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Metal fluorides, a new family of negative thermal expansion materials Lei Wang, Cong Wang*, Ying Sun, Kewen Shi, Sihao Deng, Huiqing Lu, Pengwei Hu, Xiaoyun Zhang Center for Condensed Matter and Materials Physics, Department of Physics, Beihang University, Beijing 100191, China Received 4 January 2015; revised 16 January 2015; accepted 20 February 2015 Available online 24 April 2015

Abstract In the past decades, the families of negative thermal expansion (NTE) materials have been in the uninterrupted growth with more new NTE materials reported; in particular, metal fluorides as the new members begin to draw attention. Herein, recent progress on the NTE properties of metal fluorides is reviewed, including compounds, mechanisms and the control of thermal expansion. Although some achievements have been made, there are still great development prospects. More in-depth investigations on metal fluorides with NTE behavior are expected. © 2015 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Metal fluorides; Negative thermal expansion

1. Introduction Most materials expand on heating owing to the anharmonicity of chemical bond. However, as a very exceptional phenomenon, negative thermal expansion (NTE), i.e., volume shrinks on heating, can be observed in a small number of materials [1e4]. In fact, NTE phenomenon has been known for some time in several compounds such as ice, amorphous or crystalline forms of SiO2, zeolites, perovskite ferroelectrics, tetrahedral semiconductors [5e8]. In these systems, NTE occurs over a limited temperature range and is often anisotropic. In 1996, the discovery of giant and isotropic NTE behavior over a board temperature range (from 0.5 to 1030 K) in ZrW2O8 triggers great research interest [1]. Over the past two decades, the field of NTE has rapidly expanded. Experimental and theoretical studies revolving around the NTE materials have been in full swing [9e15]. For example, the discovery of new NTE materials, the promotion in process technology, the development of composites using NTE materials as thermal-

* Corresponding author. E-mail address: [email protected] (C. Wang). Peer review under responsibility of The Chinese Ceramic Society.

expansion compensators, the control of NTE properties by doping in single-phase material, and the exploration of NTE mechanisms, etc. The NTE materials have emerged in both inorganic and organic fields. Presently, the NTE materials are mainly concentrated in the following several series: (1) metal oxide, including AM2O8 (A ¼ Zr, Hf; M ¼ W, Mo), AM2O7 (A ¼ Zr, Hf; M ¼ V, P), A2M3O12 (A ¼ Al, Y, Sc, Ga, etc; M ¼ W, Mo), A2O (A ¼ Ag, Cu) [16e22]; (2) metal cyanide, including MIIPtIV(CN)6 (M ¼ Mn, Fe, Co, Ni, Cu, Zn, Cd), M(CN)2 (M ¼ Zn, Cd, Ni) [23,24]; (3) PbTiO3 (PT)-based perovskite compounds [11,12]; (4) Mn3AN/C-based (A ¼ Cu, Ge, Zn, Sn, Ag, etc.) antiperovskite compounds [9,10,25e31]; (5) alloy system, such as Invar alloys (Fe65Ni35), FeCo, FePd, FePt, FeC and so on [32e34]; (6) low-dimensional materials, for example, zero-dimensional fullerene and clusters, onedimensional carbon nanotubes, and two-dimensional thin film (graphite, grapheme, etc.) [35,36]; (7) metal-organic frameworks (MOFs), polymers, fibers, etc. [37,38]; (8) metal fluorides, AFx (A ¼ Sc, Zn, Ti, Mn, etc.) [39e49]. In recent years, metal fluorides as new NTE members begin to attract attention. Among them, ScF3 with a cubic ReO3-type structure behaves the most conspicuous NTE properties. The volumetric contraction can be observed in a wide temperature range from

http://dx.doi.org/10.1016/j.jmat.2015.02.001 2352-8478/© 2015 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

L. Wang et al. / Journal of Materiomics 1 (2015) 106e112

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10 to 1100 K [39]. Compared with other NTE compounds, the strong NTE behavior in such a simple structure is really amazing. Additionally, some meaningful researches on NTE properties in metal fluorides have been reported in succession. In this article, we review the research progress on NTE properties of metal fluorides. Moreover, some views are put forward based on the existing achievements.

determined if this was significant. Because of larger temperature interval measured in experiments, more detailed information about the thermal expansion of TiF3 in the range 0e100 K was lacked. Very recently, Wang et al. put forward definitely the NTE behavior of rhombohedral TiF3 at low temperature and discussed the NTE mechanisms within the framework of first principle calculations [44] (see Fig. 1(d)).

