1. Introduction

Materials exhibiting negative thermal expansion (NTE) property are that the materials volumes would decrease with increasing temperature, which is opposite to the conventional materials with positive thermal expansion coefficients [1]. The most popular example of NTE materials is the water in the temperature range of 273-277 K. Since 1990s, some new families of NTE materials have been discovered including AM₂O₇ [2], AM₂O₈ [3-5], A₂M₃O₁₂ [6-8], alloy [9] and zeolites [10], etc. Among these materials, the orthorhombic A₂M₃O₁₂ (A: trivalent cations, M: W⁶⁺ or Mo⁶⁺) have drawn more and more attention especially in recent years, for the reason that A cation in A₂M₃O₁₂ could be many ions from Al³⁺ (radius of 0.51 Å) to rare earth ions, e.g. Gd³⁺ (radius of 0.94 Å) [11-13], and it is the A cation which mainly determines the different positive or negative thermal expansion properties of A₂M₃O₁₂. Therefore, A cation can be partially replaced by other trivalent cations in order to achieve artificial control of thermal expansion coefficient of A₂M₃O₁₂.

The A₂M₃O₁₂ compounds, adopting orthorhombic crystal structure (Pnca or Pbcn space group, No. 60), contain independent rigid AO₆ octahedra sharing all six corners with independent rigid MO₄ tetrahedra. When the temperature is rising, the bending or rotation about the A-O-M linkages causes polyhedral rotation and slight distortion in some or all the rigid polyhedra, which is known as quasi rigid unit modes (QRUMs) and results in NTE phenomenon [14]. In terms of molybdate, A₂Mo₃O₁₂ (A = Y³⁺, Yb³⁺, Ho³⁺, Tm³⁺, Lu³⁺, Sc³⁺, In³⁺, etc.) compounds have negative linear coefficients of thermal expansion (α_l =α_V/3) [15-19]. Upon reducing the A cation size, the AO₆ octahedra decrease in size, thus oxygen-oxygen distances contract resulting in increase in repulsion. The increased interaction strength in oxygen repulsions enhances the rigidity of the metal-oxygen polyhedra which inhibiting distortions and rotations [20]. Hence, it is implied that the NTE coefficients of A₂Mo₃O₁₂ can be controlled by adjusting the rigidity of polyhedra. This was confirmed by experimental results on Y₂Mo₃O₁₂ which had a stronger negative coefficient of thermal expansion, α_l = -12.6 ×10^-6 K^-1 [7], differing from orthorhombic A₂Mo₃O₁₂ with smaller A cations as Lu₂Mo₃O₁₂ (α_l = -5.59 ×10^-6 K^-1) and Sc₂Mo₃O₁₂ (α_l = -2.1 ×10^-6 K^-1) [21, 22]. Consequently, it is obvious that the decrease of A cation size could inhibit thermal contraction of A₂Mo₃O₁₂ materials remarkably. On the basis of above analysis, we performed a research work of control on thermal expansion property of rare earth molybdate in which rare earth ions were substituted by small metal ions step by step.

In this study, Yb³⁺ (radius of 0.86Å) was partially substituted by Fe³⁺ (radius of 0.64Å) in order to form Yb_2-xFe_xMo₃O₁₂ (x=0.0, 0.6, 1.0, 1.1, 1.4) solid solutions. The AO₆ octahedra therefore decreased in size with doping of Fe³⁺ inducing stronger repulsions in oxygen anions, and the linear thermal expansion coefficients of Yb_2-xFe_xMo₃O₁₂ increased synchronously, as expected. For the reason that the framework of Fe₂Mo₃O₁₂ adopts monoclinic structure at a temperature range from room temperature to 773K differing from the orthorhombic crystal structure of Yb₂Mo₃O₁₂ [23, 24], Yb³⁺ could not be substituted by Fe³⁺ in all composition ranges. Otherwise, the detailed investigations on crystal structures of Yb_2-xFe_xMo₃O₁₂ revealed the fundamental causes for the positive or negative thermal expansion.

