Phase transition temperature and negative thermal expansion of Sc-substituted In₂(MoO₄)₃ ceramics

Abstract

A series of Sc-substituted In₂Mo₃O₁₂ ceramics were synthesized by the chemical co-precipitation method. The results reveal that In³⁺ can be substituted by Sc³⁺ and form a single phase with high purity for all In_2−xSc_xMo₃O₁₂ (x = 0, 0.3, 0.6, 0.9, 1.2 and 1.5) samples. The crystal structure of In_2−xSc_xMo₃O₁₂ changes from monoclinic to orthorhombic symmetry with increasing Sc³⁺-content, confirmed by X-ray diffraction and Raman spectroscopy (Raman). With increasing concentration of A-site Sc³⁺ cations, the microstructure of In_2−xSc_xMo₃O₁₂ becomes denser and the shape and size distribution of grains is more regular and uniform. The monoclinic-to-orthorhombic phase transition temperature of In₂Mo₃O₁₂ is successfully decreased from 343 °C to room temperature via the substitution of In³⁺ by Sc³⁺. When x = 1.5, the occurrence of the monoclinic-to-orthorhombic phase transition for In_0.5Sc_1.5Mo₃O₁₂ solid solution is at around 7 °C. It has an average linear coefficient of thermal expansion of − 5.08 × 10⁻⁶ °C⁻¹ in 25–600 °C. The phase transition results obtained by theoretical calculation using the framework of spin-polarized DFT accord well with the experimental evidences.

Introduction

In general, most of the materials expand as the temperature rises, but some materials exhibit anomalous thermal expansion, which is called negative thermal expansion (NTE). Such materials contract as they are heated up and expand as they are cooled down. They have attracted extensive attention due to their special physical properties, which have potential applications in optical and microelectronic devices. Previous studies in A₂Mo₃O₁₂ (A = trivalent main group metal or transition metal and M = W, Mo) reveal that many of them exhibit NTE [1,2,3,4,5,6]. When the A-site is occupied by Y³⁺, Ho³⁺, Tm³⁺, Er³⁺, Yb³⁺ and Lu³⁺, these A₂Mo₃O₁₂ materials form hydrated polymorphs that display positive thermal expansion (PTE) at room temperature because they are highly hygroscopic in the air. The water that is incorporated into the crystal structure hinders the transverse vibrations of the A–O–M linkages, ultimately leading to the complete loss of NTE. Only when the absorbed water is volatilized by heating can these A₂Mo₃O₁₂ materials exhibit strong NTE. This reversible hygroscopicity severely restricts any practical applications of such materials [7,8,9,10,11,12,13,14,15,16]. No hygroscopicity has been observed in A₂Mo₃O₁₂ (A = Sc, Al, In, Cr, Fe) molybdates as well as Sc₂W₃O₁₂ tungstate [3, 4, 17]. However, in the above cases, A₂Mo₃O₁₂ materials exhibit PTE with a monoclinic structure at low temperature, and NTE behavior can only be observed in an orthorhombic structure at high temperature upon undergoing a phase transition from monoclinic to orthorhombic.

In₂Mo₃O₁₂ exhibits very strong NTE in its orthorhombic phase, making it a promising candidate for tuning coefficients of thermal expansion (CTE) in composites. In₂Mo₃O₁₂ undergoes the monoclinic-to-orthorhombic phase transition at 340 °C [4]. Its solid solution suffers, however, from destruction by thermal cracking caused by the occurrence of the phase transition throughout the working temperature.

The dependence of the phase transition temperature for A₂(MO₄)₃ on the electronegativity of the A-site cation has been reported. For example, the electronegativity of Sc³⁺ is the lowest among the non-hygroscopic A-site cations in the A₂M₃O₁₂ series. Accordingly, the phase transition temperatures of Sc₂Mo₃O₁₂ and Sc₂W₃O₁₂ are also lowest, at about − 95 °C and − 263 °C (or lower), respectively. In an attempt to stabilize the orthorhombic phase at room temperature, the A-site cation in In₂Mo₃O₁₂ is partially substituted by low-electronegativity Sc³⁺ to suppress the undesirable phase transition. In previous work by our group, a new series of In_2−xSc_xMo₃O₁₂ solid solutions synthesized by the solid-state method suffer from high energy consumption, incomplete reaction and low density [18]. It is well known that the chemical co-precipitation method can overcome these disadvantages of the solid-state method.

