The formation energy, phase transition, and negative thermal expansion of Fe_2−xSc_xW₃O₁₂

Abstract

Tungstates with a molecular formula A₂W₃O₁₂ exhibits a wider negative thermal expansion (NTE) temperature range than molybdates but are challenging to synthesize, especially when A = Fe or Cr with metastable structures. To enhance the structural stability of Fe₂W₃O₁₂, Sc with lower electronegativity is adopted to substitute Fe according to Fe_2−xSc_xW₃O₁₂, considering the thermodynamic stability of Sc₂W₃O₁₂. It is shown that the solid solutions can be easily synthesized and the phase transition temperature (PTT) can be tuned to well below room temperature (RT). Theoretical calculations and experimental results show that the formation energy decreases and the W–O bond in Fe–O–W gradually strengthens as the substitution of Sc in Fe_2−xSc_xW₃O₁₂ increases, indicating an increase in structural stability. NTE is enhanced after phase transition with an increase in the Sc content. The reduction in PTT and the enhancement in NTE properties of Fe₂W₃O₁₂ could result in a decrease in the effective electronegativity of the Fe-site elements, resulting in a low formation energy and strengthened W–O bond in Fe–O–W, which corresponds to a more stable structure.

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1 Introduction

Materials with negative thermal expansion (NTE) properties have potential advantages in modulating the coefficients of thermal expansion (CTEs) and improving the thermal shock resistance of devices and instruments. In recent years, significant progress has been made in NTE materials, such as framework oxides,^1–9 fluorides,^10–12 and cyanides.^13–17

However, NTE materials still have some disadvantages in practical applications, such as hygroscopicity,¹⁸ toxicity,¹⁹ a narrow NTE temperature range,²⁰ sensitivity toward high temperatures,²¹ negative environment impacts,²² and difficult synthesis.²³

Oxide-based NTE materials with a stable structure and wide NTE temperature range offer an excellent platform for designing novel NTE materials with the desired properties for potential applications. One of the oxide-based NTE materials, A₂M₃O₁₂, where A is a trivalent transition metal or rare earth element and M is Mo⁶⁺ or W⁶⁺, generally has an NTE in a wide temperature range and is chemically flexible for the design of NTE materials with desired properties.^24–30 However, their NTE is observed only after the phase transition from a low-temperature monoclinic to a high-temperature orthorhombic structure. Moreover, they are hygroscopic and, except for Sc₂M₃O₁₂, their NTE generally appears after the complete depletion of water molecules. Furthermore, tungstates are more challenging to synthesize than molybdates. These limiting factors seriously restrict their industrial applications. Much effort has been devoted to regulating the phase transition and reducing the hygroscopicity toward designing NTE materials with desired properties.^1,31

Fe₂W₃O₁₂ is compositionally cheap, but it is challenging to obtain a high purity regardless of the solid-state reaction or sol–gel method owing to its metastable structure.^32,33 Its monoclinic to orthorhombic phase transition is reported at about 687 K and is accompanied by abrupt volume thermal expansion.³⁴ Mary et al. reported that Sc³⁺ substitution could promote Ga₂W₃O₁₂ to form a pure phase material.³⁵ Varga et al. reported that Sc₂W₃O₁₂ is thermodynamically stable, while other tungstates in the A₂W₃O₁₂ series were only entropically stabilized at high temperatures.³⁰ Therefore, it is reasonable that the metastable structure of Fe₂W₃O₁₂ could be stabilized by introducing Sc. In this paper, we report a method for synthesizing Fe₂W₃O₁₂ and reducing its phase transition temperature (PTT) below room temperature (RT) by introducing Sc. Theoretical calculations show that the formation energy decreases and the W–O bond in Fe–O–W gradually strengthens as the substitution amount of Sc in Fe_2−xSc_xW₃O₁₂ increases.

2 Materials and methods

Analytical grade reagents of Fe₂O₃, Sc₂O₃, and WO₃ were used as raw materials, which were weighted and ground according to the molar ratios of the target materials of Fe_2−xSc_xW₃O₁₂. The mixed raw materials were pressed into cylinders with a diameter of 10 mm and a thickness of 5 mm using a 769YP-15A tablet machine with a pressure of about 200 MPa on the cylinder's green body. Twice sintering processes at about 1323 K for 4 h with intermediate grinding are needed for the desired products.

