Rietveld Refinement, Structural Characterization, and Methylene Blue Adsorption of the New Compound Ba_0.54Na_0.46Nb_1.29W_0.37O₅

Abstract

Using the solid-state process, the new compound Ba_0.54Na_0.46Nb_1.29W_0.37O₅ was effectively produced in a single crystalline phase. The material’s characteristics were determined by X-ray diffraction and Raman techniques. The Rietveld method was applied to refine the structural properties of this sample using X-ray diffraction data and derive the diffraction line profile. The cell parameters a = b = 12.37843 ± 0.02 and c = 3.93526 ± 0.02 were accustomed to crystallizing this compound in the tetragonal tungsten bronze (TTB) structure of the space group P4bm. Thanks to Raman measurements, we were able to detect numerous vibration modes in this crystalline phase. The adsorption of methylene blue (MB) on crystalline phase was studied by UV–visible spectroscopy. On account of methylene blue adsorption on Ba_0.54Na_0.46Nb_1.29W_0.37O₅, it was discovered that this material can be used to remove organic pollutants and thus be used for water treatment.

1. Introduction

Among the most prevalent pollutants that can damage water are organic dyes. Because industrial waste is harmful, the adsorption and separation of dye contaminants are essential for wastewater treatment. Methylene blue (MB) is a frequent cationic dye used in the textile industry because of its chemical stability. On the other hand, it might have an impact on human health, living species, and the ecosystem. At ambient temperatures, methylene blue is extremely resistant to oxidation and disintegration [1,2,3]. The majority of the more important scientific issues when it comes to pollution remediation address the creation and use of an adsorbent with good adsorption qualities for organic dyes [4,5,6,7]. There have been several ways proposed so far to reduce methylene blue as an organic contaminant in wastewater [8,9,10]. Different nanomaterials have been introduced to remove the organic molecules in wastewater as a result of their highest adsorption capacity, such as activated carbon, TiO₂, SnO₂, WO₃/(WO₃,H₂O), etc. [11,12,13,14]. However, the development of the new materials characterized by high capacity for adsorption, low cost, and abundance is still an ongoing work. In this context, many scientists have actively researched niobate materials, because they have unique structures and physico-chemical properties that can be applied to heterogeneous catalysts, ferroelectric substances, piezoelectrics, photocatalysis, and so on [15,16,17,18,19]. The reaction method has seen widely used to create the complex of Nb–W–O oxides. According to our knowledge, the only work prepared by Juhyon Yu et al. is concerned with the synthesis of niobium-tungsten oxide Nb₁₈W₁₆O₉ by using the hydrothermal method, which has been used in the adsorption of methylene blue [20]. Regardless of the fact that articles on the combination of Nb–W–O have indeed been provided, there is no more discussion anywhere on the methylene blue adsorption on compounds of the tetragonal tungsten bronze type prepared by the solid state technique. In this work, we outline the procedure for preparing a new compound, Ba_0.54Na_0.46Nb_1.29W_0.37O₅, which is investigated as an adsorbent material prepared by the solid-state method to examine its adsorption capacity for removing methylene blue adsorption from wastewater.

2. Methods and Materials

2.1. Manufacturing of Adsorbent

The crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O₅ were synthesized from the raw materials BaCO₃, NaCO₃, WO₃, and Nb₂O₅ purchased from Merck (Merck, Darmstadt, Germany, 99.95%). These raw materials were ground in an agate mortar during one hour of grinding. Then, the mixture was placed in an alumina crucible for thermal treatment at 600 °C and 1200 °C, respectively, for 24 h and 48 h. After this step, the mixture is reground with ethanol for around an hour for calcination. The calcination was performed at a final heating temperature of 1300 °C for 24 h in an alumina crucible. To complete the chemical processing of the chemicals, the grinding and calcination steps were performed twice. The X-ray diffraction technique was applied to evaluate the compound’s purity and formation.

