Figure 1a,b show the SEM images of Gd₂InSbO₇ and Gd₂FeSbO₇ with low magnification. Figure 1c,d show the TEM images of Gd₂InSbO₇ and Gd₂FeSbO₇ with high magnification. The results showed that the particle diameter of Gd₂FeSbO₇ was 240 nm and the particle diameter of Gd₂InSbO₇ was 310 nm. The nanosized particles of Gd₂FeSbO₇ and Gd₂InSbO₇ were obtained, and these particles were in inhomogenous global shapes. Figure 1 revealed that the average particle size of Gd₂FeSbO₇ was smaller than that of Gd₂InSbO₇. There were two reasons to obtain nanocrystals in this experiment, while synthesizing Gd₂InSbO₇ and Gd₂FeSbO₇ powders by the solid-state method. Firstly, the powders, which were obtained after a sintering process by an electric furnace, would be ground by mortar three times and then would be ground in a ball mill three times. The total time for grinding the above photocatalyst powders was approximately 15 h. Secondly, the sizes of the photocatalyst particles were different. We utilized a centrifuge to realize separation of the photocatalyst particles, which had different sizes by adjusting the rotation speed of the centrifuge, and the small particles were obtained. SEM-EDS spectrum taken from the prepared Gd₂FeSbO₇ indicated the existence of gadolinium, iron, antimony and oxygen. As to the prepared Gd₂InSbO₇, gadolinium, indium, antimony and oxygen were detected and other elements were not identified.

X-ray powder diffraction patterns of Gd₂FeSbO₇ and Gd₂InSbO₇ are shown in Figure 2. Figure 3 displays the powder X-ray diffraction patterns of Gd₂InSbO₇ together with full-profile structure refinements of the collected data as obtained by the RIETAN™ [45] program, which is based on Rietveld analysis. The results of the final refinement for Gd₂FeSbO₇ and Gd₂InSbO₇ manifested an excellent consistency between the observed and calculated intensities for the pyrochlore-type structure, a cubic crystal system and a space group Fd3m (O atoms were included in the model). The lattice parameters of Gd₂InSbO₇ and Gd₂FeSbO₇ were 10.449546 Å and 10.276026 Å, respectively. All the diffraction peaks for Gd₂FeSbO₇ and Gd₂InSbO₇ could be successfully indexed based on the lattice constant and above space group. The atomic coordinates and structural parameters of Gd₂FeSbO₇ and Gd₂InSbO₇ are listed in Tables 1 and 2, respectively. In addition, Our XRD results showed that Gd₂FeSbO₇ and Gd₂InSbO₇ crystallized with the same structure, and 2 theta angles of each reflection of Gd₂InSbO₇ changed with the substitution of In³⁺ by Fe³⁺. The lattice parameter decreased from α = 10.449546 Å for Gd₂InSbO₇ to α = 10.276026 Å for Gd₂FeSbO₇, indicating a decrease in the lattice parameter of the photocatalyst with the decrease of M ionic radii, Fe³⁺ (0.78 Å) < In³⁺ (0.92 Å). Figure 1e,f show the selected area electron diffraction patterns of Gd₂InSbO₇ and Gd₂FeSbO₇, respectively. It could be seen that Gd₂InSbO₇ and Gd₂FeSbO₇ crystallized with a cubic crystal system, and the lattice parameters α of Gd₂InSbO₇ and Gd₂FeSbO₇ were proved to be 10.449546 Å and 10.276026 Å, respectively. According to the calculation results from Figure 1e,f the main diffraction peaks (222), (440), (400) and (622) for Gd₂InSbO₇ and Gd₂FeSbO₇ could be found and indexed within Figure 1e,f.

Our X-ray diffraction outcomes showed that Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇ crystallized with the same pyrochlore-type structure. The cubic system structure with space group Fd3m for Bi₂InTaO₇ remained unchanged, with Ta⁵⁺ being substituted by Sb⁵⁺ and with Bi³⁺ being substituted by Gd³⁺. The cubic system structure with space group Fd3m for Bi₂InTaO₇ also remained unchanged with Ta⁵⁺ being substituted by Sb^5+, with In³⁺ being substituted by Fe³⁺ and with Bi³⁺ being substituted by Gd³⁺. The result of refinements for Gd₂FeSbO₇ generated the unweighted R factors, R_P = 16.20% with space group Fd3m. Similarly, the result of refinements for Gd₂InSbO₇ generated the unweighted R factors, R_P = 12.13% with space group Fd3m. Zou et al.[46] refined the crystal structure of Bi₂InNbO₇ and obtained a large R factor, which was owing to a slightly modified structure model for Bi₂InNbO₇. Based on the high purity of the precursors that were used in this study and the EDS results that did not trace any other elements, it was unlikely that the observed space groups originated from the presence of impurities. Therefore, it was suggested that the slightly high R factor for Gd₂FeSbO₇ or Gd₂InSbO₇ was due to a slightly modified structure model of Gd₂FeSbO₇ or Gd₂InSbO₇. It should be emphasized that the defects or the disorder/order of a fraction of the atoms could result in the change of structures, including different bond-distance distributions, thermal displacement parameters and/or occupation factors for some of the atoms.

The XPS spectra of Gd₂FeSbO₇ and Gd₂InSbO₇ were obtained. The various elemental peaks, which are corresponding to specific binding energies, are given in Table 3. The results further suggested that the oxidative valence state of Gd, Fe, Sb and O ions from Gd₂FeSbO₇ were +3, +3, +5 and −2, respectively. For Gd₂FeSbO₇, the mean atomic ratios of Gd: Fe: Sb: O were 2.00: 1.02: 0.99: 6.96 based on averaging our XPS, SEM-EDS and XFS results. Similarly, the oxidation state of Gd, In, Sb and O ions from Gd₂InSbO₇ were +3, +3, +5 and −2, respectively. For Gd₂InSbO₇, the mean atomic ratios of Gd: In: Sb: O were 2.00: 1.03: 0.97: 6.98 based on averaging our XPS, SEM-EDS and XFS results. Consequently, it could be deduced that the final materials were of high purity under our preparation conditions. It was noteworthy that neither shoulders nor widening of any XPS peaks of Gd₂FeSbO₇ or Gd₂InSbO₇ were observed, suggesting the absence of any other phases.

Figures 4 and 5 present the absorption spectra of Gd₂FeSbO₇ and Gd₂InSbO₇, respectively. In contrast to the well-known TiO₂, whose absorption edge was less than 380 nm, the absorption edges of newly synthesized Gd₂FeSbO₇ and Gd₂InSbO₇ were found to be 586 nm and 428 nm, respectively, which were in the visible region of the spectrum. It was noteworthy that the apparent absorption (defined hereby as 1-transmission) could not take into consideration reflection and scattering. As a result, the apparent absorbance at sub-bandgap wavelengths (600 to 800 nm for Gd₂FeSbO₇ and 425 to 800 nm for Gd₂InSbO₇) was higher than zero.

For a crystalline semiconductor compound, the optical absorption near the band edge followed the equation [47,48]: αhν = A (hν-E_g)ⁿ. Here, A, α, E_g and ν denoted proportional constant, absorption coefficient, band gap and light frequency, respectively. In this equation, n determined the character of the transition in a semiconductor compound. E_g and n could be calculated by the following steps: (i) plotting ln(αhν) versus ln(hν-E_g) assuming an approximate value of E_g, (ii) deducing the value of n based on the slope in this graph and (iii) refining the value of E_g by plotting (αhν)^1/nversus hν and extrapolating the plot to (αhν)^1/n = 0. According to this method, Figure 6 shows the plot of (αhν)^1/nversus hν for Gd₂FeSbO₇ and Gd₂InSbO₇. It was evidently to be found from Figure 6 that the values of E_g for Gd₂FeSbO₇ and Gd₂InSbO₇ were calculated to be 2.151 eV and 2.897 eV, respectively, while the values of n for Gd₂FeSbO₇ and Gd₂InSbO₇ were calculated to be 0.50 and 0.50, respectively, indicating that Gd₂FeSbO₇ possessed a narrower band gap compared with that of Gd₂InSbO₇.

Generally, the photocatalytic process by semiconductors begins with the direct absorption of supra-bandgap photons and the generation of electron–hole pairs within semiconductor particles. This is followed by diffusion of the charge carriers to the surface of the semiconductor particle. Changes in the UV-Vis spectrum of rhodamine B (RhB) upon exposure to visible light (λ > 400 nm) with the presence of Gd₂FeSbO₇ or Gd₂InSbO₇ are depicted in Figure 7a,b, respectively. The measurements were performed under oxygen-saturation conditions ([O₂]_sat = 1.02 × 10⁻³ M). The degradation of RhB did not occur in darkness within the Gd₂FeSbO₇/RhB suspension or Gd₂InSbO₇/RhB suspension or Bi₂InTaO₇/RhB suspension or RhB suspension. It could be seen from Figure 7a and Figure 7b that a reduction of typical RhB peaks at 553.5 nm and 525 nm was clearly noticed. The results showed that the initial degradation rate of RhB was about 2.413 × 10⁻⁹ mol L⁻¹ s⁻¹, and the initial photonic efficiency was estimated to be 0.05069% (λ = 420 nm) for Gd₂FeSbO₇. Similarly, the initial degradation rate of RhB was about 2.322 × 10⁻⁹ mol L⁻¹ s⁻¹, and the initial photonic efficiency was estimated to be 0.04877% (λ = 420 nm) for Gd₂InSbO₇. For Bi₂InTaO₇, after visible light irradiation for 200 min, the RhB concentration decreased only from 0.0293 mM to 0.0161 mM, and the initial degradation rate of RhB was about 1.1 × 10⁻⁹ mol L⁻¹ s⁻¹. The initial photonic efficiency was estimated to be 0.02311% (λ = 420 nm) for Bi₂InTaO₇. By contrast, the photonic efficiency of Bi₂InTaO₇ was inferior to that of Gd₂FeSbO₇ or Gd₂InSbO₇.

The kinetics of RhB degradation deduced according to the spectral changes under visible light irradiation are shown in Figure 8, which describes the kinetics not only with Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇ as catalysts, but also without any photocatalyst. As expected, reduction of RhB signal in the controlled measurements in the absence of a photocatalyst was promising. In addition, the photodegradation removal rate of RhB was 90.35%, 77.80% and 26.62% after visible light irradiation for 80 min with Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇ as catalysts, respectively. Complete removal of rhodamine B was observed after visible light irradiation for 225 min or 260 min with Gd₂FeSbO₇ or Gd₂InSbO₇ as photocatalyst. Based on the above outcomes, it was much faster for Gd₂FeSbO₇ and Gd₂InSbO₇ to photodegrade RhB compared with Bi₂InTaO₇, and the photocatalytic degradation activity of Gd₂FeSbO₇ or Gd₂InSbO₇ for degrading RhB was higher than that of Bi₂InTaO₇; moreover, Gd₂FeSbO₇ showed higher photocatalytic degradation activity than Gd₂InSbO₇. The main reason was that the lattice parameter α = 10.746410 Å for Bi₂InTaO₇ was larger than the lattice parameter α = 10.449546 Å for Gd₂InSbO₇, and the lattice parameter α = 10.449546 Å for Gd₂InSbO₇ was larger than the lattice parameter α = 10.276026 Å for Gd₂FeSbO₇, which probably resulted in a decrease for the migration distance of photogenerated electrons and holes to reach the reaction site on the photocatalyst surface; subsequently, the creation of more active sites was realized. As a result, it would probably improve the photocatalytic activities by decreasing the lattice parameter of the photocatalyst.

The first order nature of the photocatalytic degradation kinetics with Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇ as catalysts is clearly exhibited in Figure 9, which describes a linear correlation between ln(C/C₀) (or ln(TOC/TOC₀)) and the irradiation time for the photocatalytic degradation of RhB under visible light irradiation by using Gd₂FeSbO₇ or Gd₂InSbO₇ or Bi₂InTaO₇ as catalyst. Here, C represented the RhB concentration at time t, and C₀ represented the initial concentration of RhB. TOC represented the total organic carbon concentration at time t, and TOC₀ denoted the initial total organic carbon concentration. According to the relationship between ln(C/C₀) and the irradiation time, the apparent first-order rate constant k was estimated to be 0.02220 min⁻¹ with Gd₂FeSbO₇ as catalyst, 0.01606 min⁻¹ with Gd₂InSbO₇ as catalyst and 0.00329 min⁻¹ with Bi₂InTaO₇ as catalyst, indicating that Gd₂FeSbO₇ and Gd₂InSbO₇ were more effective than Bi₂InTaO₇ for the photocatalytic degradation of RhB under visible light irradiation. Meanwhile, Gd₂FeSbO₇ showed more effective photocatalytic activity for degrading RhB than Gd₂InSbO₇. According to the relationship between ln(TOC/TOC₀) and the irradiation time, the apparent first-order rate constant k was estimated to be 0.02024 min⁻¹ with Gd₂FeSbO₇ as catalyst, 0.01348 min⁻¹ with Gd₂InSbO₇ as catalyst and 0.00317 min⁻¹ with Bi₂InTaO₇ as catalyst, indicating that the photodegradation intermediate products of RhB were probably produced during the photocatalytic degradation of RhB under visible light irradiation.

The photodegradation intermediate products of RhB in our experiment were identified as succinic acid (m/z = 118), terephthalic acid (m/z = 166), pentanedioic acid, 3-Hydroxybenzoic acid (m/z = 138), 1,2-benzenedicarboxylic acid and maleic acid (m/z = 116). Based on the intermediate products detected in this work, a possible photocatalytic degradation pathway for RhB is proposed in Figure 10. This pathway was similar, but not identical, to the pathway proposed by Horikoshi et al.[49] for the photodegradation of RhB under ultraviolet light illumination assisted by microwave radiation with TiO₂ as catalyst. According to the research from Zhang et al.[32], the photodegradation of RhB occurred through two competitive processes: one was N-demethylation and the other one was the destruction of the conjugated structure. Thus, we considered that chromophore cleavage, opening-ring and mineralization would be the main photocatalytic degradation pathway of RhB in our experiment. RhB was converted to smaller organic species, which were ultimately mineralized into inorganic products, such as CO₂ and water. Figure 11 shows CO₂ yields during the photocatalytic degradation of RhB with Gd₂FeSbO₇, Gd₂InSbO₇ or Bi₂InTaO₇ as catalyst under visible light irradiation. The results indicated that the yielded CO₂ increased gradually with the increase of reaction time by using Gd₂FeSbO₇, Gd₂InSbO₇ or Bi₂InTaO₇ as catalyst. The production rate of CO₂ with Gd₂FeSbO₇ or Gd₂InSbO₇ as catalyst was higher than that with Bi₂InTaO₇ as catalyst, which was in line with the absorption curves (Figures 4 and 5) of Gd₂FeSbO₇ and Gd₂InSbO₇. For example, after visible light irradiation for 200 min, the CO₂ production was 0.2366 mmol with Gd₂FeSbO₇ as catalyst, 0.2280 mmol with Gd₂InSbO₇ as catalyst and 0.1080 mmol with Bi₂InTaO₇ as catalyst.

Figure 12 shows the change of the total organic carbon (TOC) for photocatalytic degradation of rhodamine B during visible light irradiation with Gd₂FeSbO₇, Gd₂InSbO₇ or Bi₂InTaO₇ as catalyst. The TOC measurements revealed the disappearance of organic carbon when the RhB solution containing Gd₂FeSbO₇, Gd₂InSbO₇ or Bi₂InTaO₇ was exposed under visible light irradiation. The results showed that 86.70%, 70.49% or 25.26% of TOC decrease was obtained after visible light irradiation for 80 min with Gd₂FeSbO₇, Gd₂InSbO₇ or Bi₂InTaO₇ as catalyst, respectively. The turnover numbers, which were the ratio between total amount of evolved gas and exhausted catalyst, were calculated to be more than 0.18 or 0.19 for Gd₂FeSbO₇ or Gd₂InSbO₇ after 200 min of reaction time under visible light irradiation. The reactions ceased when the light was turned off, indicating an obvious photic response.

The photocatalytic performance of Gd₂FeSbO₇ and Gd₂InSbO₇ was remarkable under visible light irradiation. This superior quality could be even more bracing if one considered the fact that the specific surface areas of Gd₂FeSbO₇ and Gd₂InSbO₇ were further smaller than that of titanium dioxide. In this experiment, BET isotherm measurements gave a specific surface area of 4.12 m² g⁻¹, 3.26 m² g⁻¹ and 1.26 m² g⁻¹ for Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇, respectively, which was almost 12-times smaller than that of TiO₂ (46.24 m² g⁻¹). The particle sizes of Gd₂InSbO₇ and Gd₂FeSbO₇ were uneven. We provide SEM images with low magnification of Gd₂InSbO₇ and Gd₂FeSbO₇. Simultaneously, we give the TEM images of Gd₂InSbO₇ and Gd₂FeSbO₇, which represent the average particle size. Because the particle size of Gd₂InSbO₇ and Gd₂FeSbO₇ compounds were greater than 230nm, their specific surface areas were less than 5 m² g⁻¹.

There are three main reasons to choose Gd for producing Gd₂FeSbO₇ and Gd₂InSbO₇ in this paper. Firstly, the substitution of Bi³⁺ by Gd³⁺ and the substitution of Ta⁵⁺ by Sb⁵⁺ in Bi₂InTaO₇ will produce smaller catalyst particles and increase the specific surface area, because the radii of Gd³⁺, Bi³⁺, Ta⁵⁺ and Sb⁵⁺ are 1.053 Å, 1.17 Å, 0.74 Å and 0.60 Å, which shows that the radius of Gd³⁺ is smaller than the radius of Bi³⁺, and the radius of Sb⁵⁺ is smaller than the radius of Ta⁵⁺. Similarly, the substitution of Bi³⁺ by Gd³⁺, the substitution of In³⁺ by Fe³⁺ and the substitution of Ta⁵⁺ by Sb⁵⁺ in Bi₂InTaO₇ will produce smaller catalyst particles and increase the specific surface area, because the radii of In³⁺ and Fe³⁺ are 0.92 Å and 0.78 Å, which shows that the radius of Gd³⁺ is smaller than the radius of Bi³⁺, the radius of Fe³⁺ is smaller than the radius of In³⁺ and the radius of Sb⁵⁺ is smaller than the radius of Ta⁵⁺. Thus, the active sites and the catalytic activity will increase. Secondly, the smaller catalyst particles probably result in a decrease of the migration distance of photogenerated electrons and holes, which are formed under visible light irradiation from the grain interior to reach the reaction site on the photocatalyst surface. Subsequently, the photogenerated electrons and the photogenerated holes that reach the surface of the particles in unit time increase, and the creation of more active sites is realized. As a result, it will probably improve the photocatalytic activities with decreasing the particle size of the photocatalyst. Thirdly, some literatures reported that Gd-containing catalyst had excellent catalytic performance [50–53].

Figure 4 and Figure 5 show the action spectra of RhB degradation in the presence of Gd₂FeSbO₇ or Gd₂InSbO₇ under visible light irradiation. A clear photonic efficiency (0.03921% at its maximal point for Gd₂FeSbO₇ and 0.03145% at its maximal point for Gd₂InSbO₇) at wavelengths that corresponded to sub-Eg energies of the photocatalysts (λ from 425 to 800 nm) was observed for Gd₂FeSbO₇ and Gd₂InSbO₇. The existence of photonic efficiency at energies where photons were not absorbed by the photocatalysts, and the correlation between the low-energy action spectrum and the absorption spectrum of RhB clearly demonstrated that any photodegradation at wavelengths above 479 nm should be attributed to the photosensitization by RhB dye itself, the mechanism showing as follows:

According to this mechanism, RhB adsorbed on Gd₂FeSbO₇ or Gd₂InSbO₇ was excited by visible light irradiation. Subsequently an electron was injected from the excited RhB to the conduction band of Gd₂FeSbO₇ or Gd₂InSbO₇, where the electron was scavenged by molecular oxygen. Scheme I served to explain the results obtained with Gd₂FeSbO₇ or Gd₂InSbO₇ as catalyst under visible light irradiation, where Gd₂FeSbO₇ or Gd₂InSbO₇ might serve to reduce recombination of photogenerated electrons and holes by scavenging of electrons [54].

The situation was different below 479 nm, where the photonic efficiency correlated well with the absorption spectra of Gd₂FeSbO₇ and Gd₂InSbO₇. This result evidently showed that the mechanism, which was responsible for the photodegradation of RhB, went through band gap excitation of Gd₂FeSbO₇ or Gd₂InSbO₇. Although detailed experiments about the effect of oxygen and water on the degradation mechanism were not performed, it was sensible to assume that the mechanism in the first steps was similar to the observed mechanism for Gd₂FeSbO₇ or Gd₂InSbO₇ under supra-bandgap irradiation, namely showing below:

Previous luminescent studies had shown that the closer the M–O–M bond angle was to 180°, the more delocalized was the excited state [55]; As a result, the charge carriers could move easily in the matrix. The mobility of the photoinduced electrons and holes influenced the photocatalytic activity, because high diffusivity increased the probability that the photogenerated electrons and holes would reach the reactive sites of the catalyst surface. Based on the above results, the lattice parameter α = 10.276026 Å for Gd₂FeSbO₇ was smaller than the lattice parameter α = 10.449546 Å for Gd₂InSbO₇, thus the photoinduced electrons and holes inside Gd₂FeSbO₇ was easier and faster to reach the reactive sites of the Gd₂FeSbO₇ surface than those inside Gd₂InSbO₇; as a result, the photocatalytic degradation activity of Gd₂FeSbO₇ was higher than that of Gd₂InSbO₇. Moreover, in this experiment, for Gd₂FeSbO₇, the Fe–O–Fe bond angle was 116.424°; at the same time, for Gd₂InSbO₇, the In–O–In bond angle was 123.338°. The above results showed that the Fe–O–Fe bond angle of Gd₂FeSbO₇ or the In–O–In bond angle of Gd₂InSbO₇ was close to 180°, thus the photocatalytic activity of Gd₂FeSbO₇ or Gd₂InSbO₇ was accordingly higher. Moreover, the In–O–In bond angle of Gd₂InSbO₇ was larger than the Fe–O–Fe bond angle of Gd₂FeSbO₇, which led to an increase of photocatalytic activity for Gd₂InSbO₇ compared with that of Gd₂FeSbO₇. The crystal structures of Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇ were the same, but their electronic structures were considered to be a little different. For Gd₂FeSbO₇ or Gd₂InSbO₇, Sb or In was a 5p-block metal element, Gd was a 5d-block rare earth metal element and Fe was a 3d-block metal element, but for Bi₂InTaO₇, Ta was a 5d-block metal element and Bi was a 6p-block metal element, indicating that the photocatalytic activity might be affected not only by the crystal structure of the photocatalysts, but also by the electronic structure of the photocatalysts. According to the above analysis, the difference of RhB photocatalytic degradation among Gd₂FeSbO₇, Gd₂InSbO₇ and Bi₂InTaO₇ could be mainly attributed to the difference of their crystalline structure and electronic structure.

Figure 13 shows the suggested band structures of Gd₂FeSbO₇ and Gd₂InSbO₇. The positions and width of the conduction band (CB) and the valence band (VB) were investigated by calculating the electronic band structure of Gd₂FeSbO₇ and Gd₂InSbO₇ with the plane-wave-based density functional method. The band structure calculations of Gd₂FeSbO₇ and Gd₂InSbO₇ were performed with the program of cambridge serial total energy package (CASTEP) and first-principles simulation. The CASTEP calculation was composed of the plane-wave pseudopotential total energy method according to the density functional theory. The generalized gradient approximation (GGA-PBE) and the geometry optimization were adopted. The selected unit cell for calculation was [Gd₂FeSbO₇]₂ or [Gd₂InSbO₇]₂. The pseudo-atomic calculations were accomplished for Gd₂FeSbO₇ with 5d¹6s² (Gd), 3d⁶4s² (Fe), 5s²5p³ (Sb) and 2s²2p⁴ (O). The pseudo-atomic calculations were accomplished for Gd₂InSbO₇ with 5d¹6s² (Gd), 5s²5p¹ (In), 5s²5p³ (Sb) and 2s²2p⁴ (O). The self-consistent field tolerance was 1.0 × 10⁻⁶ eV/atom. The core electrons were replaced by the ultra-soft pseudopotentials. The FFT grid of the basis was 40 × 30 × 30. The kinetic energy cutoff was 400 eV. 4 × 5 × 5 k-point, and the ultrasoft pseudopotential was applied in the above calculation. The total and partial density of the states of Gd₂FeSbO₇ and Gd₂InSbO₇ was taken into consideration. We determined the band structures of Gd₂InSbO₇ and Gd₂FeSbO₇ by borrowing ideas from the relevant literature [56–62]. Recently, the electronic structures of InMO₄ (M = V, Nb and Ta) and BiVO₄ were reported by Oshikiri et al. based on the first principles calculations [63]. The conduction bands of InMO₄ (M = V, Nb and Ta) were mainly composed of a dominant d orbital component from V 3d, Nb 4d and Ta 5d orbitals, respectively. The valence bands of BiVO₄ were composed of a small Bi 6s orbital component and a dominant O 2p orbital component. The band structures of Gd₂FeSbO₇ and Gd₂InSbO₇ should be similar to that of the above compounds. Therefore, we concluded that the conduction band of Gd₂FeSbO₇ was composed of Gd 5d, Fe 3d and Sb 5p orbital components; meanwhile, the valence band of Gd₂FeSbO₇ was composed of a small dominant O 2p orbital component. Similarly, the conduction band of Gd₂InSbO₇ was composed of Gd 5d, In 5p and Sb 5p orbital components; moreover, the valence band of Gd₂InSbO₇ was composed of a small dominant O 2p orbital component. Direct absorption of photons by Gd₂FeSbO₇ or Gd₂InSbO₇ could produce electron–hole pairs within the catalyst, indicating that larger energy than the band gap of Gd₂FeSbO₇ or Gd₂InSbO₇ was necessary for decomposing RhB by photocatalysis.

The presented results indicated that the Gd₂FeSbO₇ (or Gd₂InSbO₇)-visible light photocatalysis system might be regarded as a method for practical treatment of diluted colored waste water. Our Gd₂FeSbO₇ (or Gd₂InSbO₇)-visible light photocatalysis system could be utilized for decolorization, purification and detoxification in the textile, printing and dyeing industries within semi-arid countries. We designed Gd₂FeSbO₇ (or Gd₂InSbO₇)-visible light photocatalysis system without demanding chemical reagents or using the high pressure of oxygen or heating. The decolorized and detoxified water was submitted to our new system for treatment, and the results showed that the Gd₂FeSbO₇ (or Gd₂InSbO₇)-visible light photocatalysis system might provide a valuable treatment for purifying and reusing colored aqueous effluents.