Thermal Expansion Anomaly in TTB Ferroelectrics: The Interplay

Article pubs.acs.org/IC

Thermal Expansion Anomaly in TTB Ferroelectrics: The Interplay between Framework Structure and Electric Polarization Kun Lin,† Li You,‡ Qiang Li,† Jun Chen,† Jinxia Deng,† and Xianran Xing*,† †

Department of Physical Chemistry and ‡State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, P. R. China S Supporting Information *

ABSTRACT: Tetragonal tungsten bronze (TTB) makes up a large family of functional materials with fascinating dielectric, piezoelectric, or ferroelectric properties. Understanding the thermal expansion mechanisms associated with their physical properties is important for their practical applications as well as theoretical investigations. Fortunately, the appearance of anomalous thermal expansion in functional materials offers a chance to capture the physics behind them. Herein, we report an investigation of the thermal expansion anomalies in TTBs that are related to ferroelectric transitions and summarize recent progress in this field. The special role of Pb2+ cation is elucidated. The interplay between the thermal expansion anomaly, electric polarization, and framework structure provides new insight into the structure−property relationships in functional materials. ferroelectric materials after perovskite structures.11,12 In particular, the TTB niobates have attracted a lot of attention because of their structural diversity and technological appeal. For example, PbNb2O6 (Pb5Nb10O30) can be used in hightemperature piezoelectric transducers because of its high Curie temperature (TC ≈ 570 °C), low mechanical quality factor Q, and large anisotropy of its electromechanical coupling coefficient kt.13−19 Ba- and Sr-based TTBs exhibiting fascinating dielectric responses were developed by Chen’s group in recent decades.20−27 However, until very recent years, little attention had been paid to the thermal expansion of TTBs. Knowledge of the thermal expansion in TTBs will be highly helpful for their technological applications. TTBs can be viewed as A-site-deficient perovskites.28 Unlike for perovskites, however, there are more structural varieties, such as different tunnel sizes and more vacancy probabilities, which give the TTBs both framework structural features and typical ferroelectric material features. The balance between the structure and ferroelectricity could provide a direction for the design of ferroelectric materials with controllable thermal expansion behavior. In this contribution, we focus on the thermal expansion anomaly in TTB ferroelectrics and review the recent progress in the study of thermal expansion behavior and its relationship to crystal structure. Particular attention is focused on Pb-based TTBs, which usually have special polarizations. Toward this end, a series of Pb-based TTBs

1. INTRODUCTION Multifunctional electronic materials with ferroelectric, piezoelectric, dielectric, and mechanical properties, among others, play crucial roles in modern electronic industries.1 Since the discovery of BaTiO3, perovskite and its topological oxides have been widely investigated and applied in electronic devices, such as ferroelectric random access memories (FeRAMs), magnetic field sensors, ultrafast switching detectors, and sonars, because of their excellent chemical stabilities and diverse physical properties.2,3 In practical applications, however, devices usually suffer from severe environmental instabilities. For example, humidity changes with the seasons, illumination variations with the weather, and temperature fluctuations with day and night can significantly affect material functionalities. A possible solution to these problems is to use electronic packaging to isolate materials from external stimuli.4 However, the heat exerted by electron conductivity cannot be avoided. The resulting fluctuations in temperature, or even thermal shock, would cause thermal stress and inevitably affect the stability and shorten the lifetimes of devices.5 Thus, multifunctional materials with controllable thermal expansion are highly desirable for the fabrication of thermal expansion-matchable devices. In the past 10 years, controllable thermal expansion in PbTiO3-based perovskite ferroelectrics and ANM3-based antiperovskite magnets has been achieved by modulating the spontaneous volume ferroelectrostriction (SVFS)6,7 and spontaneous volume magnetostriction (SVMS),8−10 respectively. Tetragonal tungsten bronze (TTB) structures, one type of perovskite analogue, constitute the largest species of © 2016 American Chemical Society

Received: May 21, 2016 Published: August 3, 2016 8130

DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139

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Figure 1. (a) TTB structure (viewed along the c axis) built up of (i) BX6 octahedra and (ii) A1, A2, and C tunnel sites. (b) Coordinated polyhedra stacked along the [001] direction, where the B, A1, A2, and C atoms form 6-, 12-, 15-, and 9-coordinated polyhedra, respectively. (c−e) Three different types of polarizations: (c) order−disorder ferroelectric, (d,e) displacive ferroelectrics adopting macroscopic polarization along the (d) [110]TTB and (e) [001] directions.

TTB structures, K0.475WO3 and K0.57WO3, were reported by Magneli29 in 1949. The as-synthesized materials have tetragonal symmetry with centrosymmetric space group P4/mbm and cell parameters of (12.3 Å, 12.3 Å, 3.8 Å);29 since then, these materials have become the archetype of TTBs. The general formula of TTBs can be expressed as (A2)4(A1)2(C)4(B1)2(B2)8X30. The TTB structures are composed of corner-sharing BX6 octahedra and intermediate A-site cations (Figure 1). The BX6 octahedra build up the TTB framework, and viewed along the c axis as illustrated in Figure 1a, they form tunnel caves of three different shapes: quadrangular A1, pentagonal A2, and triangular C (Figure 1b). For most cases, the “X” is oxygen, although some TTBs are fluorides or oxyfluorides.30−36 The B sites favor highvalence transition metals such as W6+, Nb5+, and Ta5+ and are prone to form intense covalent bonds with coordinated oxygen to stabilize the BO6 octahedral framework. In contrast, in TTB fluorides such as K3Fe5F15 and K3Cr2Fe3F15,36 the B sites are occupied by low-valence cations such as Cr2+, Fe2+, and Fe3+, as a result of the high electronegativity of F−. In contrast, the A sites are much more flexible: They can be occupied by a large variety of cations including alkali metals, alkali earth metals, transition metals, lanthanide metals, and even ammonium ion.32 The number of A-site cations can vary in large ranges.29,37,38 Ferroelectric Polarization. Ferroelectricity in TTBs was first reported in PbNb2O6 (Pb2.5Nb5O15) by Goodman in 1953.13 Before that, ferroelectric compounds were mainly limited to the ABO3-type perovskites.2 The term “ferroelectricity” derives from “ferromagnetism”, in which the materials establish electric

was studied to further understand the structure−property relationships.

2. EXPERIMENTAL SECTION Samples Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na), Pb3TiNb4O15, and Ba2NaNb5O15 were synthesized by a solid-state method. The stoichiometric raw materials were PbO, Rb2CO3, K2CO3, Ag2CO3, Li2CO3, Na2CO3, Ba2CO3, and Nb2O5. The raw materials were ground in ethanol with an agate mortar. After being allowed to dry, the fine powders were calcined at 800−900 °C for 4h. The calcined products were ground again for 10 h. Then, some of the powders were made into pellets and sintered at 1150−1250 °C for 2−4 h, after which the furnace was turned off and allowed to cool to room temperature. Hightemperature X-ray diffraction (XRD) (X’Pert3 Powder, PANalytical B.V., Almelo, The Netherlands, Cu Kα, λ = 1.5406 Å) data were collected using an Anton-Paar TTK450 chamber. The heating rate was 10 °C/min, and the sample was held for 10 min at the specified temperature to reach heat equilibrium. Selected-area electron diffraction (SAED) experiments were performed on a Tecnai G2 F30 S-TWIN transmission electron microscope at an accelerating voltage of 300 kV. A double-tilt sample stage (α, ±40°; β, ±30°) was used to rotate the sample to specific zone axes. The sample for the SAED experiments was prepared by ion thinning. X-ray absorption near-edge structure (XANES) spectra were collected on the 1W1B beamline at Beijing Synchrotron Radiation Facility (BSRF), Institute of High Energy Physics, Chinese Academy of Sciences (CAS). The data was recorded at the Pb LIII edge at room temperature in transmission mode. There is no significant hazard in this work.

3. RESULTS AND DISCUSSION 3.1. Tungsten Bronze Structures and Their Ferroelectric Polarizations. Crystal Structures of TTBs. The first 8131

DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139

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Table 1. Space Groups (SGs), Curie Temperatures (TC), Spontaneous Polarization (PS) Directions, Cell Parameters, and Axis Ratios for Some Selected TTB Compositions no. 1 2 3 4 5 6

7

8

9 10 11 12 13 14 15 16 a

TC (°C)

formula PbNb2O6 Pb2KNb5O15 Pb2K0.5Li0.5Nb5O15 PbK2LiNb5O15 Pb0.75K1.8Li1.7Nb5O15 Pb2(1−x) K(1+x)GdxNb5O15: x < 0.35 x > 0.35 Pb2Na0.8R0.2Nb4.8Fe0.2O15

PbxBa1−xNb2O6: x > 0.7 x < 0.54 Pb2AgNb5O15 Pb3TiNb4O15 Ba3TiNb4O15 PbBiNb5O15 BaBiNb5O15 PbTa2O6 Pb4.5KTa10O30 Pb2KTa5O15

57013 460 500 36642 355

R3+ R3+ R3+ R3+ R3+

= = = = =

La3+ Nd3+ Sm3+ Eu3+ Dy3+

450 430 415 395 360 300−450

450 600 230 100 600 °C, tetragonal, P4/mbm), the cell parameters a for BNN and PNN are very close [√2aBNN = 17.7836(3) Å ≈ √2aPNN = 17.7740(0), where the superstructures (discussed below) are not considered for simplification]. Upon decreasing the temperature from the paraelectric phase, BNN exhibits two phase transitions from the high-temperature tetragonal P4/ mbm phase (paraelectric) to the tetragonal P4bm phase (polar, c axis), and then to the orthorhombic Ccm21 phase (polar, c axis) at room temperature,77 whereas PNN displays only one transition from P4/mbm (paraelectric) to tetragonal Cm2m (polar, b axis); see Figure 3. It is interesting to note that the polar b axis of PNN abnormally increases by 1.1(1)% over the temperature range of 550−25 °C (uniaxial NTE), resulting in a large orthorhombic distortion at room temperature compared to that of BNN [(b/a)PNN = 1.0186(1), (b/a)BNN = 1.0017(1)], whereas the polar c axis of BNN increases by 0.6(1)% during the P4/mbm-to-P4bm transition (600−400 °C). Apparently, there is a close correlation between electric polarization and the thermal expansion anomaly. Understanding the role of polarization could help researchers to tailor the thermal expansion behavior by modifying the ferroelectric properties. The uniaxial NTE along the polar c axis in BNN can be explained by the ferroelectrovolume effect (FVE); this mechanism accounts for NTE in PbTiO3-based materials,6,7 where the ferroelectricity gives rise to elongation of the NbO6 octahedra along the polar axis.72 However, the uniaxial NTE in PNN can be attributed to both the FVE and the framework structure effect. The NTE induced by the FVE has been published elsewhere;6,7 here, we focus on the special characteristics of the NTE in PNN and related materials. The large unit cell induced by the superstructure, as discussed in the next section, makes further study of the local structure change in PNN problematic. In fact, abnormal negative thermal expansion along the b axis was reported in some other Pb-based TTB niobates such as PbNb2O6,62 Pb2KNb5O15,72 and Pb2AgNb5O15,49 as well. Such horizontal Yshaped thermal expansion curves (Figure S1) are characteristic of Pb-based niobates among the TTBs. Figure 4a illustrates the evolution of the [Nb5O25] supercluster and the inner Pb atoms in Pb2KNb5O15.72 At low temperature, Pb2+ with a 6s2 lone pair displaces from the center along the polar b axis to form a covalent bond with coordinated oxygen. With increasing temperature, thermal vibrations weaken the Pb−O bond, as well as the polarization, gradually driving the Pb2+ back to the center. This process is accompanied by synergistic rotation of the octahedra, which directly gives rise to NTE of the b axis. The visualization of the Pb−O bond was performed by firstprinciples calculations based on density functional theory (DFT) on Pb2KNb5O15.72 As shown in Figure 4b, the electron densities of the Pb−O and Nb−O bonds are evident compared to that of the K−O bond. It suggests that the ferroelectric

Figure 4. (a) Schematic representation of octahedral synergic rotations induced by anisotropic Pb−O interactions with the coordinated oxygen. (b) Electron density distribution of Pb2KNb5O15 revealed by DFT calculations in different sections showing the Pb−O and Nb−O covalency, according to Lin et al.72

polarization can be mainly attributed to Pb−O and Nb−O covalency.72 The 6s2 lone pair of Pb2+ in TTB niobates could greatly strengthen the total polarization and, hence, raise the Curie temperature (Table 1). Here, it is worth noting that lone pairs are not a prerequisite for a high Curie temperature. For example, BNN also has a high Curie temperature (∼600 °C, Figure 3), comparable to that of Pb3TiNb4O15 (Table 1). Analogously to Pb2+, Bi3+ also has a 6s2 lone pair, and their ionic radii are close (1.17 Å for Bi3+ and 1.26 Å for Pb2+, CN = 8).78 However, because of a difference in charge, directly replacing Pb2+ by Bi3+ would reduce the number of A-site atoms, which weakens the A−O interactions and the total polarization. For example, the Curie temperature of PbBiNb5O15 relaxor is as low as 100 °C,51 much lower than that of Pb2KNb5O15 with TC = 460 °C.40 Although PbBiNb5O15 in the ferroelectric phase has the same polar direction as Pb2KNb5O15, its macroscopic polarization is not strong enough to drive an increase of polar axis that favors shrinking upon heating.51 As shown in Figure 5a, PbBiNb5O15 normally displays positive thermal expansion in all three dimensions. The contribution of polarization might be embedded in the weakened thermal expansion of the b axis relative to the a axis. Instead, the distribution of one Pb2+ ion and one Bi3+ ion in three of the A sites produces strong local dipole moments, but the macroscopic polarization is suppressed by unusually strong incommensurate modulations.51 This suggests that what affects the thermal expansion in ferroelectrics is the long-range/ macroscopic electric order, not the local order. Anomalous thermal expansions have also been reported in some other non-Pb and non-Bi TTB niobates such as Sr0.75Ba0.25Nb2O6 [from −120 to 100 °C, αc = −0.6(1) × 8134

DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139

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Figure 5. Temperature dependence of cell parameters for (a) PbBiNb5O15 and (b) Sr0.75Ba0.25Nb2O6 (error bars are too small to show), according to Lin et al.51 and Qadri et al.79

Figure 6. (a−d) Coefficients of thermal expansion (CTEs, from room temperature to TC), (e) Curie temperature (TC, and (f) orthogonality at room temperature (b0/a0) as functions of the average A-site ionic radius for Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15. The error bars are too small to show.

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DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139

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Figure 7. (a,b) Electron diffraction patterns along the [001] and [100] zone axes for Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15. The Miller indexes are labeled according to the orthorhombic lattice, namely, a (√2aTTB, √2bTTB, cTTB)-type cell. (c) Schematic presentation of the relationship between the superstructure and thermal expansion in the [001] direction: Where the superstructure (c axis) is enhanced (Na > Rb), the thermal expansion (c axis) is strengthened (Δd2 > Δd1). (d) Normalized Pb LIII-edge XANES spectra measured at room temperature for the samples Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15. Comparisons were made with standard samples PbO2 (Pb4+), yellow PbO (Pb2+), and Pb foil (Pb0+). The data for Pb foil were obtained from ref 87. In this figure, the XANES spectra of the TTBs are severely overlapped, and only the standard samples PbO2, PbO, and Pb foil are clearly distinguished and labeled here. An enlarged figure is available in the Supporting Information (Figure S2). The positions of absorption edge are indicated by a shadow.

10−5 °C−1],79,80 Ca0.28Ba0.72Nb2O6 [25−180 °C, αc = −0.4(1) × 10−5 °C−1],81,82 and Sr2NaNb5O15 [from −150 to 25 °C, αc = −0.21(1) × 10−5 °C−1].83 These NTEs, caused by the FVE, are very weak and are limited to a narrow temperature range (Figure 5b). In the TTB fluoride K3Fe5F15, the sudden contraction of the a axis at ∼297 °C can be attributed to a structural phase transition that occurs in a narrow temperature window of ∼10 °C.70 3.3. Design of Thermal Expansion by Modification of Ferroelectricity. The uniaxial NTE over a wide range of temperatures in the high-Curie-temperature TTB ferroelectrics provides possibilities for the design of multifunctional materials with desirable thermal expansion, ferroelectricity, or mechanical properties. Because there are three different types of A sites and two B sites in TTB structures, more flexibility can be introduced compared to perovskite structures. For the control of the thermal expansion behavior of TTBs by chemical substitutions, there is an interesting example of the Pb2RNb5O15 system, in which the thermal expansion behavior and Curie temperature can be effectively controlled by adjusting the R cation species. Figure 6 depicts the coefficients of thermal expansion (CTEs), Curie temperatures, and axis ratios (b/a, at room temperature) for the systems Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15. All of these compositions display uniaxial NTE along the polar b axis and positive thermal

expansion along the other two axes. The average A-site ionic radius, rA, increase in the sequence of Na < K0.5Li0.5 < Ag < Pb < K < Rb. The rA value was calculated as rA̅ = (2rPb2+ + rRn+)/3, where the ionic radii are the values at CN = 8.78 Figure 6e shows that the Curie temperature, reflecting the firmness of the ferroelectric long-rang Coulomb forces,84 decreases with rA, indicating stronger spontaneous polarization with the smaller R radius. The smaller R cation results in reduced cell parameters and hence shortens the Pb−O and Nb−O distances, which might strengthen the Pb−O and Nb−O covalency. In particular, Pb3TiNb4O15 has the highest Curie temperature of ∼600 °C (Figure 6e), with A1 and A2 fully occupied by Pb; for Pb2AgNb5O15, the Pb−O covalency is somewhat weakened by the transition metal Ag forming a Ag−O covalency, resulting in a relatively low Curie temperature.49 In addition, the positive CTE along the a axis is comparatively small (Figure 6a), in the range of (0.6−1.6) × 10−5 °C−1, not strongly influenced by the R radius and generally decreasing with the R radius, whereas the negative CTE along the b axis and positive CTE along the c axis are relatively large (Figure 6b), in the ranges (−1.6 to −2.4) × 10−5 and (1.5−2.7) × 10−5 °C−1, respectively. The negative CTEs of the polar b axis strengthen with decreasing Asite radius, in good agreement with the higher Curie temperature and larger orthorhombic distortion (b/a) (Figure 6e,f), suggesting larger electric polarization for compositions with small R cations. However, the smaller R cations could not 8136

DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139

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Inorganic Chemistry

obvious in displacive ones, which might due to their stronger electric polarizations. In particular, the Pb-rich TTB niobates usually have high Curie temperatures and exhibit large uniaxial NTEs along the polar b axis over a wide temperature range, as a result of the combined ferroelectrovolume effect and framework synergistic effect. These understandings provide new insight into the crystal chemistry of TTB ferroelectrics. However, for future applications, there is still a long way to go, for example, achieving multifunctional materials with proper thermal expansion, mechanical, and electronic properties at the same time; determining the situation in the thin film; and investigating the size effect. It is also expected that these materials will be used for novel applications, such as nonlinear optical properties and lithium/sodium ion electrode materials. Nevertheless, the relationship between the framework structure, electric polarization, and negative thermal expansion in TTBs can be helpful in the future design and application of this type of material.

lead to small or negative volumetric thermal expansion, because the CTEs of both of the other two axes, especially the layered c axis, increase rapidly. As a result, the superposition of threedimensional thermal expansion makes the volumetric thermal expansion decrease with the R cation radius (Figure 6d). The volumetric CTE, αV, is 1.8 × 10−5 °C−1 for R = Na, which is normal for ceramics, whereas the αV value is 0.4 × 10−5 °C−1 for R = Rb, which is rather low. Thus, Pb2RbNb5O15 is a lowthermal-expansion ferroelectric material. The strengthening of the positive thermal expansion along the layered c axis can be understood by the geometric configurations of the framework structures. Figure 7 shows the [001] and [100] planes of the electron diffraction patterns for the Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15 systems. The superstructure reflections in the [001] plane indicate multiples of the unit cell in the a−b plane referring to charge order related to the A-site cations, whereas the appearance of extra reflections lining up between 0kl and 0k(l + 1) indexes (Figure 7b) indicates the doubling of the c axis, which is mainly caused by the tilt of the NbO6 octahedra. For R = Rb, the material keeps basic orthorhombic structure with cell parameters of (17 Å, 17 Å, 4 Å). By decreasing the R cation radius, superstructures inside both the a−b and b−c planes were observed. It can be seen from Figure 7a that partial charge order inside the a−b plane starts from R = K0.5Li0.5, evidenced by the odd reflections depicted by the arrows, and becomes nearly complete ordered for R = Na. The possible origin of charge ordering inside the a−b plane might be the positional modulation of A-site cations coupled with the tilt of the NbO6 octahedra when the R cations are small. As revealed in Figure 7b, the tilt of the NbO6 octahedra is already evident from R = Pb and becomes increasingly evident as the R cation radius is decreased. The small R cations tend to form negative pressure for the A-site tunnels they fill in, which can be balanced by the tilting of the NbO6 octahedra (Figure 7b). However, the tilted octahedra would gradually be stretched upon heating, and the tilt angle ∠O1−O2−O3 in Figure 7c increases to 180° after the transition to the tetragonal phase, accompanied by sharp expansion of the layered c axis (Figure 7c). Thus, the smaller the R cation, the stronger the thermal expansion along the layered c axis. The valence states of Pb and the existence of 6s2 lone pairs were confirmed by the X-ray absorption near-edge spectrum (XANES) of the Pb L3 edge (Figure 7d). The pre-edge peak A in Figure 7d that appear in PbO2 is due to the 2p3/2 → 6s transition because the 6s level is unoccupied in quadrivalent Pb4+.85,86 The absence of peak A for Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15 suggests that the lone pairs are not deprived from Pb. Moreover, the positions of the absorption edges, the energies at the slope maxima, of Pb in the TTBs are adjacent to PbO, revealing that Pb was in the Pb2+ form. Thus, for the Pb2RNb5O15 system, the macroscopic thermal expansion was determined by contradictory factors: lone-pair-induced ferroelectricity favoring NTE along the polar b axis and octahedron tilting favoring large positive thermal expansion along the layered c axis. The volumetric thermal expansion is determined by a synergistic effect.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b01242. Temperature dependence of cell parameters for the samples Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15 and enlarged XANES spectra of Pb2RNb5O15 (R = Rb, K, Pb, Ag, K0.5Li0.5, Na) and Pb3TiNb4O15 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 91022016, 21031005, 21231001, and 91422301) and the Fundamental Research Funds for the Central Universities, China (Grant FRF-SD-13-008A). We thank Dr. Lirong Zheng for his help with XANES measurements (1W1B, Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences). The various-temperature XRD experiments for PbBiNb5O15 were performed at the BL44B2 of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2015B1127 and No. 2016A1060).

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REFERENCES

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4. SUMMARY In summary, the thermal expansion anomalies related to electric polarization in TTB ferroelectrics were systematically investigated in this work. Compared with those in order−disorder ferroelectrics, the thermal expansion anomalies were more 8137

DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139

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DOI: 10.1021/acs.inorgchem.6b01242 Inorg. Chem. 2016, 55, 8130−8139