTIR spectroscopy, and field-emission scan-electron microscope (FE-SEM). The I–V characteristic curves were recorded using the two-point probe method. The optical features were analyzed and discussed in detail. The obtained films are promising for optoelectronic applications and energy storage.
2 Experimental procedures
2.1 Precursors and preparation
Chromium(ii) acetate (CrA) [Cr2(CH3CO2)4·2(H2O), 376.2 g mol−1, LOBA Chemie] and chromium nitrate (CrN) [Cr(NO3)3·9H2O, 400.15 g mol−1, LOBA Chemie] were used as the Cr source. 2-Methoxyethanol (M) [C3H8O2, 76.1 g mol−1, Merck] and absolute (Et) [C2H5O, 46.1 g mol−1, Merck] were used as solvents. Monoethanolamine (M) [C2H7NO, 61.1 g mol−1, Merck] and AA [C2H4O2, 60.05 g mol−1, Merck] were used as stabilizing agents. These precursors were used as received. Three different solutions with a 0.35 M concentration were prepared as follows: solution (1) was prepared by dissolving a certain amount of CrA in 10 mL of 2-methoxy ethanol. After 10 min of magnetic stirring at a speed of 1,200 rpm and heating at 60°C, a few drops of monoethanolamine were added to make the solution clear. The stirring was continued for 2 h at RT. Solution (2) was prepared by dissolving a similar amount of CrA in 10 mL of ethanol. For the solutions (1) and (2), the required mass of CrA is calculated using the equation: Mass(CrA) = 0.35 × 10 × 10–3 × 376.2 = 1.317 g. The solution (3) was prepared by dissolving the required mass CrN (Mass(CrN) = 0.35 × 10 × 10–3 × 400.15 = 1.401 g) in 10 mL of ethanol, and after 10 min of stirring, a few drops of AA were added to make the solution clear. The speed, time, and temperature during the magnetic stirring process were the same for the three solutions. The final volume of the three solutions was the same. The solution was stirred continuously for 2.0 h at RT. Next, the solutions were aged at RT for 24 h. For simplicity, the solutions (1), (2), and (3) and the resultant films were named CrA/M/M, CrA/Et, and CrN/Et/AA, respectively.
Before the deposition process, the glass substrates (1 × 2 × 0.15 cm3) were cleaned in an ultrasonic bath using a detergent, acetone, and ultraclean water for 5 min for each step. An air gun was used to dry the substrates. The solutions (1), (2), and (3) were deposited using a spin coater operated at 2,500 rpm for 45 s. After each layer, the formed film was pre-heated on a hotplate at 200°C for 5 min. The deposition and drying procedure was repeated five times to increase the film thickness. Finally, the films deposited on the substrates were annealed at 500°C for 2.0 h in a ceramic furnace. After returning to RT, the films were put in plastic Zipper bags to avoid moisture.
2.2 Characterization and devices
A PANalytical X’Pert Pro (high-resolution), Holland, XRD system was used to study the influence of precursors on the structure and crystallite size of spin-coated Cr2O3 films. The device was operated in the 2θ range of 5°–80°; applying a Cu source provides a K α radiation of wavelength λ ∼1.541 Å. The Cr2O3 film’s surface morphology and cross-sectional investigations (thickness evaluation) were performed using FE-SEM (ZEISS-SUPRA-55-VP). FTIR spectra were gathered using a spectrophotometer of model Bruker-vertex 70 in the wavenumber range of 400–4,000 cm−1. Direct current–voltage (IV) characteristics were determined using the two-point probe technique using Keithley 2400. Ultraviolet-visible-near infrared (UV-Vis-NIR) optical spectra (transmittance and reflection) were recorded using the spectrophotometer (Shimadzu; UV-3600/UV-Vis-NIR) in the λ range of 200–2,000 nm, in normal incidence mode.
3 Results and discussion
3.1 XRD, FTIR, and FE-SEM analyses
Figure 1(a) illustrates the influence of precursor materials on the crystal structure (XRD patterns) of the deposited films. The charts of all films contain peaks at
where