2.2. X-ray Diffraction Technique

The prepared powder was acquired by using a Bruker D8 Advance diffractometer with the following settings: 0.01 rad cuts on direct and scattering photons, a 0.5° diverging interval, and a 1° antiscatter funnel; 1° collecting cut. Copper (Cu) is used as an anticathode and the radiation is at a voltage of 40 KV and a current of 40 mA. The diffractogram was beamed in steps of 0.01 (2θ), in the range of 10–100 (2θ), with a specific time count of 12 s. The GSAS-II program was used to improve the Rietveld pattern analytical method [21].

2.3. Raman Spectrometer

The Raman spectrometer used is a T64000 marketed by the company HORIBA-Jobin Yvon; it is provided with a single network part (600 or 1800 lines/mm) and a pre-monochromator part offering the possibility of working in triple network mode (1800 lines/mm). The accessible frequency range is very wide, from 5 cm⁻¹ to 4000 cm⁻¹. Sample analysis is performed in backscatter mode, and the laser light is incident on the material through the lens of a microscope (×10, ×50, ×50 LWD, ×100). The spectrum measurement process and pretreatments are approximated to have a 1.5 cm⁻¹ accuracy in spectral measurements. The accuracy of the recorded highest points, as measured by the error margin from fit peaks, ranged from 0.2 to 0.7 cm⁻¹, with the low value in accordance with the 650 cm⁻¹ mode and the high value corresponding to intersecting peaks within the range of 150–350 cm⁻¹. The acquisition time was, on average, 10 s.

2.4. Study of Adsorption

In a 1000 mL volumetric flask, to make the adsorbate, 1 g of methylene blue powder was mixed with a small volume of distilled water. To compensate for the disparity, more distilled water was added. To ensure thorough dissolution, the stock solution was rapidly agitated for five minutes and homogenized. This yielded a 1000 mg/L stock solution. Serial dilution was used to create different concentrations, contact time, adsorbent dosage, and dye concentration effects. A 100 mL dye solution (50 mg. L⁻¹) was poured into a cylindrical bottle with a 0.5 g adsorbent dose and placed inside an agitator. At room temperature, the mixture was stirred for 10–180 min. After each time t, the dye solution was extracted from the adsorbent using a micropipette. Then, the solution was analyzed by UV-Visible spectroscopy (JASCO UV/Vis-550). The influence of the adsorbent’s mass was examined. The adsorbent dosage was changed from 0.02 to 0.20 g/100 mL. The various adsorbent masses employed were investigated to see how this parameter affects the adsorption process. The adsorbent material’s adsorption capability, denoted as $q_e$ and represented in mg/g adsorbent, must be determined for the adsorption efficiency assessment Equation (1):

$$q_e=\frac{\left(C_0-C_e\right)\mathrm{V}}{\mathrm{m}}$$

(1)

with:

• $q_e$: adsorbed amount (mg/g),
• V: volume of solution (l),
• m: mass of adsorbent (g),
• C₀: initial adsorbate concentration (mg/L),
• (C_e): steady-state concentration of adsorbate (mg/L).

3. Results and Discussion

3.1. Characterization of the Adsorbent

3.1.1. Characterization by X-ray Diffraction

The prepared powder was produced after the precursors were calcined for various lengths of time and at various temperatures. In the X-ray pattern, it has not been found to contain any other crystalline phases, which indicates that the used raw materials have been totally mixed through the calcination steps. The crystallinity of the current materials containing niobate was comparable to structures of the type TTB generated by a solid-solid reaction method, such as K₆Nb_10.8O₃₀ [22,23,24] and Sr_2−xK_1+xNb₅O_15−xF_x [25]. The Rietveld method was used to refine the sample’s diffraction pattern [26]. As a result, the GSAS-II software was used to figure out the chemical formula, lattice parameters ($\mathrm{a}$, $\mathrm{b}$, and $\mathrm{c}$), and symmetry group [27]. The phase identified had a chemical formula of Ba_0.54Na_0.46Nb_1.29W_0.37O₅.

In the refinement procedure for the Ba_0.54Na_0.46Nb_1.29W_0.37O₅ sample (Figure 1), the atomic positions and space group of the system Ba_2.15-xNa_0.7+xNb_5-xW_xO₁₅ with ($0\le x\le 1$) were served as first sets [28]. The background was assimilated using a third-order polynomial, while a pseudo-Voigt function was used to fit the peaks. The Caglioti equation was used to evaluate the half width of the diffraction peaks [29]. The scale factor and background coefficients were optimized throughout the initial cycles. As a result, the lattice parameters and the profile parameters were evaluated as gathered in

Table 1. Rietveld refinement data of the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O_5.

Formula	Ba0.54Na0.46Nb1.29W0.37O5
Crystallographic data
Symmetry	Tetragonal
Space group	P4bm
Z	6
Lattice parameters (Å)	$\mathrm{a}=\mathrm{b}=12.37843 \left(7\right) \mathrm{c}=3.93526 \left(5\right)$
Volume (Å3)	602.983 (12)
Calculated density (g/cm3)	5.836
Experimental conditions for data collection
Wavelength (Å)	$k_1=1.5406$ and $k_2=1.5444$
2θ range (°)	10.00–100.00
Step (2θ)	0.01
Integration time (s)	30
Rietveld data
Program for Rietveld analysis	GSAS-II
Chemical formula weight (g/mol)	353.18
Z	6
Rp	7.50
Rwp	9.76
χ2	1.50
GOF	1.23

. In addition, the refined atomic positions are listed in

Table 2. Refined atom positions of the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O₅.

Atom	Wyckoff	x	y	z	Occupation	Uiso
Ba1	2a	0.0	0.0	0.05	0.716	0.800 (12)
Na1	2a	0.0	0.0	0.05	0.284	0.01442
Ba2	4c	0.17611 (14)	0.67611 (14)	0.02135 (14)	0.454	0.00157
Na2	4c	0.16428 (14)	0.66428 (14)	−0.07711 (14)	0.546	0.02092
Nb1	2b	0.0	0.5	0.5	0.82	0.0033
W1	2b	0.0	0.5	0.5	0.164	0.00014
Nb2	8d	0.08364 (17)	0.20650 (18)	0.4759 (30)	0.761	0.0229 (6)
W2	8d	0.06475 (32)	0.21564 (32)	0.518 (4)	0.239	0.0206 (12)
O1	8d	0.1535 (7)	0.0650 (8)	0.501 (24)	1.0	0.0520 (27)
O2	8d	0.3514 (13)	0.0389 (17)	0.771 (12)	1.0	0.5757 (27)
O3	8d	0.0574 (8)	0.2069 (8)	−0.037 (9)	1.0	0.0312 (27)
O4	4c	0.2753 (7)	0.7753 (7)	0.419 (6)	1.0	0.01142
O5	2b	0.0	0.5	−0.02	1.0	0.7505 (27)

. and the selected interatomic distances are presented in

Table 3. Some interatomic distances (Å) of the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O_5.

Principal Interatomic Distances (Å) Ba1/Na1–O
Ba1/Na1–O1	2.99 (7) × 4
Ba1/Na1–O1	2.72 (7) × 4
Ba1/Na1–O3	2.680 (11) × 4
(Ba1/Na1–O)	2.7967
Principal interatomic distances (Å) Ba2/Na2–O
Ba2/Na2–O1	3.25 (6) × 2
Ba2/Na2–O1	3.15 (6) × 2
Ba2/Na2–O2	1.67 (3) × 2
Ba2/Na2–O2	1.99 (3) × 2
Ba2/Na2–O4	2.755 (18) × 2
Ba2/Na2–O4	2.777 (18) × 2
(Ba2/Na2–O)	2.59866
Principal interatomic distances (Å) Nb1/W1–O
Nb1/W1–O2	2.18 (3) × 4
Nb1/W1–O5	2.04634 (3)
Nb1/W1–O5	1.88892 (3)
(Nb1/W1–O)	2.03842
Principal interatomic distances (Å) Nb2/W2–O
Nb2/W2–O1	1.782 (11)
Nb2/W2–O1	1.956 (12)
Nb2/W2–O2	2.34 (3)
Nb2/W2–O3	1.76 (4)
Nb2/W2–O4	2.149 (11)
Nb2/W2–O4	1.956 (10)
hNb2/W2–O	1.99050

. It was found that the structure of the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O₅ has two sorts of crystallography of niobium or tungsten atoms, each one characterized by an octahedral oxygen environment with an average distance W/Nb–O of around 1.92–1.93 Å. As the sodium and barium atoms occupied large sites of the coordination numbers 15 and 12, respectively, they were enclosed by oxygen atoms, forming distorted and non-uniform surroundings, where the average distance of the Ba/Na–O is approximately 2.75–3.02 Å.

The crystalline structure can be schematized as follows:

Figure 2 shows the projection of the crystal structure Ba_0.54Na_0.46Nb_1.29W_0.37O₅ along the c-axis ([0 0 1]). The cations Na⁺ and Ba²⁺ occupied sites of coordination 15 and 12, respectively (Figure 2a). Moreover, the two cations Nb⁵⁺ and W⁶⁺ occupied the octahedral sites (Figure 2b). Furthermore, the present crystal structure is characterized by the non-centrosymmetric space group (P4bm), which allows Nb and/or W to undergo small, off-center displacements within the (Nb/W)O₆ octahedra, leading to a polar c-axis. The barium (1)/sodium (1) atoms are surrounded by 12 oxygen atoms (coordinance 12), which they share with the faces of the octahedra Nb(1)/W(1)–O₆. Polyhedra distances range from 2.66 Å to 3.36 Å with an average value equal to d(Ba(1)/Na(1)–O) = 2.7967 Å. At least 15 oxygen atoms surround barium (2) and sodium (2) atoms at distances ranging from 2.5613 Å to 3.3627 Å, with an average distance of 2.59866 Å d(Ba(2)/Na(2)–O). However, the barium (2) and sodium (2) atoms have a subtle difference in their atomic positions, despite having the same Wyckoff site, 4c (see Table 2). The Niobium (1) or Tungsten (1) atoms are surrounded by six oxygen atoms and form octahedrons which are bound together by the tops. The average distance between Nb(1)/W(1)–O is 2.03842, and the O–Nb(1) and W(1)–O angles range from 84.45° to 180.00°. The niobium (1) and tungsten (1) atoms are characterized by the same atomic positions and the same Wyckoff site (2b), in contrast to the niobium (2) and tungsten (2) atoms, which are different in atomic positions but have the same Wyckoff site (8d).

3.1.2. Characterization by Raman Spectroscopy

Figure 3 shows Raman spectrum of Ba_0.54Na_0.46Nb_1.29W_0.37O₅ in the frequency range 1200–100 cm⁻¹, and the frequencies corresponding to the Raman bands are illustrated in

Table 4. Attributed Raman bands of the Ba_0.54Na_0.46Nb_1.29W_0.37O₅ within the frequency range 1200–100 cm⁻¹.

Frequency (cm−1)	Band Assignment
485→115	Octahedra (W/NbO6) or cation translation vibrations (Ba2+, Na+)
650→485	W/Nb–O stretching vibrations caused by deformation
840→650	W/Nb–O bonds

.

The literature states that the assignment of different entities is predicated on a comparison with compounds that have comparable structures and the sequence of tetragonal tungsten bronze vibrations below, in order of increasing frequency [30,31,32,33,34]. The main Raman bonds observed in Figure 3 can be divided into three regions: (i) the modes at the region 840–650 cm^–1 are identified as the W/Nb–O bonds; (ii) the modes between 650 cm^–1 and 485 cm^–1 are attributed to the W/Nb–O stretching vibrations caused by deformation; (iii) the bands approximately at the region 485–115 cm^–1 as associated with W/Nb–O in octahedra (W/NbO₆) or cation translation vibrations (Ba²⁺, Na⁺). Elsewhere, Shudong Xu et al. attributed the band at position 250 cm^–1 to the O–Nb–O bending vibrations, and the bands below 200 cm^–1 are associated with A-site displacements associated with the NbO₆ octahedral structure [33]. These assignments suppose that the intensity change and phase shift of Raman peaks arising from bonds, such as Ba–Nb/WO₆ and Na–Nb/WO₆, at the same crystal positions are neglected. Both the strongest higher-frequency bands near 280–650 cm⁻¹ are apparently connected with NbO₆-octahedra bending and stretching vibrations, respectively. This is comparable to the 248 cm⁻¹ and 628 cm⁻¹ modes observed in LiNbO₃ and to the 260–280 cm⁻¹ and 630–650 cm⁻¹ modes reported for Pb_2(1−x)K_1+xGd_xNb₅O₁₅ [34]. Finally, in analogy with perovskites [32], the highest-frequency mode around 850–938 cm⁻¹ might be connected with a stretching vibration of (Nb/W)O₆ octahedra. The Raman spectrum of Ba_1.62Na_1.38Nb_3.87W_1.11O₁₅ is characterized by a broad and intense peak around 650 cm⁻¹ and another intense peak around 280 cm⁻¹, both of which are connected to the Nb–O vibrations in NbO₆ octahedra, as shown in Figure 3 [33].

3.2. Application of Methylene Blue Adsorption to TTB

The elimination of dissolved metals by adsorption requires contact of the Ba_0.54Na_0.46Nb_1.29W_0.37O₅ (adsorbent) phase with the ions of methylene blue (the adsorbate). After a period of contact, the adsorbent retains metal ions on its surface.

3.2.1. Effect of Mass on Methylene Blue Adsorption

At a pH of 6.5, ambient temperature, and a concentration of 50 mg/L, the influence of the mass of the adsorbent was investigated. Adsorbent masses of 20–200 mg were used (Figure 4). The various adsorbent masses employed are being investigated to see how this parameter affects the adsorption process.

According to the findings, increasing the mass of the compound Ba_0.54Na_0.46Nb_1.29W_0.37O₅ from 20 mg to 200 mg causes a rise in the dye adsorption (from 30.05 mg/g for a mass of 20 g to 98.02 mg/g for a mass of 200 mg). This is because the accessibility of the available sites on the adsorbent surface for the fixation of the dye, which is methylene blue, favors the discoloration phenomena.

3.2.2. Influence of the Contact Time on Methylene Blue Adsorption

The goal of this study is to see how the methylene blue adsorption capacity on Ba_0.54Na_0.46Nb_1.29W_0.37O₅ changes over time. The methylene blue concentration in the solution reduces over time, according to the data. This decline is rapid during the first 40 min of contact between methylene blue and Ba_0.54Na_0.46Nb_1.29W_0.37O₅ (Figure 5). It then slows down until the methylene blue concentration at equilibrium (C_e) is nearly constant.

By analyzing the curve shown in Figure 5, we deduce that the capacity of the adsorption for methylene blue rises when the time of the Ba_0.54Na_0.46Nb_1.29W_0.37O₅ increases. The balance is reached after exceeding the first 40 min. As a result, each time that is greater will be considered an equilibrium time. Figure 5 shows the absorbance of methylene blue on a Ba_0.54Na_0.46Nb_1.29W_0.37O₅ synthesized sample as a function of adsorption time by a UV–Vis spectrometer. The sample, as illustrated in Figure 5, can adsorb and remove more than 97% of methylene blue (initial concentration of 10 mg/L) in 5 min at ambient temperature before changing to a colorless solution. The maximum adsorption capacity of the prepared sample Ba_0.54Na_0.46Nb_1.29W_0.37O₅ was 19.41 mg/g (see Figure 5). It was shown that the compound Ba_0.54Na_0.46Nb_1.29W_0.37O₅ has a significant capacity for the adsorption of methylene blue.

3.3. Isotherm Studies

The adsorption isotherms show how the methylene blue dye is distributed between the solution and the adsorbent, Ba_0.54Na_0.46Nb_1.29W_0.37O₅, as the adsorption process nears equilibrium. There are various isotherm models that can be utilized, but the Langmuir and Freundlich models are the most commonly applied. The two models given below were used to examine the data from adsorption isotherms [35,36].

To represent the adsorption behavior of homogenous surfaces, the Langmuir Equation (2) has been modified. The Langmuir adsorption model is used with the following assumptions: (1) adsorption sites that are uniformly strong; (2) monolayer coverage; and (3) no lateral contact between adsorbed molecules. The linear form of this isotherm is shown below [37]:

$$\frac{1}{q_e}=\frac{1}{q_m}+\left(\frac{1}{K_L{q}_m{C}_e}\right)$$

(2)

where:

$q_e$ (mg/g) is the amount of dye adsorbed at equilibrium.

