Introduction

Water contamination is crucial issues worldwide due to the increasing utilize of organic compositions, particularly in the industrial source such as textile, agricultural, paper, leather, pharmaceutical, printing, and tannery (Liyun et al. 2023). Natural water is mostly classified into groundwater and surface water (Gopalan Saianand et al. 2023). Surface water implicates rivers, reservoirs, lakes, streams, and ponds, each with its own dynamics and exposed to both land surfaces and the atmosphere (Piyawan Nuengmatcha et al. 2023). Water can include toxic compositions such as organic compounds, metalloids, and metals (2023). Contamination is realized by the concentration and existence of these compounds and is highly dependent on the size and type of the water (Mohammad 2023). Dyes are organic pollutants used in the food and textile industries that negatively affect the aquatic ecosystem, human health, and the environment (Joy Sankar Roy and Messaddeq 2023). With an annual output of 700,000 tons, more than 10,000 types of commercial textile dyes are liberated into watercourses without suitable treatment (Alterkaoui et al. 2022) (Aazam Jafarinejad and Salavati-Niasari 2023). Many traditional physical techniques have been used in the treatment of water contamination such as adsorption, ultrafiltration, photodegradation, and advanced oxidation processes (AOPs) (Shabna SSJD 2023). Currently, photocatalysis, membrane-based methods, sonocatalysis, adsorption, and a diversity of other methods have been utilized to eliminate dyes from water (Shaghayegh Naghdi et al. 2023). Newly, the photocatalysis technology has attracted massive attention because of its energy savings from solar energy utilization, ease of use, low levels of toxic byproducts, environmental protection, and remove dyes from water (Zahoor et al. 2022) (Piyawan Nuengmatcha et al. 2023). Heterogeneous photocatalysis is a well-characterized redox procedure that starts with absorption of light via a semiconductor material (Cruz HBO-O et al. 2023). The following steps manifest in the process (Sridhar et al. 2023): (i) adsorption of reactants on the surface of photocatalyst, (ii) absorption of photons with equal or higher than the band gap, (iii) Electrons move from the valence band (VB) to the conduction band (CB), iv) Transfer of photogenerated electrons (e−) and holes (h+) towards the surface of the catalyst, v) Redox reactions with adsorbent substrates, and finally vi) adsorption of the outputs. In photocatalysis, parameters such as photocatalyst dose, band gap, surface area, and production of electron–hole pairs influence the photocatalytic efficiency (Munyai NCH-M. 2023). In the near future, the properties of photocatalysts have been extensively investigated in many environmental applications using semiconductor materials as a photocatalyst to generate reactive species such as (_OH) to react with a dye molecule under visible light (Sohier et al. 1963). Semiconductor photocatalysis is widely applied to solve a number of environmental issues such as energy shortage and pollution. Semiconductor photocatalyst materials are well reported because of their remarkable catalytic activity, simplicity, ease of synthesis, cost-effectiveness, and environmental friendliness (Guddappa Halligudra et al. 2023). The catalysts like TiO2, Fe3O4, ZnO, Fe2O3 and metal chalcogenides such as CdS, WS2, SnS2, MoS2, ZnS have been utilized to solving inorganic and organic effluents in water (Khatun et al. 2023) (Graphene, inorganic nanocomposites 2023). Among these catalysts, CdS has attracted researchers because of its low toxicity (Gizem Basaran Dindas and Yatmaz 2023). CdS is one of the significant (II–VI) semiconductors with wide bandgap, excellent luminescence, and photochemical features (Amiezatul Amirulsyafiee and Harunsani 2023). CdS has the capability to decompose toxic organic compositions due to its wide absorption band in the electromagnetic spectra (Recent progress in photoelectrocatalysis of g-C3N4 for water environment remediation. 2023). However, various problems like large band gap, easy agglomeration, and easy recombination of carriers have been demonstrated in the CdS studies (Zhang et al. 2023). To overcome the above issues, studies have examined a large number of modulations to enhance the photocatalytic efficiency of CdS (Ari Sulistyo Rini et al. 2023). Attempts to develop the photocatalytic performance of CdS have involved changing the structure surface of CdS NPs by dominating morphology, metal/non-metal doping into CdS, depositing CdS to graphene layers, sensitizing enrichment, and crystallinity improvement (Nida Qutub et al. 2022). Gadolinium (atomic number 64) is a metal of the lanthanide group during the rare earth constituents (REEs) combination, which clearly appear in trivalent state (Gd3+) (El-Morsy NSA et al. 2023). Gadolinium oxide (Gd2O3) is widely used as an n-type photocatalyst for semiconductors and large bandgap around (5.4) eV (Sugyeong Jeon J-WKaW-BK 2021). Gadolinium oxide (Gd2O3) has a relatively high thermal stability, good chemical durability, exhibits features, and low phonon energy identical to those of Fe3+ and Al3+ that are used to the arsenic removal [(Lingamdinne et al. 2021). In addition, Gd2O3 exhibits a magnetic property that can be useful for water recovery using an external magnetic field. In particularly, Gd(III) displays seven unpaired electrons and thus a strong magnet (Lingamdinne et al. 2021). The Gd2O3 a good candidate in numerous novel applications such as UV detectors, biomedical devices, luminescent, optical coating, magnetic resonance, fluorescence imaging, high-resolution X-ray medical imaging, and electronic visual displays (El-Morsy NSA 2023). Graphene oxide is a promising nanomaterial which has aroused a massive deal of interest among scientists due to its several features and diversity of applications (Ali et al. 2018). It has two-dimensional (2-D) material, in which the carbon atoms are sp2 hybridized in a hexagonal lattice (Sukumaran et al. 2018). Graphene oxide (GO) is a zero band gap semiconductor (Yi et al. 2019). It is widely used in optoelectronic devices, photodetectors, energy, drug delivery, and environmental cleaning due to edge effects and the quantum confinement (Jiang et al. 2020). Moreover, GO can absorb co-existing traditional pollutants such as heavy metals and organic contaminants in water due to its large surface areas and considerable functional oxygen groups (Cao et al. 2019). The graphene oxide offer certain characteristics such as good conductivity, excellent optical properties, thermal stability, electrical field resistivity, good lubricating properties, and non-toxicity (Rohan Bahadur and Bando 2023). Many researchers have confirmed that graphene-related nanoparticles such as ZnO, TiO2, CdS, and SnO2, exhibit superior photoreduction properties (Zaman et al. 2022). Methylene blue (MB) is the most commonly used dye for wool and silk. May cause eye burns resulting in permanent eye damage in humans and animals. Inhalation may cause transient shortness of breath or difficulty breathing, while oral ingestion can cause a burning sensation that may lead to nausea, vomiting, profuse sweating, confusion, etc. Therefore, the treatment of wastewater containing such dyes is of concern due to their detrimental effects on receiving water bodies (Kyzas and Kostoglou 2014). The dynamic adsorption process depends on the adsorbate–adsorbent interaction, and the suitability of the system state for water pollution control is investigated (Nafees et al. 2023). Mechanism and response rate are two critical factors in evaluating an adsorption process unit. The residence time necessary for the adsorption reaction to complete is governed by the solute uptake rate, which may be calculated via kinetic analysis. Many kinetic models describe the reaction order of adsorption systems. One of these is the reversible and irreversible Langmuir models. Furthermore, adsorption isotherms are significant in identifying the interaction between the adsorbate and the adsorbent as well as the ideal adsorption capacity of the adsorbent. The adsorption kinetics are best understood by analyzing the adsorption kinetics data (Pan et al. 2023). The purpose of this study is to look at the powder composites of pristine CdS, Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO utilized to improve photocatalytic activity, stability, and the capacity to remove MB dyes. The structural, morphological, and optical properties of the resulting composites were investigated using various techniques such as XRD, SEM, and UV–Visible spectroscopy. Different elastic properties of the as-prepared composites were examined using various methods such as the modified Scherrer method, the W–H plot, and the H–W approach based on the broadening of the XRD peak.