This study is devoted to the preparation of a series of In_2−xSc_xMo₃O₁₂ solid solutions with high density and the stabilization of the orthorhombic phase of In₂Mo₃O₁₂ at room temperature or lower by tuning the content of Sc³⁺-substitution. In this paper, In_2−xSc_xMo₃O₁₂ solid solutions are synthesized by the chemical co-precipitation method. The effects of Sc³⁺-substitution on its crystal structure, phase transition, micromorphology, density as well as negative thermal expansion of In₂Mo₃O₁₂ have been studied. From the combined experimental results, the correlation between Sc³⁺-substitution and NTE as well as the phase transition temperature of In₂Mo₃O₁₂ can be well established. In this work, to investigate the phase transfer process of In_2−xSc_xMo₃O₁₂, the total energies of both monoclinic and orthorhombic phase In_2−xSc_xMo₃O₁₂ with various doping atomic ratios of Sc³⁺ are also calculated using spin-polarized density functional theory.

Experimental details

The series of In_2−xSc_xMo₃O₁₂ solid solutions were synthesized by the chemical co-precipitation method using commercially available In(NO₃)₃·xH₂O, Sc(NO₃)₃·6H₂O and (NH₄)₆Mo₇O₂₄·4H₂O as raw materials. The starting reactants were weighed in stoichiometric amounts corresponding to In³⁺:Sc³⁺:Mo⁶⁺ molar ratios of 2:0:3, 1.7:0.3:3, 1.4:0.6:3, 1.1:0.9:3, 0.8:1.2:3 and 0.5:1.5:3 and dissolved in deionized water. The three solutions were mixed in a total volume of 25 ml of deionized water while stirring at 80 °C. The pH value of the solution was kept around 10, which was controlled by dripping in ammonia as needed. The corresponding slurries were stirred for 2 h and then dried at 90 °C. The obtained powder was pre-sintered at 500 °C, followed by cold isostatic pressing into pellets (7 mm in diameter), and finally sintered at 760 °C for 6 h in air.

The structural characterization was determined by the X-ray diffraction (XRD) technique, using a Shimadzu XRD-7000 with CuKα radiation. Data were collected with a scanning speed of 5°/min. Raman spectra were collected (Thermo Fisher, DXRxi) in the scanning range of 100–1200 cm⁻¹ with a power of 0.2 mW using a laser with a wavelength of 532 nm. Elemental mapping was done by energy-dispersive X-ray spectroscopy (EDX) on a high-resolution transmission electron microscopy (HRTEM, FEI Tecnai F30 S-TWIN). X-ray photoelectron spectroscopy (XPS, Thermo Scientific, ESCALAB 250Xi) was used to study the valence state of all elements. The cross-sectional microstructure was characterized by scanning electron microscopy (SEM, TESCAN VEEGA3). Dilatometric studies were performed on pellets at a heating rate of 5 °C/min from room temperature to 600 °C using thermal mechanical analysis (TMA/SS, Seiko 6300). Differential scanning calorimetry (DSC) measurements were carried out using PerkinElmer DSC-8500, with the heating rate of 5 °C/min from room temperature to 350 °C.

Results and discussion

Crystal structure analysis

The crystal structure of the samples was determined by X-ray diffraction. The XRD patterns of as-synthesized In_2−xSc_xMo₃O₁₂(0 ≤ x ≤ 1.5) heat-treated at different temperatures are shown in Fig. 1. As shown in Fig. 1a, the samples are crystallized during pre-sintering at 500 °C. The crystallization temperature is relatively lower compared to that of solid-state reaction method [18], which means that the chemical co-precipitation synthesis can cause good sinterability of samples. To improve the crystallinity and density, the sintering temperature was further increased to 760 °C and the corresponding XRD patterns are shown in Fig. 1b. All the diffraction peaks become stronger and sharper with no variation in positions, revealing that the crystallinity of the samples is improved with increased sintering temperature. For comparison, the reference pattern for monoclinic In₂(MoO₄)₃ is also displayed. All In_2−xSc_x(MoO₄)₃ ceramics with Sc³⁺-content (x) ranging from 0.3 to 1.2 appear to be a well-crystallized single phase with monoclinic In₂(MoO₄)₃-type structure, and no impurity phases are detected. As the Sc³⁺-content (x) is increased to 1.5, In_0.5Sc_1.5Mo₃O₁₂ crystallizes in an orthorhombic Sc₂(MoO₄)₃-type structure (space group Pbcn, JCPDS card No.21-1329), as marked by the disappearance of the diffraction peaks at 2θ = 25°–27.5° (Fig. 2).

