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Thermal Expansion Behavior in the A2M3O12 Family of Materials

School of Physical Science and Technology, Yangzhou University, Yangzhou 225002, China
Guangling College, Yangzhou University, Yangzhou 225002, China
Department of Chemistry and Biochemistry, The University of Toledo, 2801 W. Bancroft St., Toledo, OH 43606, USA
Authors to whom correspondence should be addressed.
Solids 2021, 2(1), 87-107;
Submission received: 30 December 2020 / Revised: 9 February 2021 / Accepted: 11 February 2021 / Published: 19 February 2021
(This article belongs to the Special Issue Feature Papers of Solids 2021)


Over the past several decades, research on anomalous thermal expansion materials has been rapidly growing, and increasing numbers of compounds exhibiting negative thermal expansion (NTE) have been reported. In particular, compounds with formula A2M3O12 have attracted considerable attention. A2M3O12 family materials offer a wide range of possible compositions due to the chemical flexibility of the A and M sites. According to published research, more than half of them possess NTE properties. This paper reviews the range of physical properties displayed by materials in the A2M3O12 family. Research on improving material imperfections and controlling the coefficient of thermal expansion in the A2M3O12 family are systematically summarized. Finally, challenges and questions about the developments of these A2M3O12 NTE compounds in future studies are also discussed.

1. Introduction

In recent years, the fields of microelectronics, photoelectric communications and aerospace have rapidly expanded. Materials with high-precision size are in growing demand, and dimensional stability and long lifetime of devices at different operating temperatures is of high importance. A mismatch of thermal expansion coefficients combined with a temperature variation of the materials’ environment can result in thermal stress, thus leading to performance degradation or permanent damage to devices. Therefore, low, and especially near-zero expansion materials, are beneficial to improve the geometrical stabilities of these materials and devices. The discovery of negative thermal expansion (NTE) behavior in compounds provides the possibility of developing materials with controllable or near-zero thermal expansion coefficients for specific applications.
Previous research on NTE materials has focused on the following families: Metal cyanides [1,2,3,4,5,6], metal fluorides [7,8,9,10,11,12,13,14,15,16], Mn3AN (A = Cu, Zn, Ge, Sn, Ag) [17,18,19,20,21,22,23], intermetallics [24,25,26,27,28,29,30,31], metal oxides including AM2O8 (A = Zr, Hf; M = W, Mo) [32,33,34,35,36,37,38], AM2O7 (A = Zr, Hf; M = V, P) [39,40,41,42], A2O (A = Ag, Cu) [43,44,45,46,47] and A2M3O12 (A = trivalent cation; M = W, Mo) [48,49,50]. Compared to the other families, the A2M3O12 stoichiometry has received special attention because of the broad range of metals that can be incorporated into the structure. The A-site can be fully occupied by a single trivalent metal ranging in size from Al3+ to the smaller lanthanides, or partially substituted by most lanthanides and many transition metals, whereas the M-site is usually occupied by tungsten or molybdenum. Aliovalent substitution of both metal sites has also been reported. The wide range of compositions accessible in the A2M3O12 family is unique. This paper reviews the thermal expansion properties of the A2M3O12 family with a focus on compounds displaying NTE behavior. Recent advances are discussed in detail as well as promising future prospects.

2. Positive Thermal Expansion

The A2M3O12 family consists of a large number of compounds that can adopt several different structure types. The identity of the A and M site elements determines the preferred structure type which is intimately related to the thermal expansion properties of the compounds. According to the systematic research conducted by Nassau et al. [51], when the A-site is occupied by the larger lanthanides ranging from La3+ to Tb3+, these tungstates and molybdates display positive thermal expansion. Dy2Mo3O12 also belongs to this group of compounds, while Dy2W3O12 does not [52,53]. The crystal structures of these positive thermal expansion A2M3O12 compositions are orthorhombic in space group Pba2 or monoclinic in space group C2/c, and contain edge-shared AO7-polyhedra, which are generally considered as an unfavorable factor for NTE behavior. For instance, Figure 1 shows the typical structure of Gd2Mo3O12 [54]. Gd3+ is coordinated by seven oxygen atoms, while Mo6+ is bonded to four oxygen atoms. The GdO7 units share common edges, causing oxygen atoms to be coordinated by three instead of two atoms. This connection mode hampers transverse vibration of oxygen atoms, the typical basis of NTE in the A2M3O12 family.

3. Negative Thermal Expansion

In the field of NTE research, the A2M3O12 family is also referred to as the scandium tungstate family. Scandium tungstate adopts an orthorhombic structure in the space group Pnca at all temperatures (Figure 2) [55,56]. The crystal structure is composed of a corner-sharing framework of octahedral ScO6 and tetrahedral WO4 units. No edge-sharing is observed, in contrast to the Gd2Mo3O12-type structure discussed earlier. As the bond lengths of Sc-O and W-O show little change with temperature, the global expansion behavior is dominated by transverse motions of the corner-sharing oxygens. Diffraction data demonstrate that these vibrations give rise to a reduction of the Sc-O-W bond angle and a shortening of the next-nearest neighbor distances on a microscopic level and macroscopic NTE of the material [55]. The resulting rocking motions of the polyhedral building blocks are accompanied by some distortion of the polyhedra. Larger A-site cations can more readily accompany these distortions, and thus favor more significant NTE [57].
When the A-site is occupied by Ho3+, Y3+, Er3+, Tm3+, Yb3+, Lu3+, Sc3+, In3+, Fe3+, Cr3+, Ga3+ or Al3+, almost all tungstates and molybdates have been reported to form stable compounds that adopt the same structure as Sc2W3O12 and display NTE behavior [50,58]. Some compositions can undergo a phase transition from the orthorhombic NTE phase at high temperatures to a denser monoclinic positive thermal expansion (PTE) structure at low temperatures [59]. This phase transition can also be induced by applying pressure, which will be discussed later in this review.
Many attempts to synthesize single phase Fe2W3O12 and Cr2W3O12 using different approaches, such as solid-state, co-precipitation and sol-gel methods failed to obtain single phase Fe2W3O12 and Cr2W3O12 [60,61]. This is mainly because both Fe2W3O12 and Cr2W3O12 are metastable phases, which decompose to FeWO4 or CrWO4 and WO3 during heating. Other researchers reported successful synthesis, but did not display diffraction data [62,63] or displayed data that cannot exclude the presence of an amorphous component or small impurity phases [64,65]. Recently, Yang et al. fabricated Mo-doped single-phase Fe2W3O12 using rapid solid-state reactions with excess MoO3 [66]. Fe2W3O12 still showed positive thermal expansion after the monoclinic-to-orthorhombic phase transition with a coefficient of thermal expansion of 1.35 × 10−6 °C−1 (445–600 °C) as measured by dilatometry. Ga2Mo3O12 is another difficult to synthesize composition, which can only be obtained by non-hydrolytic sol-gel chemistry [67], and remains monoclinic with positive expansion until its decomposition temperature around 650 °C.
It is generally accepted that the coefficient of thermal expansion (CTE) is related to the size of the A-site trivalent cation, and that it decreases with increasing size of the A-site ion. To date, Y3+ has the largest ionic radius (0.90 Å) of the materials adopting the orthorhombic Pnca structure, and Y2Mo3O12 and Y2W3O12 display intrinsic linear thermal expansion coefficients of −9.36 × 10−6 °C−1 [68] and −7.0 to −7.4 × 10−6 °C−1 [69,70], respectively, in the temperature range of 200 to 800 °C. Only Ho2Mo3O12 has been reported to possess an even larger negative intrinsic αl value of −11.56 × 10−6 °C−1 [71], although several rare earth molybdates and tungstates show similar magnitudes of linear NTE [52,68,72]. These A-site cations are very similar in size to Y3+. However, many A2M3O12 compounds with large A-site ions possess the ability to absorb water, which inhibits the NTE behavior of the materials.

3.1. Mechanism of Negative Thermal Expansion in the A2M3O12 Family

Several excellent reviews discussing the origins of NTE in different classes of compounds have recently been published [73,74]. Both intrinsic structural features, and structural or magnetic phase transitions, can contribute to the observed behavior. The negative thermal expansion observed in Pnca-A2M3O12 compounds is categorized as intrinsic structural NTE. It arises from transverse vibrational motions of the 2-coordinated oxygens. In materials that contain mostly 2-coordinate linkers in approximately linear coordination, these vibrations result in concerted bending and torsional motions that reduce the distances between next-nearest neighbor metal centers. When these reductions outweigh the bond expansion due to longitudinal vibrations, NTE results. This visual concept for explaining NTE behavior was introduced early on for ZrW2O8 [34], and has since been applied to many other NTE materials that possess corner-sharing polyhedral networks. Other authors refer to it as the “tension effect” to indicate that the vibrations result in forces that cause rocking motions of the polyhedral building blocks [75,76]. In physics terms, these lattice vibrations are described as phonon modes, and both optical and acoustic transverse phonon modes with negative Grüneisen parameters can contribute to NTE, which is observed when the overall Grüneisen parameter is negative over an extended temperature range. If these modes occur without distortion of the polyhedra, they are referred to as rigid unit modes (RUMs), whereas modes in solids that show some changes within the polyhedra are often called quasi rigid unit modes (QRUMs) [37,77]. Tao and Sleight showed that the A2M3O12 family can only support QRUMs [78]. Evidence for transverse phonon modes in NTE materials was obtained by heat capacity and phonon density of states measurements [38,79]. Theoretical calculations have also been used to elucidate NTE mechanisms [80,81].

3.2. Hygroscopicity in the A2M3O12 Family

When the A-site is occupied by the smaller rare earth elements or pseudo-lanthanides, more specifically, Ho3+, Y3+, Er3+, Tm3+, Yb3+ and Lu3+, the A2M3O12 materials display strong NTE and remain orthorhombic to the lowest temperatures studied [68,69,71,72,82,83,84]. The large negative CTEs are attributed to the large ionic radii. However, the large ionic radii also cause hygroscopicity, as this gives rise to the emergence of microchannels accessible to water in the crystal structure [82,84,85]. Moisture from the atmosphere results in formation of trihydrates, with the water molecules interacting with the structure via strong hydrogen bonds. The presence of water and hydrogen bonding networks weakens or in most cases eliminates NTE behavior [86], and removal of the water is necessary to reclaim the NTE properties. Marinkovic et al. researched NTE and hygroscopicity of Y2Mo3O12 in detail, and found that the microchannels in the lattice are large enough for water molecules to enter freely and play a part in causing partial amorphization of Y2Mo3O12 upon hydration. A summary of CTEs and the corresponding temperature ranges for these hygroscopic materials can be found in Table 1.
Ample research has been performed with the materials in Table 1 to synthesize controllable thermal expansion materials that are less hygroscopic by chemical modification. Substitution of small amounts of Al, Cr, Fe or Sc generally did not eliminate water uptake [87,88,89,90,91,92,93], while lanthanide poor compositions showed less tendency to absorb moisture. For Al, Cr and Fe, hygroscopicity was overcome for compositions that resulted in formation of the denser monoclinic PTE phase, which is less favorable for water incorporation. For Sc, a non-hygroscopic material was obtained for Sc1.75Y0.25W3O12. A length change of −7.13 × 10−6 °C−1 was detected by dilatometry. Substitution of a larger rare earth ion that favors edge-shared structures has also been explored [88,94,95,96,97]. In this context, we previously prepared Y2−xCexW3O12 solid solutions to adjust the magnitude of the CTE and to overcome the hygroscopicity of Y2W3O12 [97]. Results showed that moisture absorption was no longer observed for x ≥ 1.5 at room temperature, however, compositions with x ≥ 0.5 also showed the presence of the denser monoclinic C2/c structure, with coexistence of the orthorhombic and monoclinic phases for x = 0.5. Dilatometer measurements still showed NTE for compositions up to Y0.25Ce1.75W3O12 (−0.82 × 10−6 °C−1), suggesting that such monoclinic ceramics could be promising near-zero thermal expansion materials. Double ion substitution such as (LiMg)3+ has also been implemented to reduce hydrophilicity in Y2Mo3O12 by Cheng et al. [98]. The hygroscopicity of the sample was eventually eliminated, but the thermal expansion of the material increased with the addition of (LiMg)3+. In addition to the method of ion-doping, Liu et al. chose C3N4 as a coating material to protect Y2Mo3O12 from water exposure [99]. This successfully prevented hydration, and retained similar expansion coefficients.

3.3. Non-Hygroscopic A2M3O12 Compositions with Corner-Shared Networks

When the A-site is occupied by Sc3+, In3+, Fe3+, Cr3+, Ga3+ and Al3+, A2M3O12 compositions do not absorb water molecules from air. Most of these materials undergo a reversible temperature-induced phase transition from a low temperature monoclinic structure in the space group P21/a to the orthorhombic Sc2W3O12 structure in the space group Pnca at higher temperatures. Exceptions are Sc2W3O12, which remains orthorhombic to the lowest temperatures investigated [55], and Ga2Mo3O12, which decomposes to the binary oxides before transforming to the orthorhombic phase [67]. Only Pnca-A2M3O12 materials exhibit notable negative thermal expansion. In general, the phase transition temperature increases with increasing electronegativity of the A-site ion. This can be attributed to the fact that A-site cations with higher electronegativity reduce the partial negative charge of the oxygen atoms and weaken the repulsive forces between them, which stabilizes the denser monoclinic structure to higher temperatures. The transition temperature can be determined by refinement of diffraction data, Raman spectroscopy, dilatometry or thermal analysis. The temperatures of the monoclinic to orthorhombic phase change are summarized in Table 2.
The exact relationship between the monoclinic and orthorhombic structures was demonstrated for Sc2Mo3O12 by Evans et al. [59]. This material adopts a monoclinic structure below −93 °C that displays PTE with an expansion coefficient of 2.19 × 10−5 °C−1. Above −93 °C, orthorhombic Sc2Mo3O12 shows NTE with a linear expansion coefficient of −6.3 × 10−6 °C−1. Figure 3 shows the two crystal structures of Sc2Mo3O12 and their crystallographic relationship, which is given by am ≈ −bo + co, bm ≈ −ao, and cm ≈ −2co.
Scandium tungstate is the only non-hygroscopic compound that does not undergo a phase transition to the lowest temperatures investigated [55]. It shows stable NTE performance over a wide temperature range from −263 °C to 800 °C and is non-hygroscopic in air. Because of this, it is considered to be one of the most promising NTE compounds in the A2M3O12 family. Sc2Mo3O12 [59] and Al2W3O12 [101] possess phase transition temperatures that are below room temperature, while the rest of the non-hygroscopic phase change materials undergo the transition at temperatures between 200 and 500 °C [66,100,101,102,103,104]. High phase transition temperatures are considered undesirable for fabricating devices, and approaches that allow lowering of the transition temperatures would be beneficial. To date, this has mainly been attempted by doping with different A-site elements, which showed that controlling the phase transition temperature to meet specific environments is promising and feasible [100,103,104].

