Abstract
Controlling the physicochemical features of chromium sesquioxide α-Cr2O3 (chromia) films is essential to widening their utilization. This work investigates the influence of heat treatment (HT) and La doping on the physical characteristics of chromia films spin-deposited on glass. X-ray diffraction/Fourier transform infrared spectroscopy and field-emission transmission electron microscopy techniques reveal that the crystallinity, size, and modes of vibration in chromia (eskolaite phase) can be tuned by HT and La doping. Energy-dispersive X-ray analysis confirms the presence of La in the hexagonal chromia films. All films display high transmittance (T%) and improved absorption indices in the UV and near-infrared regions. The films’ reflection and refractive indices are in the range of 6–15% and 1.77–1.97, respectively. The impact of HT and La content on the optical band gap, lattice dielectric constant, and electron-effective mass is reported. The current–voltage characteristic curves reveal the Ohmic resistance, and the films’ sheet resistance demonstrates sensitivity to HT and La content. The findings of this study illustrate the possible development of optoelectronic devices and chromia-based IR sensors.
1 Introduction
Various cutting-edge technologies, such as green energy, energy storage, networks, and superconductivity, have some form of metal oxide coatings or thin films [1]. Metal oxides are fascinating multifunctional materials that could be introduced in various technological applications. The filled s-shells acquire good chemical and thermal stability, and their partially filled d-shells provide interesting electronic properties [2]. Among the metal oxides, chromium sesquioxide (α-Cr2O3 or chromia) is an attractive multifunctional material due to its low cost (wide availability), low humidity dependency, good chemical and color stability, high thermal stability and corrosion resistance, and adjustable band structure [3]. Chromia is an antiferromagnetic insulator with a Neel temperature of 307 K (34°C) [4]. These properties make chromia suitable for several applications, such as a hard coating or protection layer for tools and machines for high-temperature applications [5]. According to Tian et al. [6], adding 0.1% chromia to ZnO-based varistor ceramics improves I–V nonlinearity and reduces the leakage current. Owing to its interesting photoelectric properties, Li et al. [7] suggested the use of microfibers decorated with chromia, grown by magnetron sputtering, as a saturable absorber for ultrafast fiber laser technology. Alotabi et al. [8] used the photo-deposited chromia layer on different material particles to prevent the reverse reaction in photocatalytic water splitting.
A fundamental step in the application of chromia coatings is controlling the synthesized material by adjusting the processing technique [9]. In other words, the preparation technique and preparative parameters determine the physicochemical and biological features of chromia nanoparticles (NPs) and thin films, and introducing foreign atoms (dopants) can enhance and broaden these features. Heating Cr(NO₃)₃ at above 350°C in KOH solution resulted in green nano-crystalline Cr2O3 pigments for reflection purposes in the wavelength region 750–2,500 nm [10]. Tsegay et al. [11] utilized drop-casting and spin-coating to obtain quasi-spherical, nanorod, and meso-spherical-shaped chromia that can act as a spectrally selective solar absorber. The pulsed-laser deposited (PLD) Ni-doped chromia films showed improved photoresponse for solar cells and photoelectrodes [12]. According to Erickson et al. [13], B doping and adjusting the Cr2O3/V2O3 film thickness, via PLD, can be used to increase the Neel temperature of Cr2O3 for voltage control due to its antiferromagnetic properties. The nano-sized Fe-doped chromia exhibited weak ferromagnetism and therefore can be used in logic and spintronic data storage devices [14]. In addition, Bhardwaj et al. [15,16] prepared chromia NPs by the co-precipitation method and found that doping with 10% Co and Mn can reduce the E g value from 2.96 to 2.82 eV, or 2.51 eV, which made the doping materials useful for optoelectronic applications. Moreover, the PLD films made from these materials demonstrated p-type conductivity and room-temperature (RT) ferromagnetism, making them suitable for spintronic device applications. By covering chromia NPs made by the microemulsion method with Ni or Co NPs, Yıldırım [17] improved their specific capacitance and ability to store energy. The X-ray diffraction (XRD) peak intensities of Cr2O3 in the composites were greatly reduced compared with those of the uncovered Cr2O3 NPs. Furthermore, Gyawali et al. [3] prepared Ag/chromia NPs by liquid impregnation and annealing with enhanced antibacterial efficiency. Additionally, the Pd/chromia electrode prepared by reactive dc magnetron co-sputtering was found to be a viable candidate for utilization in supercapacitors as future energy storage devices [18].