$C_e$ (mg/L) is the equilibrium concentration.

$K_L$ (L/mg) is the Langmuir constant and $q_m$ is the monolayer adsorption capacity.

A dimensionless term known as the $R_L$ Equation (3) separation factor can also be used to explain the basic property of the Langmuir isotherm. This factor is applied to assess the “favorability” of an adsorption system. The following is its definition [38]:

$$R_L=\frac{1}{1+K_L{C}_0}$$

(3)

On the other hand, Freundlich accepts the surface’s heterogeneity and assumes that absorption occurs at places with various adsorption energies. The amount of adsorption energy depends on the covering area [39]. In Equation (4), the Freundlich isotherm is depicted:

$$q_e=K_F{C}_e^{\frac{1}{n}}$$

(4)

where:

$q_e$ is the amount of solute adsorbed per unit weight of adsorbent (mg.g⁻¹).

$C_e$ is the equilibrium concentration.

$K_F$ is the Freundlich constant, it stands for the adsorption capacity.

(n) is the heterogeneity factor. At n = 1, adsorption is linear, meaning that sites are homogeneous and there is no interaction between the adsorbed species.

$\frac{1}{n}$ represents the adsorption intensity:

Adsorption is advantageous when $\frac{1}{n}<1$ adsorption sites appear;

Adsorption is favorable when $\frac{1}{n}=1$, adsorption sites appear, the adsorption capacity increases while new adsorption sites appear;

When $\frac{1}{n}>1$ adsorption is less advantageous, adsorption bonds weaken and adsorption capacity decreases [40,41].

Let’s have a look at the models mentioned above. To measure the adsorption capacity of the Ba_0.54Na_0.46Nb_1.29W_0.37O₅ powders, the Langmuir isotherm equation (Equation (2)) was used to calculate the adsorption data. The data had a good linear fit on the Langmuir plot (Figure 6), and the calculated q_m and $K_L$ parameters from slope and intercept are listed in

Table 5. The Freundlich and Langmuir models’ adsorption characteristics.

Isotherme of Langmuir	Isotherme of Freundlich
$K_L$ (L/mg) = 0.002	$K_F$ (mg/g) = 0.022
qm,cal (mg/g) = 20.83 monocouche	n = 1.56
R2 = 1	R2 = 0.98625
$R_L$ = 0.02

. The coefficient of the correlation (R²) is equal to 1. The $R_L$ value calculated is 0.02, demonstrating that the adsorption is effective. This good agreement between the results and the Langmuir adsorption model is based on methylene blue monolayer coverage on homogeneous Ba_0.54Na_0.46Nb_1.29W_0.37O₅ sites, uniform adsorption energy, and no interaction between methylene blue species adsorbed on surrounding sites. The Freundlich model was used to plot the adsorption data (Figure 7). Table 5 lists the calculated numerical values of $K_F$ and (n). The numerical result of n = 1.56 implies that heterogeneous site adsorption is advantageous. Nonetheless, the Langmuir isotherm provides the greatest fit for the experimental data based on the correlation coefficient (R²) values in this investigation.

3.4. Kinetics Studies

The literature provides several formalisms for describing adsorption kinetics. All of these formalisms provide some information about the adsorption rate and process. The pseudo-first-order and pseudo-second-order models were used to characterize the adsorption kinetic mechanism in this investigation [42,43,44].

The pseudo-first-order kinetic model Equation (5) is written as follows:

$$\frac{d{q}_t}{dt}=k_1\left(q_e-q_t\right)$$

(5)

$q_e$ and $q_t$ are adsorption capacity (mg/g) at equilibrium and at time t, respectively.

$k_1$ is the adsorption rate constant (min⁻¹).

Once the boundary conditions have been applied and the integration has been completed, Equation (6) can be expressed linearly:

$$\log \left(q_e-q_t\right)=\log \left(q_e\right)-k_1\frac{t}{2.303}$$

(6)

The curve of $\log \left(q_e-q_t\right)$ as a function of time (t) is shown in Figure 8. The values of the $k_1$ and $q_e$ parameters are determined from the Figure 8 and are provided in

Table 6. Details of the kinetic models during the adsorption of methylene blue on the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O_5.

