Mechanosynthesis of Mesoporous Bi-Doped TiO₂: The Effect of Bismuth Doping and Ball Milling on the Crystal Structure, Optical Properties, and Photocatalytic Activity

Abstract

In this work, we reported obtaining mesoporous Bi-doped TiO₂ by mechanosynthesis and bismuth loading of 0%, 1%, 3%, 5%, and 10% (milled TiO₂, TiO₂ Bi 1%, TiO₂ Bi 3% TiO₂ Bi 5%, and TiO₂ Bi 10%, respectively). The effect of bismuth doping and ball milling on the crystal structure, optical properties, and photocatalytic performance of Bi-doped TiO₂ mesoporous samples under UV, visible, and sun irradiation was investigated. According to the results of the Rietveld refinement, the estimated chemical formulas for the TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi10% samples were Ti_0.99Bi_0.01O₂, Ti_0.97Bi_0.03O₂, Ti_0.96Bi_0.04O₂, and Ti_0.91Bi_0.09O₂ respectively. The incorporation of Bi into the TiO₂ lattice causes the crystallite size to decrease and, consequently, the absorption spectrum of TiO₂ to extend into the visible region of the electromagnetic spectrum, resulting in a lower band gap (E_g) value. Bi-doped TiO₂ mesoporous samples had E_g values of 2.90 eV, 2.83 eV, 2.77 eV, and 2.70 eV for the TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi 10% samples, respectively. Photocatalytic removal of methylene blue (MB) data fit well for second-order kinetics. Photocatalytic activity increase followed the order of TiO₂ Bi 5% > TiO₂ Bi 10% > TiO₂ Bi 3% > TiO₂ Bi 1% > pristine TiO₂. The TiO₂ Bi 5% sample exhibited excellent photocatalytic performance for MB photodegradation under natural sunlight (89.2%).

1. Introduction

Titanium oxide (TiO₂) has now become a major material due to its applications within the environmental arena, especially in sustainable energy. Amongst these applications, its use as a photo-anode in solar cells [1], a photocatalyst in the degradation of organic pollutants [2], in the production of H₂ [3], and in the manufacture of lithium batteries [4] are the most prominent. The last is mainly due to its chemical and physical properties and relatively low cost [5].

TiO₂ has been widely used as a photocatalyzer to degrade a large number of organic molecules, such as dyes [6,7,8,9,10,11], drugs [12,13,14,15], and pesticides [16,17,18], amongst other molecules. However, its use is limited to processes in which the light source is in the UV range due to its forbidden energy gap or band gap value (E_g), which ranges from 3.0 to 3.2 eV, depending on its crystalline phase. The anatase crystalline phase is preferred in photocatalysis because it is obtained at lower temperatures and has a higher degree of hydroxylation on its surface with respect to rutile and brookite, which contributes to the better performance in the adsorption and photodegradation of organic molecules [5].

Numerous efforts have been made to extend the energy absorption to the visible region of the electromagnetic spectrum and decrease the value of the band gap of the TiO₂ anatase phase, with the aim of achieving the activation of this semiconductor with visible and even solar light. The doping of TiO₂ anatase phase with metallic and nonmetallic elements serves to achieve the modification of this optical property; some of the most-used elements are C, N, and Fe [19,20,21,22]. The degree of modification of the optical and photocatalytic properties of doped TiO₂ depends on its characteristics, such as porosity, morphology, crystallite size, and the presence of other phases such as rutile and brookite; in turn, these characteristics depend a lot on the method and synthesis variables.

There are some interesting research papers in which TiO₂ doping has been reported with Bi using the solvothermal and sol–gel methods, the latter being the most researched. The literature reports that the absorption spectrum of Bi-doped TiO₂ has been shifted towards the visible region of the electromagnetic spectrum, significantly reducing the value of E_g and improving its photocatalytic activity; however, improving both properties strongly depends on the level of bismuth doping, morphology, and crystalline phase, and, at the same time, on the synthesis method. Wang et al. obtained photocatalysts of Bi-doped anatase TiO₂ hollow thin sheets by the hydrothermal method with Eg values of 3.16 eV and 2.97, the former corresponding to a sample with 0.6 ato. % Bi, and the latter to a sample containing 0.8 at. % Bi into TiO₂ and with the presence of Bi₂O₃ [23]. Xu et al. obtained Bi-doped titania-coated carbon spheres by the sol–gel method and using carbon spheres; they investigated the effects of Bi content on the physical structure and photocatalytic activity of hollow titanium spheres, and reported that the crystallite size of the titania becomes smaller when the doping amount of Bi ions increases, and that Bi species in the sample with Bi at. percent of 4% were present in the form of Bi₂O₃ [24].