To identify the crystalline phase and analyze cell volume changes, temperature-dependent XRD patterns were carried out with a Rigaku (Japan, SmartLab 3 kW) diffractometer with Cu Kα radiation (λ = 1.5406 Å), equipped with a high-temperature attachment of the model multi-temperature, with a scan speed of 4° min⁻¹ and a step of 0.01° and 40 kV/40 mA power. The samples were held at each temperature for 20 min to maintain thermal equilibrium before the XRD measurement. Crystal structure refinement was performed using Rietveld refinement with Fullprof software. Raman spectra were recorded with HORIBA Lab RAM HR Evolution (HORIBA Scientific, France), equipped with a Linkam THMS600 Heating and Freezing Stage (Japan Hightech) (an accuracy of ±0.1 K). A laser excitation wavelength of 532 nm was used. The sample was held for about 5 min at each temperature to attain thermal equilibrium before the Raman measurements. The linear CTEs were measured by applying a dilatometer (Linseis DILL76) with a heating rate of 5 K min⁻¹. Differential scanning calorimetry (DSC) measurements were carried out using a thermal analyzer (Netzsch STA 449F3) with a 10 K min⁻¹ heating rate. Scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS) was tested using a field-emission scanning electron microscope (JSM-7001F).

3 Results and discussion

The XRD patterns at RT of Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, 2.0) are shown in Fig. 1a. The primary diffraction peaks for the sample with x = 0.5 correspond to PDF no. 38-0200 of monoclinic Fe₂W₃O₁₂. Fe₂W₃O₁₂ is a metastable material that is difficult to synthesize through solid-state reactions. Substitution of Sc³⁺, even in a small quantity, for Fe³⁺ in Fe₂W₃O₁₂ benefits pure phase synthesis, which could be related to the reduction in the formation energy of Fe₂W₃O₁₂. A comparison of the XRD patterns of x = 1.5 and 2.0 with those of x = 0.5 and 1.0 shows that the featured peak for the monoclinic phase at 26.2° disappears, and a peak at around 22° splits up. The results indicate that Fe_2−xSc_xW₃O₁₂ adopts a monoclinic phase for x = 0.5 and 1.0, and an orthorhombic phase for x = 1.5 and 2.0 at RT. The theoretical calculation optimization of the adopted structure is used to find the suitable element substitution position, and the stable structure is depicted in Fig. 2. Fig. 3 shows the refinement results of (a) Fe_1.5Sc_0.5W₃O₁₂, (b) Fe_1.0Sc_1.0W₃O₁₂, (c) Fe_0.5Sc_1.5W₃O₁₂, (d) Fe_0.25Sc_1.75W₃O₁₂, and (e) Sc₂W₃O₁₂. Structure refinements by applying the Rietveld method demonstrate that Fe_2−xSc_xW₃O₁₂ adopt a monoclinic phase with space group P2₁/c for x = 0.5 and 1.0 and an orthorhombic structure with space group Pnca for x = 1.5, 1.75, 2.0 at RT. Fig. S3 (ESI†) shows the lattice parameters and volume with a substitution ratio of Sc from the refinement results (To facilitate comparison, the cell volumes of the monoclinic phase of x = 0.5, 1.0 are divided by 2, as calculated in ref. 36). With the substitution of Sc³⁺ for Fe³⁺ in Fe₂W₃O₁₂, lattice volume increases gradually. Cell parameters are depicted in Table S1 (ESI†), and structural parameters are presented in Tables S2–S6 in ESI.† It can be observed from Fig. 1a that with the increase in Sc³⁺ substitution, the peak position shifts slightly toward a smaller angle, indicating an increase in the lattice constants due to the larger cation radius of Sc³⁺ (74.5 pm) than that of Fe³⁺ (64 pm). To detect the microstructure and elemental composition, SEM-EDS was performed. In Fig. S1 (ESI†), the SEM images show that with the substitution of Sc in Fe₂W₃O₁₂, the average particle sizes increase, and the interspaces gradually disappear. As depicted in Fig. S2 (ESI†), the information from the EDS spectra is almost consistent with the molar ratio of Fe/Sc.

Fig. 1 (a) XRD patterns, (b) Raman spectra, and (c) Raman peak positions shifting with a substituting ratio of Sc³⁺ by fitting Raman peaks (b) at 800–1025 cm⁻¹, (d) the formation energy change with substituting ratio both in monoclinic phase Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0) and orthorhombic phase Sc_2−xFe_xW₃O₁₂ (x = 0.25, 0.5). (The calculation process is presented in ESI,† and the raw data are depicted in Table S7, ESI†).

Fig. 2 The stable structure and formation energy of Sc substitution in Fe₂W₃O₁₂ and Fe substitution in Sc₂W₃O₁₂ (a)–(d) corresponding to Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, and 1.75).

Fig. 3 The Rietveld analysis of XRD patterns at RT (detailed cell parameters are given in Table S1, ESI†): (a) x = 0.5 (R_p = 3.29, R_wp = 4.50, and R_exp = 2.15) and (b) x = 1.0 (R_p = 3.70, R_wp = 4.85, and R_exp = 2.07) for the monoclinic, space group P2₁/c; (c) x = 1.5 (R_p = 5.29, R_wp = 7.05, and R_exp = 1.95), (d) x = 1.75 (R_p = 5.61, R_wp = 7.47, and R_exp = 2.05) and (e) x = 2.0 (R_p = 5.40, R_wp = 7.18, and R_exp = 2.32) for the orthorhombic, space group Pnca.

The phase transition from monoclinic to orthorhombic with an increase in Sc³⁺ substitution can also be characterized by Raman spectra. Fig. 1b shows the Raman spectra of Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, 2.0). The bands at about 1000 and 800 cm⁻¹ are attributed to the stretching vibrations of WO₄ tetrahedra, and 340 and 100 cm⁻¹ are attributed to the symmetric and asymmetric bending motions of Fe/ScO₆ octahedra and WO₄ tetrahedra, respectively.¹⁸ When x = 1.0 and 0.5, the shoulder peak at about 1000 cm⁻¹ is observed only for the monoclinic phase, which is assigned to the stretching vibrations of the W–O bond. This agrees well with the XRD results. The shoulder peak is only present in the monoclinic phase and disappears with an increase in the substitution of Sc³⁺ (x = 1.5 and 2.0) for Fe³⁺ in Fe₂W₃O₁₂.

The results suggest that the x = 1.5 and 2.0 samples transformed to the orthorhombic phase. Fig. 1c shows the Raman peak positions shifting with the substitution ratio of Sc³⁺ by fitting Raman peaks in Fig. 1b at 800–1025 cm⁻¹ to explore the change in the stretching vibrations of W–O in Fe–O–W and Sc–O–W with the substitution of Sc for Fe. The peak, corresponding to the asymmetric stretching vibration of W–O, shifts to higher wavenumbers in Fe–O–W but to lower wavenumbers in Sc–O–W. The introduction of Sc strengthens the W–O bond in Fe–O–W, improving the stable performance of Fe₂W₃O₁₂.

We investigated the stability of the substituted system Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, 1.75) using the first-principles calculations. The thermodynamic stability can be expressed by the formation energy (E_form) both in monoclinic phase (1) and orthorhombic phase (2) as follows:^37,38

E_form = E_tot(subst) − E_tot(Fe₂W₃O₁₂) − nμ_Sc + nμ_Fe, (1)

E_form = E_tot(subst) − E_tot(Sc₂W₃O₁₂) − nμ_Fe + nμ_Sc, (2)

where E_tot(subst) and E_tot(prist) are the total energies of the system with and without substitution (pristine), respectively; μ_Fe and μ_Sc represent the chemical potential for single Fe and Sc atoms, respectively; and n is the number of substitution atoms in a primitive cell. In both the monoclinic and orthorhombic phases, increasing the substitution of Sc³⁺ lowers the formation energy (Fig. 1d), which means that the material becomes more stable. The lower the electronegativity, the stronger the ability to lose electrons to oxygen, forming a stable structure.