Experimental Details

Chemicals and Materials

Cadmium chloride (CdCl2. 2H2O) 98%, sodium sulfide (Na2S) 99.5%, and gadolinium oxide (Gd2O3) 99.0% were all acquired from LOBA (India). Sigma–Aldrich (USA) provided the graphene oxide (99.5%), ammonium solution (25%), and deionized water (DI).

Synthesis of Powder Compositions

The co-precipitation method was used to prepare CdS. Separately, 250 mmol of (CdCl2. 2H2O) and 90 mmol of (Na2S) were dissolved in 50 mL of deionized water (DI) with magnetic stirring for 1 h. The (CdCl2. 2H2O) solution was then dropped wisely into the (Na2S) container, while the pH value was kept at 10. Gadolinium oxide (Gd2O3) was combined with cadmium sulfide (CdS) and mixed in 50 mL of DI water under highly powerful sonication for 30 min. The solution then was left for precipitation and drying. After that, 50 mg of graphene oxide (GO) and gadolinium oxide (Gd2O3) was added individually to cadmium sulfide (CdS). Finally, the product was dried at 60 °C. Figure 1 depicts the instruments and steps used in sample preparation.

Fig. 1
figure 1

Preparation of CdS, Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO compositions

Full size image

Characterization and Measurements

The crystalline size and the structure were analyzed via the XRD technique (XRD, analytical, Pertpro, Netherlands). The morphology of the composition was examined using Field Emission Scanning Electron Microscope (FE-SEM, QUANTA-FEG250, Netherlands). Furthermore, the particle size distribution was identified by a transmission electron microscope (HRTEM) (JEOL/ JME—2100, Japan). Fourier-transformed infrared (FT-IR) spectra were attained by JASCO-6300 in the range of 4000–400 cm−1, to investigate the functional group of the compound. Thus, UV–Visible Spectroscopy (Bio Aquarius CE 7250, UK) was used to characterize the optical properties of the prepared compositions. Furthermore, XPS has studied the chemical composition of K-ALPHA (Thermo Fisher Scientific, USA).

Dye Degradation Studies

There are several processes for treating solvent extraction, electrolytic reduction, and ion exchange that require the use of more effective remediation technologies such as adsorption, which allows for high pollutant removal percentages. As a photocatalyst, the photocatalytic performance of CdS, Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO powdered compositions was calculated. The mixing solution was held in the dark for 60 min prior to lighting to reach adsorption/desorption equilibrium, and the concentration of the solution was measured as the initial concentration (Co) of the dye solution. The dye degradation experiment was carried out in a closed box at room temperature with a halogen lamp (500W) and a container of 30 mL containing MB (0.5 ppm) and 100 mg of powdered composition. The reaction's progress will be determined by the reactant with a considerably lower concentration. The solution was kept in a dark environment for 60 min, and the halogen lamp was 18 cm away from the compound. A spectrophotometer was used to monitor the 30 mL of MB solution every 10 min.

The degrading activity (%) was estimated using the equation below (Shubha et al. 2023):

$$\eta = \left( {\frac{{{C_o} - C}}{{C_o}}} \right)x100\% ,$$
(1)

where C0 and C are the first and final concentrations of the dye, respectively.

Results and Discussion

X-Ray Powder Diffraction Study

XRD was used to determine the phase structure and crystallite composition of the produced compounds. The XRD patterns of the compositions are depicted in Fig. 2a. Growing grain boundaries may cause grain size to increase when adding CdS to Gd2O3 and GO. The presence of CdS deposition causes the size of nanoparticles to increase. The broadening peak of CdS composition denotes that the particles are in small size. The diffraction peaks at 2 ϴo = 26.5°, 30.7°, 43.9°, and 52.1° indicate that the planes of (111), (200), (220), and (311) are corresponding to cubic symmetry of CdS, according to the ICDD card of (00–042-1411). The diffraction peaks at 2 ϴo = 20.19°, 28.56°, 33.19°, 47.70°, and 52.17°, which correspond to the cubic phase of Gd2O3, refer to the planes of (211), (222), (400), (440), and (611), respectively, at reference card (00–043-1014). Furthermore, the peaks estimated at 2ϴ = 28.56°, 43.61°, 47.70o, and 52.17° are part of the CdS hexagonal system as (101), (110), (103), and (201) with reference to card (00-006-0314). The weakening and broadening of these diffraction peaks indicated that the CdS/Gd2O3 has a weak crystalline structure, which could reduce the order of structure. Impurities were not observed, indicating that the compounds were synthesized with high crystalline and purity (El-Morsy et al. 2023). Because of the comparatively high crystallinity, the peaks of CdS/Gd2O3@GO are sharper than those of CdS. The crystal size, micro-strain, and dislocation density based on the diffraction result were calculated, as detailed in the next section.

Fig. 2
figure 2

a XRD pattern with different powdered compositions pristine CdS, pure Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO and b, c the crystallite size modified Scherrer model (MSM) and Halder–Wagner method (HWM) and their particle size distribution

Full size image

The Calculation of Crystallite Size via Various Methods

Modified Scherrer Method (MSM)

Generally, this method was also employed for calculating the crystallite size of compositions. The histogram of particle size distribution is displayed in Fig. 2b. The modified Scherrer equation can be written as follows (Marzieh Rabiei and Monshi 1627):

$$\beta=\frac{K\lambda}{{D}_{s}}\times \frac{1}{{{\rm cos}}\theta},$$
(2)

where Ds is the Scherrer’s crystallite size (nm), K is the dimensionless shape factor (0.94), λ is the wavelength of X-ray, β is full width at half maximum (FWHM), θ is Bragg’s angle, and ε is the micro-strain. Taking logarithm on both sides and the equation becomes:

$${\text{ln}}\beta ={\text{ln}}\frac{K\lambda }{{D}_{s}}+{\text{ln}}\frac{1}{{\text{cos}}\theta }.$$
(3)

Plot of ln β (in y-axis) versus with ln (1/cos \(\theta\)) (in x-axis) is shown in Fig. 3. The plot's linear fitting can be contrasted with the straight line equation (y = mx + c) used in the following equations. The (Ds) was calculated using Eq. (5). As a result, the crystallite size was calculated to be 30.03 nm (as shown in Table 1).