Figure 1

XRD patterns of In_2−xSc_xMo₃O₁₂ (x = 0, 0.3, 0.6, 0.9, 1.2 and 1.5) sintered for 6 h at a 500 °C and b 760 °C

Figure 2

a X-ray diffraction pattern of In_0.5Sc_1.5Mo₃O₁₂ and b Sc₂Mo₃O₁₂ reference pattern

As the small differences between the monoclinic and orthorhombic crystal structures of In_2−xSc_xMo₃O₁₂ can make them difficult to distinguish through XRD, Raman analysis was carried out to further characterize the different phases, and the results are depicted in Fig. 3. For x = 0, the recorded Raman spectrum of In₂Mo₃O₁₂ agrees well with literature reports [19]. As seen in the spectrum, In₂Mo₃O₁₂ presents strong Raman bands with some shoulders in the 970–1030 cm⁻¹ and 790–970 cm⁻¹ region that can be related to Mo–O symmetric and asymmetric stretching modes, respectively. In addition, the distinct peaks in the 300–400 cm⁻¹ range originate from bending modes of the MoO₄ tetrahedra and InO₆ octahedra. Comparison of the spectra as a function of composition reveals that the three characteristic peaks located at 175, 862 and 994 cm⁻¹ are gradually weakened with increasing Sc³⁺-content (x) and disappear completely around x = 1.5 (Fig. 3f). The Raman spectrum of In_0.5Sc_1.5Mo₃O₁₂ corresponds to the typical spectrum of orthorhombic Sc₂Mo₃O₁₂ in exact accordance with literature data [19]. This observation suggests that the crystal structure of In_0.5Sc_1.5Mo₃O₁₂ has changed from monoclinic to orthorhombic symmetry at room temperature, in good agreement with the above XRD analysis.

Figure 3

The Raman spectra of In_2−xSc_xMo₃O₁₂ solid solutions a In₂Mo₃O₁₂, b In_1.7Sc_0.3Mo₃O₁₂, c In_1.4Sc_0.6Mo₃O₁₂, d In_1.1Sc_0.9Mo₃O₁₂, e In_0.8Sc_1.2Mo₃O₁₂ and f In_0.5Sc_1.5Mo₃O₁₂

To further confirm the successful synthesis of single-phased samples, EDX, STEM and XPS were performed on the In_0.5Sc_1.5Mo₃O₁₂ solid solution. In, Mo, O, Sc and C used for calibration are detected in In_0.5Sc_1.5Mo₃O₁₂ (Fig. 4a), and the corresponding high-resolution XPS spectra of the In 3d and Sc 2p are shown in Fig. 4b, c, respectively. Two peaks at the binding energy of 445 eV and 453 eV are assigned to In 3d_5/2 and In 3d_3/2 of trivalent indium. In addition, the two peaks with binding energies of 403 eV and 407 eV are attributed to Sc 2p_3/2 and Sc 2p_1/2, indicating the existence of trivalent scandium. The homogeneity of the elemental composition of In_0.5Sc_1.5Mo₃O₁₂ was further demonstrated through EDX analysis, as shown in Fig. 4d. No elements other than In, Mo, O, Sc and Cu are detected. The strong Cu signal originates from the copper net used to mount the sample. Moreover, as shown in Fig. 4e–i, the STEM image and elemental maps of a selected particle for In_0.5Sc_1.5Mo₃O₁₂ powder demonstrate that the four elements are uniformly distributed throughout the investigated region. Based on the above analysis, these results clearly confirm that In³⁺ is substituted by Sc³⁺ in In₂Mo₃O₁₂ to form a single phase with high purity.

Figure 4

XPS spectra of a In_0.5Sc_1.5Mo₃O₁₂, b In 3d peaks, c Sc 2p peaks, d EDX spectrum and e STEM micrograph of In_0.5Sc_1.5Mo₃O₁₂ powder and f In, g Mo, h O, i Sc elemental mapping images

To better understand the crystal structure of In_2−xSc_xMo₃O₁₂, the ball-and-stick model presentations are given in Fig. 5; In₂Mo₃O₁₂ takes on a monoclinic structure (see Fig. 5a), while In_0.5Sc_1.5Mo₃O₁₂ adopts an orthorhombic structure at room temperature (see Fig. 5b), and the frameworks of both are composed of a network of InO₆ (ScO₆) octahedra and MoO₄ tetrahedra. Mo⁶⁺ occupies the center of MoO₄ tetrahedra. In³⁺ occupies the center of InO₆ octahedra. With the increase in Sc³⁺-substitution content, Sc³⁺ gradually replaces In³⁺ and occupies the A-sites in the center of InO₆ octahedra, which is shown in Fig. 5c. Sc³⁺-substitution leads to the change in crystal structure from monoclinic to orthorhombic symmetry.

Figure 5

Ball-and-stick model presentations of a monoclinic structure for In₂Mo₃O₁₂, b orthorhombic structure for In_0.5Sc_1.5Mo₃O₁₂, c schematic diagram of Sc³⁺ substituting In³⁺ in the crystal structure

Microstructure analysis

To reveal the relationship between the microstructure and substituted Sc³⁺-content (x), the typical cross-sectional morphologies of In_2−xSc_xMo₃O₁₂ solid solutions are shown in Fig. 6. It is observed that all samples exhibit a dense microstructure without significant pores in contrast to the solid solutions synthesized by the solid-state method [18], indicating a great improvement in the density of solid solutions. In the case of pure In₂Mo₃O₁₂, the average size of particles varies from 2 to 10 µm and the shapes of particles are not regular (Fig. 6a). Moreover, SEM micrographs clearly reveal the dependence of grain size, as well as the homogeneity of grain sizes, on Sc³⁺-content (x): The average grain size is gradually reduced and the uniformity of the grain size is improved with increasing Sc³⁺-content. For x = 1.2, the average grain size is reduced to 2–3 µm, and the microstructure morphology of In_0.8Sc_1.2Mo₃O₁₂ solid solution is clearly more regular with spherical shapes (Fig. 6e). For composition x = 1.5, In_0.5Sc_1.5Mo₃O₁₂ solid solution displays a uniform grain size distribution and the particle size is further reduced to 1 µm, as shown in Fig. 6f.

Figure 6

SEM micrographs of In_2−xSc_xMo₃O₁₂ solid solutions a In₂Mo₃O₁₂, b In_1.7Sc_0.3Mo₃O₁₂, c In_1.4Sc_0.6Mo₃O₁₂, d In_1.1Sc_0.9Mo₃O₁₂, e In_0.8Sc_1.2Mo₃O₁₂ and f In_0.5Sc_1.5Mo₃O₁₂

To attempt to investigate the effect of substituted Sc³⁺-content (x) on the relative densities of In_2−xSc_xMo₃O₁₂ solid solutions, Archimedes’ method was performed on all samples. It can be found that the relative densities for In_2−xSc_xMo₃O₁₂ slightly increase with the increase in Sc³⁺-content (x), which is consistent with the SEM observations. Furthermore, the average relative densities of In_2−xSc_xMo₃O₁₂ solid solutions were found to be about 93% (Fig. 7). Obviously, compared with samples prepared by the solid-state method [18], it can be generalized that the microstructure of In_2−xSc_xMo₃O₁₂ solid solutions becomes denser without raising the temperature through use of the chemical co-precipitation method.

Figure 7

The effect of Sc³⁺-content on the relative densities of In_2−xSc_xMo₃O₁₂ solid solutions prepared by the chemical co-precipitation method and solid-state reaction method, respectively