There are less popular synthesis methods, but these are more simplified and more environmentally sustainable, such as mechanosynthesis, which allows for the incorporation of atoms as dopants into the crystalline structure of metal oxides, due to the high energy generated with elastic shocks between reagents and grinding media, in addition to causing defects in the crystal lattice [25]. Moreover, this method is considered a type of green synthesis, as the use of solvents is not required. It is to be expected that the incorporation of a dopant such as Bi³⁺ into the TiO₂ anatase phase will improve the absorption of energy into the visible region of the electromagnetic spectrum, regardless of the synthesis method; however, the magnitude of such an improvement depends on the synthesis method and the degree of doping achieved. For these reasons, it is important to investigate how doping and grinding affect the crystal structure of TiO₂, crystallite size, and morphology, and how these, in turn, are related to the modification of the Eg values of the samples.

This research reported the obtaining of Bi-doped TiO₂ mesoporous samples by mechanosynthesis. The effect of bismuth doping and grinding on structural, morphological, and porosity characteristics, as well as their effect on optical properties and photocatalytic activity, was investigated.

2. Materials and Methods

2.1. Chemicals

TiO₂ anatase phase (pristine TiO₂ sample), previously obtained following the methodology of our working group [26], involved Bi(NO₃)₃·5H₂O (98%, Aldrich, Saltillo, Mexico) and C₁₆H₁₈ClN₃S (MB, 99%, Aldrich, Saltillo, Mexico).

2.2. Synthesis of Bi-Doped TiO₂

TiO₂ pristine sample and a certain previously determined amount of Bi (NO₃)₃·5H₂O were manually mixed in an agate mortar; the mixture was placed in a zirconia container with zirconia grinding media, and mechanically ground at 300 rpm using a High Energy Planetary ball mill Fritsch, Pulverisette 6 model. The load-to-balls ratio was 1:20 and the grinding time was two periods of 30 min. At the end of the grinding time, the product was heat-treated at a temperature of 450 °C for 4 h and subsequently characterized. The experiment was repeated several times by varying the amount of the bismuth precursor to obtain different degrees of doping (Ti_1−xBi_xO₂, x = 0–0.1). Samples synthesized with values of x = 0, x = 0.01, x = 0.03, x = 0.05, and x = 0.1 were identified as milled TiO₂, TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi 10%, respectively.

2.3. Photocatalytic Activity Evaluation

The photocatalytic performance of the samples was evaluated using MB as a model molecule. The standard solution used for photocatalytic experiments (100 mg/L) was prepared by dissolving 100 mg of MB in 1 L of deionized water. An aqueous dilution of this dye (100 mL, 20 mg/L) was put in contact with each of the catalysts (1.0 g/L), and a solution of 0.1 M NaOH was used to adjust the pH value to 8. The mixture was stirred for 2 h in the dark to reach the adsorption equilibrium. Next, the solution with the catalyst was irradiated with visible light using a Pen-Ray^® Xenon Lamp (λ = 467 nm, 1.8 Watts).

Aliquots of 2 mL were collected at the following time intervals: 5, 10, 15, 30, 45, and 60 min. Subsequently, each aliquot was centrifuged and its absorbance at 664 nm was read with a UV–Vis spectrophotometer (Jenway-6705); the MB concentration was calculated using a calibration curve that was obtained previously with standard solutions at different concentrations. A double-jacketed glass reactor and a water-cooling bath were used to keep the temperature at 25 ± 1 °C. The photolysis of MB solution was performed with visible light for 2 h. A magnetic stirrer was used to ensure the homogeneity of the solution.

The effect of the amount of catalyst (0.5 g/L, 1.0 g/L, and 2.0 g/L) and the type of irradiation (UV light, visible light, and natural sunlight) on the photodegradation efficiency of MB was investigated; an irradiation time of 1 h was used. For photodegradation experiments under UV light irradiation, a Pen-Ray^® Mercury Lamp (λ = 254 nm, irradiance = 4400 µW/cm², 300 V) was used, and for photodegradation experiments under natural sunlight, an irradiance of 320.68 W/m² was registered. A catalyst concentration of 0.5 g/L and an irradiation time of 60 min were used. Photocatalysis and photolysis experiments were performed in triplicate.

2.4. Characterization

The infrared spectra were collected in the range of 4000 to 400 cm⁻¹ with 4 cm⁻¹ resolution using a Thermo Scientific Nicolet iS10 spectrometer (Waltham, MA, USA) with attenuated total reflectance (ATR) modality. X-ray photoelectron spectra (XPS) measurements were performed with a Thermo Scientific K-Alpha+ Model spectrometer, using the AlKα X-ray beam (1486.6 eV) with the C 1s (peak at 284.8 eV) as a reference. N₂ adsorption–desorption measurements were performed in a Quantachrome Instruments Autosorb 1 model (Boynton Beach, FL, USA). The samples were degassed at 100 °C for 12 h; the specific surface areas were calculated using the Brunauer–Emmett–Teller (BET) theory, and the pore size distributions and pore volumes were calculated with the desorption data from adsorption-desorption isotherms (based on the Barrett–Joyner–Halenda (BJH) theory). The morphologies of the samples were investigated with a JEOL JSM-7800F electron microscope (Salem, MA, USA). The diffractograms of the samples were obtained using a Rigaku model Ultima IV equipment with D/teX detector (The Woodlands, TX, USA), Bragg–Brentano geometry, with Cu k_α X-ray source at a voltage of 40 kV and current of 40 mA, and scanning in the 10–80° 2θ range at a speed of 2° min⁻¹. Rietveld refinement of the observed XRD patterns was performed with the FULLPROF suite software, using the conditions described above. The spatial group I4₁/amd was used for the anatase and lattice parameters previously obtained by the Le Bail setting of the diffractograms with the FullProf software. The UV–Vis diffuse reflectance spectra and the UV–Vis absorbance spectra were obtained using a Perkin-Elmer Lambda 35 UV–Visible spectrophotometer (Houston, TX, USA).

3. Results

3.1. Synthesis and Characterization

Figure 1 shows the ATR-FTIR spectra of Bi-doped TiO₂ samples obtained by mechanosynthesis; the spectra of all samples showed the typical broad band of the Ti–O bond stretch from 800 cm⁻¹ to 400 cm⁻¹, as well as absorption bands of the bending and stretching of the O–H bond of the OH group in 1640 cm⁻¹ and between 3600 and 3000 cm⁻¹, respectively. The small absorption bands around 3725 and 3693 cm⁻¹ correspond to the O–H bond stretch of the groups OH free on the surface of the material, which are associated with the planes with higher electronic density; in the case of anatase, the plane with the highest electronic density was (101). In addition, it has been reported that such superficial OH groups occur when oxygen vacancy exists on the surface of the material [27]. The presence of an OH group on the surface of the material is favorable because they react with the holes (H⁺) generated in photocatalysis when the material is activated, forming hydroxyl radicals (HO*) and making the photocatalytic process more effective [23].

The XPS technique was used to analyze the chemical structures and electronic states of pristine TiO₂ and Bi-doped TiO₂ samples. Figure 2A shows the XPS survey spectra of TiO₂ Bi 1% and TiO₂ Bi 5% samples, which contain the peaks of Ti, Bi, O, and C elements; for purposes of comparison, the XPS survey spectrum of pristine TiO₂ is also shown in this figure, which contains the peaks of Ti, O, and C. The observed C 1s peak was used as an energy reference for determining the peak positions of core-level spectra.

Figure 2B–D show the high-resolution XPS spectra of the Ti 2p, Bi 4f, and O 1s regions, respectively, on the surface of TiO₂ Bi 1% and TiO₂ Bi 5% samples, as well as pure anatase (pristine TiO₂). The Ti2p spectra are shown in Figure 2B, where it is possible to observe two peaks at 458.88 eV and 464.64 eV assigned to Ti2p_3/2 and Ti2p_1/2, which are characteristic of Ti⁴⁺. The spectra of doped samples show a shift of these peaks towards smaller binding energies due to the formation of Ti–O–Bi bonds and the creation of surface defects [28]; this same effect was observed by Li et al., who synthesized titanium oxide doped with Bi³⁺ using a modified sol–gel method [29]. The Bi4f region (Figure 2C) is formed by three peaks; the first peak located at 156.9 eV is attributed to Bi⁰. According to Wu et al., the reason for Bi⁰ species formation in samples is uncertain; the remaining carbonaceous species might have reduced partial Bi³⁺ to Bi⁰ during the calcination [30] and during the ball milling, this last considering that high temperature and energy values can be reached during grinding. Other authors report that such species also cause modifications to the X-ray diffraction pattern of samples, causing displacement at a larger 2θ degree [31]. Bi⁰ could be decorating the surface of the TiO₂ Bi 1% and TiO₂ Bi 5% samples.

The peaks at 164.6 eV and 159.3 eV for both samples can be ascribed to Bi 4f_5/2 and Bi 4f_7/2, respectively, corresponding to Bi³⁺, whereas the peaks centered at 163.4 and 158 eV for the TiO₂ Bi 1% sample and the peaks at 163.1 and 158 for the TiO₂ Bi 5% sample are attributed to Bi 4f_5/2 and Bi 4f_7/2 of Bi ⁴⁺. The peaks at 159.3 and 158 eV ascribed to Bi 4f_7/2 are the signals corresponding to Bi³⁺ and Bi⁴⁺, respectively, indicating a partial oxidation of the centers from Bi³⁺ to Bi⁴⁺; Wang et al., (2016) and Hao et al., (2019) mention that the peaks at 163.7 eV and 164.5 eV, corresponding to Bi 4f_5/2, and the peaks at 159.2 eV and 158.4 eV, corresponding to Bi 4f_7/2, are attributed to the oxidized bismuth layers [23,32].

The O1s peak of the pristine TiO₂ sample consists of two signals at 530.08 and 531.97 eV corresponding to the O–Ti bond and the O–H bond of hydroxyl groups on the surface of the material, respectively. Bi-doped samples show three signals: one around 529.78 eV corresponding to the O–Ti bond, which is displaced to lower bond energy values due to the incorporation of bismuth into the crystal lattice [33], another at 530.58 eV indicating the presence of the O–Bi bond and increasing with respect to the amount of bismuth present in the sample, and, finally, one at 531.38 eV attributed to the O–H bond, indicating the presence of hydroxyl groups on the surface of the material (Ti–OH) [29,34]. The intensity of the signal of the O–H bond decreases as the degree of doping increases, which may be an indication that hydroxyl groups interact with Bi, forming Bi–O–Ti (Figure 2D).

Figure 3A–F shows the micrographs of pristine TiO₂, milled TiO₂, and Bi-doped TiO₂ samples. It is observed that the pristine TiO₂ sample (Figure 3A) had a porous morphology, consisting of agglomerates of small particles. On the other hand, it is observed in the micrographs of the undoped sample (milled TiO₂, Figure 3B) and in those of TiO₂ samples doped with bismuth (Figure 3C–F) that the morphology changed markedly and had less porosity than the pristine TiO₂ sample. It is well known that mechanical grinding produces changes in morphology, particle size distribution, and porosity. Porosity in photocatalyst materials is a desirable characteristic, because the number of active sites for the adsorption of molecules or compounds to be photodegraded increases with porosity. The elemental mapping of Ti, Bi, and O on the TiO₂ Bi3% sample is presented in Figure 4; a uniform dispersion of the three elements in this sample is observed.

Figure 5 shows N₂ adsorption–desorption curves of the TiO₂ powder prepared by mechanosynthesis at different Bi-doping concentrations and calcined at 450 °C. It can be observed that the pristine TiO₂, milled TiO₂, and TiO₂ 1% samples have an isotherm of type IV, which is characteristic of mesoporous powders. On the other hand, the sample with 5% bismuth (TiO₂ Bi 5% sample) presents a mixture of isotherm types II and IV. At a high relative pressure from 0.40 to 0.95, all isotherms of milled samples exhibited a hysteresis loop of type H₃, indicating that they contain mesopores (2–50 nm).

Table 1. Specific surface area (S_BET), mean pore diameter (D_p) and mean pore volume (V_p) of the samples pristine TiO₂, milled TiO₂, TiO₂ Bi 1%, and TiO₂ Bi 5%.

Sample	SBET (m2/g)	Dp (nm)	Vp (cm3/g)
pristine TiO2	138.7	5.86	0.300
milled TiO2	74.0	3.50	0.191
TiO2 Bi 1%	116.7	3.40	0.196
TiO2 Bi 5%	59.1	3.48	0.201

presents the values of the specific surface area (S_BET) determined by the BET technique, in which it can be observed that the pristine TiO₂ sample had a S_BET value of 138.7 m²/g and that the milled sample without doping (milled TiO₂) and the milled and doped samples with bismuth (TiO₂ Bi 1% and TiO₂ 5%) had smaller specific surface area values.

Figure 5 also shows the Barrett–Joyner–Halenda (BJH) pore size distribution of the samples, determined from the desorption branches. It can be seen that the pristine TiO₂ sample had a high quantity of pores with a size less than 10 nm; on the other hand, samples subjected to mechanical grinding and bismuth doping had a wider pore distribution. However, the size of their pores is in the range of mesopores, as can be seen from the mean pore diameter values (D_p) listed in Table 1, ranging from 3.40 to 3.50 nm. The pristine TiO₂ sample had an average pore size value of 5.86 nm and a relatively high mean pore volume value (V_p) of 0.300 cm³/g, compared with the ground sample and ground and doped samples. The milled TiO₂ sample had two maximum peaks, and its pore size distribution was not monodisperse. The decrease in S_BET value is related to the decrease in D_p and V_p; such a decrease is due to both grinding and bismuth doping, as can be seen from the S_BET, D_p, and V_p values listed in Table 1. Mechanical grinding produces changes in the morphology, particle size, and porosity (Figure 3C–F); the action of the grinding media on the TiO₂ pristine sample (V_p = 0.300 cm³/g) causes the partial destruction of the pores, leading to a reduction in porosity up to 33% for the TiO₂ 5% sample (V_p = 0.201 cm³/g). Henych et al., (2014) mentioned that the pores of a sample must be large enough that the light affecting the photocatalysis process can enter them and activate the surface [35]. The Bi-doped TiO₂ samples obtained in this work by mechanosynthesis remained mesoporous, a characteristic that will allow them to have high photocatalytic activity.

Figure 6A shows the diffraction patterns of the synthesized samples; diffractograms of all samples show that the main phase obtained corresponds to anatase (PDF #21-1272). The diffractogram of the sample that was milled without the addition of bismuth salt (milled TiO₂) mainly presents the diffraction peaks of the anatase phase, and a small diffraction peak at 2θ equal to 30.8°, which is assigned to the plane (121) of the TiO₂ brookite phase (PDF #29-1360). It is well known that the energy produced by mechanical grinding promotes the formation of structural defects [36], which at the same time leads to the partial transformation of the anatase phase to the brookite phase. The incorporation of the Bi³⁺ dopant into the crystal lattice of anatase also contributes to the formation of brookite, as can be seen in the diffractograms of TiO₂ samples Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi 10%. It is known that phase transformations can occur when oxygen vacations are formed, especially on the surface of the material, where the breaking of bonds is favored, thus resulting in a rear coupling of atoms [37].

The presence of brookite in the Bi-doped TiO₂ samples has previously been observed by doping with other types of atoms such as Sn [38] and even Bi [35]. Although it is possible to form other polymorphs such as rutile, nitrate ions (which are present in bismuth nitrate salt) may facilitate the formation of brookite [39]. On the other hand, a weak diffraction peak corresponding to a bismuth oxide (Bi₂O₃, PDF #50-1088) in the diffractogram of the sample TiO₂ Bi 10% is observed (Figure 6A), which is because a greater number of atoms of this element were used. With increasing Bi content, the peaks slightly broaden and the crystallite size is reduced, indicating a slight distortion in the crystal structure. This may be attributed to the formation of crystallographic point defects due to the substitution of Ti⁴⁺ by Bi³⁺ ions. Most bismuth ions might be inserted into the structures of TiO₂ located at the interstices or might occupy some of the titanium sites to form a solution with bismuth–titanium solids. It has been reported that, because the ion radius of the Bi³⁺ (1.03 Å) is greater than that of the Ti⁴⁺ (0.61 Å) [40,41], it is first introduced in the interstitials of the crystal lattice of the anatase, causing a contraction in the lattice parameters [35]. The higher the degree of doping, the more bismuth is placed in the sites corresponding to Ti⁴⁺, which causes the expansion of the unit cell. The latter effect has previously been reported when TiO₂ is doped with bismuth using the sol–gel method [42].

An amplification was performed at the highest intensity peak of the diffractograms, which corresponds to the plane (101) of the anatase (Figure 6B); from this figure, it is possible to appreciate its displacement to 2θ degrees greater than 2 with little dopant and then to smaller 2θ degrees when we increase the amount of bismuth, which is also indicative of the modification of the unit cell of the anatase. The shift to degrees greater than 2θ may also be related to the presence of Bi⁰ on the sample surface [31]. The TiO₂ Bi 1% and TiO₂ Bi 5% samples contain Bi⁰, based on the XPS spectra presented in Figure 2C.

To corroborate the above, an analysis by the Rietveld method of structural refinement was performed on pristine TiO₂, TiO₂ Bi0% (milled TiO₂), and on the Bi-doped TiO₂ samples. Figure 7 shows the adjustments of pure anatase, as well as samples subjected to mechanical grinding with and without doping.

Table 2. Parameters of the anatase structure for the samples.

	Pristine TiO2	Milled TiO2	TiO2 Bi 1%	TiO2 Bi 3%	TiO2 Bi 5%	TiO2 Bi 10%
Space group	I41/amd	I41/amd	I41/amd	I41/amd	I41/amd	I41/amd
a (Å)	3.7829 (3)	3.7837 (16)	3.7765 (2)	3.7858 (1)	3.7853 (10)	3.7842 (3)
c (Å)	9.4930 (9)	9.4834 (6)	9.4715 (3)	9.4910 (6)	9.4868 (10)	9.482 (13)
V (Å3)	135.847	135.768	135.08	136.02	135.915	135.783
Formula	TiO2	TiO2	Ti0.99Bi0.01O2	Ti0.97Bi0.03O2	Ti0.96Bi0.04O2	Ti0.91Bi0.09O2
Rp, Rwp, Rexp	8.30, 9.13, 4.34	7.60, 8.35, 4.56	11.5, 11.3, 4.90	9.05, 9.44, 4.70	3.78, 4.94, 2.68	18.4, 16.5, 13.1
X2	4.43	3.40	5.29	4.03	3.40	1.59
% Brookite	0	17	11.85	7	19.05	0

shows the lattice parameters of the anatase present in each of the synthesized samples. The table shows that the TiO₂ Bi 1% sample has a decrease in cell volume, while samples loaded with 3% and 5% of bismuth have an expansion in the unit cell, since, as mentioned above, the unit cell of the anatase is distorted due to the incorporation of Bi³⁺ atom, which is larger than that of Ti⁴⁺. According to the results of the Rietveld refinement, the quantities of the doping incorporated in the TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi10% samples were 1%, 3%, and 4%, respectively, so, the estimated chemical formula for these samples are Ti_0.99Bi_0.01O₂, Ti_0.97Bi_0.03O₂, Ti_0.96Bi_0.04O₂, and Ti_0.91Bi_0.02O₂ respectively.

The lattice parameters and cell volume of the milled TiO₂ sample were smaller than those of the pristine TiO₂ sample (Table 2), indicating that grinding causes distortion of the crystal lattice of the TiO₂ anatase phase, causing the formation of TiO₂ brookite phase by 17%, and an increase in crystallite size. Table 2 also shows that the percentage of TiO₂ phase brookite was between 7% and 19.05% for doped samples with 1%, 3%, and 5% of Bi; the brookite phase was not formed in the TiO₂ Bi 10% sample, but bismuth oxide (B₂O₃) was formed in a small amount. It has previously been reported that TiO₂ phase mixtures may be beneficial for photocatalysis processes, as the recombination of electron–hollow pairs can be reduced [43].

The average crystallite sizes of TiO₂ anatase in Bi-doped samples were determined from the Debye-Scherrer equation, Equation (1):

$$\mathrm{D}=\raisebox{1ex}{$\mathrm{K}\mathsf{\lambda }$}\!\left/ \!\raisebox{-1ex}{$\mathsf{\beta }\cos \mathsf{\theta }$}\right.$$

(1)

where D is the size of crystallite, K is a dimensionless shape factor (0.89), λ is the wavelength of Cu Kα radiation having a value of 1.5406 Å, β is the broadening of the peak of higher intensity (101), and θ is the angle of X-ray diffraction. The average crystallite size of all the samples was 18.28, 19.11, 18.12, 18.05, 17.78, and 17.15 nm, corresponding to the pristine TiO₂, milled TiO₂, TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi 10% samples, respectively. It is observed that the crystallite size of anatase increased from 18.28 nm (TiO₂ pristine) to 19.11 nm (milled TiO₂) by grinding action, which is because the energy that is generated causes changes in the crystal lattice of TiO_2, decreasing the lattice parameter c and the cell volume; such a change in the lattice in turn causes brookite to form, as can be seen in Table 2 and Figure 6A. On the other hand, it is observed that the average crystallite size decreased with an increasing concentration of Bi. Since the ionic radius of Bi³⁺ is different from that of Ti⁴⁺, an increase in Bi concentration leads to reduced intensity with increased full width at the half-maximum of the Bragg peak. Furthermore, it is very challenging to substitute smaller-radius Ti⁴⁺ (0.61 Å) with larger-radius Bi³⁺ (1.03Å). The substitution of Ti⁴⁺ for Bi³⁺ might create oxygen vacancies for the charge compensation in the TiO₂ lattice. Moreover, besides Bi³⁺ at the Ti⁴⁺ sites, a large fraction of ions may stay on the surface of particle and, hence, the doping of Bi³⁺ can inhibit the grain growth of the TiO₂, which typically leads to a reduction in crystallite size. Ali et al., (2020) reported this same behavior in TiO₂ samples doped with Mg²⁺ [44]. Xu et al., (2011) obtained Bi-doped TiO₂ composite hollow spheres by the sol–gel method, and reported a decrease in the crystallite size of the anatase from 16.7 to 10.7 nm when increasing the content of Bi³⁺, which was because the bismuth species located at the edges of the crystallite prevented growth [24]. Similar crystallite sizes up to 17 nm were reported by Murcia-Lopez et al., (2011), who synthesized TiO₂ doped with Bi³⁺ by the hydrothermal method [45]. Compared to the hydrothermal and sol–gel methods, mechanosynthesis has the advantages of being inexpensive, solvent-free, and applicable on an industrial scale.

Figure 8A presents the absorption spectra of the Bi-doped TiO₂ samples; absorption spectra of pristine and milled TiO₂ are also included. With the incorporation of Bi³⁺ into the TiO₂ crystal lattice, it is possible to increase the absorption of light in the visible range of the electromagnetic spectrum; the samples with the highest absorption of light in the visible region are those containing a greater amount of the dopant. The shift of the absorption edge to the visible region indicates the modification of the E_g value; the values of this optical property were calculated using the Tauc plot (Figure 8B) considering n = 2 for allowed indirect transitions. The calculated values of E_g are listed in Table 3 and it is seen that the value of E_g decreased with an increasing concentration of Bi in the TiO₂ crystal lattice. The shift in the absorption band edge in doped TiO₂ samples might also be due to the shallow trap states created by oxygen vacancies associated with Ti³⁺ and Bi³⁺.

It has been reported that the presence of vacancy states just below the conduction band is related to the oxygen vacancy associated with Ti³⁺ and is responsible for the band narrow gap in TiO₂ [46]. In this work, doping with Bi is the main reason for lowering the E_g of TiO₂.

Table 3. E_g values of Bi-doped TiO₂ samples obtained by mechanosynthesis compared with the reported values in the literature for Bi-doped TiO₂ samples obtained with other methods.