According to Zekaik et al. [19], the E
g of 0.0–12 at% Cu-doped chromia in the dip-coated films reduced from ∼2.9 to 2.5 eV and the resistance from 87 to 12.8 Ω. Ishtiaq et al. [20] found that the hardness of the chromia films deposited on soda lime glass substrates improved with Cu doping to 2.0%, and the antibacterial activity of the films increased with increasing Cu/Cr ratio. Bio-synthesized chromia NPs, 15–24 nm in size, showed
The rare earth (RE) ions can form strong bonds with the metal oxide’s functional groups due to the presence of 4f empty orbitals [23], and therefore RE dopants can alter the physical characteristics of chromia. A few reports on the effect of RE on the chromia films’ features are recounted in the literature. Ikram et al. [23] studied the impact of Sr doping on the bactericidal potential and catalytic activity of nano-sized chromia for wastewater treatment. Jia et al. [5] used Y-doping and the ion-plating technique to fabricate chromia films with improved friction and wear resistance performance, as well as reasonable stability at high temperatures. The trivalent doping could induce vacancy complexes (vacant Cr sites proximal to oxygen vacancies), and these structural defects may encourage the researchers to develop spintronic devices based on Cr2O3 doped with La3+ [24]. In addition, the La electronic 4f–4f transitions result in strong emission peaks with wavelengths in the visible and infrared regions. This enhances the photoluminescence features of the host material for optoelectronic applications [25].
The current work aims to investigate the influence of HT and La doping on the structure and electrical and optical properties of chromia thin films, which have not been reported yet. Most of the physical and chemical synthetic techniques require specialized devices with high costs and high temperatures. However, the sol–gel preparation combined with the spin-coating technique is more affordable and cost-efficient [26]. The solutions were sol–gel-prepared and then spin-coated on glass substrates. The influence of HT/La doping on the structural and morphological features of the films was studied by XRD/Fourier transform infrared (FTIR) spectroscopy and field-emission scanning electron microscopy (FESEM) and energy-dispersive X-ray spectroscopy (EDAX/EDS). The results of optical and electrical properties revealed the possible development of these films for photoelectrooptical devices.
2 Experimental section
2.1 Film preparation
Chromium acetate (Cr2C8H16O10, ∼376 g mol−1, >97%; LOBA Chemie, India), 2-methoxyethanol (C3H8O2, ∼76 g/mol; Merck), and monoethanolamine (C2H7NO, ∼61 g/mol; Merck) were used as the precursor, solvent, and stabilizer, respectively, for chromia thin film preparation. LaCl3.7H2O (371.4 g/mol, >97%; WINLAB, India) was used for La doping. About 0.94 g of Cr source was dissolved in 10 mL of solvent (0.25 M) using a magnetic stirrer. Some drops of stabilizing agent were added during stirring for 1.0 h at 45°C until a clear and homogeneous solution was formed. To prepare 2.5 and 5.0 at% La-doped chromia films, the same procedure was repeated by adding the required mass of the La source. The solutions were kept at RT for 1 day. The glass substrates were washed with neat ethanol and neat water, 5 min for each, using an ultrasonic bath and then air dried. The prepared solutions were coated at 2,100 rpm for 25 s. The deposited (six) layers were pre-heated at 220°C on a hotplate for 5 min to yield films with 200–230 nm thickness. Finally, the samples were heat-treated at 400, 500, and 600°C for 2 h in a furnace. The La-doped films were also annealed at 600°C. The furnace was left to cool naturally to RT. In the following sections, the names (codes) of the samples will be Cr/400, Cr/500, Cr/600, 2.5% La-Cr/600, and 5.0% La-Cr/600.