(a) XRD patterns and (b) FTIR spectra of Cr2O3 thin films.
Crystallite size (
Film |
|
d (nm) |
|
|
|
n at 550 nm |
---|---|---|---|---|---|---|
CrA/M/M | 24.96 ± 3.5 | 208 | 22.70 | 0.302 | 2.90 ± 0.05 | 1.92 |
CrA/Et | 19.30 ± 4.2 | 198 | 20.14 | 0.284 | 2.75 ± 0.03 | 2.25 |
CrN/Et/AA | 17.56 ± 4.5 | 203 | 10.66 | 0.305 | 2.60 ± 0.05 | 2.15 |
For further structural and compositional investigations of the spin-coated Cr2O3 films, FTIR spectroscopy was applied to obtain the transmittance spectra as shown in Figure 1(b). The two bands at 490
In addition, the weak band at 1,030
Figure 2(a)–(c) depicts the FE-SEM surface pictures of the Cr2O3 films prepared using different precursors. In addition, Figure 2(a′)–(c′) shows the cross-section of the films, and the measured thickness is listed in Table 1. The CrA/M/M film is crack-free and consists of closely spaced spherical particles of approximately the same size. Using ethanol as a solvent without a stabilizing agent resulted in smaller particles, as shown in Figure 2(b), compared to the particle size, as shown in Figure 2(a). This note is consistent with the

FE-SEM images and the cross-section for thickness determination for (a, a′) CrA/M/M, (b, b′) CrA/Et, and (c, c′) CrN/Et/AA.
The acetate salt (CrA), used in the preparation of Cr/M/M and Cr/Et films, hydrolyzes easily in the solvent medium and gives soluble products that can be decomposed to volatile materials under upon heating [23]. The CrN/Et/AA film appears rough and has a different morphology in which its particles agglomerate and appear with sizes in the range of 15
3.2 IV curves
The I–V characteristic curves of the Cr2O3 thin films prepared by sol–gel route and spin-deposition using different sources are shown in Figure 3. The linear behavior indicates a good ohmic feature. The sheet resistance (

IV characteristic curves for the Cr2O3 thin films spin-coated using different precursors.
The
3.3 Optical analyses
The optical transmittance (T%) in the
To correlate the optical and electrical features of the films, the new figure of merit (
where HR stands for high resolution, and s can take 10, 12, and other values, and
The optical band gap (
where
A similar result was found by Fan et al. [22] for the PLD Cr2O3 thin films, which exhibited T% in the order of 53–90% in the UV and visible regions and
3.4 Films’ optical constants and conductivity
The interaction of photons with the films involves absorption, dispersion, scattering, and attenuation. Considering the complex f-dependent function
where R is the reflectance. Figure 4(a) and (b) shows the dependence of k and n on the applied

Optical constant of Cr2O3 thin films: (a) absorption index and (b) refractive index distribution; the inset show the reflection (R%) of the films.
The inset of Figure 4(b) displays the measured R (%) values. Table 1 lists the n values for the films at 550 nm. The n values decrease with increasing

(a) UV–Vis–NIR transmittance and (b) Tauc’s plots for band gap determination of Cr2O3 thin films spin-deposited on glass substrates.
The polarizability of the Cr2O3 films is in relation to the density of states inside the forbidden E
g and can be described in terms of the function:

Optical constant of Cr2O3 thin films obtained from different precursors: (a) real dielectric and (b) fictional dielectric constants and (c)
Finally, the optical conductivity
where c is the light speed. The obtained

Optical conductivity of sol–gel spin-deposited Cr2O3 films on glass substrates.
4 Conclusion
Cr2O3 thin films were prepared from different precursors (CrA/M/M, CrA/Et, and CrN/Et/AA) using the sol–gel route and spin deposition techniques. XRD showed the formation of a rhombohedral structure. The composition CrA/M/M yielded film with improved crystallinity,
Acknowledgments
The author extends his appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research work through the Project Number “NBU-FFR-2024-885-05.”
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Funding information: This research work was funded through the Project Number “NBU-FFR-2024-885-05” by the Deanship of Scientific Research at Northern Border University, Arar, KSA.
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Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The author states no conflict of interest.
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Data availability statement: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
- Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
- Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
- The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
- Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
- Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications