The Local and Electronic Structure Study of LuxGd1−xVO4 (0 ≤ x ≤ 1) Solid Solution Nanocrystals

Rare-earth-doped mixed crystals have demonstrated tunable optical properties, and it is of great importance to study the structural characteristics of the mixed-crystal hosts. Herein, LuxGd1-xVO4 (0 ≤ x ≤ 1) solid solution nanocrystals were synthesized by a modified sol–gel method, with a pure crystalline phase and element composition. The X-ray diffraction (XRD) and Rietveld refinement results showed that LuxGd1−xVO4 nanocrystals are continuous solid solutions with a tetragonal zircon phase (space group I41/amd) and the lattice parameters strictly follow Vegard’s law. The detailed local structures were studied by extended X-ray absorption fine structure (EXAFS) spectra, which revealed that the average bond length of Gd-O fluctuates and decreases, while the average bond length of Lu-O gradually decreases with the increase in Lu content. Furthermore, the binding energy differences of core levels indicate that the covalent V-O bond is relatively stable, while the ionicity of the Lu-O bond decreases with the increasing x value, and the ionicity of the Gd-O bond fluctuates with small amplitude. The valence band structures were further confirmed by the first-principles calculations, indicating that the valence band is contributed to by the O 2p nonbonding state, localized Gd 4f and Lu 4f states, and the hybridized states between the bonding O 2p and V 3d. The binding energies of the Lu core and the valence levels tend to decrease gradually with the increase in Lu content. This work provides insight into the structural features of mixed-crystal hosts, which have been developed in recent years to improve laser performance by providing different positions for active ions to obtain inhomogeneous broadening spectra.


Introduction
Benefiting from excellent optical, electronic, magnetic, and thermal properties, rareearth orthovanadates (REVO 4 , RE = Sc, Y, and La-Lu) have wide applications in many fields, such as phosphors, laser hosts, scintillators, catalysts, polarizers, photovoltaic cells, dielectric ceramics, magnetocaloric materials, photothermal therapy, and optical probes [1][2][3][4][5][6][7][8][9]. Due to the strong UV absorption of VO 4 3− groups and the efficient energy transfer from VO 4 3− groups to emitting ions, REVO 4 materials have been used as highly efficient host materials [10]. Their similar ionic radii are conducive to the doping of some active ions, such as all lanthanide active ions, Bi 3+ , etc. Due to the abundant energy levels of 4f n configurations, the 4f -4f and 5d-4f transitions of lanthanide active ions can emit light from ultraviolet to infrared [11]. In recent years, nanosized REVO 4 materials with well-controlled shape, size, phase purity, and different active ions and doping concentrations have been widely studied to learn their luminescent properties and have been identified as promising materials for a wide range of optical applications [12][13][14][15][16]. In order to further expand the optical applications of REVO 4 -series materials, the influence of mixed-crystal hosts on the luminescence properties has also been explored. For example, Robinson et al. proved that Bi 1−x Dy x VO 4 showed broader XRD peaks compared to DyVO 4 , and a progressive decrease in the bandgap with the increase in Bi concentration and crystal field effects should not be negligible for the 4f -4f transitions [17]. Kang et al. confirmed that the adjustment of the cation fractions could tune the excitation tail and emission band maximum of Bi 3+ ions through bandgap modulation in the (Y,Sc)VO 4 host [18]. For Nd:Lu x Y 1−x VO 4 mixed crystals, although the absorption and emission peak locations were unchanged, the full width at half-maximum (FWHM) exhibited obvious inhomogeneous broadening compared to the two single crystals, meaning better Q-switched and mode-locked laser performance [19].
As mentioned above, the doped mixed-crystal materials may also have better performance than the single-crystal materials, besides the tunability of the physical properties of the materials. Thus, it is of great importance to study the structural characteristics of the mixed-crystal hosts. Among all of the REVO 4 nanomaterials, GdVO 4 and LuVO 4 have been extensively studied for their unit cell structures, properties, and applications. They both possess a tetragonal zircon structure, belong to the space group I4 1 /amd, and can be used as catalysts and as hosts for luminescent materials [1,4,6,[20][21][22][23][24]. Mixed crystals of the two orthovanadates Lu x Gd 1−x VO 4 doped with Nd 3+ have been grown by the Czochralski method, and the XRD results revealed that GdVO 4 and LuVO 4 can form solid solutions in any proportion and maintain the zircon-phase structure [25]. By changing the composition of the solid solutions, the basic physical properties of the materials can be adjusted. Yu et al. demonstrated that the thermal, optical, and laser properties of Nd:Lu x Gd 1−x VO 4 show variation as a function of x [26]. Additionally, compared to pure crystals, the laser performance of mixed crystals is improved, due to the inhomogeneous broadening of the fluorescence lines generated by the mixed-crystal hosts, which indicate that although the spectroscopic and laser properties are mainly determined by the eigen multiplet of the active ions, they are also partly influenced by the crystal field [2,27]. As far as we know, there have been some previous reports on the growth and properties of large rare-earthion-doped Lu x Gd 1−x VO 4 crystals, but the local and electronic structures of nanosized Lu x Gd 1−x VO 4 solid solution materials are less studied.
It is known that the properties of a material are strongly dependent on its lattice structure. In the unit cell of zircon-type Lu x Gd 1−x VO 4 , the Gd (Lu) atom coordinates with eight oxygen atoms to form an irregular dodecahedron with four longer and four shorter chemical bonds and occupies D 2d sites, while the V atom coordinates with four oxygen atoms to form a regular tetrahedron [28]. Active ions can substitute Lu 3+ or Gd 3+ to occupy the center of GdO 8 or LuO 8 dodecahedrons. Previous reports suggested that the reason for the inhomogeneous broadening of the spectral peaks is that active ions are randomly distributed in mixed-crystal hosts, occupying different lattice locations and experiencing different local crystal fields, so the spectral peaks are contributed by many different structural centers [19]. Therefore, compared with GdVO 4 and LuVO 4 , the application of Lu x Gd 1−x VO 4 nanomaterials can be expanded to present as promising host materials.
In this work, a series of Lu x Gd 1−x VO 4 (0 ≤ x ≤ 1) nanocrystals were prepared by a simple sol-gel method. The changes to the unit cell, local and electronic structures, and composition were studied by experimental and theoretical methods. In terms of experimental technology, we combined X-ray powder diffraction (XRD), extended X-ray absorption fine structure (EXAFS), and X-ray photoelectron spectroscopy (XPS) to study the unit cell structures, the local structures of the Lu 3+ and Gd 3+ ions, the chemical states of elements, the covalency or ionicity of metal-oxygen (M-O) chemical bonds, and the valence band structures of the series solid solutions. The valence band structures were also investigated by comparison with the density of electronic states (DOS) calculated by the LSDA + U method. Our findings could provide a comprehensive understanding of the mixed-crystal structures of Lu x Gd 1−x VO 4 nanocrystals, which will be helpful to explore more applications.

Materials and Methods
A series of Lu x Gd 1−x VO 4 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1) nanocrystals were synthesized by the sol-gel method. Stoichiometric Gd 2 O 3 and Lu 2 O 3 (Aladdin, 99.9%) were dissolved in diluted HNO 3 solution under heating and stirring to obtain a transparent nitrate solution. Then, citric acid (C 6 H 8 O 7 ·H 2 O, Sinopharm, AR) with a molar ratio of 2:1 to metal cations (Gd 3+ and Lu 3+ ions) was added as the chelating agent. After the citric acid was completely dissolved, ammonium metavanadate solution obtained by dissolving NH 4 VO 3 (Sinopharm, AR) in hot deionized water was added dropwise to the above solution. After stirring and heating, viscous gels formed. The gels were then dehydrated at 100 • C for 6 h and calcined in air at 800 • C for 6 h to obtain pale-yellow powders with a heating and cooling rate of 50 • C/h. The powders were then finely ground for subsequent experiments.
The series of powder samples were identified by powder X-ray diffraction performed on a Bruker D8 advance powder diffractometer with Cu K α1,2 radiation (λ average = 1.54184 Å). The molar contents of the constituent elements were measured using an EPMA-1720H (Shimadzu, Japan) Electron Probe Microanalyzer with the following parameters: AccV = 15.0 kV, BC = 9.9 nA, beam size = MIN, and SC = 6.8 nA. Additionally, YVO 4 , Gd 3 Ga 5 O 12 , and LuSiO 5 were used as standard samples for the quantitative analysis of V, Gd, and Lu, respectively.
The local structures of the cations were investigated by extended X-ray absorption fine structure (EXAFS) measured at the beamline 14W1 of Shanghai Synchrotron Radiation Facility (SSRF, Shanghai, China). Gd L 3 -edge X-ray adsorption spectra at 7243 eV and Lu L 3 -edge X-ray adsorption spectra at 9244 eV of the samples were recorded in transmission and Lytle fluorescence (when the concentration was too low) modes at room temperature. The EXAFS spectra were normalized using Athena software, and the corresponding Fouriertransformed (FT) k 3 χ(k) plots were obtained by selecting the Hanning window. The FT plots were fitted using Artemis with k 3 -weighting to determine the distances between the central atoms and their coordination shells.
X-ray photoelectron spectroscopy (XPS) was performed using an ESCALAB 250XI spectrometer (Thermo Fisher Scientific) with monochromatized Al K α X-ray radiation (1486.6 eV) in an ultrahigh vacuum (<10 −7 Pa). A flood gun was used for charge neutralization. Survey scans were taken between 0 and 1300 eV with an energy step of 1 eV, fine scans of the elements' characteristic peaks were taken with an energy step of 0.1 eV, and the valence bands were recorded between 0 and 37 eV with an energy step of 0.05 eV. All data were analyzed using the version 5.9918 of Thermo Avantage software.
Electronic structure calculations of Lu 0.5 Gd 0.5 VO 4 ( Figure S1) were performed using a LSDA + U approach [29] based on density functional theory (DFT) [30] implemented through the Cambridge Serial Total Energy Package (CASTEP) [31] program. The Hubbard-U corrections were introduced because simple local density approximation (LDA) [32] or generalized gradient approximation (GGA) [33] failed to describe the strong correlation between the highly localized 4f electrons of Gd and predicted a metallic band structure for GdVO 4 , which is inconsistent with its insulating nature. The calculations with several U values showed that Hubbard U has a significant impact on the Gd 4f energy level and the bandgap, and the Gd 4f is located at a deeper energy level when the U value is large. The U value (0.01 eV) added to the Gd 4f electrons was finally determined semi-empirically by comparing it to the XPS valence band spectra, but the calculated Gd 4f level was still deeper than the experimental binding energy. Vanderbilt-type ultra-soft pseudo-potentials were adopted to describe the electron-ion interactions. The atomic levels 4f 14 5p 6 5d 1 6s 2 of the Lu atom, 4f 7 5s 2 5p 6 5d 1 6s 2 of the Gd atom, 3s 2 3p 6 3d 3 4s 2 of the V atom, and 2s 2 2p 4 of the O atom were treated as valence electrons. The plane-wave cutoff energy of 600 eV was chosen for the calculations of the energy and properties. The (3 × 3 × 3) Monkhorst-Pack grid was used for Brillouin zone integrations.

XRD and Rietveld Refinement
All Lu x Gd 1−x VO 4 powder samples had a pure tetragonal zircon-phase structure with no impurity phase as identified by X-ray diffraction (Figure 1), which is indicative of continuous solid solutions. In the inset in Figure 1, a gradual shift to high angles for the positions of the diffraction peaks with increasing Lu content can be seen clearly, which is consistent with the trends of bulk mixed crystals [25]. This shift is probably due to the substitution of Lu 3+ with a smaller ionic radius for Gd 3+ . The diffraction peaks of the Lu x Gd 1−x VO 4 (0 < x < 1) solid solutions show a broadening compared to the peaks of the two end members, which is also suggestive of compositional inhomogeneity due to the mismatch in radius between Lu 3+ and Gd 3+ ions.

XRD and Rietveld Refinement
All LuxGd1−xVO4 powder samples had a pure tetragonal zircon-phase structure with no impurity phase as identified by X-ray diffraction (Figure 1), which is indicative of continuous solid solutions. In the inset in Figure 1, a gradual shift to high angles for the positions of the diffraction peaks with increasing Lu content can be seen clearly, which is consistent with the trends of bulk mixed crystals [25]. This shift is probably due to the substitution of Lu 3+ with a smaller ionic radius for Gd 3+ . The diffraction peaks of the LuxGd1−xVO4 (0 < x < 1) solid solutions show a broadening compared to the peaks of the two end members, which is also suggestive of compositional inhomogeneity due to the mismatch in radius between Lu 3+ and Gd 3+ ions.  Based on the XRD data, the unit cell parameters a and c, along with the unit cell volume (V) of the Lu x Gd 1−x VO 4 samples, were calculated by Rietveld refinement using FullProf Suite software (Table S1). They all decreased linearly with the increase in Lu content, as can be seen from Figure 2, which conforms to Vegard's law [34]. When x changes from 0 to 1, the values of a, c, and V decrease by 2.6%, 1.9%, and 6.8%, respectively, showing anisotropy. Based on the XRD data, the unit cell parameters a and c, along with the unit cell volume (V) of the LuxGd1−xVO4 samples, were calculated by Rietveld refinement using Full-Prof Suite software (Table S1). They all decreased linearly with the increase in Lu content, as can be seen from Figure 2, which conforms to Vegard's law [34]. When x changes from 0 to 1, the values of a, c, and V decrease by 2.6%, 1.9%, and 6.8%, respectively, showing anisotropy.

EPMA
EPMA was used to determine the actual compositions of the series of LuxGd1−xVO4 (x = 0.1, 03, 0.5, 0.7, 0.9) samples. It can be seen from Table 1 that the molar ratios of Lu/RE were very close to the nominal ratios (x values); therefore, x values are used to denote the actual Lu contents in this work. Because only metal elements were measured, V molar contents close to 50% for all of the samples indicate that they were also consistent with the stoichiometric ratios.

TEM
The morphology and grain sizes of the LuxGd1−xVO4 nanocrystals were observed from the TEM images ( Figure 3). The crystalline grains of all of the samples were irregular in shape and easily agglomerated. Under the same calcination temperature and time, the grain size of these nanocrystals decreased with increasing x values, and the average grain sizes were about 30-50 nm. Therefore, continuous LuxGd1−xVO4 (0 ≤ x ≤ 1) solid solution nanocrystals with a tetragonal zircon-type structure were successfully synthesized by the sol-gel method.

EPMA
EPMA was used to determine the actual compositions of the series of Lu x Gd 1−x VO 4 (x = 0.1, 0.3, 0.5, 0.7, 0.9) samples. It can be seen from Table 1 that the molar ratios of Lu/RE were very close to the nominal ratios (x values); therefore, x values are used to denote the actual Lu contents in this work. Because only metal elements were measured, V molar contents close to 50% for all of the samples indicate that they were also consistent with the stoichiometric ratios.

TEM
The morphology and grain sizes of the Lu x Gd 1−x VO 4 nanocrystals were observed from the TEM images ( Figure 3). The crystalline grains of all of the samples were irregular in shape and easily agglomerated. Under the same calcination temperature and time, the grain size of these nanocrystals decreased with increasing x values, and the average grain sizes were about 30-50 nm. Therefore, continuous Lu x Gd 1−x VO 4 (0 ≤ x ≤ 1) solid solution nanocrystals with a tetragonal zircon-type structure were successfully synthesized by the sol-gel method. Nanomaterials 2023, 13, x FOR PEER REVIEW 6 of 15

Local Structure of Lanthanide Atoms in LuxGd1−xVO4 Solid Solutions
In order to further study the linear evolution of the unit cell parameters of the LuxGd1−xVO4 solid solutions caused by cation substitution, the local structures of the lanthanide cations were investigated by EXAFS. Because they share the same zircon-type structure, the atomic distributions of the coordination shells of Gd atoms in GdVO4 and Lu atoms in LuVO4 are similar. The first, second, and third coordination shells of Gd/Lu atoms consist of eight O atoms, two V atoms, and four Gd/Lu and four V atoms, respectively, as shown in Figure 4. More precisely, the first coordination shell consists of two subshells, with the same coordination number (4) and a bond length difference of 0.12 Å for GdVO4 and 0.15 Å for LuVO4. The interatomic distances of the first two coordination shells from the central atoms were obtained by fitting the Fourier-transformed (FT) EX-AFS spectra; the values, along with the fitting parameters and the average bond lengths of the two subshells, are listed in Tables S2 and S3.

Local Structure of Lanthanide Atoms in Lu x Gd 1−x VO 4 Solid Solutions
In order to further study the linear evolution of the unit cell parameters of the Lu x Gd 1−x VO 4 solid solutions caused by cation substitution, the local structures of the lanthanide cations were investigated by EXAFS. Because they share the same zircon-type structure, the atomic distributions of the coordination shells of Gd atoms in GdVO 4 and Lu atoms in LuVO 4 are similar. The first, second, and third coordination shells of Gd/Lu atoms consist of eight O atoms, two V atoms, and four Gd/Lu and four V atoms, respectively, as shown in Figure 4. More precisely, the first coordination shell consists of two subshells, with the same coordination number (4) and a bond length difference of 0.12 Å for GdVO 4 and 0.15 Å for LuVO 4 . The interatomic distances of the first two coordination shells from the central atoms were obtained by fitting the Fourier-transformed (FT) EXAFS spectra; the values, along with the fitting parameters and the average bond lengths of the two subshells, are listed in Tables S2 and S3.

Local Structure of Lanthanide Atoms in LuxGd1−xVO4 Solid Solutions
In order to further study the linear evolution of the unit cell parameters of the LuxGd1−xVO4 solid solutions caused by cation substitution, the local structures of the lanthanide cations were investigated by EXAFS. Because they share the same zircon-type structure, the atomic distributions of the coordination shells of Gd atoms in GdVO4 and Lu atoms in LuVO4 are similar. The first, second, and third coordination shells of Gd/Lu atoms consist of eight O atoms, two V atoms, and four Gd/Lu and four V atoms, respectively, as shown in Figure 4. More precisely, the first coordination shell consists of two subshells, with the same coordination number (4) and a bond length difference of 0.12 Å for GdVO4 and 0.15 Å for LuVO4. The interatomic distances of the first two coordination shells from the central atoms were obtained by fitting the Fourier-transformed (FT) EX-AFS spectra; the values, along with the fitting parameters and the average bond lengths of the two subshells, are listed in Tables S2 and S3.   (Table S4). The average Gd-O bond lengths reduced from 2.398 to 2.357 Å as x increased from 0 to 0.9, while the average Lu-O bond lengths reduced gradually from 2.356 to 2.314 Å as x increased from 0.1 to 1 (Figure 6). This suggests that the irregular REO 8 dodecahedron is not rigid enough to remain unchanged in Lu x Gd 1−x VO 4 solid solutions but will shrink or relax slightly with the change of the unit cell. Although the Gd-O and Lu-O bond lengths did not follow Vegard's law, the average RE-O bond lengths were distributed near the linear fits, following Vegard's law. The Gd-V interatomic distances reduced gradually while the Lu-V interatomic distances first increased and then decreased as the Lu content increased. Moreover, the average RE-V interatomic distances followed Vegard's law.
Nanomaterials 2023, 13, x FOR PEER REVIEW 7 of 15 the peak shape of the first coordination shell was probably due to the change in the distortion index of the REO8 dodecahedron (Table S4). The average Gd-O bond lengths reduced from 2.398 to 2.357 Å as x increased from 0 to 0.9, while the average Lu-O bond lengths reduced gradually from 2.356 to 2.314 Å as x increased from 0.1 to 1 ( Figure 6). This suggests that the irregular REO8 dodecahedron is not rigid enough to remain unchanged in LuxGd1−xVO4 solid solutions but will shrink or relax slightly with the change of the unit cell. Although the Gd-O and Lu-O bond lengths did not follow Vegard's law, the average RE-O bond lengths were distributed near the linear fits, following Vegard's law. The Gd-V interatomic distances reduced gradually while the Lu-V interatomic distances first increased and then decreased as the Lu content increased. Moreover, the average RE-V interatomic distances followed Vegard's law.

X-ray Photoelectron Spectroscopy of LuxGd1−xVO4 Solid Solutions
The elements, chemical states, and valence band structures of the LuxGd1−xVO4 nanocrystals were studied by XPS. The survey scans (Figure 7) confirmed the existence of only Lu, Gd, V, and O in all samples, except for the ubiquitous contaminated carbon. The intensity of characteristic peaks of Gd 3d, 4d and Lu 4p, 4d was enhanced with the increase in their respective contents; that is, they varied inversely with the change of x. Nanomaterials 2023, 13, x FOR PEER REVIEW 7 of 15 the peak shape of the first coordination shell was probably due to the change in the distortion index of the REO8 dodecahedron (Table S4). The average Gd-O bond lengths reduced from 2.398 to 2.357 Å as x increased from 0 to 0.9, while the average Lu-O bond lengths reduced gradually from 2.356 to 2.314 Å as x increased from 0.1 to 1 ( Figure 6). This suggests that the irregular REO8 dodecahedron is not rigid enough to remain unchanged in LuxGd1−xVO4 solid solutions but will shrink or relax slightly with the change of the unit cell. Although the Gd-O and Lu-O bond lengths did not follow Vegard's law, the average RE-O bond lengths were distributed near the linear fits, following Vegard's law. The Gd-V interatomic distances reduced gradually while the Lu-V interatomic distances first increased and then decreased as the Lu content increased. Moreover, the average RE-V interatomic distances followed Vegard's law.

X-ray Photoelectron Spectroscopy of LuxGd1−xVO4 Solid Solutions
The elements, chemical states, and valence band structures of the LuxGd1−xVO4 nanocrystals were studied by XPS. The survey scans (Figure 7) confirmed the existence of only Lu, Gd, V, and O in all samples, except for the ubiquitous contaminated carbon. The intensity of characteristic peaks of Gd 3d, 4d and Lu 4p, 4d was enhanced with the increase in their respective contents; that is, they varied inversely with the change of x.  The core-level O 1s, V 2p, Gd 4d, and Lu 4d XPS spectra (Figures 8-10) were analyzed to determine the chemical states of these elements in the LuxGd1−xVO4 solid solutions. The C 1s spectra all showed two peaks with a separation of about 4.6 eV, in which the stronger C 1s peak (284.6 eV) of the adventitious carbon (C-C/C-H) was used as a reference for binding energy calibration [35].
Due to the small overlap between the O 1s and V 2p1/2 peaks, it was essential to analyze the O 1s and V 2p spectra together [36]. The V 2p spectra contained two peaks due to spin-orbit splitting-an asymmetrical 2p1/2 and a symmetrical 2p3/2-and the 2p1/2 peak was broadened because of the Coster-Kronig effect [37]. The O 1s peaks were located at the higher-energy side of V 2p1/2 peaks. All of these O 1s and V 2p spectra showed a similar shape but a small amount of peak position shift, as can be seen from Figure 8a. The binding energy of O 1s changed from 529.9 to 530.2 eV, and it first increased and then decreased with the increases in x (Table S5). In addition to the predominant lattice O 1s peak, a low-intensity component located at 1.5 eV higher (inset of Figure 8a) could be attributed to the surface-adsorbed hydroxyl groups [38][39][40]. The binding energy of V 2p3/2 changed from 517.1 to 517.4 eV, similar to the change in the lattice O 1s (Figure 8b and Table S5). All of the binding energies were about 517.4 eV, indicating that V ions have only one +5 valence state in these solid solutions [36,41,42].

Chemical States of O, V, Lu, and Gd in Lu x Gd 1−x VO 4 Solid Solutions
The core-level O 1s, V 2p, Gd 4d, and Lu 4d XPS spectra (Figures 8-10) were analyzed to determine the chemical states of these elements in the Lu x Gd 1−x VO 4 solid solutions. The C 1s spectra all showed two peaks with a separation of about 4.6 eV, in which the stronger C 1s peak (284.6 eV) of the adventitious carbon (C-C/C-H) was used as a reference for binding energy calibration [35]. All of the Lu 4d spectra (Figure 9a) exhibited a doublet character due to the spinorbit interaction. The 4d3/2 and 4d5/2 peaks had almost the same FWHM, due to the 4f 14 filled shell of Lu 3+ , whereas metal Lu 4d peaks usually show extra broadening [43]. A separation of about 9.9 eV was observed, and the peak area ratios were in the range of 0.60- All of the Lu 4d spectra (Figure 9a) exhibited a doublet character due to the spinorbit interaction. The 4d3/2 and 4d5/2 peaks had almost the same FWHM, due to the 4f 14 filled shell of Lu 3+ , whereas metal Lu 4d peaks usually show extra broadening [43]. A separation of about 9.9 eV was observed, and the peak area ratios were in the range of 0.60-0.69-close to the theoretical values of 10.00 eV and 2/3, respectively [44]. The binding energy of the Lu 4d5/2 peak decreased gradually from 196.8 to 196.1 eV as x increased from 0.2 to 1 (Figure 9b and Table S5). Meanwhile, in the case of the Gd 4d core level, due to the existence of strong Coulomb-exchange interactions between 4d and the half-filled 4f 7 states together with the spin-orbit interaction in the 4d state, the Gd 4d XPS spectra exhibited a broad multiplet splitting structure including four peaks (A, B, C and D), as shown in Figure 10a [45]. Kowalczyk et al. qualitatively described the multiplet with spin antiparallel 7 DJ (J = 1, …, 5) (peaks B, C and D) and spin parallel 9 DJ (J = 2, …, 6) (peak A) final states [46]. In this work, the 9 D states were fitted by five sharp peaks with the same FWHM (1.66-1.83 eV) and a separation of 1.1 eV, and peak B was fitted by a broad Lorentzian-Gaussian mixed peak, according to the high-resolution XPS and lifetime broadening effect [41,45,47]. The fitting peaks of partial Gd 4d of GdVO4 are shown in the inset of Figure 10a as an example. The 9 D5 states (141.5-141.8 eV) with the strongest intensity were selected to observe the evolution of the binding energies of the Gd 4d level. The binding energies of Gd 4d showed a 0.1-0.3 eV chemical shift with the variation in the Lu content (Figure 10b and Table S5).  Table S5 and Due to the small overlap between the O 1s and V 2p 1/2 peaks, it was essential to analyze the O 1s and V 2p spectra together [36]. The V 2p spectra contained two peaks due to spin-orbit splitting-an asymmetrical 2p 1/2 and a symmetrical 2p 3/2 -and the 2p 1/2 peak was broadened because of the Coster-Kronig effect [37]. The O 1s peaks were located at the higher-energy side of V 2p 1/2 peaks. All of these O 1s and V 2p spectra showed a similar shape but a small amount of peak position shift, as can be seen from Figure 8a. The binding energy of O 1s changed from 529.9 to 530.2 eV, and it first increased and then decreased with the increases in x (Table S5). In addition to the predominant lattice O 1s peak, a low-intensity component located at 1.5 eV higher (inset of Figure 8a) could be attributed to the surface-adsorbed hydroxyl groups [38][39][40]. The binding energy of V 2p 3/2 changed from 517.1 to 517.4 eV, similar to the change in the lattice O 1s (Figure 8b and Table S5). All of the binding energies were about 517.4 eV, indicating that V ions have only one +5 valence state in these solid solutions [36,41,42].
All of the Lu 4d spectra (Figure 9a) exhibited a doublet character due to the spin-orbit interaction. The 4d 3/2 and 4d 5/2 peaks had almost the same FWHM, due to the 4f 14 filled shell of Lu 3+ , whereas metal Lu 4d peaks usually show extra broadening [43]. A separation of about 9.9 eV was observed, and the peak area ratios were in the range of 0.60-0.69-close to the theoretical values of 10.00 eV and 2/3, respectively [44]. The binding energy of the Lu 4d 5/2 peak decreased gradually from 196.8 to 196.1 eV as x increased from 0.2 to 1 ( Figure 9b and Table S5).
Meanwhile, in the case of the Gd 4d core level, due to the existence of strong Coulombexchange interactions between 4d and the half-filled 4f 7 states together with the spin-orbit interaction in the 4d state, the Gd 4d XPS spectra exhibited a broad multiplet splitting structure including four peaks (A, B, C and D), as shown in Figure 10a [45]. Kowalczyk et al. qualitatively described the multiplet with spin antiparallel 7 D J (J = 1, . . . , 5) (peaks B, C and D) and spin parallel 9 D J (J = 2, . . . , 6) (peak A) final states [46]. In this work, the 9 D states were fitted by five sharp peaks with the same FWHM (1.66-1.83 eV) and a separation of 1.1 eV, and peak B was fitted by a broad Lorentzian-Gaussian mixed peak, according to the high-resolution XPS and lifetime broadening effect [41,45,47]. The fitting peaks of partial Gd 4d of GdVO 4 are shown in the inset of Figure 10a as an example. The 9 D 5 states (141.5-141.8 eV) with the strongest intensity were selected to observe the evolution of the binding energies of the Gd 4d level. The binding energies of Gd 4d showed a 0.1-0.3 eV chemical shift with the variation in the Lu content (Figure 10b and Table S5).
As mentioned above, changes existed in the core-level binding energies of the elements in the series of solid solutions. Furthermore, the binding energy difference The XPS valence band spectra (Figure 11a) of the samples were analyzed in comparison with the first-principles-calculated density of states (DOS) and partial density of states (PDOS) of Lu0.5Gd0.5VO4 (Figure 11b). The valence band spectra (0-37 eV) are mainly composed of peaks of the Lu 5p, Lu 4f, Gd 5p, Gd 4f, O 2s, O 2p, and V 3d states, in which the doublet peaks at ~33.7 eV and ~27.3 eV are assigned to the Lu 5p1/2 and Lu 5p3/2 states [54]. The wide band ranging from 12.0 eV to 30.0 eV, with lower intensity, is attributed to the Gd 5p 7 P final state and the hybridization between the Gd 5p 9 P final state and the O 2s state [55]. The predominant peak with a bump on its lower-binding-energy side, ranging from 2.5 eV to 12.5 eV, is the valence band (VB). The strongest splitting peaks located at ~9.0 eV and ~7.8 eV, in the middle of the VB, should be assigned to Lu 4f5/2 and 4f7/2 doublets [17]. Meanwhile, the Gd 4f state presents as an asymmetric peak with much lower intensity located at ~8.2 eV, which is overlapped with the Lu 4f doublet and a bump (broad and very low intensity) of the hybridized states between the bonding O 2p and V 3d. Nevertheless, the Gd 4f and Lu 4f states are highly localized and do not participate in chemical bonding with ligand O atoms, as can be seen from the DOS and PDOS. The valence band maximum (VBM) is a bump and is contributed to by the O 2p nonbonding state. The hybridized states between the bonding O 2p and V 3d determine the minimum and width of the VB, leading to a broader and broader VB as the x value decreases. Due to the higher intensity and specific  [54]. The wide band ranging from 12.0 eV to 30.0 eV, with lower intensity, is attributed to the Gd 5p 7 P final state and the hybridization between the Gd 5p 9 P final state and the O 2s state [55]. The predominant peak with a bump on its lower-binding-energy side, ranging from 2.5 eV to 12.5 eV, is the valence band (VB). The strongest splitting peaks located at~9.0 eV and~7.8 eV, in the middle of the VB, should be assigned to Lu 4f 5/2 and 4f 7/2 doublets [17]. Meanwhile, the Gd 4f state presents as an asymmetric peak with much lower intensity located at~8.2 eV, which is overlapped with the Lu 4f doublet and a bump (broad and very low intensity) of the hybridized states between the bonding O 2p and V 3d. Nevertheless, the Gd 4f and Lu 4f states are highly localized and do not participate in chemical bonding with ligand O atoms, as can be seen from the DOS and PDOS. The valence band maximum (VBM) is a bump and is contributed to by the O 2p nonbonding state. The hybridized states between the bonding O 2p and V 3d determine the minimum and width of the VB, leading to a broader and broader VB as the x value decreases. Due to the higher intensity and specific doublet shape, it is obvious that the binding energies of the Lu 5p and 4f levels tend to decrease gradually with the increase in the Lu content, which is consistent with the evolutionary trend of the binding energy of the Lu 4d core level. This gradual change in the binding energies of the Lu core and valence levels originates from the variations in the lattice parameters induced by the displacement of Lu 3+ with Gd 3+ .

Conclusions
A series of Lu x Gd 1−x VO 4 (0 ≤ x ≤ 1) nanocrystals of 30-50 nm in size were synthesized by a citric acid sol-gel process. XRD demonstrated that the as-synthesized nanocrystals were single-phase zircon-type continuous solid solutions, and the lattice parameters decreased linearly with the increase in the x value-a decreased from 7.21287 Å to 7.02852 Å, while c decreased from 6.35552 Å to 6.23600 Å, following Vegard's law. The local structures of the central atoms of the GdO 8 and LuO 8 dodecahedrons studied by EXAFS showed that, to adapt to the shrunk unit cell, the Gd-O interatomic distances fluctuate reduced and Lu-O interatomic distances gradually reduced as the x value increased. The core-level electronic structures of all of the composition elements in Lu x Gd 1−x VO 4 , as functions of the x values, were analyzed by XPS. With the Lu content increasing from 0 to 1, the binding energy values of O 1s and V 2p first increased and then decreased, and their differences remained unchanged, indicating that the covalency of V-O bonds is less affected by composition. The ionicity of the Lu-O bonds weakened with the increasing x, while the ionicity of the Gd-O bonds fluctuated with small amplitude. The valence band electronic structure of Lu x Gd 1−x VO 4 was also studied by the combination of XPS and first-principles calculations. The O 2p nonbonding state was located at the top of the VB, the Gd 4f and Lu 4f states were highly localized and located in the middle of the VB, while the hybridized state between the bonding O 2p and V 3d was located at the bottom of the VB and overlapped with Gd 4f and Lu 4f states. The Lu 5p, 4f levels and 4d core level tended to decrease gradually with the increase in the x value. In conclusion, due to the lanthanide contraction, the Gd-O and  Table S1: Rietveld-refined cell parameters and R factors for Lu x Gd 1−x VO 4 solid solutions; Table S2: Fitting results of Lu x Gd 1−x VO 4 for the nearest and next-nearest neighbor coordination shells at the Gd L3-edge; Table S3: Fitting results of Lu x Gd 1−x VO 4 for the nearest and next-nearest neighbor coordination shells at the Lu L3-edges; Table S4: Average distances from the dodecahedron central atoms to the first and second coordination shells and the dodecahedron distortion indices for the Lu x Gd 1−x VO 4 solid solutions; Table S5: Binding energies of the characteristic peaks of all component elements and binding energy differences (∆BE) between metal and oxygen characteristic peaks of the Lu x Gd 1−x VO 4 solid solutions. Reference [56] is cited in the supplementary materials.