2. Metal fluorides with NTE behavior

3. NTE mechanisms

Early in 2004, an unusual NTE behavior in the simple perovskite MnF3 was experimentally obtained below the Neel point where the spins were ordered in an A-type magnetic structure (see Fig. 1(a)) [47]. In 2010, Greve et al. observed a giant NTE behavior (linear coefficient of thermal expansion (CTE), aL ¼ 14 106 K1) of cubic ScF3 [39], larger than that of ZrW2O8 (aL ¼ 9 106 K1) [1] (see Fig. 1(b)). Besides the cubic zirconium tungstate, ScF3 is the best known example of large isotropic negative expansion persisting over a wide temperature range. Thereafter, Li et al. investigated the structural relationship between NTE and quartic anharmonicity in ScF3 [40]. In 2011, Chatterji et al. discovered the NTE behavior at low temperatures (below 100 K) in rutiletype ZnF2 [41] (see Fig. 1(c)). Then, Wang et al. have given the theoretical study on NTE mechanism of ZnF2 by means of the first principle calculations [42]. The cubic-torhombohedral phase transition of TiF3 was once investigated by powder X-ray diffraction [43]. By the way, a clue was supplied that below 100 K the volume appeared to be essentially constant although the volume at 20 K, in fact, slightly larger than that measured at 100 K and it remained to be

To predict the new NTE materials and gain in-depth insight into NTE mechanisms, important tests of the ability of first principle theory in probing various macroscopic physical properties of NTE are necessary. Generally, the origin of NTE behavior can be classified into two aspects, one is vibrational mode effects, and the other is non-vibrational mode effects. Lattice vibration, i.e. phonon, plays a decisive role in the NTE materials with open-framework structures. Some NTEcontributing phonon modes have been identified. In certain materials (e.g. ZrW2O8), polyhedra can rotate through coupled librations without distortion, called a “rigid unit mode” (RUM), as shown in Fig. 2. While, in some others (e.g. ZrW2O7), there are many vibrations involving librations with only small distortions of the polyhedra. These are titled quasirigid unit modes (QRUM). The RUMs and QRUM can lead to a rotary coupling between two adjacent polyhedra, contributing to the NTE behavior [17]. Additionally, non-linear A-OM bridge as another vital mode is applied in some NTE materials such as A2M3O12 series, where the O atom vibrates perpendicular to the A-O-M linkage and shortens the distance between A and M atoms [50]. For metal cyanides, the

Fig. 1. (a) Temperature dependence of the unit-cell volume of MnF3. The Neel point is shown [47]. (b) The temperature dependence of cell parameter and coefficient of thermal expansion (CTE) of ScF3 [39]. (c) Temperature variation in DV/V0 of ZnF2 [41]. (d) The calculated volumeetemperature curve of rhombohedral TiF3, insets show the experimental measurement and calculated CTE, respectively [44].

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Fig. 2. Schematic diagram of coupling rotation of rigid unit mode (RUM).

transverse vibration mode of C and N atoms also shorten the distance between M and M0 atom [15]. The NTE-contributing phonon modes in nanoporous MOF-5 can be viewed as the results of local deformations (translation, rotation, twisting) of BDC (1,4-benzenedicarboxylate) linker and zinc clusters [51]. The non-vibrational mode effects mainly deal with some orderingedisordering transitions including the crystal or magnetic phase transitions and so on which can be as the NTE mechanisms for PbTiO3 (PT)-based perovskite compounds, Mn3AN-based (A ¼ Cu, Ge, Zn, Sn, Ag) antiperovskite compounds and alloys [9,12]. To date, for the concerned metal fluorides, magnetostriction is correlated with the NTE of MnF3. The observed magnetostriction is a consequence of spin ordering in the absence of charge ordering. That spin ordering alone can lead to an abnormal thermal expansion is very well known for Invar alloys, while it is very rare in metal fluorides [47]. Firstprinciple calculations would be valuable to clarify the underlying mechanisms. For other compounds such as ScF3, ZnF2 and TiF3, the RUM mechanism is applicable. To study the role of different phonons in the thermal expansion, one need calculate the Gru¨neisen parameter, which is defined as gn(q)¼vlnu(q)n/vlnVn, where u(q)n is the frequency of the nth mode of vibration, which itself is a function of wavevector (q) in the first Brillouin zone, and V is the volume. The correlation between the volumetric PCTE and Gru¨neisen parameter can be expressed as aV ¼ B10 gn ðqÞCV;n ðqÞ. This sum goes over all vibrational modes. B0 is the bulk modulus and CV,n(q) is the contribution of mode jn; q〉 to the specific heat. Due to the weak interaction force in the crystal when the lattice expands, the Gru¨neisen parameters are usually positive in most materials. However, the occurrence of negative values of Gru¨neisen parameters indicates that the volume contracts when heating. The coupling rotating of MF6 (M ¼ Sc, Zn, Ti) octahedra, which is responsible for NTE behavior, is mainly populated in low-frequency region. It has been confirmed that, in tetragonal ZnF2 and rhombohedral TiF3, the lowestfrequency optical mode possesses the largest negative Gru¨neisen parameters through the analysis on phonon mode classification, calculated frequencies and corresponding Gru¨neisen parameters [42,44]. Besides, the internal vibration also may contribute to the NTE in spite of smaller effect. With

increasing temperature, the relatively high-frequency modes (gi > 0) can be dominating and surpasses gradually the RUM's effect, causing normal positive expansion on heating. Moreover, the intrinsic phonon anharmonic interactions containing an explicit temperature dependence of phonon frequencies play an important role in cubic ScF3 [40]. In despite of the uniform RUM mechanism, the NTE behavior of these metal fluorides such as ScF3, ZnF2 and TiF3 is diverse. This depends on the space group as well as the bond nature, bond strength. Generally speaking, a lowering of the space group can lead to an increase of lattice flexibility and have more produced effect on compressive rather than expansive flexibility [52]. From the perspective of density, the bulk density of cubic ScF3 is smaller. The above indicates that cubic ScF3 may provide more degrees of freedom where the RUM mechanism can be exerted to the greatest extent. Furthermore, the bond nature and bond strength which can influence the length and rigidity of the linker are also of importance. Weaker bonding interaction between the atoms makes the linker more flexible. The different NTE behavior between cubic ScF3 and ReO3 might reflect the role of this factor [53]. 4. The control of NTE in Sc1-xMxF3 The NTE materials have a promising potential application on tuning the overall thermal expansion of materials. The coefficient of thermal expansion (CTE) can be tailored by either formation of composites or chemical modification of single-phase materials. In the preparation of composite, the condition of interfaces and the amount of voids are important factors. The over thermal expansion of composites depends on their microstructure. Some drawbacks in composites such as binding capacity, interfacial mismatch, thermal stress, or chemical reaction at interface could be introduced inevitable. In principle, solid solution formation, which provides a means of controlling the CTE of single-phase material without forming a composite, can effectively overcome the above shortcomings. Most recently, the experimental work on the control of CTE in ScF3 has been reported. Chen et al. reported that: the zero thermal expansion (ZTE) can be obtained between 300 and 900 K in cubic Sc0.85Ga0.05Fe0.1F3 (see Fig. 3(a)), where a ferromagnetism state was introduced [54]. Through PDF analysis, they proposed the local distortion from the bending Sc/MF-Sc/M linkage might impede the transverse vibration of rigid (Sc,M)F6 polyhedra and thus was presumably responsible for the ZTE performance. The results from Morelock et al. indicated that through cation substitution by MF3 (M ¼ Y, Ti, Al), the thermal expansion properties of ScF3-based solid solutions can be controlled (see Fig. 3(b)e(d)). By more doping content, there would be a phase transition from cubic to rhombohedral structure [55e57]. In comparison, the solubility limit of YF3 in ScF3 is restricted by the significant difference in ionic radius between Sc3þ and Y3þ (0.74 and 0.90 Å, respectively). TiF3 is fully soluble in ScF3 at a synthesis temperature of 1338 K. The temperature for cubic-rhombohedral phase transition in


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Fig. 3. (a) Temperature evolution of lattice constant of (Sc0.85Ga0.05Fe0.1)F3 [54]. (b) Temperature dependence of the volume CTE for each Sc1-xYxF3 sample [55]. (c) Normalized unit cell volumes for Sc1-xTixF3 plotted with respect to temperature [56]. (d) Temperature dependence of volume CTE for Sc1-xAlxF3 [57].

Sc1xTixF3 varies linearly with composition and the transition is clearly first-order at large x. The CTE of rhombohedral Sc1xAlxF3 is strongly positive; above 600 K, the CTE of cubic structure varies from negative to near zero (x ¼ 0.15) to positive (x > 0.2), providing a greater possibility for tuning CTE than either cubic Sc1xYxF3 or cubic Sc1xTixF3. Whereas, the Sc1xAlxF3 system does not provide a tunable CTE in a cubic symmetry at room temperature. Among Sc1xMxF3 (M ¼ Y, Ti, Al), on the whole, Ti-substitution is the most useful approach to tailor the thermal expansion characteristics of ScF3-based solid solutions. Due to similar elemental characteristic of titanium and scandium such as ionic radius and electronegativity, the solubility as well as the CTE, phase transition temperature of Sc1xTixF3 has a better performance. Theoretical studies on Sc1xTixF3 have been performed with the first principle calculations [58]. There is good agreement between theoretical results and experimental measurements. For solid solution Sc1xTixF3, the Ti3þ can introduce Jahn-Teller active [59]. In cubic framework structure, each Sc atom is at the center of a corner sharing fluoride atoms, forming an octahedral coordination environment. Under this case, with the incorporation of Ti3þ cation, the triply degenerate t2g orbital in which only one 3d electron occupies will be split for favorable energy and hence a JahnTeller instability may be expected. Below a certain concentration, the local structural distortions that are associated with a disordered arrangement of fluoride displacements can be accommodated by cubic Sc1xTixF3. Whereas, considerable disorder introduced by more Ti doping breaks the original cubic symmetry, and eventually leads to the displacement-type

transition from cubic to rhombohedral phase. It has noticed that the Jahn-Teller effect plays a key role in the phase transition of Sc1xTixF3, and is also responsible for controlling the thermal expansion. As far as we know, the Jahn-Teller effect can be also observed in other transition-metal trifluorides such as VF3, CrF3, MnF3, CoF3 and NiF3 [60e63]. It is inspired that may be the doping of these Jahn-Teller active trivalent cations will also be an effective approach to tune the thermal expansion of Sc1xMxF3. 5. Abnormal thermodynamic properties Almost all materials become stiffer when compressed, owing to the constituent atoms being squeezed together. Therefore, it comes as something of a shock that some NTE materials such as amorphous silica, ZrW2O8 and Zn(CN)2, actually become softer under compression [64e66]. Formally, the bulk modulus B0, which is defined as B0 ¼ V0 ðvV0 =vPÞ1 T , represents the ability of a solid to resist compression deformation within the limits of the elastic regime. It is a critical property to indicate stiffness, especially for cubic crystal. Fang et al. demonstrated that pressure-induced softening may be as a common feature of framework structures with NTE behavior based on a series of molecular dynamics simulations [67]. The origin of softening is rooted in the dependence of frequencies of the NTE phonon modes on strain. However, the bulk modulus B0 of the solid solutions Sc1xMxF3 (M ¼ Y, Al) increases with temperature over the entire temperature range examined (see Fig. 4), contrary to the behavior of the most NTE materials. Recently, it is emphasized that the intrinsic

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Fig. 4. (a) Average isothermal bulk moduli of Sc1-xYxF3 plotted with respect to temperature [55]. (b) Temperature dependence of average isothermal bulk modulus for Sc1-xAlxF3 [57].

phonon anharmonic interactions containing an explicit temperature dependence of phonon frequencies play an important role in some NTE materials including ScF3, ReO3, Cu2O and so on [40,68,69]. A possible theoretical basis is supplied that the thermal stiffening might occur in some highly anharmonic NTE materials. Besides, Li et al. have reported that the large anharmonic effect contributes a thermal stiffening of some modes in ScF3 through the temperature dependence of lattice dynamic measured by inelastic neutron scattering experiments [40]. Thus, to a certain extent, apart from Sc1xMxF3 (M ¼ Y, Al), ScF3-based solid solutions with other cation-doping can also be expected to stiffen upon heating. The unusual thermal stiffening is atypical in most NTE materials and still needs indepth exploration from the experimental as well as the theoretical work. 6. Final remarks and future prospects As the new members in NTE families, the metal fluorides NTE materials have aroused great attention. Related work has been carried out from experimental and theoretical studies. Some achievements have been obtained, including the discovery of new NTE materials in metal fluorides, underlying NTE mechanisms, and the controlling of thermal expansion in solid solutions. In spite of this, more in-depth explorations are still needed. In our opinion, there is a great possibility that NTE behavior may exist in other metal fluorides. Besides the cation-doping in pure phase, the preparation of the composites containing metal fluorides can also be developed as an approach to tune the thermal expansion. Quasi-harmonic lattice dynamics, which readily takes account of quantum effects that determine low temperature behavior as well as mechanisms, are widely adopted in theoretical work on NTE materials. However, it is inappropriate at high temperatures where phonon anharmonic interactions have a great influence, for instance, cubic ScF3. Thus, other approaches such as molecular dynamics, Monte Carlo simulations, and some methods containing quartic anharmonicity based on ab initio, should be adopted as complementary techniques.

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Dr. Lei Wang, Beihang University Dr. Lei Wang is a postdoctoral of Dept. of Physics, Beihang University, Beijing, China. She graduated from Zhengzhou University in 2014. Her research focuses on negative thermal expansion materials by the first-principles calculations.

Prof. Dr. Cong Wang: a Professor in Dept. of Physics, Beihang University in Beijing, China. He got his Ph. D in 1995 from Inst. of Physics, Chinese Academy of Science (CAS), China. He was also an Alexander von Humboldt (AvH) research fellow. His research focuses on condensed matter and materials physics, including ①structure, magnetic and electronic transport of antiperovskite structured Mn3XN(C) materials; ②solar selective absorbing films for concentrated solar power; ③photocatalytic nanomaterials. He has published more than 160 papers and 10 national patents. He is committee member of Chinese Crystallography Society, member of International Center for Diffraction Data (ICDD, USA).