3.3.1. Single Ion Substitution

Single ion substitution can be used to improve performance in A2M3O12 NTE compounds that display high phase transition temperatures (A = Al, In, Cr, Fe; M = W and Mo). This has been applied to solid solutions to tune phase transition temperatures in the 200 to 500 °C range [100,104]. However, from an applications point of view, suppressing the phase transition temperature to room temperature or below is desirable. This can mainly be achieved by incorporation of A-site cations with low electronegativity, which is known to lower the phase transition temperature [101]. In our previous work, we prepared solid solutions of In2−xScxW3O12 (0 ≤ x ≤ 2) using solid state reaction methods to reduce the phase transition temperature of In2W3O12 [103]. Sc3+ was shown to effectively replace In3+, and the monoclinic-to-orthorhombic phase transition temperature was shifted from 248 °C to 47 °C for x = 1. The average linear thermal expansion coefficient of InScW3O12 determined by dilatometry is −7.13 × 10−6 °C−1 in the temperature range 58 to 700 °C. The obtained thermal expansion curve for this sample is shown in Figure 4a. We have also prepared AlScMo3O12 by non-hydrolytic sol-gel routes [105], and found that it remains orthorhombic to −173 °C, but approaches the phase transition to the monoclinic structure at that temperature. The thermal expansion curve for this sample is shown in Figure 4b.
Wu et al. synthesized Ln2−xCrxMo3O12 (Ln = Er and Y) and showed via differential scanning calorimetry that the phase transition of Cr2Mo3O12 could be suppressed from 400 to 197 °C by substitution of 10% Er [93]. Similarly, Li et al. showed that with increasing Y3+ content in the solid solution Fe2−xYxMo3O12, the phase transition temperature could be decreased significantly, with Fe1.5Y0.5Mo3O12 showing the transition below −170 °C [87]. Substitution of Fe2−xLnxMo3O12 by other lanthanides (Ln = Er, Lu, Yb) resulted in orthorhombic materials at or below room temperature [87,90,91]. These reports demonstrate that single ion substitution can successfully broaden the temperature range in which the orthorhombic NTE phase is stable. However, these compounds become hygroscopic even after incorporation of small quantities of lanthanides, making substitution by Sc3+ most attractive. Work on single ion doping on the M-site to reduce the phase transition temperature is rare. Shen et al. prepared Al2Mo3−xWxO12 solid solutions to adjust the coefficient of thermal expansion of Al2Mo3O12 and found a less significant reduction of the phase transition temperature of Al2Mo3−xWxO12 with increasing W6+ content [106]. Liu et al. later suggested that this could be explained by the lower electronegativity of W6+ compared to Mo6+, which is consistent with the effect of the electronegativity of the A3+ cation on the transition temperatures [107]. Table 3 gives an overview of selected mono-substituted compounds for which phase transition temperatures and expansion coefficients have been reported.
Figure 5 shows the relationship between average A-site electronegativity and phase transition temperature for A2−xA’xM3O12 compositions. Compounds with reported transition temperatures below room temperature are marked by name. The molybdates generally follow a linear trend, with the exception of AlScMo3O12 and Fe1.5Y0.5Mo3O12. These compounds both contain two A-site cations with a significant size difference, which according to Truitt et al. can result in the suppression of the phase transition temperature [105]. Interestingly, the behavior of the tungstates is more varied, resulting in two distinct branches with some scattered values in-between. It is worth noting that all compounds on the lower branch contain aluminum as one of the A-site cations, while all compositions on the upper branch contain indium. The two reported Al2−xInxW3O12 compositions contribute the datapoints between the two lines. The formation of these two branches is related to the large difference in phase transition temperature for Al2W3O12 and Inl2W3O12 combined with the very similar electronegativities of aluminum and indium.

3.3.2. Aliovalent Substitutions

Considerable work has been performed on single ion substitution with cations of the same charge (trivalent A-site or hexavalent M-site cations). In addition, both the A- and M-site of A2M3O12 can be substituted by a number of aliovalent cations. The guiding principles of single or double ion doping to reduce the phase transition temperature of A2M3O12 materials all center around choosing A-site cations with lower electronegativity. Lower electronegativity reduces the ability of the A-site cations to attract surrounding electrons, causing an increase of the partial negative charges on oxygen. The enhanced oxygen-oxygen repulsion favors the less dense orthorhombic structure, in which these atoms are separated by a larger distance. Therefore, phase transitions require less energy and occur at lower temperatures.
Aliovalent doping requires double substitution to maintain charge balance. In all cases, the A-site is at least partially occupied by a tetravalent atom (Zr4+, Hf4+). The extra positive charge can either be balanced by an A-site divalent metal (Mg2+, Mn2+, also partial substitution by Zn2+) [120,121,122,123,124,125,126,127,128,129], or by partial substitution of the M-site with a pentavalent atom (P5+, V5+) [130,131,132,133]. The earliest reports of such substitutions were Zr2MP2O12 and Hf2MP2O12, which were shown to be isostructural to Sc2W3O12 and possess NTE by Evans et al. [58,134]. These materials remain orthorhombic to the lowest temperatures studied, and display intrinsic NTE with αl values of −4 to −5 × 10−6 °C−1 [58,135,136].
The first aliovalent double substitution of the A-site was accomplished when Suzuki et al. synthesized HfMgW3O12 [124]. The equivalent Zr- and Mo-substituted compositions were reported as well [126,137]. In contrast to Zr2MP2O12 and Hf2MP2O12, these materials adopt a cation-ordered structure in the space group Pna21 [138] and show small negative to small positive intrinsic αl values [122,124,126,129,138,139]. Evidence for a monoclinic phase at low temperatures has been observed as well [127], and some authors detected hygroscipic behavior [140,141]. Significant ion conductivity was reported as well [142]. For the molybdates, Mg2+ can also be replaced by Mn2+, which enhances the NTE of the orthorhombic phase slightly, but also results in formation of a monoclinic phase with PTE below 90 °C [125]. Partial substitution by Zn2+ (up to ZrMg0.65Zn0.35Mo3O12 [143] and HfMg0.5Zn0.5Mo3O12 [120]) has also been achieved, and also increases the phase transition temperature to the monoclinic structure. Based on the consideration of valence balance, partial substitution of a trivalent A-site cation with a +2/+4 cation combination has also been explored to further tune the properties of A2M3O12 compounds. These include (ZrMg) doping of Al2W3O12 [140], Cr2Mo3O12 [123] and In2Mo3O12 [144] as well as (HfMg) doping of Al2W3O12 [145], Fe2Mo3O12 [146] and In2Mo3O12 [147,148]. Similarly to single ion substitution, the lower electronegativity of Mg and Zr contributes to the reduction in phase transition temperature.
Another interesting set of materials has been created by matching partial substitution of the A-site by Zr4+ or Hf4+ with the equivalent amount of P5+ or V5+ incorporation on the M-site. The majority of investigations focused on Sc3+ as the trivalent A-site cation [131,132,133,149,150,151], but materials containing Mn3+, Cr3+, Fe3 + and Y3+ have also been reported [130,152,153,154]. Phase transition temperatures considerably below room temperature were observed for many materials. In addition, several compositions exhibit intense photoluminescence. Relevant expansion coefficients and phase transition temperatures (where investigated) are summarized in Table 4.

