A. Crystal system at room temperature and hygroscopicity of In_0.5(ZrMg)_0.75Mo₃O₁₂

FE-SEM analysis [Fig. 1(a)] showed that the calcined powder was constituted of faceted sub-micron to micron-sized particles, in the general range 0.7–1.6 μm. EDS analysis [Fig. 1(b)] indicated that the stoichiometric ratio of the chemical elements is in agreement with the proposed formula In_0.5(ZrMg)_0.75Mo₃O₁₂ (Table SI in Supplementary Material).

FIG. 1.

(a) FEG-SEM image of In_0.5(ZrMg)_0.75Mo₃O₁₂ powder, (b) EDS spectrum, and (c) room-temperature XRPD pattern, illustrating the Le Bail fit to the monoclinic P2₁/a space group (a = 16.2694 Å, b = 9.5610 Å, c = 18.9782 Å and β = 125.56°); the experimental pattern is black, the calculated pattern is red and the difference plot is green [inset: magnified view of XRPD in the range between 21° and 27° (2θ), with two weak diffraction lines at 25.8° and 23.7° (2θ) related to the monoclinic system marked as *].

The room-temperature XRPD pattern [Fig. 1(c)] indicated that the calcined powder was monophasic and monoclinic (P2₁/a space group), not orthorhombic. Two weak diffraction peaks at 25.8° and 23.7° (2θ), marked in the inset of Fig. 1(c), can be associated with a lower symmetry monoclinic space group (P2₁/a), ^{Reference Miller, Johnson, White and Marinkovic10} and are absent in the orthorhombic space groups (Pbcn and Pna2₁) adopted by members of the A₂M₃O₁₂ and ABM₃O₁₂ families. Therefore, the substitution of 1/4 of the low electronegativity Zr (1.4) and Mg (1.2) atoms by In with higher electronegativity (1.7) significantly increases the thermal stability range of the monoclinic phase in comparison to the end-member compound ZrMgMo₃O₁₂ (transition temperature of −126 °C).

Note that In_0.5(ZrMg)_0.75Mo₃O₁₂ is not hygroscopic: its mass loss on heating to 600 °C was negligible (<0.3 mass%) (Fig. 2). However, above 700 °C significant mass loss occurs because of partial decomposition of In_0.5(ZrMg)_0.75Mo₃O₁₂ into its constituent oxides followed by sublimation of MoO₃. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15} The absence of hygroscopicity is not unexpected since the end-members ZrMgMo₃O₁₂ and In₂Mo₃O₁₂ are not hygroscopic, ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15} and hygroscopicity in the A₂M₃O₁₂ family is generally reported for the orthorhombic phases with large trivalent cations, such as rare earths from Y to Ho. ^{Reference Sleight and Brixner24} The evidence of partial molybdate decomposition above 700 °C (Fig. 2) might be an obstacle to attaining high densities during sintering.

FIG. 2.

TGA curve of In_0.5(ZrMg)_0.75Mo₃O₁₂ powder.

B. Phase transition in In_0.5(ZrMg)_0.75Mo₃O₁₂

The DSC thermogram of In_0.5(ZrMg)_0.75Mo₃O₁₂ [Fig. 3(a)] shows an endothermic event on heating, associated with a monoclinic to orthorhombic phase transition, with an enthalpy change of 2.5 kJ/mol and an onset temperature of 82 °C. This kind of phase transition for the compounds belonging to the A₂M₃O₁₂ family is reported to be structurally subtle and comprises very low enthalpy changes (ΔH ≤ 2 kJ/mol), ^{Reference Varga, Moats, Ushakov and Navrotsky8} i.e., on the same order of magnitude as observed here for In_0.5(ZrMg)_0.75Mo₃O₁₂. This is a displacive phase transition due to the breakage of secondary oxygen–oxygen bonds (the same ones responsible for the existence of molecular solid tetraoxides, such as RuO₄ and OsO₄) between neighboring polyhedra, ^{Reference Evans, Mary and Sleight1,Reference Pley and Wickleder26} resulting in more empty space within the orthorhombic crystal structure. No primary bonds are broken during this event. Therefore, the phase transition is thermodynamically driven by the increase of vibrational entropy in the transition to a less dense structure (orthorhombic), causing more disorder (i.e., increase of distinctive configurations) in distribution of thermal energy over harmonic oscillators (atoms). The dilatometric curve of a pre-sintered specimen confirms this transition through an abrupt increase of sample length (thermal deformation) between 70 and 90 °C [Fig. 3(b)], characteristic of a phase transition from a dense to a more open crystal structure, such as in the case of the monoclinic (P2₁/a) to orthorhombic (Pbcn or Pna2₁) transition, inherent to the A₂M₃O₁₂ and ABM₃O₁₂ families. This abrupt change of specimen length is not associated with water loss since the latter is insignificant for In_0.5(ZrMg)_0.75Mo₃O₁₂.

FIG. 3.

(a) DSC curve of In_0.5(ZrMg)_0.75Mo₃O₁₂ powder and (b) dilatometric curve of a pre-sintered specimen of In_0.5(ZrMg)_0.75Mo₃O₁₂.

In the A₂M₃O₁₂ family, the subtle structural differences that exist between Pbcn, Pna2₁, and P2₁/a phases can be difficult to resolve by x-ray diffraction alone. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Gindhart, Lind and Green18} Raman spectroscopy provides an important complementary technique because it is sensitive to different structural features. Specifically, there exist stretching modes of the AO₆ and MO₄ coordination polyhedra that are sensitive to the identity of the A and M cations. ^{Reference Paraguassu, Maczka, Filho, Freire, Melo, Filho and Hanuza27} Unlike the low-energy bending and librational modes, which involve coordinated motions of atoms throughout the unit cell, the energies of the stretching modes show significant differences for the Pbcn, Pna2₁, and P2₁/a phases. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Paraguassu, Maczka, Filho, Freire, Melo, Filho and Hanuza27} However, the number of Raman-active vibrational modes in A₂M₃O₁₂ materials is large due to their large unit cells and the absence of atoms at special positions. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Paraguassu, Maczka, Filho, Freire, Melo, Filho and Hanuza27} Therefore, to quantify differences in the vibrational spectra between phases, a deconvolution approach has been used, using Fityk software. ^{Reference Wojdyr28} This approach fits the spectra to peaks that represent bands rather than individual vibrations, an approach which is supported by previous computational and Raman studies. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Paraguassu, Maczka, Filho, Freire, Melo, Filho and Hanuza27,Reference Sivasubramanian, Ravindran, Nithya and Arora29–Reference Ravindran, Sivasubramanian and Arora33}

In Fig. 4 the fitted stretching regions of the Raman spectra of In_0.5(ZrMg)_0.75Mo₃O₁₂ at 40 and 250 °C are shown. The fits were performed with pseudo-Voigt profile functions, with the goal of finding the minimum number of peaks required for a satisfactory fit. The criterion used was to deem the fit satisfactory when the addition of a new peak resulted in a reduction in the residual which was larger than the residual resulting from the error in fitting the shape of the largest stretching peak. Eight peaks were needed to fit the spectrum acquired at 40 °C [Fig. 4(a)], whereas the spectrum acquired at 250 °C [Fig. 4(b)] required only five peaks, indicating an increase in symmetry upon heating. This result is consistent with previous reports of transitions between monoclinic and orthorhombic phases in the A₂M₃O₁₂ family. ^{Reference Sivasubramanian, Ravindran, Nithya and Arora29,Reference Li, Yuan, Song, Liang and Yuan32,Reference Ravindran, Sivasubramanian and Arora33} However, peak deconvolution has not previously been applied to these materials. Therefore, we have additionally determined and deconvoluted the room-temperature Raman spectra of A₂M₃O₁₂ and ABM₃O₁₂ materials such as In₂Mo₃O₁₂, Al₂Mo₃O₁₂, ZrMgMo₃O₁₂, and Sc₂W₃O₁₂; all these phases synthesized as described elsewhere, ^{Reference Marinkovic, Ari, Jardim, de Avillez, Rizzo and Ferreira25} are known and were used here to make comparisons with In_0.5(ZrMg)_0.75Mo₃O₁₂.