Fig. 4a shows the thermal expansion property with increasing temperatures of Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, 1.75, 2.0). The sample with x = 0.5 shows a normal thermal expansion from RT to 490 K in the monoclinic phase and a low NTE following an abrupt expansion corresponding to the monoclinic–orthorhombic phase transition. By increasing the substitution amount of Sc³⁺ for Fe³⁺ in Fe₂W₃O₁₂, the PTT decreases gradually from 490 to 320 (x = 1.0) and 210 K (x = 1.5). After the phase transition, Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, 1.75, 2.0) show an NTE property with linear thermal expansion coefficients of −0.566 × 10⁻⁶ K⁻¹ (523–673 K), −0.606 × 10⁻⁶ K⁻¹ (385–673 K), −3.54 × 10⁻⁶ K⁻¹ (210–673 K), −2.48 × 10⁻⁶ K⁻¹ (160–673 K), and −2.92 × 10⁻⁶ K⁻¹ (160–673 K), respectively.

Fig. 4 (a) Relative length change measured using a dilatometer. (b) DSC curves (endothermic peak represents phase transition process), (c) temperature-dependent XRD patterns of Fe_1.5Sc_0.5W₃O₁₂, (d) an increase in cell volume with an increase in temperature of Fe_1.5Sc_0.5W₃O₁₂. (To facilitate comparison, the cell volumes of the monoclinic phase, as calculated in ref. 30, were divided by 2. The corresponding cell parameters change with temperature as shown in Fig. S4, ESI†).

The DSC curves for the samples are shown in Fig. 4b. The endothermic peaks appear for the x = 0.5 and 1.0 curves, corresponding to the phase transition observed in the thermal expansion and temperature-dependent Raman results (Fig. 3).

Fig. 4c displays the temperature-dependent XRD patterns of Fe_1.5Sc_0.5W₃O₁₂. The phase transition process can be recognized with the disappearing and splitting of specific peaks. Fig. 4d shows the cell volume change with temperature. This agrees well with the thermal expansion curves acquired by the dilatometer shown in Fig. 2a.

The temperature-dependent XRD of Fe_0.5Sc_1.5W₃O₁₂ is also investigated (Fig. 5a). Fig. 5b shows a schematic diagram of the crystal structure of Fe_0.5Sc_1.5W₃O₁₂. Fig. 5c depicts the changes in lattice constants for the a-, b- and c-axes with temperatures ranging from RT to 1073 K from the refinement of temperature-dependent XRD patterns, showing anisotropy in thermal expansion. Fig. 5d shows the thermal expansion curve of the sample from RT to 1073 K measured by a dilatometer and the volume change acquired from temperature-dependent XRD. The lattice constants of the a- and b-axes decrease, whereas those of the c-axis increase with heating, yielding a linear thermal expansion coefficient of a cell volume contraction of −1.3 × 10⁻⁶ K⁻¹ from 300–1000 K, which is slightly smaller than that measured by the dilatometer. Yuan et al. proposed a linear scaling law in which effective electronegativity can scale the interaction between oxygen atoms and further predicate the phase transition of A₂M₃O₁₂-based compounds.³¹ Owing to the lower electronegativity of Sc (1.20, Allred-Rochow^39,40) than that of Fe (1.64, Allred-Rochow^39,40), with the substitution of Sc³⁺ for Fe³⁺ in Fe₂W₃O₁₂, more effective charges on oxygen produce more significant oxygen–oxygen repulsion, preferring the less compact crystal structure that contributes to the phase transition from the monoclinic to the orthorhombic of Fe_2−xSc_xW₃O₁₂ (x = 0.5, 1.0, 1.5, 1.75, 2.0). The PTT (T_t) could also be estimated by averaged effective electronegativity χ_eff, and the scaling law is given by eqn (3) and (4):

T_t = c·χ_eff + d, (4)

where c = 8444.61 and d = 1190.93, obtained by linear fitting from the reference.³¹χ_Fe/Sc, χ_W, 6, and 4 are the electronegativities and coordination numbers of Fe/Sc and W atoms, respectively. For Fe_2−xSc_xW₃O₁₂, the measurement data T_t have obvious differences with scaling law prediction, which may be related to the influence of different elements in the M site (Mo → W) and the magnetism of Fe. The linear fitting of T_t and the scaling law prediction curve are presented in Fig. 6a. The proposed scaling law depends on summarizing many molybdates owing to few reported tungstates, which should be appropriate for A₂Mo₃O₁₂ materials. An equivalent compilation of tungstates could result in a line with a slightly different y-axis intercept. The linear scaling law still holds when the y-axis intercept shifts for the tungstates. The predicted T_t agrees well with the measured T_t, where for x = 0, the T_t of Fe₂W₃O₁₂ is about 687 K from our recent investigation.³⁴ To obtain a scaling law suitable for tungstates, we found some studies on the phase transition of tungstates.^{29,31,35,41–46} A similar graph to that shown for tungstates (Fig. 6b) is obtained. (Raw data can be found in Tables S8 and S9, ESI†). By fitting, we obtain a similar formula (5) with different constants:

T_t = 7176.92 χ_eff + 1124.27. (5)

Fig. 5 (a) Temperature-dependent XRD patterns of Fe_0.5Sc_1.5W₃O₁₂. (b) A schematic diagram of the crystal structure and (c) lattice constant change of Fe_0.5Sc_1.5W₃O₁₂ obtained from the Rietveld refinement of XRD, and (d) relative length change obtained from the dilatometer and cell volume change obtained from Rietveld refinement of XRD of Fe_0.5Sc_1.5W₃O₁₂ from RT = 1073 K.

Fig. 6 The linear fitting of and the scaling law predication curve of Fe_2−xSc_xW₃O₁₂ (x = 0.0, 0.5, 1.0, and 1.5) (a), tungstates (b).^29,42–46

Fig. 7a shows the temperature-dependent Raman spectra of Fe_2−xSc_xW₃O₁₂ with x = 0.5 ranging from 100 to 700 K. The featured Raman peak for the monoclinic phase at about 1003 cm⁻¹ appears from 100 to 510 K and then disappears above 510 K. For the sample with x = 1.5 in Fig. 7b, the featured Raman peak at about 1032 cm⁻¹ for the monoclinic phase appears at about 210 K, suggesting the monoclinic to orthorhombic phase transition of the sample. However, no monoclinic featured peak appears from 90 to 670 K for the sample with x = 1.75 in Fig. 7c, suggesting that the phase transition occurs at a lower temperature than 90 K for x = 1.75. The temperature-dependent Raman results are consistent with the phase transition observed by the thermal expansion curves, as depicted in Fig. 4a. According to previous reports on temperature-dependent Raman and high-pressure Raman spectra of A₂M₃O₁₂ framework materials, the phase transition from the orthorhombic to the monoclinic is always accompanied by the appearance of a featured Raman peak aside from the main stretching Raman mode. It is located on the left side of the main peak if M = W and on the right-hand side of M = Mo.^28,29,47,48

Fig. 7 The temperature-dependent Raman spectra of (a) Fe_1.5Sc_0.5W₃O₁₂, (b) Fe_0.5Sc_1.5W₃O₁₂, and (c) Fe_0.25Sc_1.75W₃O₁₂.

4 Conclusions

The solid solutions of Fe_2−xSc_xW₃O₁₂ are developed by the substitution of Sc³⁺ for Fe³⁺ in Fe₂W₃O₁₂, and the PTT can be tuned to well below RT. The much easier synthesis of the solid solutions than Fe₂W₃O₁₂ is attributed to the reduced formation energy by incorporating Sc, as demonstrated by the theoretical calculations. Fe_2−xSc_xW₃O₁₂ crystallizes in a monoclinic structure for x = 0.5 and 1.0 and an orthorhombic phase for x ≥ 1.5 at RT. The PTT from the monoclinic to orthorhombic decreases from 490 K to 320 K, 210 K, and temperatures lower than 160 K for x = 0.5, 1.0, 1.5, and 1.75, respectively. The linear scaling law can explain the regulation of the PTT. NTE is observed for the samples above their PTTs. The wider range of NTE for x ≥ 1.5 suggests potential applications in many fields.

Author contributions

Erjun Liang, Xiansheng Liu and Gaojie Zeng conceived the idea. Gaojie Zeng designed the experiments, prepared the samples, performed the measurements and analysis and prepared the manuscript. Chunyan Wang conceived the DFT calculations idea and did calculation with Xi Zhen. Qilong Gao, Juan Guo, and Mingju Chao give some suggestions for the prepare process.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11874328, 11574276).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp04816k

‡ Gaojie Zeng and Chunyan Wang contributed equally to this work.

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