Sample	Eg (eV)	Synthesis Method
TiO2 Bi 1% (This work)	2.90	Mechanosynthesis
TiO2 Bi 3% (This work)	2.83	Mechanosynthesis
TiO2 Bi 5% (This work)	2.77	Mechanosynthesis
TiO2 Bi 10% (This work)	2.70	Mechanosynthesis
Bi-doped TiO2: 0.6–1.7% [23]	3.16–2.97	Hydrothermal
Bi/Ti: 0.25–1 [42]	3.04–2.90	Sol gel/supercritical drying
Bi-doped TiO2: 0.25–5% [47]	3.19–2.97	Sol gel/Ultrasound assisted
Bi-doped TiO2: 0–10% [48]	3.08–2.80	Sol gel/assisted with propylene oxide

Table 3. E_g values of Bi-doped TiO₂ samples obtained by mechanosynthesis compared with the reported values in the literature for Bi-doped TiO₂ samples obtained with other methods.

Sample	Eg (eV)	Synthesis Method
TiO2 Bi 1% (This work)	2.90	Mechanosynthesis
TiO2 Bi 3% (This work)	2.83	Mechanosynthesis
TiO2 Bi 5% (This work)	2.77	Mechanosynthesis
TiO2 Bi 10% (This work)	2.70	Mechanosynthesis
Bi-doped TiO2: 0.6–1.7% [23]	3.16–2.97	Hydrothermal
Bi/Ti: 0.25–1 [42]	3.04–2.90	Sol gel/supercritical drying
Bi-doped TiO2: 0.25–5% [47]	3.19–2.97	Sol gel/Ultrasound assisted
Bi-doped TiO2: 0–10% [48]	3.08–2.80	Sol gel/assisted with propylene oxide

Table 3 also lists E_g values for Bi³⁺ anatase samples that were obtained by other methods. This work reported obtaining Bi-doped TiO₂ samples with lower E_g values than obtained by the hydrothermal method of the sol–gel method assisted with supercritical drying and ultrasound [23,42,47,48]. The E_g values of Bi-doped TiO₂ samples obtained by mechanosynthesis in this work are even lower than those obtained by this same method, using dopants such as sulfur and silver. Ji et al., (2009) prepared doped sulfide TiO₂ nanoparticles by ball milling, using as commercial precursors TiO₂ P25 and thiourea, and obtaining E_g values of 3.1 eV for the undoped sample and values of 2.76 and 2.83 eV for the TiO₂ P25 samples doped with 5% and 11% sulfur [49]. Ellouzi et al., (2021) prepared silver-doped biphasic TiO₂ composites via the glucose-assisted ball milling method; both anatase and rutile phases were identified in the obtained sample, and the best E_g value was 3.65 eV for the doped sample with 3% silver [50].

It is well known that the crystallite size of a semiconductor oxide affects its E_g value: the smaller the crystallite size, the lower the value of E_g, and vice versa. The crystallite size and the E_g value of the Bi-doped TiO₂ samples decreased almost linearly with the increase in the amount of bismuth used for synthesis, as can be seen in Figure 9, which indicates that the incorporation of bismuth into the TiO₂ lattice causes the crystallite size to decrease and, consequently, the absorption spectrum of TiO₂ to extend into the visible region of the electromagnetic spectrum, resulting in a lower E_g value. It is also important to consider that doping promotes the creation of new electronic levels in the band structure; possibly, this also contributed to the change in E_g values.

Figure 10 presents an outline of how mechanical grinding provides the energy needed for the formation of defects, such as oxygen vacancies, into the tetragonal structure of anatase, and, together with the heating treatment, promotes the incorporation of bismuth into the crystalline lattice of TiO₂, causing a distortion in the lattice parameters of the cell.

3.2. Photocatalytic Activity

The photocatalytic activity of the as-synthesized mesoporous Bi-doped TiO₂ samples was investigated by degrading MB. Photodegradation of this dye with mesoporous Bi-doped samples (TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi 10%) and the pristine TiO₂ sample, using visible light as a function of irradiation time, is shown in Figure 11A. MB photodegradation percentages of 38%, 54%, 60%, 74%, and 63% were obtained with pristine TiO₂, TiO₂ Bi 1%, TiO₂ Bi 3%, TiO₂ Bi 5%, and TiO₂ Bi 10%, respectively, at 60 min of irradiation (Figure 11B). The first- and second-order kinetic models (Equations (2) and (3), respectively) were used to investigate the kinetics of MB photodegradation:

$$\ln \left({\mathrm{C}}_{\mathrm{t}}|{\mathrm{C}}_0\right)=-{\mathrm{K}}_1 t$$

(2)

$$\frac{1}{{\mathrm{C}}_{\mathrm{t}}}={\mathrm{K}}_{2}t+\frac{1}{{\mathrm{C}}_0}$$

(3)

where C₀ and C_t (mol/L) are the MB concentrations at times 0 and t (min), respectively; K₁ (min⁻¹) and K₂ (mg⁻¹· L· min⁻¹) are the first- and second-order rate constants, respectively.

The variation in –ln(C_o/C_t) and 1/C_t as a function of irradiation time is shown in Figure 11B,C, for first- and second-order models, respectively, by which the rate constants (K₁ and K₂) were calculated and listed in

Table 4. Rate constants for kinetic studies of MB photodegradation using pristine TiO₂ and Bi-doped TiO₂ photocatalysts under visible light (λ = 467 nm, 1.8 Watts); 100 mL of MB solution of 20 mg/L; 1.0 g/L of catalyst concentration.

Sample	First-Order		Second-Order
	K1 (min−1)	R2	K2 (mg−1·L·min−1)	R2
pristine TiO2	7.51 × 10−3	0.8502	5.08 × 10−4	0.8796
TiO2 Bi 1%	8.98 × 10−3	0.9116	6.88 × 10−4	0.9437
TiO2 Bi 3%	1.1910−2	0.9482	1.09 × 10−3	0.9777
TiO2 Bi 5%	1.84 × 10−2	0.9796	2.02 × 10−3	0.9968
TiO2 Bi 10%	1.4210−2	0.9652	1.37 × 10−3	0.9877

. Photocatalytic removal of MB data fit well for second-order reaction kinetics. The rate constant values, K₂, followed the order TiO₂ Bi 5% > TiO₂ Bi 10% > TiO₂ Bi 3% > TiO₂ Bi 1% > pristine TiO₂; enhanced removal of MB from solution under visible light irradiation is mainly ascribed to bismuth doping. The excitation energy was extended from the UV region to the visible region and the absorbance of the samples at a wavelength of 467 nm increased following the order TiO₂ Bi 5% > TiO₂ Bi 10% > TiO₂ Bi 3% > TiO₂ Bi 1% > pristine TiO₂, which is equal to the increasing order of the photocatalytic activity. The results from photocatalytic experiments agree with the absorbance spectra (Figure 8A). The TiO₂ Bi 5% sample had the highest photocatalytic activity (K₂ = 2.02 × 10⁻³ mg⁻¹·L·min⁻¹) because it has a low E_g value (2.77 eV) and higher absorbance in the visible region.

Figure 12A shows that the photocatalytic activity of the TiO₂ Bi 5% sample to degrade MB under visible light does not depend on the catalyst concentration in the range studied from 0.5 g/L to 2.0 g/L; it was also observed that the photocatalytic activity of this sample was higher than the P25 catalyst, reaching a photodegradation of 75.87% and 37.5%, respectively, using a catalyst concentration of 1 g/L; this is due to the fact that the P25 catalyst does not absorb photons in the visible region, it only absorbs in the UV region. The effect of the type of light used on MB photodegradation with the TiO₂ Bi 5% sample is shown in Figure 12B; it is observed that photodegradation percentages of 79.5%, 74.4%, and 89.2% were reached using UV light, visible light, and natural sunlight, respectively. The highest percentage of MB photodegradation was obtained with natural sunlight irradiation, since the TiO₂ Bi 5% sample had higher absorbance in the visible region of the electromagnetic spectrum, from 400 to 700 nm (Figure 8A). As already mentioned, the higher photocatalytic activity of the TiO₂ Bi 5% sample is mainly associated with its higher level of bismuth doping and with its low E_g value.

4. Conclusions

In this work, mesoporous Bi-doped TiO₂ catalysts were successfully prepared by mechanosynthesis. This green method allowed for the incorporation of bismuth into the crystal lattice of the TiO₂ anatase phase by up to 9%, achieving interstitial doping when small amounts of bismuth are used, as well as substitute doping when the amount of this atom was increased. This was demonstrated with the results of Rietveld refinement, which indicated a contraction of the unit cell of the anatase and subsequent expansion of the cell. The presence of brookite phase in the Bi-doped TiO₂ samples is due to the formation of defects caused by mechanical grinding and by the incorporation of bismuth into the TiO₂ crystal lattice. The crystallite size of the TiO₂ phase anatase decreased from 18.28 nm to 17.5 nm by increasing the amount of Bi used from 0% to 10%, and this in turn caused a decrease in the E_g value from 2.97 eV to 2.70 eV. The results of bond energy characterization by XPS suggest that Bi-doped TiO₂ samples have Bi⁰ on their surface and that there are OH groups on the surface of pristine TiO₂ and Bi-doped TiO₂ samples. The Bi-doped TiO₂ mesoporous samples obtained by mechanosynthesis in this work have good porosity and adequate E_g values that allow them to have excellent photodegradation of MB under UV, visible, and natural solar irradiation. The higher photocatalytic activity of the TiO₂ Bi 5% sample under visible and natural sunlight irradiation (79.5% and 89.2%, respectively) is mainly associated with its higher level of bismuth doping (4%) and with its low E_g value (2.77 eV). The absorbance of the samples at a wavelength of 467 nm increased following the order: TiO₂ Bi5% > TiO₂ Bi10% > TiO₂ Bi3% > TiO₂ Bi1% > TiO₂ pristine, which is equal to the increasing order of the photocatalytic activity.