FIG. 4.

Stretching regions of the Raman spectra of In_0.5(ZrMg)_0.75Mo₃O₁₂ at (a) 40 °C and (b) 250 °C, showing experimental data (black circles), the fit to the data (blue line), and the peaks composing the fit (orange lines).

Figure 5 shows the stretching regions of the Raman spectra of In₂Mo₃O₁₂ and Al₂Mo₃O₁₂, two A₂M₃O₁₂ materials that adopt a monoclinic P2₁/a phase at room temperature. ^{Reference Marinkovic, Ari, Jardim, de Avillez, Rizzo and Ferreira25,Reference Harrison, Cheetham and Faber34} In both cases, the deconvolution procedure revealed eight peaks. The significant differences in the positions and intensities of the peaks between the two materials can be attributed to the Al³⁺ cation participating in the stretches to a greater extent than Sc³⁺ due to the greater rigidity of the AlO₆ polyhedron. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Paraguassu, Maczka, Filho, Freire, Melo, Filho and Hanuza27} The identification of eight peaks in the spectra shown in Fig. 5 corroborates the P2₁/a phase at room temperature for In_0.5(ZrMg)_0.75Mo₃O₁₂.

FIG. 5.

Stretching regions of the Raman spectra of (a) In₂Mo₃O₁₂ and (b) Al₂Mo₃O₁₂ at room temperature, showing experimental data (black circles), the fit to the data (blue line), and the peaks composing the fit (orange lines). Both materials are in the P2₁/a phase at this temperature. ^{Reference Marinkovic, Ari, Jardim, de Avillez, Rizzo and Ferreira25,Reference Harrison, Cheetham and Faber34}

In Fig. 6, the stretching regions of the Raman spectra of ZrMgMo₃O₁₂ and Sc₂W₃O₁₂, two materials whose orthorhombic phases are stable at room temperature, ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Evans, Mary and Sleight35} are shown. Sc₂W₃O₁₂ adopts a Pbcn structure typical for A₂M₃O₁₂ materials, ^{Reference Evans, Mary and Sleight35} whereas the related Pna2₁ phase of ZrMgMo₃O₁₂ has ordered Zr⁴⁺ and Mg²⁺ cations. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15} A′_2x (A″Mg)_1−x M₃O₁₂ materials such as In_0.5(ZrMg)_0.75Mo₃O₁₂ can adopt Pna2₁ phases where the A″(Zr or Hf) and Mg atoms are ordered and the A′ atom is disordered, ^{Reference Suzuki and Omote23} or Pbcn phases where all three A site atoms are disordered. ^{Reference Suzuki and Omote23} Deconvolution of the stretching regions of the Raman spectra revealed 11 peaks for ZrMgMo₃O₁₂ and five for Sc₂W₃O₁₂. The large differences between the two can be attributed to the decrease in symmetry between Pbcn and Pna2₁, and the differences in chemical bonding between the ZrO₆ and MgO₆ polyhedra. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15} The presence of five peaks in the stretching region of the Raman spectrum of In_0.5(ZrMg)_0.75Mo₃O₁₂ at 250 °C therefore corroborates its assignment to the Pbcn phase, while the presence of eight peaks in the room temperature spectrum confirms the assignment of this phase to the monoclinic P2₁/a space group as previously ascribed through XRPD [Fig. 1(a)]. The increased breadth of the peaks in Fig. 4 can be attributed to disorder at the A site.

FIG. 6.

Stretching regions of the Raman spectra of (a) ZrMgMo₃O₁₂ and (b) Sc₂W₃O₁₂ at room temperature, showing experimental data (black circles), the fit to the data (blue line), and the peaks composing the fit (orange lines). ZrMgMo₃O₁₂ is in the Pna2₁ phase while Sc₂W₃O₁₂ is in the Pbcn phase at this temperature. ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15,Reference Evans, Mary and Sleight35}

C. Thermal expansion of orthorhombic In_0.5(ZrMg)_0.75Mo₃O₁₂

Suzuki and Omote ^{Reference Suzuki and Omote23} showed for Al_2x (HfMg)_1−x W₃O₁₂ that when x increases from 0 to ∼0.3, the space group changes to Pbcn from a lower symmetry orthorhombic space group (originally thought to be Pnma but now known to be Pna2₁). ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15} This agrees with our analysis of the Raman spectra of In_0.5(ZrMg)_0.75Mo₃O₁₂ (x = 0.25), which attributed the spectrum at 250 °C, i.e., above the phase transition temperature, to the orthorhombic space group Pbcn [see Supplementary Materials for all Raman spectra of In_0.5(ZrMg)_0.75Mo₃O₁₂ from room temperature to 250 °C]. In situ XRPD (Fig. 7) additionally corroborates that the high temperature phase adopts the Pbcn space group due to the absence of two closely spaced diffraction lines at around 13.5° (2θ), present in the case of Pna2₁ space group in accordance to the findings of Suzuki and Omote. ^{Reference Suzuki and Omote23} Figure 8 presents the dependence of the natural logarithm of unit-cell volume of In_0.5(ZrMg)_0.75Mo₃O₁₂ in the orthorhombic (Pbcn) phase with temperature. The intrinsic linear CTE, calculated from the slope of this curve, gives a value very close to zero (−0.16 ± 0.07) × 10⁻⁶ K⁻¹ between 100 and 500 °C, in reasonable agreement to the value estimated by the rule of mixtures (−0.3 × 10⁻⁶ K⁻¹), using the CTE of the end-member ZrMgMo₃O₁₂ reported by Romao et al., ^{Reference Romao, Perras, Werner-Zwanziger, Lussier, Miller, Calahoo, Zwanziger, Bieringer, Marinkovic, Bryce and White15} The CTE of In_0.5(ZrMg)_0.75Mo₃O₁₂ is in the same range as ZrMgMo₃O₁₂ (0.16 × 10⁻⁶ K⁻¹), which is considered a near-zero thermal expansion material with a CTE similar to that of fused quartz and Invar.

FIG. 7.

In situ XRPD patterns of In_0.5(ZrMg)_0.75Mo₃O₁₂ powder in the temperature range between 25 and 500 °C.

FIG. 8.

Natural logarithm of the unit-cell volume of orthorhombic (Pbcn space group) In_0.5(ZrMg)_0.75Mo₃O₁₂ as a function of temperature.

It is worth noting that In_0.5(ZrMg)_0.75Mo₃O₁₂ shows anisotropic expansion along its three crystallographic axes, as the a-axis expands and b- and c-axes contract on heating (Supplementary Material, Fig. S3). Thermal expansion anisotropy can be quantitatively expressed as the maximum difference between the axial thermal expansion coefficients (Δα_max) as proposed by Srikanth ^{Reference Srikanth, Subbarao and Rao36} and it was determined here to be Δα_max = 9.2 × 10⁻⁶ K⁻¹ (from 100 to 500 °C). This value is almost the same as previously determined for In(HfMg)_0.5Mo₃O₁₂ ^{Reference Miller, Romao, Bieringer, Marinkovic, Prisco and White16} and is significantly lower than the values generally estimated for the phases from A₂M₃O₁₂ and ABM ₃O₁₂ families. ^{Reference Miller, Romao, Bieringer, Marinkovic, Prisco and White16} The CTE can also be obtained from the dilatometric curve, however, pronounced hysteresis [Fig. 3(b)] indicates microcrack healing within bulk specimens. Thus, the bulk CTE (1.5 × 10⁻⁶ K⁻¹) determined dilatometrically on heating from 100 to 500 °C is biased due to the microcracking contribution increasing the CTE compared with the intrinsic CTE, a phenomenon previously documented that can occur on heating and cooling of bulk specimens. ^{Reference Jardim, Garcia and Marinkovic37} It is possible that sintered bodies of In_0.5(ZrMg)_0.75Mo₃O₁₂ with nanometric grains could exhibit a bulk CTE close to the intrinsic value due to reduction of microcracks in accordance with Griffith theory. ^{Reference Carter and Norton38}