#
Synthesis and Basic Properties of Y_{1−x}Yb_{x}VO_{4} Obtained by High-Energy Ball Milling and High-Temperature Treatment

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{1−x}Yb

_{x}VO

_{4}is formed in the pseudo-binary system YVO

_{4}–YbVO

_{4}, and to investigate its basic unknown properties as a function of composition for 0.00 < x < 1.00. To date, such a solid solution has been obtained and characterized to a limited extent, but only for a few selected compositions. This solution was obtained by a high temperature and, for the first time, using mechanochemical methods. For the solution obtained by the high-energy ball-milling method, unknown physicochemical properties were established over its entire range of homogeneity. The solution was synthesized from mixtures of yttrium orthovanadate (V) with ytterbium (III) orthovanadate (V) of different compositions and investigated by XRD, IR, SEM, and UV-Vis(DRS) methods. It was found that Y

_{1−x}Yb

_{x}VO

_{4}crystallizes in a tetragonal system. The results confirmed that the solid solution Y

_{1−x}Yb

_{x}VO

_{4}has a structure of YVO

_{4}and YbVO

_{4}, and its structure is composed of YbO

_{6}and YO

_{6}octahedrons and VO

_{4}tetrahedrons. Moreover, if the parameter (x) in the solid solution Y

_{1−x}Yb

_{x}VO

_{4}increases, its crystalline lattice contracts and the value of the energy gap decreases. This solid solution is stable in the air atmosphere at least up to ~1500 °C. The estimated band gap for this solid solution indicates that it belongs to the semiconductors.

## 1. Introduction

_{2}O

_{5}–Yb

_{2}O

_{3}–Y

_{2}O

_{3}oxides is the YVO

_{4}–YbVO

_{4}system [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]. Yttrium orthovanadate(V) and ytterbium are well characterized in the literature [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. Methods for their syntheses are known, ranging from the solid-state reaction method to hydrothermal, Pechini, or co-precipitation [5,6,9,15,16,17,27,34,41]. It is also known that YVO

_{4}and YbVO

_{4}crystallize in a tetragonal system [7,11,30,31,32,35]. Depending on studies, the congruent melting temperature of YVO

_{4}varies from 1780 to 1810 °C, while YbVO

_{4}melts at ~1820 °C [18,19].

^{3+}, Eu

^{3+}, Dy

^{3+}, Sm

^{3+}, or Er

^{3+}ion results in materials able to be applied in high-resolution devices, such as cathode ray tubes (CRT), flat panel displays, and field emission displays (FED) [20,36,37,39,42,43,44,45,46]. Data on the properties of YVO

_{4}also point out that the compound is a useful matrix for the listed rare earth ions, making it possible to produce phosphors that emit light of different colors [20,21,33,42]. Yttrium orthovanadate(V) activated with Eu

^{3+}ions is an important red phosphor used in color television, cathode ray tubes, and high-pressure mercury lamps. On the other hand, YVO

_{4}activated with Dy

^{3+}ions is a potential component of white phosphors and Nd

^{3+}ions of blue ones [20,33,37].

_{4}with ytterbium ions and using it as a host material is a promising solution in the prospect of developing a low-threshold and high-performance solid-state erbium laser [12,20,38,40,41]. It is also possible to dope orthovanadium(V) ytterbium with other rare earth ions, such as neodymium, to produce lasers with a wavelength of 1.35 μm. YbVO

_{4}crystals doped with neodymium can produce red, green, or blue light with high efficiency and beam quality [13,20]. The phases obtained in the work are most often with general formulas YVO

_{4}:Yb

^{3+}and Yb:YVO

_{4}. The methods for obtaining such phases do not differ significantly from those for the synthesis of pure yttrium and ytterbium orthovanadates(V) [5,6,16,17,28,38]. The doping of YVO

_{4}with Yb

^{3+}ions using ytterbium orthovanadate(V) is rare, and if so, it is in a limited range of YbVO

_{4}concentrations, namely in the range of 0.4 to 25% molar of orthovanadate(V) in a mixture with YVO

_{4}[22,23,24,25]. In summary, to our knowledge and based on the performed literature review, comprehensive studies of the reactivity of yttrium orthovanadate(V) with ytterbium orthovanadate(V) over the entire concentration range of the components of the system comprising these compounds—i.e., in the YVO

_{4}–YbVO

_{4}system—have not yet been carried out.

^{3+}ions in the YVO

_{4}crystal lattice, corresponding to the Y

_{1−x}Yb

_{x}VO

_{4}solid solution for 0.004 < x < 0.25. Importantly, the study, mostly focused on monocrystalline samples, primarily examined their optical properties.

_{4}–YbVO

_{4}system are isostructural, and that the Y

^{3+}and Yb

^{3+}ions present in their structures have similar values of ionic radii (Yb

^{3+}—86.8 pm, Y

^{3+}—90.0 pm), the primary objective of our work was to experimentally demonstrate that a continuous substitutional solid solution with the general formula Y

_{1−x}Yb

_{x}VO

_{4}is formed in the YVO

_{4}–YbVO

_{4}system. As the sustainability of solid solution Y

_{1−x}Yb

_{x}VO

_{4}is not known, the DTA-TGA measurements in the air atmosphere and in the temperature range 25–1500 °C were performed. In this range, no thermal effects were observed on DTA and TG curves. The results prove that the obtained phase is stable in an air atmosphere at least up to ~1500 °C. Considering the fact that for the first time the mechanochemical method was used to obtain the solid solution, an additional objective was to study the effect of the degree of incorporation of Yb

^{3+}(x) ions into the YVO

_{4}crystal lattice on the physicochemical properties of the Y

_{1−x}Yb

_{x}VO

_{4}solution, i.e., lattice parameters, density, particle size distribution, or energy gap value, etc. The results presented in this work have significantly advanced the knowledge of the solid solution formed in the YVO

_{4}–YbVO

_{4}system. It was shown that the Y

_{1−x}Yb

_{x}VO

_{4}solid solution forms over the entire concentration range of the components of the studied system, i.e., for 0.00 < x < 1.00, and not only for 0.004 < x < 0.25. For the first time, such a nanometric solution was obtained mechanochemically. The unknown properties of the solution obtained both by high-temperature and mechanochemical methods were examined as a function of its composition.

## 2. Materials and Methods

_{4}and YbVO

_{4}, which were synthesized from the oxides Y

_{2}O

_{3}, a.p. (Alfa Aesar, Memphis, TN, USA), Yb

_{2}O

_{3}, a.p. (Alfa Aesar, Memphis, TN, USA), and V

_{2}O

_{5}, a.p. (POCh, Poland) by the mechanochemical and high-temperature methods described in refs. [1,22,23,24,30,31,32]. For the experiments, 10 samples were prepared from separately obtained YVO

_{4}and YbVO

_{4}(Table 1) by using two different methods:

_{α}with a graphite monochromator (2θ range 7–45°); time of counting 71.40 s, step 0.013.

- –
- SEM using an FE-SEM Hitachi SU–70 microscope. Analyses were performed at an accelerating voltage of 5 and 15 kV and secondary electron images were acquired. (Thermo Fisher Scientific); the blowup of the SEM images was 20.000 and 100.000.
- –
- IR—the measurements were made within the wavenumber range of 1200–400 cm
^{−1}, using a spectrophotometer Nicolet iS5 (ThermoFisher, Memphis, TN, USA). The technique of pressing pellets with KBr at the mass ratio of 1:300 was applied. - –
- LDS using Mastersizer 3000 (Malvern Panalytical, Malvern, UK), He-Ne laser (λ = 632.8 nm), LED (λ = 470.0 nm),
- –
- UV-Vis-DR spectra were measured using a UV-Vis spectrometer V-670 (JASCO, Japan) equipped with a reflecting attachment for the solid-state investigation (integrating sphere attachment with horizontal sample platform PIV-756/(PIN-757). The spectra were recorded in the wavelength region of 200–750 nm at room temperature.

## 3. Results and Discussion

#### 3.1. Mechanochemical Synthesis

_{4}–YbVO

_{4}system began with the preparation of five mixtures of YVO

_{4}with YbVO

_{4}with the compositions shown in Table 1. The compositions of these samples were chosen to represent different ranges of concentrations of the components of the system under study.

_{hkl}, whose values ranged from those identifying YVO

_{4}(PDF-card number: 04-007-6542), to those corresponding to YbVO

_{4}(PDF-cards number: 04-019-7298 and 04-008-3642). An analysis of the diffractograms of these samples therefore indicated that they were single phase and contained only a substitutional solid solution of YVO

_{4}or YbVO

_{4}structure. A subsequent 3 h milling step did not change the phase composition of all samples.

_{4}with YbVO

_{4}over the entire concentration range of the components of the system under study. Thus, it is a continuous substitution solid solution, the general formula of which can be written either as Y

_{1−x}Yb

_{x}VO

_{4(s.s.)}or as Yb

_{1−y}Y

_{y}VO

_{4(s.s.)}. For the solution so obtained, in the further description of the results, it was assumed that the matrix of the continuous, substituted solid solution is the compound YVO

_{4}.

_{4}with YbVO

_{4}, before and after the last stage of their synthesis.

^{3+}ions into the YVO

_{4}crystal lattice in place of Y

^{3+}ions, according to the reaction:

_{4 (s)}+ x YbVO

_{4 (s)}= Y

_{1−x}Yb

_{x}VO

_{4(s.s.)}

_{4}(Figure 1a) and YbVO

_{4}(Figure 1e), compared with fragments of the diffractograms of the Y

_{1−x}Yb

_{x}VO

_{4}solid solution obtained by the method for the first time for x = 0.10 (Figure 1b), x = 0.50 (Figure 1c), and x = 0.90 (Figure 1d).

_{1−x}Yb

_{x}VO

_{4(s.s.)}solid solution, showed that since the content of YbVO

_{4}increases in the initial mixtures of reactants, i.e., the value of x in the obtained solution, the XRD lines characterizing this phase are shifted toward higher angles 2Θ. This means that they correspond to smaller values of interplane distances d

_{hkl}relative to the X-ray characteristics of YbVO

_{4}.

^{3+}ion in octahedral coordination, which equals 86.8 pm, which is smaller than the radius of the Y

^{3+}ion, i.e., 90.0 pm. During the synthesis, a substitution of these ions takes place, leading to the contraction of the crystal lattice. These results are additional evidence for the formation of a substitutive continuous solid solution.

_{1−x}Yb

_{x}VO

_{4}solid solution obtained for the first time by the mechanochemical method (Figure 2) indicate that the crystallites of the obtained phase are small in size. The crystallite sizes of mechanochemically synthesized Y

_{1−x}Yb

_{x}VO

_{4}determined using Scherrer’s method are ~17 nm (x = 0.10), ~19 nm (x = 0.25), ~18 nm (x = 0.50), ~18 nm (x = 0.75), and ~15 nm (x = 0.90).

_{1−x}Yb

_{x}VO

_{4}solid solution synthesized for the first time by the mechanochemical method shows the crystalline structure of YVO

_{4}and YbVO

_{4}, i.e., a tetragonal system. For this purpose, powder diffractograms of the obtained Y

_{1−x}Yb

_{x}VO

_{4}solution for x = 0.10, 0.25, 0.50, 0.75, and 0.90 were subjected to refinement using the REFINEMENT program. The results confirmed that the obtained solid solution crystallizes in a tetragonal system, and its lattice parameters were calculated as a function of the degree of incorporation of Yb

^{3+}ions in place of Y

^{3+}into the YVO

_{4}crystal lattice. Table 2 shows the calculated elementary cell parameters of their volumes and densities: X-ray and experimental for the synthesized solid solution.

_{1−x}Yb

_{x}VO

_{4}formula, manifesting a higher incorporation degree of Yb

^{3+}ions and lower of the Y

^{3+}, the crystal lattice contracts and the volume of elementary cells decreases. Moreover, the density of the solid solution, determined using the gas ultrapycnometer, increases with an increase in the x value, which corresponds well with the calculated X-ray density. Close values obtained from two separate techniques substantiate the correctness of the selected solutions. Somewhat lower values of the experimental density are most likely a result of the measurement error originating, e.g., from the porosity and defects of the obtained material.

_{1−x}Yb

_{x}VO

_{4}solid solution for x = 0.50 (Figure 3c), were subjected to scanning electron microscopy (SEM) studies. Images of the obtained polycrystalline samples are shown in Figure 3.

_{1−x}Yb

_{x}VO

_{4}solid solution for x = 0.50 are very similar to the crystallites of the substrates, i.e., YbVO

_{4}and YVO

_{4}, in terms of their shape. In their appearance, they resemble irregular, very fine, “disordered” polyhedrons of varying sizes with the size of a significant part of them not exceeding 100 nm (Figure 3c).

_{1−x}Yb

_{x}VO

_{4}, obtained by the mechanochemical method, was determined using the LDS method (Figure 4).

_{1−x}Yb

_{x}VO

_{4}solid solution were determined to be nanometer-sized, i.e., ~100 nm (including 10% of ~29 nm for x = 0.10), ~440 nm (including 10% of ~102 nm for x = 0.25), ~58 nm (including 10% of ~22 nm for x = 0.50), ~55 nm (including 10% of ~21 nm for x = 0.75), and ~75 nm (including 10% of ~21 nm for x = 0.90). According to the LDS curve, the Y

_{1−x}Yb

_{x}VO

_{4}solid solution was found to have bimodal distribution, that is, it does not have a homogeneous distribution. It is known that when a material is milled using high-energy ball milling technique, the milled material can be reduced to the nanosize and may have an inhomogeneous distribution [51,52].

_{1−x}Yb

_{x}VO

_{4}. For this purpose, selected single-phase samples of the solution were studied by using infrared spectroscopy (IR). In addition to the IR spectra of the compounds YVO

_{4}(Figure 5a) and YbVO

_{4}(Figure 5e), the IR spectra of the obtained solid solution Y

_{1−x}Yb

_{x}VO

_{4}for x = 0.10, 0.50, and 0.90 are also shown in the figure (Figure 5b–d, respectively).

^{−1}wavenumber range), a broad absorption band (maxima of bands at 822–835 cm

^{−1}) with an inflection on the side of lower wavenumbers (maxima of bands at 735–750 cm

^{−1}) is present. Additionally, two very low intensity bands are also registered with maxima at around ~450 and 475 cm

^{−1}, respectively. The broad band at ~830 cm

^{−1}, according to literature data [14], is caused by stretching vibrations (ν) of V-O bonds in VO

_{4}tetrahedra. However, it cannot be ruled out that the recorded band with an inflection at ~750 cm

^{−1}is also related to stretching vibrations of Y-O or Yb-O bonds in YO

_{6}or YbO

_{6}octahedra [53,54,55]. In contrast, the bands at ~450 and 475 cm

^{−1}are, according to the literature, associated with bending (deformation) vibrations (δ) of the O-Y-O and/or O-Yb-O bonds [55,56]. An analysis of the recorded spectra made it possible to conclude that the absorption bands of the individual phases studied do not differ significantly, which proves that the phases are isostructural with respect to each other. The maxima of the absorption bands with an increase in the concentration of Yb

^{3+}ions in the crystal lattice of the obtained Y

_{1−x}Yb

_{x}VO

_{4}solid solution only slightly shift towards lower values of the wave numbers. Thus, the results of IR tests are additional confirmation that a continuous substitutional solid solution of Y

_{1−x}Yb

_{x}VO

_{4}with a YVO

_{4}or YbVO

_{4}structure is formed in the YVO

_{4}–YbVO

_{4}system. The structure of this solution is built from interconnected corners and/or edges of VO

_{4}tetrahedra and Y(Yb)O

_{6}octahedra.

_{4}(Figure 6a), YbVO

_{4}(Figure 6e), and the solid solution Y

_{1−x}Yb

_{x}VO

_{4}for x = 0.10, 0.50, 0.90 (Figure 6b–d) were subjected, was the UV-Vis-DRS. The UV-Vis-DR reflectance spectra recorded for the samples as a function of radiation energy were subjected to the Kubelka–Munk transformation to estimate their energy gap value.

^{2}= f(E) with the abscissa axis, i.e., the energy, as shown in Figure 6.

_{4}and YbVO

_{4}are ~3.52 eV and ~3.21 eV, while the value of the energy gap for the solid solution decreases with increasing x, i.e., from Eg = ~3.50 eV for Y

_{0.90}Yb

_{0.10}VO

_{4}to ~3.32 eV for Y

_{0.10}Yb

_{0.90}VO

_{4}[41].

_{1−x}Yb

_{x}VO

_{4}solid solution belongs to the group of wide energy gap semiconductors.

#### 3.2. High-Temperature Treatment

_{4}–YbVO

_{4}system, five samples of the solution (with identical compositions as in the first part of this work, Table 1) were prepared using the classical method of high-temperature solid-state reactions. Adequately, the substrates for the preparation of the mixtures, i.e., YVO

_{4}and YbVO

_{4}, were also obtained by using the high-temperature method [3,5,6]. Mixtures of YVO

_{4}with YbVO

_{4}(Table 1) after homogenization were heated in the following steps: I—1000 °C (12 h) → II—1200 °C (12 h) → III—1400 °C (12 h) → IV—1500 °C (12 h) (Figure 7).

_{4}+ YbVO

_{4}(Figure 7a) before heating compared with fragments of diffractograms of the Y

_{1−x}Yb

_{x}VO

_{4}solid solution for x = 0.50 (Figure 7b) after heating at a temperature of 1500 °C (12 h).

_{1−x}Yb

_{x}VO

_{4}solid solution (Figure 7b and Figure 8).

_{1−x}Yb

_{x}VO

_{4}solid solution was present in the samples was evidenced by the lines registered on their diffractograms, which corresponded to interplane distances falling within the range of values characteristic of analogous lines in the XRD set of pure YVO

_{4}and YbVO

_{4}. Both the position of the diffraction lines and their respective intensities were consistent with the results presented in the papers [5,6,35,38,41].

_{1−x}Yb

_{x}VO

_{4}was obtained over the entire range of concentrations of the components of the studied system.

_{4}(Figure 8a) and YbVO

_{4}(Figure 8e), compared with fragments of the diffractograms of the Y

_{1−x}Yb

_{x}VO

_{4}solid solution for x = 0.10 (Figure 8b), x = 0.50 (Figure 8c), and x = 0.90 (Figure 8d).

_{1−x}Yb

_{x}VO

_{4}solid solution obtained by the high-temperature treatment method crystallizes in a tetragonal system. For this purpose, powder diffractograms of the Y

_{1−x}Yb

_{x}VO

_{4}solution for x = 0.10, 0.25, 0.50, 0.75, and 0.90 were subjected to refinement (REFINEMENT program). Based on the results obtained, it was confirmed that the solid solution obtained by this method also crystallizes in a tetragonal system, and the parameters of its elementary cells were determined. Table 4 presents the calculated parameters of the elementary cells of their volumes and X-ray and experimental densities for the synthesized solid solution.

_{1−x}Yb

_{x}VO

_{4}, i.e., with an increasing degree of the incorporation of Yb

^{3+}ions in place of Y

^{3+}—similar to this solid solution obtained by the mechanochemical method—there is a contraction of the crystal lattice, i.e., the volume of elementary cells decreases. An analysis of these data in comparison with analogous ones for the mechanochemical method indicates, moreover, that the volume of elementary cells for the solution obtained by the high-temperature method is always smaller. It is this volume, among other things, that influences the higher values of density, both X-ray and experimental. These presented differences are due to the lower degree of structure defection and porosity of the solution obtained at high temperatures (from 1000–1500 °C).

_{4}and YbVO

_{4}, as well as the solid solution Y

_{1−x}Yb

_{x}VO

_{4}for x = 0.50 (Figure 9) obtained by the high-temperature treatment method, allowed us to conclude that the crystallites of the solid solution Y

_{0.5}Yb

_{0.5}VO

_{4}are very similar to those of the matrices, i.e., YVO

_{4}and YbVO

_{4}, in terms of shape.

_{1−x}Yb

_{x}VO

_{4}solid solution obtained by the high-temperature treatment method was determined (Figure 10).

_{1−x}Yb

_{x}VO

_{4}solid solution obtained by the high-temperature treatment method, unlike those of the solution obtained by the mechanochemical method, have micrometer sizes, i.e., of ~0.61 µm for x = 0.10, ~0.64 µm for x = 0.25, ~0.31 µm for x = 0.50, ~0.36 µm for x = 0.75, and ~0.33 µm for x = 0.90. In addition, based on the LDS curves, the particle size distribution of the Y

_{1−x}Yb

_{x}VO

_{4}solution obtained by the HT method was found to be inhomogeneous (Figure 10).

_{1−x}Yb

_{x}VO

_{4}solution synthesized by the second method exhibits the YVO

_{4}structure, IR investigations were carried out. In addition to the IR spectra of the YVO

_{4}(Figure 11a) and YbVO

_{4}(Figure 11e) compounds, the IR spectra of the obtained Y

_{1−x}Yb

_{x}VO

_{4}solid solution for x = 0.10, 0.50, 0.90 (Figure 11b–d) are also shown in Figure 11.

^{−1}, two narrow absorption bands were registered (Figure 11), which are located in the same wavelength number ranges as the absorption bands registered on the IR spectra of the phases obtained by the high-energy ball milling method (Figure 5). The difference is that the bands for the HT method are much narrower and more formed. Based on the literature [53,54,55], these bands can be attributed to both the stretching vibrations of V-O bonds in VO

_{4}tetrahedra, and the stretching vibrations of Y-O or Yb-O bonds in YO

_{6}or YbO

_{6}octahedra. At the same time, it was found that as the degree of the incorporation of Yb

^{3+}ions in place of Y

^{3+}into the YVO

_{4}crystal lattice increased, the recorded absorption bands of the solid solution (Figure 11b–d) shifted slightly towards lower wave number values. The results of this part of the work also confirmed that the Y

_{1−x}Yb

_{x}VO

_{4}solid solution obtained by the high-temperature treatment method exhibits a YVO

_{4}structure and is composed of VO

_{4}tetrahedra and Y(Yb)O

_{6}octahedra.

_{4}(Figure 12a), YbVO

_{4}(Figure 12e) and the solid solution Y

_{1−x}Yb

_{x}VO

_{4}for x = 0.10, 0.50, 0.90 (Figure 12b–d) in the last stage of the work were subjected to UV-Vis-DRS to estimate their energy gap values.

_{4}and YbVO

_{4}are, respectively, ~3.66 eV and ~3.55 eV, while the value of the energy gap for the solid solution decreases with increasing x, i.e., from Eg = ~3.62 eV for Y

_{0.90}Yb

_{0.10}VO

_{4}to ~3.57 eV for Y

_{0.10}Yb

_{0.90}VO

_{4}[41]. It was additionally determined that the energy gap values for the Y

_{1−x}Yb

_{x}VO

_{4}solution obtained by high-temperature treatment are slightly higher than the gap values for this solution obtained by high-energy ball milling. These differences are undoubtedly influenced by the size of the crystallites (the larger the crystallites, the higher the Eg value). Based on the results, it was concluded that the Y

_{1−x}Yb

_{x}VO

_{4}solid solution obtained by both methods belongs to the group of semiconductors with a wide energy gap.

## 4. Conclusions

_{1−x}Yb

_{x}VO

_{4}, where 0.00 < x < 1.00, is formed in the YVO

_{4}–YbVO

_{4}system.

_{4}with YbVO

_{4}by the high-temperature method, as well as by the high-energy ball milling method, which was used for the first time for the presented purpose.

_{1−x}Yb

_{x}VO

_{4}obtained by both methods, the crystal lattice of the solid solution contracted. Based on the LDS curves, the particle size distribution of the Y

_{1−x}Yb

_{x}VO

_{4}solution obtained by the two methods was found to be inhomogeneous. The structure of the solid solution obtained by both alternative synthesis methods consists of connected VO

_{4}tetrahedra with Y(Yb)O

_{6}octahedra. The energy gap values for the Y

_{1−x}Yb

_{x}VO

_{4}solution obtained by the high-temperature treatment method are slightly higher than the gap values for this solution obtained by the high-energy ball milling method. Regardless of the method of synthesis, Y

_{1−x}Yb

_{x}VO

_{4}solid solutions belong to the group of wide energy gap semiconductors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Fragments of diffractograms: (

**a**) YVO

_{4}(◆ PDF-card no: 04-007-6542), (

**b**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}, (

**d**) Y

_{0.10}Yb

_{0.90}VO

_{4}, (

**e**) YbVO

_{4}(■ PDF-cards no: 04-019-7298 and 04-008-3642).

**Figure 4.**Particle size distribution curve of: (

**a**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**b**) Y

_{0.75}Yb

_{0.25}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}, (

**d**) Y

_{0.25}Yb

_{0.75}VO

_{4}, (

**e**) Y

_{0.10}Yb

_{0.90}VO

_{4}.

**Figure 5.**IR spectrum of: (

**a**) YVO

_{4}, (

**b**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}(

**d**) Y

_{0.10}Yb

_{0.90}VO

_{4}, (

**e**) YbVO

_{4}.

**Figure 6.**The relationship (αhν)

^{2}as a function of the photon energy hν with the determined value of the energy gap Eg for: (

**a**) YVO

_{4}, (

**b**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}, (

**d**) Y

_{0.10}Yb

_{0.90}VO

_{4}, (

**e**) YbVO

_{4}.

**Figure 7.**Fragments of diffractograms: (

**a**) YbVO

_{4}(◆) + YVO

_{4}(•), (

**b**) Y

_{0.50}Yb

_{0.50}VO

_{4}(■).

**Figure 8.**Fragments of diffractograms: (

**a**) YVO

_{4}, (

**b**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}, (

**d**) Y

_{0.10}Yb

_{0.90}VO

_{4}, (

**e**) YbVO

_{4}.

**Figure 9.**SEM images of (

**a**) YbVO

_{4}, (

**b**) YVO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}obtained by high-temperature treatment.

**Figure 10.**Particle size distribution curve of: (

**a**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**b**) Y

_{0.75}Yb

_{0.25}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}, (

**d**) Y

_{0.25}Yb

_{0.75}VO

_{4}, (

**e**) Y

_{0.10}Yb

_{0.90}VO

_{4}(high-temperature treatment).

**Figure 11.**IR spectrum of: (

**a**) YVO

_{4}, (

**b**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}(

**d**) Y

_{0.10}Yb

_{0.90}VO

_{4}, (

**e**) YbVO

_{4}.

**Figure 12.**The relationship (αhν)

^{2}as a function of the photon energy hν with the determined value of the energy gap Eg for: (

**a**) YVO

_{4}, (

**b**) Y

_{0.90}Yb

_{0.10}VO

_{4}, (

**c**) Y

_{0.50}Yb

_{0.50}VO

_{4}, (

**d**) Y

_{0.10}Yb

_{0.90}VO

_{4}, (

**e**) YbVO

_{4}.

**Table 1.**Composition of initial mixtures and results of phase analysis of samples after the last stage of their ball milling and high-temperature treatment.

No. | % mol | x in Y _{1−x}Yb_{x}VO_{4} | Phase Composition of Samples after Synthesis by High-Energy Ball Milling and High-Temperature Treatment | |
---|---|---|---|---|

YVO_{4} | YbVO_{4} | |||

1 | 90.00 | 10.00 | 0.10 | Y_{0.90}Yb_{0.10}VO_{4} |

2 | 75.00 | 25.00 | 0.25 | Y_{0.75}Yb_{0.25}VO_{4} |

3 | 50.00 | 50.00 | 0.50 | Y_{0.50}Yb_{0.50}VO_{4} |

4 | 25.00 | 75.00 | 0.75 | Y_{0.25}Yb_{0.75}VO_{4} |

5 | 10.00 | 90.00 | 0.90 | Y_{0.10}Yb_{0.90}VO_{4} |

**Table 2.**Unit cell parameters, volumes and densities of solid solution Y

_{1−x}Yb

_{x}VO

_{4}for x = 0.10, 0.25, 0.50, 0.75, and 0.90 obtained by mechanochemical method.

x in Y _{1−x}Yb_{x}VO_{4} | a, b [nm] | c [nm] | α, β, γ [°] | V [nm^{3}] | d_{xrd}/d_{exp} [g/cm^{3}] |
---|---|---|---|---|---|

0.10 | 0.70553 | 0.67501 | 90.00 | 0.3360 | 4.20/4.09 ± 0.05 |

0.25 | 0.70207 | 0.67435 | 90.00 | 0.3324 | 4.50/4.37 ± 0.05 |

0.50 | 0.70185 | 0.67130 | 90.00 | 0.3307 | 4.95/4.67 ± 0.05 |

0.75 | 0.69929 | 0.66908 | 90.00 | 0.3272 | 5.42/5.08 ± 0.05 |

0.90 | 0.69888 | 0.65875 | 90.00 | 0.3217 | 5.77/5.43 ± 0.05 |

Formula of Solid Solution | Particle Size [µm] | ||
---|---|---|---|

d_{90} | d_{50} | d_{10} | |

Y_{0.90}Yb_{0.10}VO_{4} | 1.010 | 0.105 | 0.029 |

Y_{0.75}Yb_{0.25}VO_{4} | 2.420 | 0.432 | 0.102 |

Y_{0.50}Yb_{0.50}VO_{4} | 19.500 | 0.077 | 0.022 |

Y_{0.25}Yb_{0.75}VO_{4} | 0.416 | 0.069 | 0.021 |

Y_{0.10}Yb_{0.90}VO_{4} | 0.233 | 0.067 | 0.021 |

**Table 4.**Unit cell parameters, volumes and densities of solid solution Y

_{1−x}Yb

_{x}VO

_{4}for x = 0.10, 0.25, 0.50, 0.75, and 0.90 obtained by high-temperature treatment.

x in Y _{1−x}Yb_{x}VO_{4} | a, b [nm] | c [nm] | α, β, γ [°] | V [nm^{3}] | d_{xrd}/d_{exp} [g/cm^{3}] |
---|---|---|---|---|---|

0.10 | 0.71097 | 0.62832 | 90.00 | 0.3176 | 4.44/4.40 ± 0.05 |

0.25 | 0.70933 | 0.62739 | 90.00 | 0.3157 | 4.73/4.71 ± 0.05 |

0.50 | 0.70803 | 0.62677 | 90.00 | 0.3142 | 5.20/5.19 ± 0.05 |

0.75 | 0.70566 | 0.62523 | 90.00 | 0.3113 | 5.70/5.67 ± 0.05 |

0.90 | 0.70473 | 0.62475 | 90.00 | 0.3103 | 5.99/5.97 ± 0.05 |

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**MDPI and ACS Style**

Piz, M.; Filipek, E.; Klukowski, D.; Kochmański, P.
Synthesis and Basic Properties of Y_{1−x}Yb_{x}VO_{4} Obtained by High-Energy Ball Milling and High-Temperature Treatment. *Sustainability* **2023**, *15*, 14606.
https://doi.org/10.3390/su151914606

**AMA Style**

Piz M, Filipek E, Klukowski D, Kochmański P.
Synthesis and Basic Properties of Y_{1−x}Yb_{x}VO_{4} Obtained by High-Energy Ball Milling and High-Temperature Treatment. *Sustainability*. 2023; 15(19):14606.
https://doi.org/10.3390/su151914606

**Chicago/Turabian Style**

Piz, Mateusz, Elżbieta Filipek, Daniel Klukowski, and Paweł Kochmański.
2023. "Synthesis and Basic Properties of Y_{1−x}Yb_{x}VO_{4} Obtained by High-Energy Ball Milling and High-Temperature Treatment" *Sustainability* 15, no. 19: 14606.
https://doi.org/10.3390/su151914606