${\mathit{q}}_{\mathit{e},\mathit{e}\mathit{x}\mathit{p}} (\mathbf{mg}/\mathbf{g})$	Pseudo-First Order			Pseudo-Second Order
	${\mathit{q}}_{\mathit{e},\mathit{c}\mathit{a}\mathit{l}\mathit{c}} (\mathbf{mg}/\mathbf{g})$	${\mathit{k}}_1 \left(\mathbf{min}\right)$	R2	${\mathit{q}}_{\mathit{e},\mathit{c}\mathit{a}\mathit{l}\mathit{c}} (\mathbf{mg}/\mathbf{g})$	${\mathit{k}}_2 (\mathbf{g}/\mathbf{min}.\mathbf{mg})$	R2
19.41	20.83	0.016	0.9479	20.83	3.69 10−5	0.9960

. The fact that log $\left(q_e-q_t\right)$ is not linear can be seen from the examination of $\log \left(q_e-q_t\right)$ over time, and hence the adsorption of methylene blue on Ba_0.54Na_0.46Nb_1.29W_0.37O₅ cannot be explained by the pseudo-first order equation.

Following this result, the second model was applied to fit the experimental data from the kinetic trials. The second-order pseudonym Equation (7) is written in linear form:

$$\frac{t}{q_t}=\frac{1}{k_2{q}_e^2}+\frac{t}{q_e}$$

(7)

$q_e$ and $q_t$ designate the absorption capacity (mg/g) at equilibrium and time t, respectively.

$k_2$ represents the constant rate of adsorption (g/mg.min).

Figure 9 represents the variation of the $\frac{t}{q_t}$ as a function of time (t). This figure allows us to determine the parameters $q_e$ and $k_2$. Table 6 gathers the calculated values corresponding to these parameters. Figure 9 shows a linear variation of the evolution of $\frac{t}{q_t}$ versus time (t). This linear variation explains that the pseudo-second order model is adequate for the kinetic behavior of methylene blue adsorption on the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O₅. To fit the experimental data, the following Equation (8) has been applied:

$$\frac{1}{q_t}=0.0326t+0.0476$$

(8)

The obtained value of the correlation coefficient (R²) is around 0.9960.

According to the Langmuir model of adsorption, adsorption occurs in a single monolayer on energetically equivalent adsorption sites, with no interaction between the adsorbed molecules. So, in this case study, the nature of the adsorption is physisorption [45].

4. Conclusions

During the first portion of this project, the various methods for desalinating water were examined. In the second section, we prepared a crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O₅ with a structure of the type tetragonal tungsten bronze (TTB). The characterization by X-ray diffraction and Raman spectroscopy was applied to improve the structural study. The Rietveld method was used to determine the space group (P4bm), cell parameter (a = b = 12.3687 ± 0.02 Å and c = 3.9328 ± 0.02 Å), and the atomic positions; as well as the Raman data attributed to the different bonds forming the crystalline phase Ba_0.54Na_0.46Nb_1.29W_0.37O₅. We investigated its ability to adsorb methylene blue and discovered that it is an effective material for eliminating organic impurities, suggesting that it could be used in water treatment. The removal kinetics for methylene blue adsorption is one of the most important features of this adsorption behavior. The adsorbents’ methylene blue (mg/g) adsorption capabilities at equilibrium and time t (min) are $q_e$ and $q_t$, respectively. $k_1$ is the pseudo first-order rate constant (mg/g/min), whereas $k_2$ is the pseudo second-order rate constant (mg/g/min). The slope and intercept of $\log \left(q_e-q_t\right)$ versus time (t) and $\left(\frac{t}{q_t}\right)$ versus time (t), respectively, can be used to get $k_1$ and $k_2$ values from straight lines. With R values of 0.9479 and 0.9960 for the Ba_0.54Na_0.46Nb_1.29W_0.37O₅, respectively, the pseudo-second-order kinetic model matches the adsorption kinetics data well in comparison with the pseudo-first-order model.