2. Results and discussion

Rietveld refinements were performed for every Yb_2-xFe_xMo₃O₁₂ compound using XRPD data. Details of refinement protocols for Yb_1.4Fe_0.6Mo₃O₁₂ and Yb_1.0Fe_1.0Mo₃O₁₂, as examples, are given in Table 1. XRPD patterns of the samples showing experimental, calculated, difference profiles and Bragg positions after Rietveld refinement are illustrated in Fig. 1. Atomic coordinates for Yb_1.4Fe_0.6Mo₃O₁₂ at 873K and Yb_1.0Fe_1.0Mo₃O₁₂ at 453K are presented in Tables S1 and S2 (Supporting information), respectively.

According to the XRPD patterns (Fig. 2) and Rietveld structural refinement results, Yb_2-xFe_xMo₃O₁₂ (x=0.0, 0.6, 1.0, 1.1, 1.4) adopted orthorhombic crystal structure (space group No. 60). At the same time, all diffraction lines were observed to shift to higher two-theta angles in Fig. 2 with substituting of Fe³⁺ for Yb³⁺. Diffraction line of (123) plane was marked as an example. The interplanar spacing d of (123) in Yb_2-xFe_xMo₃O₁₂ (x=0.0, 0.6, 1.0, 1.1, 1.4), calculated using Bragg equation (Table S3, in Supporting information), decreased with more Yb³⁺ replaced by the smaller Fe³⁺. In addition, Yb_2-xFe_xMo₃O₁₂ (x=1.0, 1.1) would decomposed when heated up to high temperature, which might be induced by the distortion of polyhedra, considering the over 25 percent difference in ionic radius between Yb³⁺ and Fe³⁺. This kind of instability of crystal structure had been also observed in other A₂M₃O₁₂ solid solutions even at room temperature [25]. A comparison of XRPD patterns between Yb_0.6Fe_1.4Mo₃O₁₂ and Yb_0.9Fe_1.1Mo₃O₁₂ is illustrated in Fig. 3. Yb_0.9Fe_1.1Mo₃O₁₂ was found to decompose when the temperature was up to 873K and the same instability of Yb_1.0Fe_1.0Mo₃O₁₂ was observed at 923K, while no phase transition was found in the whole testing temperature range for Yb_2-xFe_xMo₃O₁₂ (x=0.0, 0.6, 1.4). As the temperature increased from 423K to 1073K, shift of diffraction lines can also be observed in XRPD pattern of Yb_0.6Fe_1.4Mo₃O₁₂ (Fig. 3), which indicates the changes of interplanar spacing d especially when the temperature is higher than 873K (Table S4 in Supporting information).

Besides d values, unit cell volumes V and lattice parameters a, b, c of all the prepared samples at different temperature were figured out using the Rietveld refinement method. Contraction of V, as well as lattice parameters, caused by the substitution of smaller Fe³⁺ for Yb³⁺ is evident in Fig. 4. Moreover, the doping iron ions in crystal structure of Yb₂Mo₃O₁₂ resulted in decrease of average Yb-Mo or Yb/Fe-Mo nonbonded distance (Fig. 5) and increase of linear thermal expansion coefficients (Table 2). Moreover, a comparison between Figs. 4 and 5 reveals that the variation trend of average Yb-Mo or Yb/Fe-Mo nonbonded distance is very similar to that of unit cell volume V, which implies the close connection between NTE property of Yb_2-xFe_xMo₃O₁₂ and average Yb-Mo or Yb/Fe-Mo nonbonded distance.

