Review Thermal Expansion Behavior in the A2M3O12 Family of Materials Hongfei Liu 1,*, Weikang Sun 1, Zhiping Zhang 1,2, La’Nese Lovings 3 and Cora Lind 3,* 1 School of Physical Science and Technology, Yangzhou University, Yangzhou 225002, China; [email protected] (W.S.); [email protected] (Z.Z.) 2 Guangling College, Yangzhou University, Yangzhou 225002, China 3 Department of Chemistry and Biochemistry, The University of Toledo, 2801 W. Bancroft St., Toledo, OH 43606, USA; [email protected] * Correspondence: [email protected] (H.L.); [email protected] (C.L.); Tel.: +86-514-87975466 (H.L.); +1-419-5301505 (C.L.) Abstract: 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. Keywords: negative thermal expansion; scandium tungstate; hygroscopicity; phase transition; chal- lenges Citation: Liu, H.; Sun, W.; Zhang, Z.; Lovings, L.; Lind, C. Thermal Expansion Behavior in the A2M3O12 Family of Materials. Solids 2021, 2, 1. Introduction 87–107. https://doi.org/ In recent years, the fields of microelectronics, photoelectric communications and aerospace have rapidly expanded. Materials with high-precision size are in growing Academic Editor: Guido Kickelbick demand, and dimensional stability and long lifetime of devices at different operating tem- Received: 30 December 2020 peratures is of high importance. A mismatch of thermal expansion coefficients combined Accepted: 11 February 2021 with a temperature variation of the materials’ environment can result in thermal stress, Published: 19 February 2021 thus leading to performance degradation or permanent damage to devices. Therefore, low, and especially near-zero expansion materials, are beneficial to improve the geometrical sta- Publisher’s Note: MDPI stays neutral bilities of these materials and devices. The discovery of negative thermal expansion (NTE) with regard to jurisdictional claims in behavior in compounds provides the possibility of developing materials with controllable published maps and institutional affil- or near-zero thermal expansion coefficients for specific applications. iations. Previous research on NTE materials has focused on the following families: Metal cyanides [1–6], metal fluorides [7–16], Mn3AN (A = Cu, Zn, Ge, Sn, Ag) [17–23], inter- metallics [24–31], metal oxides including AM2O8 (A = Zr, Hf; M = W, Mo) [32–38], AM2O7 (A = Zr, Hf; M = V, P) [39–42], A2O (A = Ag, Cu) [43–47] and A2M3O12 (A = trivalent Copyright: © 2021 by the authors. cation; M = W, Mo) [48–50]. Compared to the other families, the A2M3O12 stoichiometry Licensee MDPI, Basel, Switzerland. has received special attention because of the broad range of metals that can be incorporated This article is an open access article into the structure. The A-site can be fully occupied by a single trivalent metal ranging in distributed under the terms and size from Al3+ to the smaller lanthanides, or partially substituted by most lanthanides and conditions of the Creative Commons many transition metals, whereas the M-site is usually occupied by tungsten or molybde- Attribution (CC BY) license (https:// num. Aliovalent substitution of both metal sites has also been reported. The wide range of creativecommons.org/licenses/by/ compositions accessible in the A2M3O12 family is unique. This paper reviews the thermal 4.0/). Solids 2021, 2, 87–107. https://doi.org/10.3390/solids2010005 https://www.mdpi.com/journal/solids Solids 2021, 1, FOR PEER REVIEW 2 Solids 2021, 2 88 Aliovalent substitution of both metal sites has also been reported. The wide range of com- positions accessible in the A2M3O12 family is unique. This paper reviews the thermal ex- pansion properties of the A2M3O12 family with a focus on compounds displaying NTE expansionbehavior. Recent properties advances of the are A2M discussed3O12 family in detail with aas focus well onas promising compounds future displaying prospects. NTE behavior. Recent advances are discussed in detail as well as promising future prospects. 