2.2 Devices
An X’Pert Pro (PANalytical) XRD system was used to examine the phase structure, purity, and size of the spin-deposited chromia films. The surface morphology and elemental (chemical) composition were investigated using a ZEISS SUPRA 55-VP field-emission scanning electron microscope attached to an EDS unit. The chromia functional groups and vibration modes were studied by gathering the FTIR spectra using a VERTEX 70 Bruker spectrophotometer in the range of 400–4,000 cm−1. The optical reflectance/transmittance (T%) in the 200–1,500 nm wavelength region was obtained using a UV-3600 Shimadzu spectrophotometer, in normal incidence mode. The reflectance spectrum was collected using an integrating sphere attachment, and a barium compound was used as reference for 100% reflectance. A Keithley-2400 unit was used for obtaining the current (I)–voltage (V) curves using the two-point probe method.
3 Results and discussion
3.1 Structural analysis (XRD, FTIR, and FE-SEM)
The structural properties of the coated chromia films that were annealed at 400–600°C and doped with La were investigated using the X-ray diffractometer in the 2θ range of 20–75° and applying a Cu K α radiation source (wavelength: λ ∼0.1541 nm). The obtained diffraction patterns are shown in Figure 1. The peak intensity grew significantly with the heat treatment (HT), indicating the improvement in crystallinity with HT at 400–600°C. The most significant peaks were observed at 2θ = 24.66, 33.57, 36.21, and 54.83°. However, doping with La reduced the peak intensity again, indicating deterioration of crystallinity; however, the Cr2O3 phase remained unaffected with doping. Similar patterns were obtained for undoped and Cu-doped chromia films prepared by spray pyrolysis on pre-heated (400°C) soda lime glass substrates [20]. In addition, increasing the ratio of the Y element shifted the chromia film toward the amorphous state [16]. According to Salari Mehr et al. [27,28], the crystallinity of the atomic layer-deposited (ALD) chromia films greatly improved and the eskolaite phase formed with the increase of the substrate temperature from 200 to 275°C but deteriorated upon the addition of Ti. According to Joshi et al. [29], doping with La content ≥ 4 at% La leads to the formation of a TiO2 rutile structure as an additional phase alongside the anatase phase. In addition, loading of 0.1–0.3 at% La2O3 to ZnO–Bi2O3 microparticles through the flash-sintering route did not change the crystal structure (phase) of the varistor, and 0.2 at% La2O3 was enough to achieve a uniform structure with the highest density and best electrical efficiency [30]. These results indicate the possibility of controlling the chromia film crystallinity. The decrease in crystallinity correlated with an increase in defects and disorder within the materials. This will improve the film conductivity and optical characteristics, which will be covered in the following sections.

XRD patterns of chromia films annealed at 400, 500, and 600°C and doped with 2.5 and 5.0 at% La.
The analysis of the obtained data (the positions and relative intensities of the peaks) revealed that the formed material is a hexagonal chromia (α-Cr2O3, eskolaite phase) with a rhombohedral primitive cell (JCPDS nos 01-072-4555 and 01-084-0313 [26]). The Miller indices were inserted on all peaks. No trace related to La or its oxides was detected in the patterns. This outcome confirmed the purity of the product and aligned with the findings reported for La-doped CuO [31] and Co3O4 [32]. La doping resulted in a peak shift that was observed for (0 1 2), (02 4), and (1 1 6) planes, indicating the successful replacement of Cr with La atoms. The smaller Cr atoms (r Cr = 0.615 Å) [33,34]) in the host lattice were substituted by larger La atoms (r La = 1.19 Ǻ [34]), so that the host atoms suffered compression, and the lattice parameters contracted, resulting in a compressive strain [20].
The crystallite size C
s was determined using the well-known Scherrer equation:
Crystallite size (C
s), transmittance (T%), optical band gap (E
g),
Film | C s (nm) | T (%) | E g (eV) |
|
|
R
sheet (
|
|
---|---|---|---|---|---|---|---|
at λ = 380 nm | at λ = 500 nm | ||||||
Cr/400 | 24 | 46 | 68 | 2.70 | 1.052 × 10−6 | 4.44 | 27.12 |
Cr/500 | 29 | 57 | 72 | 2.80 | 1.034 × 10−6 | 3.87 | 31.64 |
Cr/600 | 38 | 64 | 78 | 2.90 | 0.313 × 10−6 | 3.50 | 113 |
2.5% La-Cr/600 | 22 | 59 | 83 | 2.85 | 0.281 × 10−6 | 3.20 | 90.4 |
5.0% La-Cr/600 | 16 | 50 | 80.5 | 2.75 | 0.391 × 10−6 | 3.35 | 45.2 |
The assessment of chemical (reactive) groups in the prepared chromia and La-doped chromia films was done via recording FTIR spectra in the wavenumber range (400–4,000 cm−1), as shown in Figure 2. The vibrations of metal–oxygen (Cr–O) bonds are prominent in the 400–1,000 wavenumber region because of the interatomic vibrations [3]. The inset of Figure 2 displays magnified vibration bands of chromia films annealed at 400°C (Cr/400) occurring at 500, 750, and 890 cm−1. These peaks are assigned to stretching vibrations of

Transmittance (FTIR) spectra of chromia films heat-treated at 400–600°C and doped with 2.5 and 5.0 at% La.
Investigating the exact position and intensity of
The film surface morphology and the chemical (elemental) composition of the spin-coated chromia films on glass substrates annealed at 400°C (Cr/400) and 600°C (Cr/600) and 5.0% La-doped chromia (5.0 % La-Cr/600) were investigated by FE-SEM and the EDX, as illustrated in Figures 3(a)–(c) and 4(a)–(c), respectively. The Cr/400 film has grains of size in the range of 35–56 nm and a large number of small cracks.

(a)–(c) FE-SEM surface images of Cr/400, Cr/600, and 5.0 %La-doped Cr/600 films.

(a)–(c) Elemental analysis of Cr/400, Cr/600, and 5.0 %La-Cr/600 films.
These cracks may be formed during the pre-heating process due to solvent evaporation. Increasing the HT to 600°C resulted in grains with large sizes in the range of 45–72 nm and a reduced number of cracks. The 5.0% La doping had an impact on the film morphology, causing the grains to appear smaller and the zigzag (curved) cracks to have smaller widths. A similar morphology was observed for 2–10% La-doped TiO2 [29]. This morphology increased the films’ surface area for efficient performance in various applications such as gas sensing, photocatalysis, and water treatment. A similar finding was reported for DC-sputtered chromia films, whose nanoflake-like morphology changed into flat-surface morphology after Pd inclusion [18]. The grain size (and morphology) evaluated by high-resolution transmission electron microscopy (HR-TEM) for the sol–gel-prepared Fe-doped Cr2O3 NPs was found to decrease from 36.56 nm (ellipsoidal shapes) to about 22.84 nm (nanorod-like) at 10 at% Fe, which then grew to 66.5 nm (spherical shape) at 30 at% Fe [24]. Huiming et al. [36] reported that La implantation at 3 × 1017 La ion/cm2 on the Co–40Cr alloy at 103 promoted the formation of the Cr2O3 film with fine-grains.
Figure 4(a)–(c) shows EDX analyses of Cr/400, Cr/600, and 5.0% La-Cr/600, respectively. These EDX spectra indicate the existence of O and Cr peaks. Two peaks attributed to Cr are observed at around 0.58 keV (Cr L α) and 5.4 keV (Cr K α). The signal of O at 0.5 keV (O K α) originates from the Cr2O3 films and also from the glass slides. Additionally, the Si (main component of glass), Na, Mg, and Ca signals are from the glass used as substrates. The EDX has a volume of interaction of about ≥ 1 μm (when the voltage of accelerating is ≥ 11 keV), which is larger than the film thickness [37]. The spectrum of 5.0% La-Cr/600 contains three (L α, L β, and L γ) lines that confirms the presence of La at 4.6, 5.4, and 5.8 keV, respectively. The ratio [Cr]/[O] in Cr/400 and Cr/600 films appears to be the same. While the [Cr] is decreased relative to [O] upon doping with 5.0 at% La.
3.2 Film transmittance and band gaps
The UV–vis–NIR transmittance (T%) spectra are shown in Figure 5. T% increases sharply in the UV region, and at λ ≥ 400 nm all films exhibit 60–90% transmittance. The inset of this figure is a magnified view for T% values in the 320–660 nm wavelength range. The values at 380 and 500 nm for all films are displayed in Table 1. The T% values of the Cr/400 film at these two wavelengths are 46 and 68%, which increase to 64 and 78% with the increase of the AT to 600°C, and then became 50 and 80.5%, respectively, after doping the Cr/600 film with 5.0% La. This result illustrates that the T% of the chromia films is adjustable, where it increases with annealing, due to the improved films’ crystallinity, and is lowered by La incorporation, where the defects induced by La absorb or scatter the incident photons. Optoelectronic and photovoltaic devices can harvest this high transmittance.

Optical T% for the spin-deposited chromia under HT and La doping.
The films’ absorption coefficient (α) can be derived from T% using the following equation:

Tauc plot for E g determination for the films under HT and La doping.
La incorporation induces a reverse effect and narrows the
The literature reported similar findings, showing that doping with 3.0% Ag reduces the E
g value of ion-impregnated chromia NPs from 3.4 to 2.82 eV, resulting from the defect sites formed in the composite films [3]. Values of 1.82 ≤
3.3 Chromia films’ optical constants
Evaluating optical constants such as the absorption index (k, where

Absorption index dependence on the HT (400–600°C) and La content in chromia films.
Figure 8 shows the dependence of the films’ reflectance (R%) on the temperature and La doping. Materials with a larger number of particles exhibit higher reflectivity. Increasing the AT from 400 to 600°C results in increasing particle (grain) size, see Figure 3(a) and (b), where the particle tends to coalesce and thus reduces the number of particles. However, La doping leads to a reduction in the particle size, as revealed by XRD and SEM images. La-doped chromia appears with a large number of particles, each particle acting as a scattering or reflecting center. The n values are derived from R and k using the relation:

Dependence of reflectance R (%) and refractive index n (the inset) on HT and La content.
Another two optical constants, the lattice dielectric constant (

n
2
vs λ
2 plot for determining the
3.4 I–V characteristic curves
Figure 10 shows the I–V plots of the spin-deposited chromia films on the glass substrate. The linear I–V curves indicate good Ohmic resistance. Bhardwaj et al. [16] also found a linear I–V relationship for chromia doped with Ni, Co, and Mn that was deposited on Al2O3 substrates. The films’ sheet resistance (

I–V characteristic curves of chromia films annealed at different temperatures and doped with La.
4 Conclusions
The influence of HT at temperatures in the range of 400–600°C and La incorporation on the physical properties of chromia thin films spin-deposited on glass substrates was investigated. XRD showed that hexagonal chromia was formed after annealing at 400°C. Raising the temperature to 600°C enhanced the films’ crystallinity and increased the C
s value from 24 to 38 nm, which then dropped to 16 nm upon doping with 5.0% La. The
Acknowledgments
The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research work through the project number NBU-FFR-2025-310-05.
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Funding information: This work was funded by the Deanship of Scientific Research at Northern Border University, Arar, KSA, through the project number NBU-FFR-2025-310-05.
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Author contributions: Adel M. El Sayed: conceptualization, methodology, data curation, writing of the original draft, and editing of the manuscript. Faisal Katib Alanazi: methodology, data curation and investigation, and reviewing and editing of the revised manuscript. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Data availability statement: All data generated or analyzed during this study are included in this published article.