Phase transition and thermal expansion studies

The thermal expansion behavior of In_2−xSc_xMo₃O₁₂ (0 ≤ x ≤ 1.5) solid solutions is shown in Fig. 8. The abrupt change in the slope of the thermal expansion curves for In₂Mo₃O₁₂ can be attributed to the structural phase transition. This means that In₂Mo₃O₁₂ maintains the monoclinic structure up to 334 °C, exhibiting positive thermal expansion with a CTE of 10.48 × 10⁻⁶ °C⁻¹. The material then undergoes a phase transition in the 334–355 °C temperature range, above which In₂Mo₃O₁₂ crystallizes in an orthorhombic structure and exhibits strong NTE with a CTE of − 8.36 × 10⁻⁶ °C⁻¹ from 360 to 600 °C. Similarly, to unsubstituted In₂Mo₃O₁₂, all In_2−xSc_xMo₃O₁₂ solid solutions follow the same trend, except for In_0.5Sc_1.5Mo₃O₁₂. It is worth noting that we have not found any changes in the slope of the curve for In_0.5Sc_1.5Mo₃O₁₂, which shows NTE throughout the testing temperature range. It can be seen that the onset of the phase transition temperature of In_2−xSc_xMo₃O₁₂ solid solutions shifts from 334 °C to a temperature of 75 °C as the Sc³⁺-content increases progressively from x = 0 to x = 1.2. In addition, A-site substitution with Sc³⁺ not only dramatically decreases the phase transition temperature of In₂Mo₃O₁₂, but also gradually narrows the transition range, which is correlated with the electronegativity of the cation. Owning to the lower electronegativity of Sc³⁺ (1.36) compared to that of In³⁺ (1.78), the reduction in the average A-site electronegativity of (In_2−xSc_x)³⁺ as Sc³⁺-content increases results in increased effective negative charges on the oxygens, and accordingly stronger O–O repulsion, which ultimately results in suppressing the phase transition temperature of In_2−xSc_xMo₃O₁₂ to a lower temperature.

Figure 8

TMA curves of In_2−xSc_xMo₃O₁₂ solid solutions a In₂Mo₃O₁₂, b In_1.7Sc_0.3Mo₃O₁₂, c In_1.4Sc_0.6Mo₃O₁₂, d In_1.1Sc_0.9Mo₃O₁₂, e In_0.8Sc_1.2Mo₃O₁₂ and f In_0.5Sc_1.5Mo₃O₁₂

The average linear thermal expansion coefficients of the measured In_2−xSc_xMo₃O₁₂ solid solutions over the corresponding testing temperature range are summarized in Table 1. In_0.5Sc_1.5Mo₃O₁₂ has an average linear CTE of − 5.08 × 10⁻⁶ °C⁻¹ throughout the testing temperature range.

Table 1 Average linear thermal expansion coefficient of In_2−xSc_xMo₃O₁₂ solid solutions (x = 0, 0.3, 0.6, 0.9, 1.2 and 1.5) over the corresponding testing temperature ranges

In order to shed more light on the precise phase transition temperature of In_2−xSc_xMo₃O₁₂ solid solutions, differential scanning calorimetry was employed to further characterize the samples, and the results are shown in Fig. 9. The DSC curve of In₂Mo₃O₁₂ (Fig. 9a) displays a sharp endothermic peak at 343 °C. We attribute the appearance of this peak to the structural change associated with the monoclinic-to-orthorhombic phase transition. It can be seen that the observed endothermic peak progressively shifts to lower temperatures as the content of Sc³⁺-substitution increases gradually from x = 0.3 to x = 1.2. As shown in Fig. 9f, the endothermic peak disappears in the testing temperature range in the case of x = 1.5, revealing that the phase transition temperature of In_0.5Sc_1.5Mo₃O₁₂ has been reduced below room temperature. The phase transition temperatures of all In_2−xSc_xMo₃O₁₂ solid solutions determined by DSC and TMA are summarized in Table 2 and show good consistency. The correlation between the variation in phase transition temperature and Sc³⁺-content (x) is established in Fig. 10, which can be used to estimate the phase transition temperature of In_2−xSc_xMo₃O₁₂ solid solutions with different contents of Sc³⁺-substitution. For instance, Sc₂Mo₃O₁₂ experiences the phase transition at about − 104.2 °C, which is consistent with the reported data. It could be inferred that the occurrence of the phase transition for In_0.5Sc_1.5Mo₃O₁₂ is at about 7 °C.

Figure 9

DSC curves of In_2−xSc_xMo₃O₁₂ solid solutions a In₂Mo₃O₁₂, b In_1.7Sc_0.3Mo₃O₁₂, c In_1.4Sc_0.6Mo₃O₁₂, d In_1.1Sc_0.9Mo₃O₁₂, e In_0.8Sc_1.2Mo₃O₁₂ and f In_0.5Sc_1.5Mo₃O₁₂

Table 2 Phase transition temperature of obtained In_2−xSc_xMo₃O₁₂ solid solutions using DSC and TMA

Figure 10

Phase transition temperature of In_2−xSc_xMo₃O₁₂ solid solutions as a function of Sc³⁺-content