Fig.3
figure 3

Linear fit plot of modified Scherrer method (MSM) for calculating crystallite size of synthesized (a) CdS, (b) Gd2O3, (c) CdS/Gd2O3, and (d) CdS/Gd2O3@GO

Full size image
Table 1 Results of the modified Scherrer model (MSM) approach for crystallite size, lattice strain, and dislocation density
Full size table
$${\text{ln}}\frac{K\lambda }{{D}_{s}}=Intercept or, \frac{K\lambda }{{D}_{s}}={e}^{(Intercept)},$$
(4)
$${D}_{s}=\frac{K\lambda }{{e}^{Intercept}}.$$
(5)

Table 1 indicates that the average crystallite size according to Modified Scherrer’s formula is fluctuated among composites, while the degree of distortion present in the crystalline lattice, micro-strain (ɛ( values 3.88, 4.63, 4.03, and 4.15 for CdS, Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO, respectively, are shown. Dislocation density (δ) is the concentration of dislocation lines per unit area of surface and is proportional to crystal size. Plastic distortion increases the influence of dislocation on material characteristics. The dislocation density was determined using the following formula (Jahil et al. 2022):

$$Dislocation density \left(\delta \right)=\frac{1}{\left({D}_{s}\right)}.$$
(6)

The dislocation density is varied from 1.10 × 10–5 to 9.12 × 10–5 for pristine Gd2O3 and CdS/ Gd2O3@GO.

Halder–Wagner Method (HWM)

Halder–Wagner (HW) investigation is another simplified method for determine the crystallite size (Article Text-2023). The size broadening of the XRD peak profile is neither a Gaussian nor a Lorentzian function (Nath et al. 2020). The results were determined and involved in Table 2, and the particle size distribution histogram is displayed in Fig. 2c. The relationship between the crystallite size and strain according to Halder–Wagner equation (Izumi and Ikeda 2014), is provided by Eq. (7):

$${\left(\frac{{\beta }^{*}}{{d}^{*}}\right)}^{2}=\frac{1}{{D}_{s}}x \left(\frac{{\beta }^{*}}{{d}^{*2}}\right)+ {\left(\frac{\varepsilon }{2}\right)}^{2},$$
(7)
$${where, \beta }^{*}=\frac{\beta {\text{cos}}\theta }{\lambda }, and\; {d}^{*}=\frac{2{\text{sin}}\theta }{\lambda }.$$
(8)

Table 2 provides all of the estimated average size values, and the (β*/d*)2 along the y-axis for each peak of the XRD method is replicated in Fig. 4. The slope of the depicted straight line represents the average size and the intercept represents the compositions' micro-strain. The plot shows that the average particle size for CdS, Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO is 7.11, 29.6, 9.52, and 13.21 nm. Whereas the value of micro-strain from Halder–Wagner plot is construct out to be 18.3 × 10–3, 4.3 × 10–3, 11.9 × 10–3, and 18 × 10–3 for CdS, Gd2O3, CdS/ Gd2O3, and CdS/ Gd2O3@GO. The increase in evaluated micro-strain value is actually due to the contribution of mid and low XRD data. Furthermore, the larger strain value obtained in the Halder–Wagner model can be attributed to lattice disturbances, which play a significant role in expanding the reflection peaks at low angles (Jahil et al. 2022).

Table 2 Results of the Halder–Wagner for crystallite size, lattice strain, and dislocation density
Full size table
Fig. 4
figure 4

Linear fit plot of Halder–Wagner method (HWM) for calculating crystallite size of synthesized compositions (a) CdS, (b) Gd2O3, (c) CdS/Gd2O3, and (d) CdS/Gd2O3@GO

Full size image

Williamson–Hall Model (WHM)

Williamson–Hall (W–H) method was utilized to determine the crystallite size of the synthesized compounds (Yendrapati et al. 2023). Moreover, W–H model extends a computational path for crystallite size as well as micro-strain (Ahmed et al. 2022). The distortions and imperfections in the crystals of a powdered material cause strain (Lim 2020). In general, the W–H technique expresses the total physical line broadening (FWHM) of an X-ray diffraction peak as a sum of strain and size effects. Clarify the modified W–H plots of the compounds (Manikandan Balakrishnan 2020):

$${\beta }_{hkl}{\text{cos}}\theta =\frac{K\lambda }{{D}_{s}}+4\; \varepsilon\; {\text{sin}}\theta .$$
(9)