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- Single-step fabrication of Ag2S/poly-2-mercaptoaniline nanoribbon photocathodes for green hydrogen generation from artificial and natural red-sea water
- Abundant new interaction solutions and nonlinear dynamics for the (3+1)-dimensional Hirota–Satsuma–Ito-like equation
- A novel gold and SiO2 material based planar 5-element high HPBW end-fire antenna array for 300 GHz applications
- Explicit exact solutions and bifurcation analysis for the mZK equation with truncated M-fractional derivatives utilizing two reliable methods
- Optical and laser damage resistance: Role of periodic cylindrical surfaces
- Numerical study of flow and heat transfer in the air-side metal foam partially filled channels of panel-type radiator under forced convection
- Water-based hybrid nanofluid flow containing CNT nanoparticles over an extending surface with velocity slips, thermal convective, and zero-mass flux conditions
- Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities
- Solving an isotropic grey matter tumour model via a heat transfer equation
- Study on the penetration protection of a fiber-reinforced composite structure with CNTs/GFP clip STF/3DKevlar
- Influence of Hall current and acoustic pressure on nanostructured DPL thermoelastic plates under ramp heating in a double-temperature model
- Applications of the Belousov–Zhabotinsky reaction–diffusion system: Analytical and numerical approaches
- AC electroosmotic flow of Maxwell fluid in a pH-regulated parallel-plate silica nanochannel
- Interpreting optical effects with relativistic transformations adopting one-way synchronization to conserve simultaneity and space–time continuity
- Modeling and analysis of quantum communication channel in airborne platforms with boundary layer effects
- Theoretical and numerical investigation of a memristor system with a piecewise memductance under fractal–fractional derivatives
- Tuning the structure and electro-optical properties of α-Cr2O3 films by heat treatment/La doping for optoelectronic applications
- High-speed multi-spectral explosion temperature measurement using golden-section accelerated Pearson correlation algorithm
- Dynamic behavior and modulation instability of the generalized coupled fractional nonlinear Helmholtz equation with cubic–quintic term
- Study on the duration of laser-induced air plasma flash near thin film surface
- Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique
- The mechanism of carbon monoxide fluorescence inside a femtosecond laser-induced plasma
- Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
- Numerical examination of the chemically reactive MHD flow of hybrid nanofluids over a two-dimensional stretching surface with the Cattaneo–Christov model and slip conditions
- Impacts of sinusoidal heat flux and embraced heated rectangular cavity on natural convection within a square enclosure partially filled with porous medium and Casson-hybrid nanofluid
- Stability analysis of unsteady ternary nanofluid flow past a stretching/shrinking wedge
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- Solitary chirp pulses and soliton control for variable coefficients cubic–quintic nonlinear Schrödinger equation in nonuniform management system
- Influence of decaying heat source and temperature-dependent thermal conductivity on photo-hydro-elasto semiconductor media
- Dissipative disorder optimization in the radiative thin film flow of partially ionized non-Newtonian hybrid nanofluid with second-order slip condition
- Bifurcation, chaotic behavior, and traveling wave solutions for the fractional (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili model
- New investigation on soliton solutions of two nonlinear PDEs in mathematical physics with a dynamical property: Bifurcation analysis
- Mathematical analysis of nanoparticle type and volume fraction on heat transfer efficiency of nanofluids
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- Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber
- Chaotic dynamics and some solutions for the (n + 1)-dimensional modified Zakharov–Kuznetsov equation in plasma physics
- Fractal formation and chaotic soliton phenomena in nonlinear conformable Heisenberg ferromagnetic spin chain equation
- Single-step fabrication of Mn(iv) oxide-Mn(ii) sulfide/poly-2-mercaptoaniline porous network nanocomposite for pseudo-supercapacitors and charge storage
- Novel constructed dynamical analytical solutions and conserved quantities of the new (2+1)-dimensional KdV model describing acoustic wave propagation
- Tavis–Cummings model in the presence of a deformed field and time-dependent coupling
- Spinning dynamics of stress-dependent viscosity of generalized Cross-nonlinear materials affected by gravitationally swirling disk
- Design and prediction of high optical density photovoltaic polymers using machine learning-DFT studies