Theoretical calculation analysis

To analyze the structural stability of the In_2−xSc_xMo₃O₁₂, the total energy of both monoclinic and orthorhombic phase In_2−xSc_xMo₃O₁₂ is calculated by the framework of spin-polarized DFT as implemented in the Vienna Ab initio Simulation Package (VASP) [20, 21]. The exchange–correlation potentials were treated by the generalized gradient approximation (GGA) parameterized by Perdew, Burke and Ernzerhof (PBE) [22]. The interaction between valence electrons and ion cores was described by the projected augmented wave (PAW) method [23]. The monoclinic and orthorhombic phases of In_2−xSc_xMo₃O₁₂ were modeled as a periodic slab by setting the lattice parameters as a = 16.34 Å/19.32 Å, b = 9.55 Å/13.23 Å and c = 18.76 Å/9.47 Å, respectively. The Monkhorst–Pack grid of 1 × 2 × 1 and 1 × 1 × 2 was used for the geometry optimization. A 400 eV kinetic energy cutoff was chosen for plane-wave basis set, and conjugated gradient (CG) atomic optimization was performed with a criterion of convergence of 0.01 eV/Å.

To address the phase transfer process of In_2−xSc_xMo₃O₁₂, we compared the stabilities of the monoclinic and orthorhombic phase In_2−xSc_xMo₃O₁₂ by displacing In atom with Sc atoms, at the ratios (R = Sc:In) of 0:6, 2:14, 4:12, 6:10, 8:8, 10:6, 12:4, 14:2 and 16:0, respectively (see Fig. 11a). Our results indicate that very close energies are found for these two phases at various doping ratios. This may be explained by the small difference in the two crystal structure. Normal XRD cannot tell the difference between monoclinic and orthorhombic phase of In₂Mo₃O₁₂ [4]. Only the XRD results obtained using a synchrotron facility can distinctly reveal the difference of the two structures. Figure 11b shows the energy difference ($\Delta E$) between the monoclinic and orthorhombic phase In_2−xSc_xMo₃O₁₂ with the same doping atomic ratio of Sc, and the $\Delta E$ is calculated as:

Figure 11

Calculated total energies (a) and energy difference (b) between monoclinic and orthorhombic phases of In_2−xSc_xMo₃O₁₂ at various doping atomic ratios of Sc

$$ \Delta E = E_{\text{monoclinic}} - E_{\text{orthorhombic}} $$

A careful examination manifested that the energy profile of two phases crosses at around R = 12:4, which can be clearly seen in Fig. 11b. When R < 12:4, ΔE < 0, indicating the In_2−xSc_xMo₃O₁₂ has stable monoclinic phase, while an orthorhombic phase is energetically favored once R ≥ 12:4. In other words, it means that the In_2−xSc_xMo₃O₁₂ (x < 1.5) crystallizes in a monoclinic In₂Mo₃O₁₂-type symmetry, and when x ≥ 1.5, the In_2−xSc_xMo₃O₁₂ shows an orthorhombic Sc₂Mo₃O₁₂-type symmetry. These theoretical results accord well with our experimental evidences.

Conclusions

For the first time, single-phased In_2−xSc_xMo₃O₁₂ solid solutions (x = 0, 0.3, 0.6, 0.9, 1.2 and 1.5) were synthesized by the chemical co-precipitation method. Sc³⁺-substitution gave rise to a change in the crystal structure of In₂Mo₃O₁₂. In_2−xSc_xMo₃O₁₂ adopts monoclinic In₂Mo₃O₁₂-type symmetry for x ≤ 1.2 and transforms to orthorhombic Sc₂Mo₃O₁₂-type symmetry in the case of x = 1.5. Meanwhile, the co-precipitation synthesis leads to better densification and sinterability in the above samples. The microstructure of In_2−xSc_xMo₃O₁₂ becomes denser with fine grain shape and narrow size distribution influenced by the increase in Sc³⁺-content. Furthermore, Sc³⁺-substitution at A-site of In₂Mo₃O₁₂ can effectively shift the phase transition temperature to below room temperature. The phase transition temperature of In_0.5Sc_1.5Mo₃O₁₂ is around 7 °C and shows stable negative thermal expansion. The corresponding average CTE of In_0.5Sc_1.5Mo₃O₁₂ ceramics is − 5.08 × 10⁻⁶ °C⁻¹ from 25 to 600 °C. The calculation results obtained using spin-polarized density functional theory agree well with the experimental results. When R < 12:4, the In_2−xSc_xMo₃O₁₂ has stable monoclinic phase, while an orthorhombic phase is energetically favored once R ≥ 12:4.