Fig. 6 shows a corner sharing framework of YbO₆ octahedra and MoO₄ tetrahedra in orthorhombic Yb₂Mo₃O₁₂, which exhibits anisotropic negative thermal expansion property with a linear thermal expansion coefficient (α_l) of -3.97 ×10^-6K^-1. The linear thermal expansion coefficients of a and b axis (α_a and α_b) are -6.59 ×10^-6K^-1 and -5.06 ×10^-6K^-1, while c axis shows a nearzero linear thermal expansion coefficient of 0.07 ×10^-6K^-1 in the temperature range of 473-1073K. When the temperature is rising, rocking of the polyhedra in the Yb₂Mo₃O₁₂ structure occurs because the average Yb-O-Mo angle reduces continually (Table 3). This contraction of A-O-Mo bridging bond angles has also been observed in other A₂Mo₃O₁₂ compounds [6, 16]. At the same time, the average apparent Mo2-O (Mo2 site in Fig. 6) bond length in Yb₂Mo₃O₁₂ (Table 3 and Fig. 7) decreases from 1.7557Å (473K) to 1.6939Å (873K) which indicates that distinct distortions took place in the Mo2O₄ tetrahedra, while change of average bond length has been hardly observed in Mo1O₄ (Mo1 site in Fig. 6) and YbO₆ (Yb sitein Fig. 6) polyhedra (Fig. 7). It isbelievedthat both the rocking and the distortion of polyhedra shorten the Yb-Mo nonbonded distances and give rise to NTE phenomenon [6, 14]. Therefore, it is conclude that the negative thermal expansion activity of Yb₂Mo₃O₁₂ could be ascribed to the reductions in both the average Yb-O-Mo angle and the average apparent Mo2-O bond length with increasing temperature, which induce decrease in average Yb-Mo nonbonded distances ultimately (Table 3). It was suggested by Liang et al. that stretching and bending modes of MoO₄ tetrahedra contribute to the NTE of Y₂Mo₃O₁₂ partially [26]. In this work, Mo2O₄ tetrahedra are confirmed playing more roles than Mo1O₄ tetrahedra in the NTE of Yb₂Mo₃O₁₂ by the changes in average apparent Mo-O bond lengths at different temperature, which is revealed for the first time.

Fig. 7 shows that Fe³⁺ dopant in crystal structure has influence on the average bond lengths of Yb/FeO₆ and MoO₄ polyhedra. Compared to the lower temperature, when the temperature increased to 873K, the distortions of Mo2O₄ tetrahedra were more remarkable than that of Mo1O₄ and YbO₆ polyhedra in Yb_1.4Fe_0.6-Mo₃O₁₂ and Yb_0.6Fe_1.4Mo₃O₁₂. As for Yb_1.0Fe_1.0Mo₃O₁₂, the average Yb/Fe-O-Mo angle reduced from 137.396° (at 435K) to 133.999° (at 873K), which indicated the slight rotations of Yb/FeO₆ and MoO₄ polyhedra.Atthesametime, theincreaseof averageYb/Fe-O and Mo1-O bond length and decrease of average Mo2-O bond length were observed in Fig. 7. Thus the cell volume of Yb_1.0Fe_1.0Mo₃O₁₂ expanded from 1204.8ų to 1206.6ų induced by the synergetic effect of rotations and distortions of metaloxygen polyhedra. Evidently, the changes of average metal-oxygen bond length are more complicated in Yb_1.0Fe_1.0Mo₃O₁₂ than in other Yb_2-xFe_xMo₃O₁₂ (x=0.0, 0.6, 1.4) compounds, indicating the instability of crystal structure as the ratio of rare earth ions to iron ions is 1/1, which can be related to the decomposition of Yb_1.0Fe_1.0Mo₃O₁₂ at 923K.

The linear relationships between the lattice parameters, unit cell volume and Fe content (x) in Yb_2-xFe_xMo₃O₁₂ at 873K are illustrated in Fig. 8, which are perfect proof for the substitution of Fe³⁺ to Yb³⁺ at Yb ³⁺ sites in crystal structures. This kind of linear relationship is exactly identical with the change of average A-Mo (A: Yb-Mo or Yb/Fe) nonbonded distances as a function of Fe content. Therefore, the average A-Mo distance is more accurate than the average A-O and Mo-O bond length and average A-O-Mo angle in studying the thermal expansion properties of Yb_2-xFe_xMo₃O₁₂ solid solutions, for the reason that neither the average A/ Mo-O bond length nor the average A-O-Mo angle can explain the changes of unit cell volume and lattice parameters independently. Furthermore, it can be deduced from Figs. 5 and 8 that the variation of average A-Mo nonbonded distances at different temperature should be a direct structural origin of negative or positive thermal expansion for orthorhombic A₂Mo₃O₁₂ compounds [16, 23].

The radius of Fe³⁺ is 0.64 Å, much smaller than that of Yb³⁺ (0.86 Å). The substitution of Fe³⁺-Yb³⁺ reduces the oxygen-oxygen distances in AO₆ octahedra directly, causing stronger repulsions between oxygen anions. The increased interaction strength in oxygen-oxygen repulsions promotes the rigidity of the polyhedra. As a result, the distortions and rotations of metal-oxygen polyhedra are inhibited [20]. Therefore, the thermal expansion coefficients of Yb_2-xFe_xMo₃O₁₂ increase from negative to positive with more ytterbium cations substituted by iron cations (Table 2), which means the NTE coefficients of A₂Mo₃O₁₂ can be controlled by doping smaller A cations at the octahedral sites in crystal structure. Yb_1.4Fe_0.6Mo₃O₁₂ has a NTE coefficient of -1.24 ×10^-6 K^-1 (473-873 K) and a positive coefficient of 7.36 ×10^-6 K^-1 (873-1073 K). Yb_1.0Fe_1.0Mo₃O₁₂ has a low positive thermal expansion coefficient of 1.19 ×10^-6 K^-1 (453-873 K). What is more interesting is that a near-zero thermal expansion coefficient of 0.55 ×10^-6 K^-1 and a very high positive thermal expansion coefficient of 22.80 ×10^-6 K^-1 for Yb_0.6Fe_1.4Mo₃O₁₂ are observed in the temperature range of 573-873 K and 873-1073 K, respectively. Such materials as Yb_0.6Fe_1.4Mo₃O₁₂ with sudden change in thermal expansion coefficient might be of potential applications in area of high-temperature ceramic components.

3. Conclusion

Rietveld structural refinements of XRPD data revealed that the reductions in average Yb-O-Mo angle and average apparent Mo2-O bond length played important roles for the NTE of Yb₂Mo₃O₁₂. The varieties of average apparent metal-oxygen bond length of AO₆ and MoO₄ polyhedra in Yb_1.0Fe_1.0Mo₃O₁₂ are more complicated than in other Yb_2-xFe_xMo₃O₁₂ (x = 0.0, 0.6, 1.4) compounds. The changes of average A-Mo distances with increasing temperature are direct structural origins of negative or positive thermal expansion for orthorhombic Yb₂Mo₃O₁₂ compound. The linear thermal expansion coefficients of Yb_2-xFe_xMo₃O₁₂ increased from negative to positive with Yb³⁺ substituted by Fe³⁺, which indicated that the thermal expansion property of Yb₂Mo₃O₁₂ (NTE coefficient of -3.97 ×10^-6 K^-1) could be efficiently adjusted by doping of Fe cations with smaller ionic radius. In addition, a near-zero thermal expansion coefficient of 0.55 ×10^-6 K^-1 for Yb_0.6Fe_1.4Mo₃O₁₂ was observed in the temperature range of 573-873K. The negative or positive thermal expansion properties of orthorhombic Yb_2-xFe_xMo₃O₁₂ solid solutions are attributed to the changes of average metal-metal nonbonded distances with increasing temperature directly.

4. Experimental

The samples were prepared by the conventional solid state techniques from stoichiometric quantities of the constituent oxides. All the starting materials were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China), and preheated to 773K before weighting to protect from H₂O and CO₂. Reactants Fe₂O₃ (purity 99.99%), Yb₂O₃ (purity 99.9%) and MoO₃ (purity 99.5%) werethoroughlygroundand heat treatedat 1073-1173K for two 24h periods with intermittent grinding in alumina crucibles. All samples were quenched in air. high temperature X-ray powder diffraction (XRPD) data were collected on PANalytical X'Pert PRO MPD with Cu K_α radiation (λ=1.54056Å, 40kV, 40mA) in 2θ range from 10° to 70° with a step size of 0.017° at Beijing Normal University. The heating rate was 30K/min and data were collected after the temperature was kept constant for 5min. Considering the hygroscopicity of orthorhombic rare earth molybdates at room temperature [13, 17], which would affect the thermal expansion property of A₂Mo₃O₁₂, XRPD data were recorded at high temperature (≥423K). Rietveld refinements of XRPD data were performed using FullProf software suite to obtain accurate parameters of crystal structure [27, 28].

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 21403129), the Project of Shandong Province Higher Educational Science and Technology Program (No. J13LD13 & J15LC09) and "Hundred Talents Project" of the Chinese Academy of Sciences.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cclet.2017.03.002.