3.4. Pressure-Induced Phase Transitions in the A2M3O12 Family

Many NTE compounds in the A2M3O12 family are also sensitive to pressure due to their open framework structures. Materials that adopt the orthorhombic structure at room temperature tend to undergo a structural change to the denser monoclinic structure at very low pressures [155,156,157], which is akin to the temperature-induced phase transition mentioned above. In addition, irreversible amorphization is observed in many of these compounds at higher pressures ranging from 5 to 20 GPa [67,155,157,158,159,160,161]. This is not surprising, as the flexible, low-density frameworks of the A2M3O12 family can readily distort or transform to denser crystalline polymorphs. Non-hydrostatic conditions favor this behavior, and can shift the onset of amorphization to even lower pressures. For a number of compositions, distinct new phases were formed at intermediate pressures. To date, it is impossible to predict the pressure and nature of these intriguing phase transitions for unstudied compositions, thus the high pressure behavior in this family still warrants further experimental and theoretical investigation. A small number of representative materials will be discussed in the following sections. For a more comprehensive summary of the high pressure behavior of these materials, the reader is referred to a review recently published by Young et al. [162].

3.4.1. High Pressure Behavior of NTE Tungstates

Orthorhombic Sc2W3O12 is thermodynamically stable in a wide temperature range from −263 to at least 800 °C. However, even moderate pressure destabilizes this phase. Garg et al. studied the pressure-induced structural changes of Sc2W3O12 using Raman scattering and X-ray diffraction [160]. Their work showed that Sc2W3O12 transformed to a monoclinic phase near 0.28 GPa and converted to another denser monoclinic phase at 1.6 GPa. Both transitions were reversible upon decompression. Above 6.5 GPa, Sc2W3O12 became increasingly disordered and irreversibly evolved into an amorphous state. Changes in the frequencies of the bending and asymmetric modes in the Raman spectra revealed that the polyhedra in the structure were highly distorted at this stage. Secco’s impedance spectroscopy study indicated that the conductivity of Sc2W3O12 increased with increasing pressure, making it a potential candidate for applications in pressure-sensing [163,164].
Orthorhombic Al2W3O12 exhibited similar pressure-induced phase transition behavior. The orthorhombic phase converted to two distinct monoclinic structures at 0.5 GPa and 3.4 GPa, respectively, both of which were assigned to the space group P21 [165]. At 18 GPa, amorphization was observed. The higher phase transition pressures can be attributed to the smaller size of Al3+ and the resulting stiffer octahedra. In contrast to Sc2W3O12 and Al2W3O12, orthorhombic Zr2WP2O12 remained stable up to ~1.7 GPa, and showed a gradual phase transition to a monoclinic cell (space group P21/n) above this pressure. In contrast to the other tungstates, no doubling of the number of formula units per unit cell and thus the cell volume was necessary to account for all peaks [161]. A second monoclinic phase was observed above 3.7 GPa (space group P21/n), followed by formation of a triclinic phase above 7.4 GPa (space group P1 or P-1) and irreversible amorphization above 14 GPa. Monoclinic In2W3O12 also underwent a phase change in the pressure range of 1.9 to 2.7 GPa, but the lattice constants of the high-pressure cell could not be determined due to the coexistence of the two phases [158]. Unlike the above compounds, orthorhombic Y2W3O12 transformed directly to a disordered phase at 3 GPa without intermediate crystalline high-pressure polymorphs [166].

3.4.2. High Pressure Behavior of NTE Molybdates

Several molybdates show comparable behavior to their tungstate counter parts. Varga et al. found that Sc2Mo3O12 undergoes similar phase transitions as Sc2W3O12 at comparable pressures [155]. A phase transition to monoclinic symmetry (space group P21/a) was observed at 0.25 GPa followed by conversion to a different monoclinic cell between 2.5 and 3.0 GPa. Above 8 GPa, broadening of diffraction peaks indicated successive amorphization. Monoclinic Al2Mo3O12, Fe2Mo3O12 and Ga2Mo3O12 undergo identical phase transition sequences to two denser monoclinic phases at pressures between 2.5 (space group P21/a) and 6 GPa (unknown space group) [167]. Young et al. showed that orthorhombic Y2Mo3O12 underwent a phase transition to the low temperature monoclinic phase (space group P21/a) below 0.13 GPa. Surprisingly, no other pressure induced crystalline-to-crystalline phase transitions or amorphization were detected up to 4.9 GPa. Similarly, no phase transitions were observed for monoclinic Cr2Mo3O12 up to 8.9 GPa [162].
While predictions of CTEs in A2M3O12 materials are possible based on the ionic radii of the A site cations, no correlations between the metals present in the structure and the pressure induced phase transition behavior of these materials have been found. The ability to predict where a novel material may undergo a pressure induced phase transition would be highly beneficial for implementation in industries such as microelectronics, thermo shock resistant materials and aerospace.

4. Controllable Thermal Expansion in the A2M3O12 Family

The A2M3O12 structure displays excellent tolerance towards elemental substitution of both the A-site and M-site, which holds the potential for tuning the overall thermal expansion of materials. Thermal expansion coefficients can be tailored by either formation of composites or chemical modification of single-phase materials. Sleight’s group began to prepare solid solutions with two or three trivalent cations as early as 1997 [58]. A number of compounds with NTE properties were synthetized successfully, such as ScAlW3O12, ScGaW3O12, ScInW3O12 and ScHoW3O12. They also effectively modulated the thermal expansion coefficient of Al2W3O12 by doping with different ratios of In3+. Finally, after adding trace amounts of Sc3+, the zero-expansion material Al1.68Sc0.02In0.3W3O12 was successfully prepared, which was a significant achievement that stimulated further research. Near-zero thermal expansion materials are attractive when dimensionally stable materials are desired. Design of intrinsic zero expansion materials through solid solution formation and heterogenous composite formation are the two main approaches to controlling thermal expansion coefficients of materials in applications.

4.1. Heterogeneous Composites

Composites that contain positive and negative thermal expansion materials present a straightforward method for the fabrication of controllable thermal expansion materials. However, for ceramic composites, this method requires two materials that possess excellent thermal stability and no reactivity with each other at the temperatures used for sintering. The first reports used an excess of MoO3 in the preparation of Fe2−xScxMo3O12 to form a Fe0.4Sc1.6Mo3O12/MoO3 composite with CTEs as low as 0.2 × 10−6 °C−1 [168]. To further reduce expansion and based on stability considerations, Yanase et al. chose ZrSiO4, which possesses good chemical stability and low thermal expansion, to fabricate ZrSiO4/Y2W3O12 composites [169]. XRD analysis showed that no reactions occurred during sintering. An average linear thermal expansion coefficient of −0.08 × 10−6 °C−1 was measured from 25 to 1000 °C. Metal matrix composites with aluminum have also been explored [170,171]. More recent work has focused on ceramic composites that contain Zr2MP2O12 (M = Mo, W) compositions, which do not undergo temperature or pressure-induced phase transitions [172,173,174]. Results from these approaches are summarized in Table 5.

4.2. Solid Solution Formation

The expansion behavior of the composites described above depends on their microstructures and interaction between the phases. Possible shortcomings of composites include interfacial mismatch, thermal stress at interfaces and potential chemical reactions. In addition, reproducibility between specimens and repeated thermal cycles can be less than optimal. In principle, solid solution formation through ion substitution provides an effective way of controlling thermal expansion coefficients of single-phase materials while circumventing the potential shortcomings of composites.

4.2.1. Single Ion Substitution at the A/M Site

The first systematic studies targeted at tuning the expansion and phase transition behavior in A2M3O12 materials were carried out by Sugimoto et al. by dilatometry [115] and Ari et al. by diffraction based methods [100]. Dilatometry based results may suffer from specimen-to-specimen variability. Ari’s research on molybdates with mixtures of Al/Cr, Al/Fe and Cr/Fe on the A-site elegantly demonstrated that both phase transition temperatures and expansion coefficients can be tuned. However, all of the compounds investigated in their work displayed transition temperatures of 200 °C or higher. Low expansion and decreased transition temperatures were achieved by doping with lanthanides, however, many of these materials still showed hygroscopic tendencies when phase transition temperatures below room temperature were achieved [91,92,93]. Dasgupta et al. [118] synthesized Al2−xScxW3O12, which can be regarded as a mixture between Sc2W3O12 with NTE and Al2W3O12 with PTE. The value of x was varied from 0 to 2.0 to identify the optimum composition to achieve the least expansion. All compositions formed a single orthorhombic phase. For x = 1.5, the lowest coefficient of thermal expansion was observed, which was −0.15 × 10−6 °C−1 from 25 to 700 °C. Al0.5Sc1.5W3O12 also exhibited high in-line transmittance in the mid infrared wavelength range, making it a candidate for application in IR night vision devices. Other near-zero thermal expansion compounds prepared by single ion substitution are listed in Table 6.

4.2.2. Aliovalent Ion Substitution at the A/M Site

Several aliovalently substituted materials display close to zero expansion. The first examples were MgZrMo3O12 and MgHfMo3O12, for which intrinsic αl values of 0.13 × 10−6 and 1.02 × 10−6 °C−1 have been reported [126,138]. Partial substitution by tungsten can further lower the intrinsic CTE of MgHfMo2.5W0.5O12 to −0.08 × 10−6 °C−1 [129]. Several compositions in which In3+ or Cr3+ were introduced on the A-site also display very low intrinsic expansion [123,147,178]. Recently, ZrFeMo2VO12, a new near-zero thermal expansion material, was prepared using solid state methods by D. Chen et al. [81] to adjust the thermal expansion of Fe2Mo3O12. The mechanism of CTE reduction was explained by the lower average expansion of the Zr(Fe)-O-V(Mo) bonds compared to Fe-O-Mo bonds, because Zr-O and V-O bonds are stiffer than Fe-O bonds. At the same time, double ion substitution also reduced the phase transition temperature of Fe2Mo3O12 due to the smaller electronegativity of Zr4+/V5+ compared to Fe3+/Mo6+. Additional results using aliovalent ion substitution are listed in Table 7.

5. Potential Challenges for Use of NTE Materials

In addition to moisture absorption and phase transitions, some additional factors need to be improved for NTE materials in the A2M3O12 family to achieve their full potential. For example, many composites have low mechanical strength, which limits their applications. Several attempts to address this issue have been reported. Liu et al. prepared Al/Y2Mo3O12 composites through uniaxial compression, which improved mechanical strength and conductivity [179]. Yang et al. [72] used a vacuum hot-pressing method to synthetize ZrMgMo3O12/Al composites, which possessed both high strength and low thermal expansion [180].

6. Conclusions

The applications of A2M3O12 materials as functional materials are limited, as additional desirable properties apart from low CTEs are necessary. Further exploration of their ionic conductivity could prove useful [181,182,183]. The ability of many ions in the structure to participate in redox reactions may have potential applications in sensing or batteries [184,185,186,187,188,189,190,191]. Researchers have started to enrich the physical or chemical properties of NTE materials with some success, which may lead to additional applications for these materials. For example, ZrScMo2VO12 and HfScW2PO12 show interesting photoluminescence properties [132,133], making them potential temperature-stable photoelectric materials for use in the field of light emitting diodes (LED). The material (HfSc)0.83W2.25P0.83O12-δ also displays photoluminescence, and may also show oxygen ion conductivity due to its composition [150]. NTE materials have been widely studied because of their abnormal thermal expansion properties and their potential for developing near-zero thermal expansion materials. These functional materials can effectively improve adverse effects on structure and precision of many devices. Compared to other NTE families, the A2M3O12 family has excellent tunability through ion substitution and a wide NTE range. Despite challenges arising from hygroscopicity and phase transitions, the A2M3O12 family still attracts much attention from researchers and warrants further exploration. Future directions for studies may include efforts dedicated to (1) in-depth research on CTEs and phase transitions of novel materials; (2) elucidation of the mechanism of pressure induced phase transitions; (3) searches for non-hygroscopic compositions with strong NTE performance; (4) extending the NTE temperature range to lower temperatures; and (5) investigating and enhancing value-added properties like electrical conductivity, thermal conductivity, mechanical properties and photonic properties.


The authors would like to thank National Natural Science Foundation of China (No.51602280 and No.51102207), Qing Lan Project of Jiangsu Province, Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX18-0794).