Equation 9 is the Williamson–Hall equation for evaluating the lattice strain and crystallite size. In this study, the crystallite size and lattice strain of the composition have been determined using different models such as uniform deformation model (UDM), uniform energy density model (UDEDM), and uniform strain deformation model (USDM). Equation 9 represents the uniform deformation model (UDM), which implicates an isotropic nature of the materials (Pijush et al. 2023). By plotting βhkl cos θ on the y-axis against 4sin θ on the x-axis in presented in Fig. 5. From the slope of the straight line between 4sinθ and βhkl cosθ, the strain (ε) could be evaluated and the average crystallite size could be evaluated via the intercept of y-axis (Sridhar et al. 2023). The results are listed in Table 3.

Fig. 5
figure 5

Linear fit plot of W–H method (WHM) of (a) CdS, (b) Gd2O3, (c) CdS/Gd2O3, and (d) CdS/Gd2O3@GO nanocomposite

Full size image
Table 3 The values of βhkl Cosθ and 4Sinθ via Williamson–Hall method of XRD pattern of CdS
Full size table
$${D}_{s}=\frac{K\lambda }{intercept (y)}$$
(10)

Morphology of Powdered Composition

The morphology of CdS/Gd2O3 and CdS/Gd2O3@GO nanocomposite was exhibited using SEM with different scale bars ranging from 300 to 500 nm, as shown in Fig. 6. The modulation of morphology has a substantial impact on the energy level and electronic structure of CdS/Gd2O3@GO, resulting in an increase in photocatalytic activity (Runda Huang and Zhang 2023). As exhibited in Fig. 6a–b, a porous bulk structure and a relatively rough surface with regular spherical particle allocation was identified. In addition, the spherical particles determine the increased roughness and hardness on the bulk surface, which results in a more porous surface area (Farhana Anjum et al. 2023). The grain size as measured from SEM images using Gwyddion software were around 7.4 nm to 85.7 nm. The reduction in particle size is an extra benefit that results in increased surface area (Fatma Mohamed et al. 2023). Figure 6c–d displays that the particles of CdS/Gd2O3@GO have shown the irregular shape of particles with the size in the range of 11.1–66.9 nm. SEM analysis shows that particles are in poly-dispersed shape, irregular in form with tendency to form agglomerates and shows the distribution of small and large nanoparticles. The size of these particles is distributed at random on the graphene layer. The particles are particularly agglomerated with few micro-particles (Kannan et al. 2021). The cracks and the surface roughness indicate the porousness of the prepared composites. It indicates the structure of large clusters, low porosity, and disorder distribution.

Fig. 6
figure 6

FE-SEM micrographs of the synthesized composition and the particle distribution: (a–b) CdS/Gd2O3 with varying scale bar started from 300 to 500 nm, (c–d) CdS/Gd2O3@GO with varying scale started from 100 to 500 nm

Full size image

Table 4 demonstrates the roughness behaviors of the powder compounds, which are exhibited in Fig. 7. Moreover, the peaks could provoke a high trend of cohesion to the ambient surroundings, which encourages the utilization of the compounds for versatile applications (Mamba et al. 2020). Moreover, the parameters Ra, Rt, and Rp are found to follow the change of dislocation density for CdS/Gd2O3 and CdS/Gd2O3@GO. Whereas Rq, Rv, and Rtm are related to micro-strain crystallize size. Generally, the rough surface might develop a photocatalytic activity as compared with the smooth surface which extends fast and effective interaction towards the ambient environment (Zhen Li and Wang 2023). Furthermore, these nanocomposites can be designed for water purification applications by controlling the morphological features of the surface, which are a function of the structural components (Han et al. 2020).

Table 4 The parameters of surface roughness of the CdS/Gd2O3 and CdS/Gd2O3@GO, powder compounds
Full size table
Fig. 7
figure 7

Surface roughness behaviors: (a) CdS/Gd2O3, (b) CdS/Gd2O3 @GO compound

Full size image

Transmission Electron Microscopy

The CdS/Gd2O3@GO nanocomposites were also examined via TEM analysis and the results are as shown in Fig. 8a–b at two different magnifications. Highly crystalline CdS/Gd2O3@GO nanocomposite of non-uniform geometry with an average particle size of 10 nm in spherical and irregular shaped aggregated nanoparticles are confirmed by TEM images. Moreover, the spherical CdS/Gd2O3@GO composition was uniformly supported on the transparent graphene nanosheet, which resemble thin nanosheets and the sheets are partially curved.

Fig. 8
figure 8

TEM micrographs of CdS/Gd2O3@GO powder composition at several magnifications

Full size image

FT-IR Analysis

FT-IR analysis was used as a qualitative analysis technique to determine the functional groups present in the synthesized materials (Muraro et al. 2020). Figure 9 shows the FT-IR spectrum ranges between 400 and 4000 cm−1 of the synthesized pristine Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO. The broadband of 3420 cm−1 could be assigned to the stretching vibration mode of O–H. The stretching vibrations of hydroxyl (OH) groups of water adsorbed by the samples were ascribed to the broad peak shown at 3100–3600 cm−1. The band of 1633 cm−1 is attributed to H–O–H bending oscillations because the molecules of water are adsorbed on the composite’s surface. The exposed band of 1517 cm−1 is assigned to the asymmetric vibrational mode belonging to the carboxyl group (C=O). The band 1393 cm−1 manifest the C–O bending. The band at 540 cm–1 is ascribed to Gd–O stretching at Gd2O3, respectively.

Fig. 9
figure 9

FT-IR spectra of pristine Gd2O3, CdS/Gd2O3, and CdS/Gd2O3@GO powder compositions

Full size image

Photocatalytic Activity Investigation of Methylene Blue (MB) Dye

The decomposition of methylene blue is widely used as an example to describe the effectiveness of photocatalysts in a wastewater treatment process (Barakat et al. 2023). Methylene blue (MB) is often used as a type dye molecule for photocatalytic degradation characterization of semiconductors. The obtained composition was allowed to resolve the photo catalytic performance via the photo degradation process with MB dye under visible light. Figure 10a, b explicates the absorption spectra of the MB solutions with catalysts Gd2O3 and CdS/Gd2O3 to visible light illumination. A sharp decrease in the absorbance was observed in the presence of catalysts due to photo degradation of the dye. With increasing irradiation time, the absorbance steadily decreases in the presence of catalysts (Shakeel Khan et al. 2023). To analyze the photo catalytic properties of the synthesized catalysts and the reaction kinetics of compositions the Langmuir–Hinshelwood model for pseudo-first-order reaction (Yao et al. 2021) is used. Photo catalytic degradation kinetics can be quantified by the following equation (Keke et al. 2023) (Fig. 11):

Fig. 10
figure 10

The absorption spectra of catalyst (a) Gd2O3 and (b) CdS/Gd2O3

Full size image
Fig. 11
figure 11

Kinetics of photocatalytic efficiency of Gd2O3, CdS/Gd2O3, and CdS/ Gd2O3@GO

Full size image
$${\text{ln}}\left(\frac{ C }{{C}_{o}}\right)= - {K}_{app}t,$$
(11)
$$Ln C=Ln {C}_{o}-{K}_{app}t,$$
(11-a)

where Co is the initial concentration of the MB at t = 0, C is the dye’s concentration at different interval times, and Kapp is the reaction rate constant (Liao et al. 2022). To analyze such kinetic, the quantity -Ln (\(C\)/C0) was plotted as a function of the irradiation time for different composites, Fig. 11. In this way, the pseudo-first-order degradation kinetics was observed for all applied catalysts. The reaction rate (degradation rate) is accelerated to clean MB contaminated water under visible light irradiation (Saravanan and Mika 2023). Figure 12 depicts the effect of dye concentration on the degradation of MB dye over time. The fit plots revealed are all straight lines, indicating that the photo catalytic degradation is strong.

Fig. 12
figure 12

Concentration versus time plots for the composition

Full size image

The quantity qt of the adsorbed die was calculated using equation:

$${q}_{t}=\frac{\left( {C}_{i}-{C}_{e}\right) V}{M},$$
(12)

where qt is the amount of adsorbed die molecules (mg/g) at time t, Ce is the concentration (mg/L) at time t, Co is the initial concentration (mg/L), V is the volume of working solution, and M is the mass of catalyst.

The maximum adsorption value (qmax) was calculated to determine the conversion capacity using the following equation (Abbas and Trari 2020):

$${q}_{t max}=\frac{\left({C}_{i }-{C}_{e}\right) V}{M},$$
(13)

where qmax acts to the optimal adsorbed quantity of MB.

Adsorption Isotherms

Adsorption isotherms are quite helpful in understanding the adsorption process. The Langmuir isotherm estimates the maximal adsorption capacity assuming that the adsorbent's surface is encompassed by a monolayer of adsorbent molecules (Ho 2006). The adsorption isotherm reflects qualitative information about the nature of the adsorbent surface contact, as well as the particular relationship between adsorbate concentration and the degree of accumulation on the adsorbent surface at constant temperature (Mina Ghorbani et al. 2023). Adsorption isotherms are crucial in maximizing adsorbent utilization; thus, examining isothermal data using various isothermal models is a critical step in determining the optimal model that may be used for design goals. (EnyewAmareZerefa SMJa. 2023). Although many factors influence adsorption capacity, such as initial adsorbate concentration, reaction temperature, solution pH value, adsorbent particle size and dose, and solute nature, a kinetic model is only concerned with the effect of observable parameters on the overall rate (Enhancing the TiO2-Ag 2023). Adsorption of metal ions, dyes, oils, and organic compounds from aqueous solutions has been successfully accomplished using the pseudo-second-order expression (Gama et al. 2006).

Pseudo-First-Order (PFO) Model

PFO describes the adsorption of solutes on adsorbents by a first-order mechanism. The Langmuir isotherm model is based on the assumption of a monolayer and uniform absorbed energy. The Langmuir constant (KL) and maximum adsorption capacity (qmax) are determined from the intercept and slope of the linear Langmuir Eq. 14. R2 is close to 1, which is a strong correlation coefficient. The intercept and slope of the Ce/qe versus Ce plot can be used to calculate qm and KL values is indicated in Fig. 13. The expression for the nonlinear form of the Langmuir isotherm is shown in the following equation (Williams and EKF 2023):

Fig. 13 (
figure 13

a–d) Plot between ce/qe on y-axis and ce on x-axis

Full size image
$$\frac{{c}_{e}}{{q}_{e}}=\frac{1}{{q}_{m}{K}_{L}}+\frac{{c}_{e}}{{q}_{m}},$$
(14)

where KL denotes the Langmuir adsorption constant and qm is the maximum adsorption capacity.

Adsorption Kinetic Analysis

Adsorption kinetics provides valuable information about possible: Adsorption mechanisms and their potentially rate-limiting steps in the adsorption process. It is also an important step to select the best conditions for optimizing parameters and large-scale removal process, in aqueous media (Abbas and Trari 2020).

Pseudo-Second-Order (PSO) Model

The PSO model assumes that the rate of solute adsorption is proportional to the available sites on the adsorbent. The reaction rate depends on the amount of solute on the surface of the adsorbent. In the form of the PSO Eq. 15, the driving force (qm–qt) is proportional to the number of active sites available on the sorbent.

$$\frac{{dq}_{t}}{{d}_{t}}={k}_{2}({q}_{m}-{q}_{t}{)}^{2},$$
(15)

where qt is adsorbate adsorbed onto adsorbent at time t (mg/g), qm is equilibrium adsorption capacity (mg/g), and k2 is PSO rate constant. Equation (15) has been treated and rearranged into the forms of Eqs. (15-a) & (15-b). Furthermore, adsorption kinetics influences the rate of solute adsorption, which in turn governs the desorption reaction's survival time (EnyewAmareZerefa SMJa. 2023). To resolve the kinetics survey of MB, the pseudo-second-order model was used (Niazi et al. 2022). Second-order models are used to fit the photo catalytic oxidation of various dyes (En Shi et al. 2023). We utilized the following two kinetic models to investigate the dye adsorption techniques, Eqs. (15-a)&(15-b) (Alexander Agafonov et al. 2023):

\(\frac{t}{{q}_{t}}=\frac{1}{{k}_{2}{q}_{e}^{2}}+\frac{t}{{q}_{e}}\), (Type 1, plotting t/qt against t) (15-a),

\(\frac{1}{{q}_{t}}=\left(\frac{1}{{k}_{2}{q}_{e}^{2}}\right)\frac{1}{t}+\frac{1}{{q}_{e}}\), (Type 2, plotting 1/qt against 1/t) (15-b).

Equations (15-a and 15-b) show the pseudo-second-order kinetic model, where k2 is pseudo-second-order rate constant. The slope 1/qt and intercept 1/k2q2e in t versus t/q2e plot was used to determine the values of the parameters of the pseudo-second-order kinetic model. However, Eq. (15-a) was found to provide better fitting results in curvilinear function compared to other forms. This behavior is compatible with the adsorption isotherms model's type-I behavior. It shows a monolayer formation tendency, achieving saturation of the adsorption surface. The adsorption mechanism was determined to be chemisorption, which involves electron transfer between the adsorbate and adsorbent (Md. Kamrul Hossain MMHaSA. 2023).

The initial sorption rate was calculated using second-order rate constants (h) (Niazi and Tanvir Shahzad. 2022) and is given by the following equation:

$$h={k}_{2}{q}_{e}^{2}.$$
(16)

While the pseudo-second-order model fitted to the highest R2 value as shown in Figs. 14 & 15. The results of pseudo-second-order kinetic models are summarized in Table 5.

Fig. 14
figure 14

The exponential fitting forms of pseudo-second-order model (type 1)

Full size image
Table 5 Parameters of pseudo-second-order model
Full size table

The pseudo-second-order model plot is illustrated in Figs. 14 and 15. The determine parameters are displayed in Table 5. The maximum adsorption capacity (qe) determined for CdS, Gd2O3, CdS/ Gd2O3, and CdS/ Gd2O3@GO adsorption for type 1 were 5, 0.067, 0.027, and 0.012 mg/g. The R2 values originated from the pseudo-second-order (type 2) plots for CdS, Gd2O3, CdS/ Gd2O3, and CdS/ Gd2O3@GO were 0.904, 0,928, 0.825, and 0.977, respectively. The initial sorption rate (h) is varied values from type 1 and type 2. Thus, the pseudo-second-order rate constant (k2) is ranged from 0.005 for CdS to 0.011 for CdS/ Gd2O3@GO in type 2 (Table 5), fitting the experimental data to pseudo-second-order kinetics yielded type 2 better correlation coefficients (R2) than fitting the experimental data to pseudo-second-order kinetics type 1 for all the systems survived.

Fig. 15
figure 15

The linear forms of pseudo-second-order model (type 2)

Full size image

Adsorption Thermodynamic Study

The MB dye adsorption process was assessed to determine the thermodynamic feasibility of the thermal effects of adsorption; the standard Gibbs free energy change (G°) was calculated using the Van't Hoff (EnyewAmareZerefa SMJa. 2023) Eq. (17):

$$\Delta G = RTLn{K_d},$$
(17)

where Kd is the distribution coefficient of adsorption and equal to the ratio between adsorption capacity (qe) to the equilibrium concentration (Ce); T is the solution’s temperature (27 + 273) in Kelvin (°K) and R is the gas constant (8.314 J/mol K).

To assess the spontaneity and feasibility of adsorption processes, the Gibbs free energy of change is utilized. A negative ∆G0 value confirms a spontaneous process, whereas a positive ∆G0 value confirms a non-spontaneous process (Table 6). This study showed that the magnitudes of the Gibbs free energy were nearly constant during the adsorption process. The result for the current study indicates a negative value of ∆G0 in the case of CdS—1706 kJ mol−1. In other circumstances, the values range between 3984.07 and 7250 kJ mol−1.

Table 6 The values of Gibbs functions (ΔG°) for adsorption of MB dye on the different catalysts
Full size table

Photo Catalytic Degradation Mechanism

The mechanism of photo catalytic MB degradation of the composition is presented in Fig. 16. During visible light irradiation, absorb light with energy equal to or greater than its band gap energy and electrons (e−) are excited from valence band (VB) to conduction band (CB) and a pair (e− & h+) is formed. Resultantly, the electrons in CB react with O2 to generate superoxide radicals, whereas holes in the VB react with the molecules of water absorbed on catalyst surface to create hydroxyl radicals (•OH˙), and the hydroxyl radicals are strong oxidizing species, which through oxidative mechanism converts the dye molecule into low molecular weight intermediates The generated hydroxyl and superoxide radicals react with MB to degrade it into CO2 and H2O and hence the MB contaminated water becomes clean (Effect of dopant on ferroelectric 2023).

Fig. 16
figure 16

Schematic mechanism of photocatalytic degradation of MB

Full size image

Conclusion

The compositions were synthesized successfully via the co-precipitation method. Different techniques were used to calculate the average crystallite size using XRD spectra. Using the Scherrer plot, Williamson–Hall plot, and Halder–Wagner method, XRD peak broadening analysis has been carried out to explore the various elastic properties of the compositions, including intrinsic strain and dislocation density. According to the Halder–Wagner plot, the average particle size for CdS, Gd2O3, CdS/ Gd2O3, and CdS/ Gd2O3@GO is 7.11, 29.6, 9.52, and 13.21 nm. Because the equations for the Halder–Wagner approach are derived from the straight line fitting in the diagram, the results are highly accurate. There is a convergence between the outcomes of the Halder–Wagner method and the outcomes of the other methods, namely the Williamson–Hall method and the Modified Scherrer equation, which rely on the graph to predict the crystal size and micro-strain. The findings also show that the adsorption mechanisms exhibit pseudo-second-order dynamics. Pseudo-second-order kinetic models were used to fit and interpret kinetic data. The benefit of utilizing this model is that the equilibrium capacity can be derived from the model as well as the initial adsorption rate, eliminating the need to know it from the tests. The Gibbs free energy change (ΔGo) is varied between —1706 and 7250 kJ mol−1.