- Robust control and preservation of quantum steering, nonlocality, and coherence in open atomic systems
- Coating thickness and process efficiency of reverse roll coating using a magnetized hybrid nanomaterial flow
- Dynamic analysis, circuit realization, and its synchronization of a new chaotic hyperjerk system
- Decoherence of steerability and coherence dynamics induced by nonlinear qubit–cavity interactions
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- Modulational instability and associated ion-acoustic modulated envelope solitons in a quantum plasma having ion beams
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- On solutions of the Dirac equation for 1D hydrogenic atoms or ions
- Entropy optimization for chemically reactive magnetized unsteady thin film hybrid nanofluid flow on inclined surface subject to nonlinear mixed convection and variable temperature
- Stability analysis, circuit simulation, and color image encryption of a novel four-dimensional hyperchaotic model with hidden and self-excited attractors
- A high-accuracy exponential time integration scheme for the Darcy–Forchheimer Williamson fluid flow with temperature-dependent conductivity
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- Development of a photoelectrode based on a bismuth(iii) oxyiodide/intercalated iodide-poly(1H-pyrrole) rough spherical nanocomposite for green hydrogen generation
- Investigation of solar radiation effects on the energy performance of the (Al2O3–CuO–Cu)/H2O ternary nanofluidic system through a convectively heated cylinder
- Quantum resources for a system of two atoms interacting with a deformed field in the presence of intensity-dependent coupling
- Studying bifurcations and chaotic dynamics in the generalized hyperelastic-rod wave equation through Hamiltonian mechanics
- A new numerical technique for the solution of time-fractional nonlinear Klein–Gordon equation involving Atangana–Baleanu derivative using cubic B-spline functions
- Interaction solutions of high-order breathers and lumps for a (3+1)-dimensional conformable fractional potential-YTSF-like model
- Hydraulic fracturing radioactive source tracing technology based on hydraulic fracturing tracing mechanics model
- Numerical solution and stability analysis of non-Newtonian hybrid nanofluid flow subject to exponential heat source/sink over a Riga sheet
- Numerical investigation of mixed convection and viscous dissipation in couple stress nanofluid flow: A merged Adomian decomposition method and Mohand transform
- Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves
- Analysis of MHD hybrid nanofluid flow over cone and wedge with exponential and thermal heat source and activation energy
- Solitons and travelling waves structure for M-fractional Kairat-II equation using three explicit methods
- Impact of nanoparticle shapes on the heat transfer properties of Cu and CuO nanofluids flowing over a stretching surface with slip effects: A computational study
- Computational simulation of heat transfer and nanofluid flow for two-sided lid-driven square cavity under the influence of magnetic field
- Irreversibility analysis of a bioconvective two-phase nanofluid in a Maxwell (non-Newtonian) flow induced by a rotating disk with thermal radiation
- Hydrodynamic and sensitivity analysis of a polymeric calendering process for non-Newtonian fluids with temperature-dependent viscosity
- Exploring the peakon solitons molecules and solitary wave structure to the nonlinear damped Kortewege–de Vries equation through efficient technique
- Modeling and heat transfer analysis of magnetized hybrid micropolar blood-based nanofluid flow in Darcy–Forchheimer porous stenosis narrow arteries
- Activation energy and cross-diffusion effects on 3D rotating nanofluid flow in a Darcy–Forchheimer porous medium with radiation and convective heating
- Insights into chemical reactions occurring in generalized nanomaterials due to spinning surface with melting constraints
- Review Article
- Examination of the gamma radiation shielding properties of different clay and sand materials in the Adrar region
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part II
- Possible explanation for the neutron lifetime puzzle
- Special Issue on Nanomaterial utilization and structural optimization - Part III
- Numerical investigation on fluid-thermal-electric performance of a thermoelectric-integrated helically coiled tube heat exchanger for coal mine air cooling
- Special Issue on Nonlinear Dynamics and Chaos in Physical Systems
- Analysis of the fractional relativistic isothermal gas sphere with application to neutron stars
- Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique
- Successive midpoint method for fractional differential equations with nonlocal kernels: Error analysis, stability, and applications