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. (a) Crystal structure of Gd2Mo3O12 and (b) three-fold coordinated oxygen.
Figure 1. (a) Crystal structure of Gd2Mo3O12 and (b) three-fold coordinated oxygen.
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Figure 2. Crystal structure of orthorhombic Sc2W3O12: blue: ScO6 octahedra; green: WO4 tetrahedra.
Figure 2. Crystal structure of orthorhombic Sc2W3O12: blue: ScO6 octahedra; green: WO4 tetrahedra.
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Figure 3. Crystal structures of (a) monoclinic and (b) orthorhombic Sc2Mo3O12.
Figure 3. Crystal structures of (a) monoclinic and (b) orthorhombic Sc2Mo3O12.
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Figure 4. (a) Expansion curve of InScW3O12 obtained by dilatometry and (b) unit cell volume of AlScMo3O12.
Figure 4. (a) Expansion curve of InScW3O12 obtained by dilatometry and (b) unit cell volume of AlScMo3O12.
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Figure 5. Monoclinic to orthorhombic phase transition temperatures for monosubstituted A2M3O12 compositions as a function of average A-site electronegativity for (a) molybdates and (b) tungstates. Triangles represent compounds that remained orthorhombic to the lowest temperatures investigated.
Figure 5. Monoclinic to orthorhombic phase transition temperatures for monosubstituted A2M3O12 compositions as a function of average A-site electronegativity for (a) molybdates and (b) tungstates. Triangles represent compounds that remained orthorhombic to the lowest temperatures investigated.
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Table 1. Intrinsic coefficients of thermal expansion (CTEs) of hygroscopic materials in the A2M3O12 family based on variable temperature diffraction data.
Table 1. Intrinsic coefficients of thermal expansion (CTEs) of hygroscopic materials in the A2M3O12 family based on variable temperature diffraction data.
Compoundαl (×10−6 °C−1)T Range (°C)Ref.
Y2Mo3O12−9.36 125–800[68]
Y2W3O12−7.34 1200–800[72]
Er2Mo3O12−7.56 125–800[68]
Er2W3O12−6.74 1200–800[72]
Lu2Mo3O12−6.02 125–800[68]
Lu2W3O12−6.18 1200–800[72]
Yb2Mo3O12−6.04 125–800[68]
Yb2W3O12−6.38 1200–800[72]
1 Collected under vacuum.
Table 2. Phase transition temperatures and CTEs of orthorhombic phases of compounds in the A2M3O12 (A = Al3+, Sc3+, Cr3+, Fe3+, Ga3+ and In3+) family. Intrinsic αl values based on variable temperature diffraction data are reported unless indicated otherwise. NR = not reported.
Table 2. Phase transition temperatures and CTEs of orthorhombic phases of compounds in the A2M3O12 (A = Al3+, Sc3+, Cr3+, Fe3+, Ga3+ and In3+) family. Intrinsic αl values based on variable temperature diffraction data are reported unless indicated otherwise. NR = not reported.
CompoundTPT (°C)αl (×10−6 °C−1)T RangeRef.
Fe2W3O12414–4451.35 1445–600[66]
Ga2W3O12NR−5 1NR[58]
In2W3O12250−3.00 1277–700[103]
1 Dilatometer data.
Table 3. Variation in phase transition temperature (TPT) by single A-site doping and corresponding intrinsic linear CTEs determined from variable temperature diffraction data, unless otherwise indicated. Elements for each site are listed in alphabetical order.
Table 3. Variation in phase transition temperature (TPT) by single A-site doping and corresponding intrinsic linear CTEs determined from variable temperature diffraction data, unless otherwise indicated. Elements for each site are listed in alphabetical order.
CompoundTPT (°C)αl
(×10−6 °C−1)
Ref.CompoundTPT (°C)αl
(×10−6 °C−1)
Al0.2Cr1.8Mo3O12374NR[100]Cr1.7Sc0.3Mo3O12276−4.34 1[108]
Al1.6Fe0.4Mo3O12273NR[100]Cr1.4Sc0.6Mo3O12177−2.81 1[108]
Al1.4Fe0.6Mo3O123053.40[100]Cr1.1Sc0.9Mo3O12149−5.87 1[108]
Al1.2Fe0.8Mo3O12399NR[100]Cr0.8Sc1.2Mo3O1265−4.57 1[108]
Al0.8Fe1.2Mo3O12399NR[100]Cr0.6Sc1.4Mo3O12<RT−11.17 1[108]
Al1.8Yb0.2Mo3O121579.5 1[88]Fe1.6Sc0.4Mo3O12376−6.25 1[112]
Al1.6Yb0.4Mo3O12<RT5.74 1[88]Fe1.2Sc0.8Mo3O122411.17[113]
Al0.4Yb1.6Mo3O12<RT−5.5 1[88]Fe0.8Sc1.2Mo3O12109−4.18 1[112]
Al0.2Yb1.8Mo3O12<RT−9.1 1[88]Fe0.7Sc1.3Mo3O121120.09[113]
Al2Mo2.5W0.5O121274.85 1[106]Fe0.4Sc1.6Mo3O12<RT−0.83[113]
Al2Mo2.5W0.5O121185.20 1[106]Fe1.8Y0.2Mo3O12348NR[87]
Al2Mo2.5W0.5O121014.00 1[106]ln2Mo3O12335−1.85[102]
Al2Mo2.5W0.5O12710.80 1[106]In1.7Sc0.3Mo3O12271−8.41 1[114]
Al2Mo2.5W0.5O12NR0.05 1[106]In1.4Sc0.6Mo3O12205−6.32 1[114]
Al2W3O12−61.51[69]In1.1Sc0.9Mo3O12137−5.83 1[114]
Al1.9Ga0.1W3O1221NR[115]In0.8Sc1.2Mo3O1277−11.27 1[114]
Al1.8Ga0.2W3O1260NR[115]In0.5Sc1.5Mo3O12<RT−5.08 1[114]
Al1.7Ga0.3W3O1291NR[115]In2W3O12250−3.00 1[103]
Al0.7In1.3W3O12118NR[116]In1.9Sc0.1W3O12224−5.29 1[103]
Al1.9Sc0.1W3O12−35~0.2 1[115]In1.5Sc0.5W3O12147−1.28 1[103]
Al1.8Sc0.2W3O12−60~0.6 1[115]In1.4Sc0.6W3O1276NR[117]
Al1.7Sc0.3W3O12−98~1.4 1[115]In1.1Sc0.9W3O12<RT−5.35 1[117]
Al1.6Sc0.4W3O12<−150~1.4 1[115]In0.8Sc1.2W3O12<RTNR[117]
1 Dilatometer data.
Table 4. Phase transition temperatures (TPT) and corresponding linear thermal expansion coefficients determined from diffraction data for aliovalently substituted A2M3O12 materials.
Table 4. Phase transition temperatures (TPT) and corresponding linear thermal expansion coefficients determined from diffraction data for aliovalently substituted A2M3O12 materials.
CompoundTPT (°C)αl (×10−6 °C−1)T RangeRef.
Hf2MoP2O12NR−4 1NR[58]
Hf2WP2O12NR−5 1NR[58]
MgZrW3O12NR−1.15 1167–698[140]
Mg0.5Zn0.5HfMo3O1250−0.11 1100–400[120]
Al1.8(MgZr)0.1W3O12−431.61 121–770[140]
Al1.4(MgZr)0.3W3O12<−1602.34 121−774[140]
1 Dilatometer data.
Table 5. Ceramic zero thermal expansion composites containing A2M3O12 materials.
Table 5. Ceramic zero thermal expansion composites containing A2M3O12 materials.
CompositionsdL/L0 (×10−6 °C−1)T Range (°C)Ref.
Zr2MoP2O12/ZrO2 −0.006525–700[173]
Table 6. Near-zero thermal expansion compounds prepared by single ion substitution. CTEs are based on diffraction data unless otherwise indicated.
Table 6. Near-zero thermal expansion compounds prepared by single ion substitution. CTEs are based on diffraction data unless otherwise indicated.
Compoundαl (×10−6 °C−1)T Range (°C)Ref.
Al2Mo0.5W2.5O120.05 125–800[106]
Al0.5Sc1.5W3O12 −0.3225–600[118]
Y0.25Ce1.75W3O12 −0.82 1182–700[97]
1 Dilatometer data.
Table 7. Near-zero thermal expansion compounds prepared by aliovalent ion substitution. CTEs are based on diffraction data.
Table 7. Near-zero thermal expansion compounds prepared by aliovalent ion substitution. CTEs are based on diffraction data.
Compoundαl (×10−6 °C−1)T Range (°C)Ref.
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Liu, H.; Sun, W.; Zhang, Z.; Lovings, L.; Lind, C. Thermal Expansion Behavior in the A2M3O12 Family of Materials. Solids 2021, 2, 87-107.

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Liu H, Sun W, Zhang Z, Lovings L, Lind C. Thermal Expansion Behavior in the A2M3O12 Family of Materials. Solids. 2021; 2(1):87-107.

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Liu, Hongfei, Weikang Sun, Zhiping Zhang, La’Nese Lovings, and Cora Lind. 2021. "Thermal Expansion Behavior in the A2M3O12 Family of Materials" Solids 2, no. 1: 87-107.

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