Characterization of Tungstates of the Type Hf_1−xLn_xW₂O_8−x/2 (Ln = Eu, Tm, Lu) Synthesized Using the Hydrothermal Method

Abstract

Pure HfW₂O₈- and Ln³⁺-containing solid solutions, Hf_1−xLn_xW₂O_8−x/2 (Ln = Eu, Tm, Lu), were synthesized using the hydrothermal method. The lanthanide ions were selected based on the differences between their ionic radii. A content of the Ln³⁺ ions in the range of 0.01–0.15 mol with a step of 0.02 was used for Hf_1−xLn_xW₂O_8−x/2 preparation, although the main research was performed on x = 0.01 and 0.05 samples because of an inhomogeneity detected by powder X-ray diffraction (XRD) when the content of Ln³⁺ was above 0.07–0.09 mol. X-ray diffraction measurements were supported by Raman and infrared spectroscopy. A new band in the Raman spectra of the samples with 0.05 mol Ln³⁺, as well as a red shift of the most intensive band (assigned to valence stretching of W-O-W bonds) as a result of the Ln³⁺ presence, was detected. The Scanning Electron Microscopy and Transmission Electron Microscopy micrographs revealed well-crystalized microcrystals with lengths in the range of 2–5 μm, with larger interplanar distances, measured in the solid solutions of the same crystal plain. The alpha-HfW₂O₈ → beta-HfW₂O₈ order-to-disorder phase transition was followed by high temperature XRD, and its reversibility was evident. The influence of the Ln³⁺ both on the unit cell parameters of the solid solutions and on the temperature of phase transition and on the coefficient of thermal expansion, CTE, was observed. A band gap energy in the range of 2.8–3.1 eV for pure HfW₂O₈ and for the solid solutions Hf_1−xLnxW₂O_8−x/2 (x = 0.01 and 0.05) was determined.

1. Introduction

Materials which contract upon heating, i.e., with negative thermal expansion (NTE), can play the role of thermal-expansion compensators, so they are considered important in the development of composites with adjustable thermal expansion [1,2,3]. Examples of these materials include various silicates [4], cyanide-bridged compounds [5], nickel-based perovskite oxide [6], and many others, reviewed in [7]. The isostructural tungstates from the group of the cubic AW₂O₈, A = Zr, Hf [8], are among these materials. The cubic AW₂O₈ have an open framework structure with WO₄ tetrahedra sharing three of their four oxygen atoms with the adjacent AO₆ octahedra [1,2,8,9,10]. ZrW₂O₈, as well as HfW₂O₈, shows an exceptionally large isotropic negative thermal expansion over an exceptionally large temperature range (0.3–1050 K) [8]. ZrW₂O₈ goes through an order–disorder change at about 440 K (167 °C) from a metastable, low-temperature cubic phase (alpha) with a coefficient of NTE of −9 × 10⁻⁶ K⁻¹ to a metastable, high temperature cubic phase (beta) with a coefficient of NTE of −5 × 10⁻⁶ K⁻¹ [8,10]. The NTE for HfW₂O₈ is less pronounced in the alpha-phase (−9 × 10⁻⁶ K⁻¹) than in beta-phase (−6 × 10⁻⁶ K⁻¹) with a temperature of order/disorder phase transition of 463 K [11], i.e., the absolute thermal expansion coefficient is slightly smaller for HfW₂O₈ than for ZrW₂O₈. Calorimetric studies show that the phase transition temperature is 24 K higher for HfW₂O₈ than for ZrW₂O₈, which is probably due to the stronger chemical bond of Hf-O than Zr-O [12]. In any case, ZrW₂O₈ and HfW₂O₈ show the low–high symmetry phase transition at similar temperatures and similar thermal contraction properties [9]. A phase transition from an alpha–phase to an orthorhombic gamma–phase induced under compression in both ZrW₂O₈ and HfW₂O₈ has been observed; significantly higher pressures are required to induce the transition in HfW₂O₈ than in ZrW₂O₈ [11]. The NTEs of those compounds originate from lattice vibrations, which could be affected by the masses and ionic radii of the constituent atoms [13]. The introduction of ions with different radii and charges can lead to a disorder in the crystalline structure of the tungstates and, consequently, to changes in their properties as detected by us for limited concentration ranges of Eu(III) on NTE and the phase transformation temperatures of ZrW₂O₈ [14]. The introduction of M⁴⁺, like Sn⁴⁺ and Ti⁴⁺ in tungstates [15,16], as well as the insertion of Y³⁺ and Lu³⁺ in HfW₂O₈, have been studied [17,18]. It has been found that even small amounts can led to essential changes in the temperatures of phase transitions, for instance, a 4% replacement decreases the temperature of the transition to 390 K for Y³⁺, 380 K for In³⁺ and 360 K for Sc³⁺ [17,18,19]. A series of solid solutions with a cubic ZrW₂O₈ structure, where the crystal sites of Zr⁴⁺ are substituted partially by lanthanide cations Ln³⁺ (Ln = Yb, Er, Eu), have been studied, and it has been found that the solubility of lanthanide cations in Zr_1−xLn_xW₂O_8−x/2 solid solutions increases as the radius of the lanthanide cations decrease [20]. In an attempt to expand the research, in this work, the influence of lanthanide ions Eu³⁺, Tm³⁺, and Lu³⁺ on the properties of HfW₂O₈ was followed by synthesis and characterization of solid solutions of the type Hf_1−xLn_xW₂O_8−x/2.

2. Materials and Methods

HfOCl₂•2H₂O (Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) and Na₂WO₄•2H₂O (Aldrich Chemie GmbH, Taufkirchen, Germany) (both ACS grade) were used as starting materials. The nitrates Ln(NO₃)₃•nH₂O were synthesized using Eu₂O₃ (Fluka Chemie GmbH, Buchs, Switzerland, p.a.), Tm₂O₃ (Sigma Aldrich, 99.99% Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany), and Lu₂O₃ (Sigma Aldrich, 99.99% Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) by dissolving them in heated diluted HNO₃ (70%, Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany), followed by crystallization after the cooling of the solution. Titration with a 0.01 M water solution of a di-sodium salt of ethylene diammine tetraacetic acid Na₂EDTA (99%+, Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) was applied to determine the amount of crystallization water in the nitrates synthesized.

The synthesis of HfW₂O₈: The initial water solutions of HfOCl₂•2H₂O (8.5 mL, 0.1 M) and Na₂WO₄ (8.5 mL, 0.1 M) were prepared with a calculated stoichiometric ratio of Hf/W = 1:2. The two solutions were added dropwise to 15 mL of distilled water simultaneously through dropping funnels. After mixing, the new solution (the white suspension) obtained was heated at 60 °C and stirred for 30 min. To obtain a homogeneous solution, 15 mL of 6 M HCl (37%, Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) was added (in order to obtain the final concentration of HCl about 3 M). An additional heating at 60 °C for 2 h was applied followed by adding of 5 mL 1-butanol. The solution obtained was heated in a 75 mL Teflon autoclave for 15 h at 180 °C, while stirring. Then, the obtained suspension was cooled down to room temperature followed by filtering, washing with water and ethyl alcohol, and drying at 50 °C. After calcination in preheated furnace for 1 h at 600 °C, the sample of HfW₂O₈ was analyzed and characterized.

The synthesis of the solid solutions: The procedure presented above for the pure HfW₂O₈ was followed for the synthesis of solid solutions, with only the exception of the first step, where a solution of Ln(NO₃)₃•nH₂O was added to obtain Hf_1−xLn_xW₂O_8−x/2 samples. The amount of the Ln³⁺ (Ln = Eu, Tm, Lu) ions used was in the range of 0.01–0.15 mol with a step of 0.02. The scheme for the typical synthesis procedure applied is presented in Figure 1.

The methods for characterization were as follows. A high temperature XRD was performed using a PANalytical Empyrean diffractometer (Malvern PANalytical Empyrean, Almelo, Netherlands) with a PIXcel 3D detector. The XRD patterns were recorded between 15–90° 2θ with a step of 0.026°. An Anton Paar HTK 16N camera (Anton Paar GmbH, Graz, Austria) was used for in situ high-temperature measurements in the interval of 25–250 °C with different steps. The unit cell parameters were calculated using the Rietveld method using the FullProf Suite software (v01-2021, Grenoble, France) [21]. Raman spectroscopy: The measurements were carried out on a HORIBA Jobin Yvon Labram HR 800 micro-Raman spectrometer (Horiba, Piscataway, NJ, USA) with a He–Ne (633 nm) laser, the absolute measurement accuracy of which was 0.5 cm⁻¹ or better. FT–IR spectroscopy: The measurements were performed on a FT–IR Nicolet 6700—Thermo Scientific (Waltham, MA, USA). UV–Vis absorption spectroscopy was applied using an Evolution 300 UV–Vis spectrometer (Thermo Scientific, Waltham, MA, USA) to measure the absorption in the range of 200–900 nm. Transmission Electron Microscopy, TEM: investigations were performed on a JEM 2100 (JEOL, Tokyo, Japan) transmission electron microscope with an accelerator voltage of 200 kV and up to 1,500,000 times magnification. SEM: A Hitachi TM4000 (Krefeld, Germany) was used, with an accelerating voltage 15 kV.

3. Results

3.1. XRD of α-HfW₂O₈ and β-HfW₂O₈

The structures of α-HfW₂O₈ and β-HfW₂O₈ were needed to evaluate the structure of the solid solutions. As long as our ICSD database did not contain .cif files of the α-HfW₂O₈ nor β-HfW₂O₈, we used the .cif file for α-ZrW₂O₈ (ICSD PDF #50-1868) to present the structure of α-HfW₂O₈, which is isostructural to α-HfW₂O₈. As for β-HfW₂O₈, the .cif file of ZrW_0.977Mo_1.023O₈ (ICSD PDF #01-070-6112), which is isostructural to β-ZrW₂O₈ and β-HfW₂O₈, was used [22]. The diffractograms of the low-temperature phase (α-HfW₂O₈) and the high-temperature phase (β-HfW₂O₈) synthesized using the hydrothermal method along with mentioned ICSD data are shown in Figure 2. The starting structural parameters used for α-HfW₂O₈ and β-HfW₂O₈ are listed in Tables S1 and S2.

3.2. Characterization of the Solid Solutions Hf_1−xLn_xW₂O_8−x/2 by XRD; Raman and IR Spectroscopy—Homogeneity of the Samples; Influence of Ln³⁺

By introducing Ln³⁺ ions to the structure of HfW₂O₈ oxygen vacancies were generated, leading to the general formula of our solid solutions, i.e., Hf_1−xLn_xW₂O_8−x/2. It is widely accepted that O-vacancies introduced in this way are considered intrinsic, but we did not follow their evolution, nor did we have a way to measure them exactly. Essential to point out is that, during the Rietveld refinement, the occupancy of all O-atoms was refined, but, due to the very low concentration of these defects, we did not notice any major deviations.

The powder X-ray diffraction patterns of the solid solutions evidenced their crystalline nature. All diffractograms show the reflection peaks typical for HfW₂O₈. XRD patterns of the samples Hf_1−xEu_xW₂O_8−x/2, 0.01 ≤ x ≤ 0.15, recorded at 25 °C, are presented in Figure 3. The reflexes observed in the samples of Hf_1−xEu_xW₂O_8−x/2 with x = 0.09 and up to x = 0.15 indicate the formation of a secondary WO₃ phase. Based on that, it can be stated that the samples of Hf_1−xLn_xW₂O_8−x/2 obtained were phase-homogeneous up to x = 0.07, as shown by the powder XRD patterns of Hf_1−xEu_xW₂O_8−x/2. Considering that, we focus our further research mainly on the solid solutions Hf_1−xLn_xW₂O_8−x/2 with x 0.01 and 0.05.

Taking into account that Raman spectroscopy is known as an effective and sensitive method to track the changes in the position of and bonding between the atoms of W and O in the crystal lattice [23], Raman spectra were recorded for the pure α-HfW₂O₈ and the solid solutions Hf_1−xLn_xW₂O_8−x/2, x = 0.01 and 0.05. The structure of α-HfW₂O₈ is viewed as a network of corner-sharing HfO₆ octahedra and WO₄ tetrahedra, and the Raman modes of tungstates are assigned as lattice modes, translation, vibrational, and internal modes of WO₄ in the range of 100–1,100 cm⁻¹ [24,25]. In the Raman spectrum of the pure α-HfW₂O₈ bands, low- and high-wavenumbers, in the range of 400–100 and 1,040–700 cm⁻¹ are observed (Figure 4). The precise values of the bands position are listed in Table S3.

The Raman spectra interpretation was based on the literature data [26]. The modes centered at 1,026, 999, 921, 896, and 859 cm⁻¹ can be assigned to the symmetric stretching vibrations vs. modes of the WO₄; the modes of 796, 746 to the WO₄ asymmetric stretching (v_as modes); the one at 373.03 to the asymmetric bending, 345.9, 322.8; and 297.1 cm⁻¹ to the symmetric bending modes. The bands at 199 and 125 cm⁻¹ are regarded as originating from lattice modes.

In the Raman spectra of the solid solutions Hf_1−xLn_xW₂O_8−x/2, a shifting of bands toward higher wavenumbers, i.e., higher frequencies, is observed (Figure 4a,b). This shifting affects the bands assigned to the stretching vibrations of W−O−W bonds, ν_s(WO₄), namely, 795.5 cm⁻¹ (the most intensive one) and 745.9 cm⁻¹ (the weaker one) of HfW₂O₈. Both bands are shifted to higher wavenumbers, i.e., 812–813 and 764–765 cm⁻¹, respectively, in the solid solutions Hf_1−xLn_xW₂O_8−x/2, x = 0.01 and x = 0.05 (Figure 4a,b). Additionally, new bands at 721, 723, and 693 cm⁻¹ were detected in the spectra of Hf_0.95Ln_0.05W₂O_8−x/2, Ln = Eu, Tm, and Lu, respectively. At the same time, the shifting of the band at 1,025.98 cm⁻¹ for pure α-HfW₂O₈ toward the higher wavenumber of 1,043 cm⁻¹ for Hf_0.99Ln_0.01W₂O_8−x/2 and Hf_0.95Ln_0.05W₂O_8−x/2 is clear evidence of the influence of Ln³⁺ on the crystal structure. Regarding the position of the band, the influence of Ln³⁺ is expressed by the essential decreasing of the intensity of the band in question, 1,043 cm⁻¹, for the samples Hf_0.95Ln_0.05W₂O_8−x/2, i.e., the effect of the incorporation of the larger amount of Ln³⁺ is detected.

In addition to the Raman, infrared spectra of the samples were recorded in the range of 4,000–400 cm⁻¹, with easily noticeable bands showing the presence of water (Figure S1). The more informative range of 1,100–400 cm⁻¹, with the absorption bands of 941, 917, 882, 832, 809, 777, and 761 cm⁻¹ accentuated with dashed lines, are shown in Figure 5.

The bands are caused by the symmetric (941, 917, 882, and 832 cm⁻¹) and asymmetric stretching vibrations of W-O in WO₄ tetrahedra (809, 777, and 761 cm⁻¹) [26]. The asymmetric and symmetric bending, as well as the lattice modes, were below 400 cm⁻¹, and so, they were not detected by the FT–IR equipment used. The influence of the Ln³⁺ doping is revealed in the spectrum of Hf_0.95Lu_0.05W₂O_8−x/2, where a broadening of the band at 761 cm⁻¹ is visible, although slightly noticeable in the spectra of the other Hf_0.95Ln_0.05W₂O_8−x/2.

3.3. The Morphology of the Samples by Electron Microscopy, SEM, and TEM

The SEM micrographs exhibit similar needle-like crystals of HfW₂O₈ (Figure 6a) and of the solid solutions Hf_0.99Eu_0.01W₂O_8−x/2 and Hf_0.095Eu_0.05W₂O_8−x/2 (Figure 6b,c), proving that the morphology is not affected by Ln³⁺. SEM micrographs of the precursor HfW₂O₇(OH;Cl)₂ and α-HfW₂O₈ verifying the method of α-HfW₂O₈ formation are shown in Figure S2.

The needle-like microcrystals, similar to those observed through SEM, were detected by TEM for α-HfW₂O₈ and the solid solutions; some more micrographs are included in the supplementary information (Figure S3). Well-formed microcrystals with high crystallinity are shown for Hf_0.99Tm_0.01W₂O_7.995 in Figure 7a. The lengths of the microcrystals vary in the range of 2 to 5 μm.

The lattice arrangements, clearly arranged crystalline planes and interplanar distances for the solid solutions Hf_0.99Lu_0.01W₂O_7.995, Hf_0.99Eu_0.01W₂O_7.995, and Hf_0.95Eu_0.05W₂O_7.975 are shown in Figure 7b–d.

The crystal plane alignments in the direction correspondent to the highest XRD diffraction peak in the cubic structure of α-HfW2O8 can be seen. The interplanar distances of the samples Hf_0.95Eu_0.05W₂O_7.975 and Hf_0.99Lu_0.01W₂O_7.995 (220) and (221) show increasing distances for Hf_0.95Eu_0.05W₂O_7.975, which is a result of the bigger ionic radius of Eu³⁺ (94.7 pm Eu³⁺; 86.1 pm Lu³⁺ [27]).

3.4. Phase Transition; Reversibility; and the Coefficients of Thermal Expansion in the Pure HfW₂O₈ and in the Solid Solutions Hf_1−xLn_xW₂O_8−x/2 (x = 0.01 and 0.05)

3.4.1. The Phase Transition α-HfW₂O₈ to β-HfW₂O₈ and its Reversibility

The X-Ray diffraction patterns recorded at 25/250/25 °C of pure HfW₂O₈ synthesized by hydrothermal method are presented in Figure 8, from them, the α-HfW₂O₈ ⇌ β-HfW₂O₈ transition and its reversibility follows. The reflex at 16.9 2Theta diminishes its intensity, while the intensity of the reflex at 31 2Theta diminishes and disappears with the temperature increase (indicated by arrows in Figure 8). As long as the latter two reflexes are typical for α-HfW₂O₈, their disappearance at 250 °C is a sign of the completed phase transition α-HfW₂O₈ → β-HfW₂O₈. After cooling down to 25 °C, these reflexes can be detected again as evidence for the reversibility of the transition (Figure 8).

3.4.2. Unit Cell Parameters and Coefficients of Thermal Expansion (CTE)

The unit cell parameters and the coefficients of thermal expansion (CTE) for pure HfW₂O₈ and Hf_1−xLn_xW₂O_8−x/2, x = 0.01 and 0.05, along with the coefficients of thermal expansion (CTE) calculated for the interval 25–100 °C (α-HfW₂O₈ phase) and 200–250 °C (β-HfW₂O₈ phase) and 25–250 °C are presented in

Table 1. Unit cell parameters and CTE for pure HfW₂O₈ and Hf_1−xLn_xW₂O_8−x/2 (x = 0.01 and 0.05).

	T °C	HfW2O8	Hf1−xEuxW2O8−x/2		Hf1−xTmxW2O8−x/2		Hf1−xLuxW2O8−x/2
			x = 0.01	x = 0.05	x = 0.01	x = 0.05	x = 0.01	x = 0.05
Unit cell parameters, Å	25	9.1244(2)	9.1246(3)	9.1245(1)	9.1245(1)	9.1245(1)	9.1244(1)	9.1243(1)
	100	9.1174(1)	9.1179(1)	9.1177(1)	9.1171(1)	9.1170(1)	9.1173(1)	9.1172(1)
	200	9.1055(1)	9.1058(2)	9.1057(1)	9.1050(3)	9.1049(1)	9.1049(1)	9.1048(1)
	250	9.1050(1)	9.1051(1)	9.1053(2)	9.1044(1)	9.1046(1)	9.1044(1)	9.1045(2)
CTE, ×10−6 K−1	25–100	−10.22	−9.79	−9.94	−10.81	−10.96	−10.38	−10.36
	200–250	−1.10	−1.54	−0.87	−1.32	−0.66	−1.10	−0.66
	25–250	−9.45	−9.49	−9.35	−9.79	−9.69	−9.74	−9.64

.

Considering that HfW₂O₈ solid solutions have isotropic negative thermal expansion, we used the classical formula for linear expansion (instead of volume expansion) [14]

$$∆a=\alpha a_{298}∆T,$$

where $∆a$ is the change in the unit cell parameter, α is the linear coefficient of thermal expansion, $a_{298}$ is the unit cell parameter at room temperature, and $∆T$ is the change in the temperature.

It can be seen that the cubic unit-cell parameter for pure HfW₂O₈ in fact diminishes with the temperature increase from 25 to 250 °C, proving that the cell shrinks and demonstrating the negative coefficient of thermal expansion. The same tendency is observed for the unit cell parameters of Hf_0.99Ln_0.01W₂O_8−x/2 and Hf_0.95Ln_0.05W₂O_8−x/2, upon the temperature increase (Table 1). When the Ln³⁺ content increases from x = 0.01 to x = 0.05, an influence on the unit cell parameters is observed; this influence is well pronounced for Eu³⁺, i.e., a slight decrease for the low-temperature phase α-Hf_1−xLn_xW₂O_8−x/2 (25 °C) and a slight increase for the high temperature phase β-Hf_1−xLn_xW₂O_8−x/2 (250 °C) (within the error range). In comparison with the pure HfW₂O₈, an increase of the cubic unit-cell parameter of Hf_1−xLn_xW₂O_8−x/2 is noticeable, especially for the Eu³⁺-containing samples (Table 1), as result of the bigger Eu³⁺ ion.

The coefficients of thermal expansion calculated were −10.22 and −1.10 × 10⁻⁶ K⁻¹, for the pure α-HfW₂O₈ and β-HfW₂O₈ phases, respectively (Table 1). They differ from the literature data, −9 × 10⁻⁶K⁻¹ and −6 × 10⁻⁶K⁻¹ [11], quite likely as a result of the different method used for synthesis. The presence of Ln³⁺ in the solid solutions is essential for the α-HfW₂O₈ phase to effect an increase of CTE, and for β-HfW₂O₈ phase, to effect a decrease of CTE when a Ln³⁺ increase is observed. For the low temperature, the α-Hf_1−xLn_xW₂O_8−x/2 phase (25–100 °C) CTE increases with Ln³⁺ especially for Eu³⁺- and Tm³⁺-containing samples. The CTE values for the high-temperature phase β-Hf_0.95Ln_0.05W₂O_8−x/2 (200–250 °C) are lower than the value for the pure high-temperature β-HfW₂O₈ phase.

The high-temperature XRD values for Hf_1−xLn_xW₂O_8−x/2 (x = 0.01; Ln = Eu, Lu) show that the temperature of 140 °C is a critical temperature for the phase transition, i.e., the reflex at 31 2Theta, typical for α- HfW₂O₈, disappears there (Figure 9a,b).

3.4.3. Order-to-Disorder Phase Transition for Hf_1−xLnxW₂O_8−x/2 (x = 0.01; 0.05) and the Role of Ln³⁺

The structure of the low-temperature α-HfW₂O₈ and β-HfW₂O₈ phase has corner-sharing HfO₆ octahedra and WO₄ tetrahedra. The difference concerns the WO₄ tetrahedra, namely, in the α-HfW₂O₈ phase, each WO₄ tetrahedron shares three of its oxygen atoms with the adjacent octahedra, while, in the high-temperature β-HfW₂O₈ phase, two WO₄ share three joined O atoms. The crystal structures of the low-temperature α-Hf_1−xLn_xW₂O_8−x/2 and the high-temperature β-Hf_1−xLn_xW₂O_8−x/2 are shown in Figure 10, where the half-filled WO₄ in β- Hf_1−xLn_xW₂O_8−x/2 are accentuated by color.

The orientations of the WO₄ tetrahedra determine the transition pf α-HfW₂O₈ → β-HfW₂O₈, which is called order-to-disorder phase transition [8]. The extent of the WO₄ tetrahedra disorder depending on the temperature can be evaluated by the parameter η_T’ [20], calculated by the following equation:

$${\eta }_T^{\prime }=\sqrt{\frac{{\left[\left(\frac{I310}{I210}\right)\right]}_T}{{\left[{\left(\frac{I310}{I210}\right)}_{HfW2O8}\right]}_{298K}}},$$

where I310 and I210 are the integrated intensities of the reflections (310) and (210), respectively; the former indicates the ordered α-HfW₂O₈ phase, the latter does not changing during the phase transition. As can be seen in Figure 11, the relative order parameter at room temperature significantly decreases when Eu³⁺ is introduced to the system, leading to a higher degree of distortion in Hf_0.99Eu_0.01W₂O_8−x/2. The effect of Tm³⁺ and Lu³⁺ on Hf_0.99Ln_0.01W₂O_8−x/2 is less pronounced, and it can be explained by the degree of solid solubility of the heavier Ln³⁺, which is much more soluble in the system due to the smaller ionic radii in comparison with Hf⁴⁺ radius (Lu³⁺ 86.1, Tm³⁺ 88.0, Eu³⁺ 94.7, Hf⁴⁺ 71 pm, CN 6 [27]).

3.5. UV–Vis Absorption of the Solid Solutions and the Energy of the Band Gaps

The absorbance in the UV–Vis range (200–450 nm) shows a clear maximum at approximately 250 nm for all samples. A weak absorbance at approximately 400 nm differs Hf_1−xTm_xW₂O₈ (x = 0.01 and 0.05) from the other samples (Figure 12a). It is quite likely that the bands between 250 and 350 nm exist due to the strong ligand-to-metal charge transfer observed both in slightly distorted monotungstate structures and polytungstates [28].

Band-gap-energy calculations were accomplished based on UV–Vis data (Figure 12a,b) and listed in

Table 2. Energy band gap of the samples, eV.

№	Sample	Band Gap Eg, eV
1	α-HfW2O8	2.87
2	α-ZrW2O8	2.84 [31]
3	Hf0.99Eu0.01W2O7,995	3.02
4	Hf0.95Eu0.05W2O7.975	2.92
5	Hf0.99Tm0.01W2O7.995	3.10
6	Hf0.95Tm0.05W2O7.975	2.78
7	Hf0.99Lu0.01W2O7.995	3.12
8	Hf0.95Lu0.05W2O7.975	2.78

. The UV–Vis data were analyzed to determine the relationship among the optical band gap, absorption coefficient, and energy (hν) of the incident photon for near-edge optical absorption. The calculations were performed from the measured curves by fits according to Tauc’s equation [29]; i.e., αhν = A(hν − Eg)ⁿ, where A is a constant independent of hν, E_g is the band gap, and n depends on the type of transition. In addition, the well-known approach for E_g determination from the intersection of the linear fits of (αhν)^1/n versus hv on the x-axis was used, n being 1/2 and 2 for direct and indirect band gaps, respectively.

The band gap value of the pure α-HfW₂O₈, 2.87 eV, obtained by the Tauc’s equation corresponds well to the value observed by Ouyang for pure α-ZrW₂O₈, 2.84 eV [30]. The values of the solid solutions for all samples of the type Hf_0.99Ln_0.01W₂O_8−x/2 increased in the range of 3.02, 3.10, and 3.12 eV, for Eu³⁺, Tm³⁺, and Lu³⁺, respectively. This can be attributed to the decrease of the crystallites due to the presence of Ln³⁺ [31]. Interestingly, the further incorporation of Ln³⁺ for Hf_0.95Ln_0.05W₂O_8−x/2 leads to the significant narrowing of the band gap, especially for Tm³⁺ and Lu³⁺ (2.78 eV), most likely due to the increased order of distortion of the WO₄ polyhedra. A similar effect was observed by Muthu and coauthors [32] due to pressure induced amorphization.

4. Conclusions

Using the hydrothermal method, pure HfW₂O₈- and Ln³⁺-containing homogeneous solid solutions Hf_1−xLn_xW₂O_8−x/2 (x = 0.01, 0.05; Ln = Eu, Tm, Lu) were obtained and characterized by XRD, Raman, FT–IR spectroscopy, and electron microscopy. The influence of Ln³⁺ was detected by (i) the Raman spectra shifting to the higher wavenumbers of the most intensive bands of Hf_1−xLn_xW₂O_8−x/2; (ii) the unit cell parameters decreasing with the temperature for the solid solutions Hf_1−xLn_xW₂O_8−x/2 in connection with the isotropic negative thermal expansion; (iii) the observed increase of CTE for the α-HfW₂O₈ phase and the decrease of CTE for the β-HfW₂O₈ phase, with a Ln³⁺ increase; (iv) the increased energy-band-gap values of the solid solutions Hf_0.99Ln_0.01W₂O_8−x/2 with decreases in the atomic radii of Eu³⁺, Tm³⁺, and Lu³⁺; and (v) the significant narrowing of the band gap for Hf_0.95Ln_0.05W₂O_8−x/2 (Ln = Tm³⁺ and Lu³⁺) due to the increased order of distortion of the WO₄ polyhedra.

The question for the potential incorporation of Ln³⁺ into the structure of the tungstates is interesting taking into account the options for the potential position of the Ln³⁺, i.e., either in the interstices or on the surface or by replacing the Hf⁴⁺ ions in the HfO₆ octahedra. This is challenging due to the fact that hafnium and lanthanides possess different atomic and ionic radii, complicating the replacement of Hf⁺⁴/Ln³⁺. On the other hand, the differences between the typical oxidation states of lanthanides and hafnium, +3 and +4, respectively, leads to the question of the neutrality of the charge of the solid solutions formed, which makes it important to follow the oxygen vacancies. In spite of the Rietveld refinement of the occupancy of all oxygen atoms, due to the very low concentration of defects, major deviations were not detected.