2. Positive Thermal Expansion 2. Positive Thermal Expansion The A2M3O12 family consists of a large number of compounds that can adopt several differentThe Astructure2M3O12 familytypes. consistsThe identity of a largeof th numbere A and ofM compounds site elements that determines can adopt the several pre- differentferred structure structure type types. which The identityis intimately of the rela A andtedM to site the elements thermal determinesexpansion theproperties preferred of structurethe compounds. type which According is intimately to the related systematic to the research thermal conducted expansion propertiesby Nassau of et the al. com-[51], pounds.when the According A-site is occupied to the systematic by the larger research lanthanides conducted ranging by Nassau from et La al.3+ [ 51to], Tb when3+, these the A-site is occupied by the larger lanthanides ranging from La3+ to Tb3+, these tungstates and tungstates and molybdates display positive thermal expansion. Dy2Mo3O12 also belongs molybdates display positive thermal expansion. Dy2Mo3O12 also belongs to this group of to this group of compounds, while Dy2W3O12 does not [52,53]. The crystal structures of compounds, while Dy2W3O12 does not [52,53]. The crystal structures of these positive thermal these positive thermal expansion A2M3O12 compositions are orthorhombic in space group expansion A2M3O12 compositions are orthorhombic in space group Pba2 or monoclinic in Pba2 or monoclinic in space group C2/c, and contain edge-shared AO7-polyhedra, which space group C2/c, and contain edge-shared AO -polyhedra, which are generally considered are generally considered as an unfavorable fa7ctor for NTE behavior. For instance, Figure as an unfavorable factor for NTE behavior. For instance,3+ Figure1 shows the typical structure 1 shows the typical structure3+ of Gd2Mo3O12 [54]. Gd is coordinated by6+ seven oxygen at- of Gd2Mo3O12 [54]. Gd is coordinated by seven oxygen atoms, while Mo is bonded to four oms, while Mo6+ is bonded to four oxygen atoms. The GdO7 units share common edges, oxygen atoms. The GdO units share common edges, causing oxygen atoms to be coordinated causing oxygen atoms 7to be coordinated by three instead of two atoms. This connection by three instead of two atoms. This connection mode hampers transverse vibration of oxygen mode hampers transverse vibration of oxygen atoms, the typical basis of NTE in the atoms, the typical basis of NTE in the A2M3O12 family. A2M3O12 family. (a) (b) FigureFigure 1. 1.( a(a)) Crystal Crystal structure structure of of Gd Gd2Mo2Mo33OO1212 and (b) three-fold coordinated oxygen.oxygen. 3.3. NegativeNegative ThermalThermal ExpansionExpansion InIn thethe fieldfield ofof NTENTE research, research, the the A A2M2M33OO1212 family is alsoalso referredreferred toto asas thethe scandiumscandium tungstatetungstate family.family. Scandium tungstate adopts anan orthorhombicorthorhombic structurestructure inin thethe spacespace groupgroup PncaPnca atat all temperatures (Figure 22))[ [55,55,56].56]. The The crystal crystal struct structureure is is composed composed of of a acorner-sharing corner-sharing framewor frameworkk of octahedral of octahedral ScO ScO6 and6 andtetrahedral tetrahedral WO4 WOunits.4 units.No edge-sharing No edge- sharingis observed, is observed, in contrast in contrast to the toGd the2Mo Gd3O212Mo-type3O12 structure-type structure discussed discussed earlier. earlier. As the As bond the bondlengths lengths of Sc-O of Sc-Oand W-O and W-Oshow show little little change change with with temperature, temperature, the theglobal global expansion expansion be- behaviorhavior is dominated is dominated by bytransverse transverse motions motions of the of thecorner-sharing corner-sharing oxygens. oxygens. Diffraction Diffraction data datademonstrate demonstrate that thatthese these vibrations vibrations give give rise rise to a to reduction a reduction of ofthe the Sc-O-W Sc-O-W bond bond angle angle and and a ashortening shortening of of the the next-nearest next-nearest neighbor neighbor distances distances on on a microscopic level and macroscopicmacroscopic NTENTE ofof thethe materialmaterial [[55].55]. TheThe resultingresulting rockingrocking motionsmotions ofof thethe polyhedralpolyhedral buildingbuilding blocksblocks areare accompaniedaccompanied byby somesome distortiondistortion ofof thethe polyhedra.polyhedra. LargerLarger A-siteA-site cationscations cancan moremore readilyreadily accompanyaccompany thesethese distortions,distortions, andand thusthus favorfavor moremore significantsignificant NTE NTE [ 57[57].]. SolidsSolids 20212021,, 12, FOR PEER REVIEW 893 Figure 2. Crystal structure of orthorhombic Sc W O : blue: ScO octahedra; green: WO tetrahedra. Figure 2. Crystal structure of orthorhombic Sc22W3O1212: blue: