Enhanced tetragonality and large negative thermal expansion in a new Pb/Bi-based perovskite ferroelectric of (1 − x)PbTiO₃–xBi(Zn_1/2V_1/2)O₃

Abstract

The exploration of a large negative thermal expansion (NTE) over a wide temperature range has been an important subject in materials science, since the overall coefficient of thermal expansion (CTE) of ordinary materials can be effectively tailored by the introduction of NTE materials. Here, we successfully achieved a large NTE within a broad temperature range in a new Pb/Bi-based ferroelectric of (1 − x)PbTiO₃–xBi(Zn_1/2V_1/2)O₃ by means of improving the ferroelectricity of PbTiO₃. The present system exhibits an unusual enhanced tetragonality, large spontaneous polarization (P_S), and high Curie temperature (T_C). Specifically, the x = 0.1 compound exhibits an enhanced CTE of −2.10 × 10⁻⁵ °C⁻¹ from room temperature (RT) up to its T_C of 600 °C, which is in contrast to that of pristine PbTiO₃ (−1.99 × 10⁻⁵ °C⁻¹, RT−490 °C). More intriguingly, a large volume shrinkage (ΔV ≈ −1%) has also been observed during the ferroelectric-to-paraelectric phase transition. According to experimental and theoretical studies, the large NTE is attributed to the enhanced P_S derived from the strong hybridization of Pb/Bi–O and Ti/Zn/V–O through the substitution of the polar Bi(Zn_1/2V_1/2)O₃ perovskite. The present study demonstrates that a large NTE within a wide temperature range can be achieved in PbTiO₃-based ferroelectrics by improving its ferroelectricity through introducing isostructural polar perovskites.

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Introduction

Most materials display a positive thermal expansion (PTE) upon heating. However, although rare, several categories of materials exhibit a negative thermal expansion (NTE), in which the volume unusually contracts on heating. There are a number of important potential applications for materials with a negative coefficient of thermal expansion (CTE). Perhaps the most immediate one is in composite materials where the overall CTE can be precisely tailored to be a specific positive, negative or even zero value.^1–6 The origins of NTE materials have been well studied in the past decades, mainly including the phonon-related transverse cooperative vibration (e.g., ZrW₂O₈, Ag₃[Co(CN)₆], and ScF₃),^7–10 the magnetovolume effect (e.g., Invar alloys and Mn₃AN),^11–14 the intermetallic charge transfer (e.g., LaCu₃Fe₄O₁₂ and BiNiO₃),^15,16 the metal–insulator transition (e.g., CuRuO₃),^17,18 and the spontaneous volume ferroelectrostriction (SVFS) in PbTiO₃-based ferroelectrics.^19,20 Recent studies in the field of NTE materials have focused on a large NTE over a wide temperature range, due to the fact that normally the stronger the NTE is, the more efficient it is to counteract PTE within composite materials.^2,4

Among the available NTE materials, there is one branch of ferroelectrics which exhibit a general phenomenon in which the unit cell volume shrinks during the ferroelectric-to-paraelectric (FE–PE) phase transition, such as perovskites of PbTiO₃,^21–23 BaTiO₃,²⁴ (Bi, La)NiO₃,¹⁶ and recently reported CH₃NH₃PbI₃,²⁵ tungsten bronze of PbNb₂O₆,²⁶ and tin-hypothiodiphosphate of Sn₂P₂S₆.²⁷ However, all the ferroelectrics except PbTiO₃, in which the NTE behavior occurs from room temperature to its Curie temperature (T_C) of 490 °C, exhibit the NTE property in a relatively narrow temperature range.²⁸ Such a wide NTE range of PbTiO₃ provides the opportunity to modify the NTE property, i.e., achieving a large NTE over a wide temperature range. The origin of NTE in PbTiO₃-based ferroelectrics has recently been well studied via the SVFS effect, which determines the crucial role of ferroelectric behavior in the NTE.¹⁹ Below T_C, PbTiO₃ exhibits ferroelectricity and NTE, while NTE disappears in the paraelectric phase above T_C. In the ferroelectric phase, the increased volume can be well maintained by the large tetragonality (c/a) resulting from the strong spontaneous polarization (P_S). It is worth noting that NTE in PbTiO₃-based ferroelectrics is mainly attributed to shrinkage of the polar c axis. Based on these, it is therefore proposed that a large NTE could be obtained through improving the c/a of PbTiO₃.

Bi(Zn_1/2V_1/2)O₃ was recently reported to be a new PbTiO₃-type perovskite, which exhibits a rather larger tetragonality (c/a = 1.26) and stronger polarization (P_S = 126 μC cm⁻²) compared to those of PbTiO₃ (c/a = 1.064, P_S = 59 μC cm⁻²).^29,30 The introduction of Bi(Zn_1/2V_1/2)O₃ in PbTiO₃ is considered to further increase its tetragonality, and therefore achieve an enhanced NTE. Herein, we successfully achieved a large NTE over a wide temperature range in the present new Pb/Bi-based binary system of (1 − x)PbTiO₃–xBi(Zn_1/2V_1/2)O₃. A continuously enhanced c/a has been observed by the substitution of the polar Bi(Zn_1/2V_1/2)O₃ perovskite. As expected, both the NTE and T_C have been improved to a certain extent. In particular, remarkably volume shrinkages have also been observed in (1 − x)PbTiO₃–xBi(Zn_1/2V_1/2)O₃ during the FE–PE phase transition, which have been well studied by the experimental and theoretical results.

Experimental section

Material synthesis and measurements

Polycrystalline samples of (1 − x)PbTiO₃–xBi(Zn_1/2V_1/2)O₃ (hereafter abbreviated as (1 − x)PT–xBZV, x = 0.1–0.5) were prepared by using a cubic anvil-type high-pressure apparatus. The raw materials of PbO, Bi₂O₃, ZnO, TiO₂, V₂O₃, and V₂O₅ were stoichimetrically mixed and sealed in a gold capsule, and then treated at 6 GPa and 1100 °C for 30 min. After the high-pressure process, the obtained compounds were carefully ground in an agate mortar, and subsequently annealed at 400 °C for 4 hours. The X-ray diffraction (XRD) patterns were collected with a Bruker D8 AVANCE diffractometer for phase identification. The high-temperature synchrotron powder diffraction (SXRD) experiment was conducted at the 11-ID-C beamline of the Advanced Photon Source with a light wavelength of 0.117418 Å.

Computational

First-principles calculation was performed by using CASTEP,³¹ a total energy package based on the plane-wave pseudopotential density functional theory (DFT).^32,33 The correlation and exchange energy was described by Perdew, Burke and Ernzerhof (PBE)³⁴ in the generalized gradient approximation (GGA)³⁵ form. The optimized norm-conserving pseudopotential³⁶ in the Kleinman–Bylander³⁷ form was adopted to model the effective interaction between the valence electrons and atom cores, allowing the choice of a relatively small plane-wave basis set without compromising the computational accuracy. The disorder occupation in 0.5PbTiO₃–0.5Bi(Zn_1/2V_1/2)O₃ was handled by virtual crystal approximation (VCA),³⁸ in which the disorder position is modeled by a ghost atom with the effective Coulomb potential weighted by its atomic constitution. A kinetic energy cutoff of 800 eV and a Monkhorst–Pack³⁹ with k-point meshes less than 0.03 Å⁻¹ in the Brillouin zones were chosen.

Results and discussion

The laboratory XRD patterns of (1 − x)PT–xBZV from x = 0.1 to 0.5 are shown in Fig. 1(a). As can be seen, all the investigated compounds exhibit a single tetragonal phase without any noticeable impurities. With the substitution of BZV, the (001) peak shows a clear shift to the lower angle, indicating the expansion of the c axis. While the (100) peak exhibits an opposite trend, it shifts slightly to the higher angle which demonstrates the shrinkage of the a(b) axis. The detailed lattice parameters were refined and plotted in Fig. 1(b). The c axis increases almost linearly, whereas the a(b) axis decreases continuously as a function of BZV. Consequently, an unusual enhanced c/a has been observed. The c/a value increases from 1.06 of pristine PT to 1.08, 1.12, 1.13, and 1.16 of x = 0.1, 0.2, 0.3, 0.4, and 0.5, respectively, which suggests that the substitution of BZV effectively enhanced the tetragonality of PT. Here, the large tetragonality results in a pyramidal rather than an octahedral coordination in the (1 − x)PT–xBZV solid solutions (see the top left of Fig. 2). The large lattice distortion can be attributed to the large P_S displacements induced by the strong Pb/Bi–O hybridization and coupling interactions between Ti/Zn/V and Pb/Bi cations, which can be evidenced by the following theoretical calculations.

Fig. 1 (a) XRD patterns and (b) lattice parameters of (1 − x)PT–xBZV (x = 0.1–0.5) at room temperature.

Fig. 2 The calculated spontaneous polarization of (1 − x)PT–xBZV (x = 0.1–0.5) at room temperature. The insets are the crystal structure (top left) and schematic diagram of P_S (bottom right).

It is well known that in ABO₃ perovskite-type ferroelectrics, P_S originates from the displacements from the centroid of the oxygen polyhedrons of the A site and B site atoms (see the bottom right of Fig. 2).²¹ Here, the P_S displacements of the A site Pb/Bi and the B site Ti/Zn/V cations can be derived from the SXRD refinement results. The detailed structure of (1 − x)PT–xBZV was refined using the Rietveld method with the FullProf software. The initial structural model corresponds to PbTiO₃ with the atomic positions being given in the noncentrosymmetric space group P4mm (no. 99).⁴⁰ The occupancies of atoms were fixed at the ideal composition. The isotropic thermal factors of Pb/Bi, Zn/Ti/V, as well as O(I) and O(II) were set equal, respectively. In addition, the anisotropic profile broadening model has been adopted in order to obtain good fitting results.⁴¹ As can be seen, the calculated diffraction profiles agree well with the observed ones (Fig. S1–S5†). The related P_S can be estimated by considering a purely ionic crystal and neglecting the electronic polarization by using the following formula,⁴²

where δz_i indicates the cation shifts along with the ferroelectric axis of the ith ion with the electric charge q_i, V represents the unit cell volume, and Z equals to 1. As shown in Fig. 2, the calculated P_S increases continuously with the solubility of BZV, ranging from 66, 70, 83, and 93, to as large as 97 μC cm⁻² for x = 0.1, 0.2, 0.3, 0.4, and 0.5, respectively, which are much larger than that of pristine PbTiO₃ (59 μC cm⁻²).³⁰ The refined results indicate that the substitution of BZV enhanced the P_S, which is consistent with the enhanced tetragonality.

Both theoretical and experimental studies have confirmed that enhanced tetragonality in the PbTiO₃-based ferroelectric could give rise to an enhanced NTE.^19,43 Generally, a large c/a indicates a large lattice distortion, and could result in large volume shrinkage with the release of high lattice energy during the heating process. As a result, an enhanced NTE could be observed, such as in Pb_1−xCd_xTiO₃,⁴⁴ PbTiO₃–BiFeO₃,⁴⁵ and recently reported Pb(Ti_1−xV_x)O₃ and (1 − x)PbTiO₃–xBiCoO₃ systems,^20,46 which exhibit abnormally enhanced c/a and NTE compared to those of PbTiO₃. In order to precisely investigate the thermal expansion property of the (1 − x)PT–xBZV system, the temperature dependence of SXRD experiments was determined (Fig. S6 and S7†). The detailed unit cell volumes were extracted by means of structure refinement based on the SXRD data (Fig. 3a). With the substitution of BZV, the 0.9PT–0.1BZV compound presents a nonlinear and strong NTE in a wide temperature range from room temperature (RT) to near T_C. This is in contrast to pristine BZV, which decomposes at a temperature higher than 730 K before reaching its T_C.²⁹ Note that the unit cell volume of 0.9PT–0.1BZV shows little dependence on temperature before the FE–PE phase transition. However, it contracts dramatically during the FE–PE phase transition. A noticeable volume shrinkage of −0.95% has been observed during the phase transition. The average CTE of the overall temperature range is −2.10 × 10⁻⁵ °C⁻¹ (RT ∼ 600 °C). With further increase of the content of BZV, the compound of 0.8PT–0.2BZV shows a tendency of PTE with a negligible CTE of 1.56 × 10⁻⁶ °C⁻¹ (RT ∼ 680 °C) before the FE–PE phase transition. Intriguingly, a more pronounced volume contraction as large as −1.08% has been observed during the FE–PE phase transition. In comparison, the present NTE is among giant NTE materials such as CuO nanoparticles (−1.1%),⁴⁷ Mn₃AN (−1.3%),¹² BiNiO₃ (−2.5%),¹⁶ Ca₂RuO_3.74 (−1.0%),¹⁸ and recently reported Pb_0.76La_0.04Bi_0.20VO₃ (−6.7%).⁴⁸ It is worth noting that the present compound of 0.9PT–0.1BZV (−2.10 × 10⁻⁵ °C⁻¹, RT ∼ 600 °C) not only enhances the NTE of PT (−1.99 × 10⁻⁵ °C⁻¹, RT ∼ 490 °C) but also extends the NTE to a much wider temperature range. The T_C of PT has been significantly increased by 100 °C, which is attributed to the enhanced polarization according to the empirical relationship of T_C = αP_S².³⁰ For further increasing the content of BZV, the compounds decompose before reaching the FE–PE phase transition temperature, which is ascribed to the increased lattice distortion and weakened thermal stability of the perovskite structure.

Fig. 3 (a) Unit cell volume and (b) calculated spontaneous polarization of (1 − x)PT–xBZV (x = 0.1 and 0.2) as a function of temperature.

Recently, a new concept of spontaneous volume ferroelectrostriction (SVFS) has been proposed to illuminate the origin of NTE in PbTiO₃-based ferroelectrics.¹⁹ According to the description of SVFS, the ferroelectric behavior plays an important role in the NTE of PT-based ferroelectrics. The NTE of PT-based ferroelectrics generally occurs in the ferroelectric phase, while it disappears in the paraelectric phase. The increased volume in the ferroelectric phase can be maintained by the high lattice distortion c/a which results from the large P_S. Therefore, how the P_S, which can reflect the magnitude of ferroelectricity, varies with temperature, will directly affect the NTE. The variation of P_S as a function of temperature for 0.9PT–0.1BZV and 0.8PT–0.2BZV is shown in Fig. 3b. The P_S values of both the two compounds exhibit a slightly decreasing tendency with increasing temperature, which is ascribed to the weakened ferroelectricity. As the temperature is raised up to near T_C, P_S still remains at a high level, with the values of 60 and 65 μC cm⁻² for 0.9PT–0.1BZV and 0.8PT–0.2BZV, respectively. Correspondingly, the unit cell volumes of 0.9PT–0.1BZV and 0.8PT–0.2BZV can be retained close to that of room temperature by the high P_S. As a result, both the two compositions exhibit little temperature dependence of unit cell volumes before reaching their T_Cs. However, P_S suddenly disappears on approaching the T_C, resulting in noticeable volume shrinkages during the FE-to-PE phase transition.

To further study the effect of BZV substitution on the hybridization with oxygen atoms, the electron density difference of (1 − x)PT–xBZV (x = 0 and 0.5) was calculated by first-principles calculation. As depicted in Fig. 4, it is revealed that in both PbTiO₃ and 0.5PbTiO₃–0.5Bi(Zn_0.5V_0.5)O₃, the concentration of the valence electrons on the Ti–O (or Ti_0.5Zn_0.25V_0.25–O) bond along the c-axis is more prominent than that within the (a,b) plane, which indicates that the orbital hybridization along the c-axis is stronger than that along the a(b)-axis. In pristine PbTiO₃, apart from the electronic cloud concentration, some electron-loss area also occurs, while in 0.5PbTiO₃–0.5BiZn_0.5V_0.5O₃, the electron concentration strongly dominates in the chemical bonds within the pyramidal anions. Moreover, the highest value of the electronic density difference in PbTiO₃ is 3.75 Å⁻³, which is smaller than that in 0.5PbTiO₃–0.5BiZn_0.5V_0.5O₃ (4.75 Å⁻³). These observations demonstrate that the Zn_0.5V_0.5/Ti substitution strongly enhanced the covalent interaction within Ti_0.5Zn_0.25V_0.25O₃ pyramid, giving rise to the larger spontaneous polarization.

Fig. 4 The electronic density difference map of (a) PbTiO₃ and (b) 0.5PT–0.5BZV. The Pb(Pb/Bi), Ti(Ti/Zn/V), and O atoms are indicated by black, blue, green, and violet balls, respectively.

Conclusions

In summary, a new Pb/Bi-based ferroelectric based on (1 − x)PT–xBZV has been designed to exhibit a large NTE over a wide temperature range. Both the tetragonality and Curie temperature are considerably increased. The 0.9PT–0.1BZV compound exhibits a large NTE with an average CTE of −2.10 × 10⁻⁵ °C⁻¹ in the temperature range from room temperature up to 600 °C, which is largely enhanced compared to that of PbTiO₃. In particular, large volume shrinkages have also been observed in 0.9PT–0.1BZV and 0.8PT–0.2BZV during the FE–PE phase transition. The large NTE is closely related to the enhanced P_S due to the substitution of BZV, which has been well elaborated by the experimental and theoretical results. The present study demonstrates that a large NTE within the extended temperature range could be achieved in PbTiO₃-based ferroelectrics through improving its ferroelectric property.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 21805215), the National Program for Support of Top-notch Young Professionals, the Program for Changjiang Young Scholars, and the General Financial Grant from the China Postdoctoral Science Foundation (2017M622536). The use of the Advanced Photon Source at the Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science (DE-AC02-06CH11357).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9qi00450e

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