Tao Yang, Longlong Fan, Yilin Wang, Kun Lin, Jun Chen, and Xianran Xing, Semi-empirical estimation for enhancing negative thermal expansion in PbTiO3-based perovskites, Int. J. Miner. Metall. Mater., 29(2022), No. 4, pp.783-786. https://dx.doi.org/10.1007/s12613-021-2390-3
Cite this article as:
Tao Yang, Longlong Fan, Yilin Wang, Kun Lin, Jun Chen, and Xianran Xing, Semi-empirical estimation for enhancing negative thermal expansion in PbTiO3-based perovskites, Int. J. Miner. Metall. Mater., 29(2022), No. 4, pp.783-786. https://dx.doi.org/10.1007/s12613-021-2390-3
Tao Yang, Longlong Fan, Yilin Wang, Kun Lin, Jun Chen, and Xianran Xing, Semi-empirical estimation for enhancing negative thermal expansion in PbTiO3-based perovskites, Int. J. Miner. Metall. Mater., 29(2022), No. 4, pp.783-786. https://dx.doi.org/10.1007/s12613-021-2390-3
Cite this article as:
Tao Yang, Longlong Fan, Yilin Wang, Kun Lin, Jun Chen, and Xianran Xing, Semi-empirical estimation for enhancing negative thermal expansion in PbTiO3-based perovskites, Int. J. Miner. Metall. Mater., 29(2022), No. 4, pp.783-786. https://dx.doi.org/10.1007/s12613-021-2390-3
Beijing Advanced Innovation Center for Materials Genome Engineering, Institute of Solid State Chemistry, Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China
2)
College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China
3)
Institute of Advanced Materials, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
Generally, most materials expand when heated and contract when cooled, whereas negative thermal expansion (NTE) materials are very rare. As a typical NTE material, PbTiO3 and related compounds have drawn particular interest in recent years. The discovery of an enhanced NTE system in PbTiO3 is beneficial to deepen our understanding of its mechanism and regulate its properties. At present, the method of discriminating an enhanced NTE material based on PbTiO3 is not universal. Here, we propose a semi-empirical method through evaluating the average lattice distortion in related systems to estimate the relative coefficient of thermal expansion conveniently. The rationality of the method was verified by the analysis of the 0.6PbTiO3–0.4Bi(GaxFe1−x)O3 system. So far, all PbTiO3-based compounds with enhanced NTE conform well to this method. This method provides the possibility to find more enhanced NTE PbTiO3-based materials.
PbTiO3 has been extensively studied due to its wide NTE temperature range and excellent ferroelectricity [1–2]. In recent years, the chemical pressure route has been applied to control the NTE property of PbTiO3. As the simplest and the most efficient way to realize chemical pressure, doping is widely used. However, most dopants weaken the NTE behavior of PbTiO3, such as Pb1−xAxTiO3 (A = La, Ca, Ba, La1/2K1/2, Bi) [3–7] and (1−x)PbTiO3–xBiMeO3 (Me = Mg1/2Ti1/2, Ni1/2Ti1/2, Zn1/2Ti1/2, Sc) [8–11], while only a few PbTiO3-based compounds could possess enhanced NTE, such as Pb1−xCdxTiO3 [12], (1−x)PbTiO3–xBiFeO3 [13] and (1−x)PbTiO3–xBiGaO3 [14]. It is helpful to reveal the NTE mechanism of doped PbTiO3 by understanding the enhanced NTE system. However, there is no regularity in the radius, valences, sites, or any other characteristics of the doping ions, making it hard to predict whether the NTE behavior in doped PbTiO3 is enhanced or suppressed. Thus, it is necessary to find a simple and efficient method to estimate and further predict whether NTE is enhanced.
The mechanism of NTE behavior in PbTiO3-based compounds has been researched over the years. Initially, the origin of NTE in PbTiO3 was thought to be the phase transition effect [15–16]. Later, the theory of charge disproportionation [17] was proposed to explain the NTE of ferroelectrics like PbTiO3 and SnP2S6. According to the theory of charge disproportionation, the increased temperature leads to changes in the valence and bond length in an anisotropic system. The anharmonicity of atomic bonds further induces NTE behavior. However, these phenomenological theories have no specific physical meanings. In fact, PbTiO3 exhibits a ferroelectric phase at room temperature and a paraelectric phase above the Curie temperature (TC = 490°C), while the phase transition is accompanied by a contraction in volume. It can be easily concluded that NTE has a close relationship with ferroelectricity. To quantitatively describe the relationship between the contribution of ferroelectricity to NTE and the spontaneous polarization, the spontaneous volume ferroelectrostriction (SVFS) theory was put forward [18]:
ωS∼δz2A
(1)
where SVFS is defined as ωS, and δzA is the displacement in z direction of the A site (in this article, Pb/Bi occupy the A site, Ti/Ga/Fe occupy the B site).
The SVFS theory expounds that there is a strong linear correlation between ωS and δz2A. The SVFS theory reasonably explains the mechanism of NTE in PbTiO3-based compounds and emphasizes the great role of δzA in NTE. The inset in Fig. 1(b) describes the definition of ωS.
The SVFS theory could well describe the contribution of ferroelectricity to volume and also explain the NTE mechanism of ferroelectric materials. However, there are still some special cases in which the ferroelectric property is enhanced and the NTE behavior is weakened in the PbTiO3-based system. For example, PbTiO3–Bi(Zn1/2Ti1/2)O3 possesses a larger c/a value and spontaneous polarization than PbTiO3 but has an obviously weakened NTE behavior, where symbols a and c represent the cell parameters. To make up for the limitations of the SVFS theory, we propose a new empirical formula based on the previous SVFS theory, which can quickly and easily determine the strength of NTE in PbTiO3-related compounds. A new PbTiO3-based NTE enhancement system, 0.6PbTiO3–0.4Bi(Ga,Fe)O3, was discovered under the guidance of the method, which is of reference significance.
Fig.
1.
(a) Relationship between (c/a − 1) and {\boldsymbol{\delta }\boldsymbol{z}}_{\mathbf{P}\mathbf{b}/\mathbf{B}\mathbf{i}}^{{\boldsymbol{2}}}of 0.6PbTiO3–0.4BiFeO3 and 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3 in 25–500°C. The inset shows the sketch of δzPb/Bi and δzTi/Ga/Fe. (b) Temperature dependence of the volume thermal expansion behavior of 0.6PbTiO3–0.4BiFeO3 and 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3. The inset shows the definition of ωS，where Vexp and Vnm are the unit cell volumes of experimental and nominal one, respectively.
As typical displacement-type ferroelectrics, the NTE behavior of PbTiO3 is closely related to the ferroelectric property. However, it is not accurate to infer the strength of NTE from the ferroelectric property. For instance, 0.6PbTiO3–0.4BiFeO3 and 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3 have similar structural distortions (c/a − 1 = 0.11 and 0.10, respectively at 25°C) and spontaneous polarization value (76.5 μC/cm2 and 74.6 μC/cm2, respectively) but opposite NTE behaviors. 0.6PbTiO3–0.4BiFeO3 possesses enhanced NTE behavior, and its coefficient of thermal expansion (CTE) can reach up to −3.54 × 10−5 °C−1, while 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3 presents a weakened NTE behavior with CTE of −0.47 × 10−5 °C−1.
To make sense of this different behavior, temperature dependence of structural change was obtained by structure refinement. Fig.1 shows a linear relationship between the structural distortion and the square of the A-site spontaneous polarization displacement (δzA). According to the results, 0.6PbTiO3–0.4BiFeO3 and 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3 have similar ratio of c/a and δzA at room temperature (TR = 25°C), whereas 0.6PbTiO3–0.4BiFeO3 shows smaller c/a and δzA than 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3 at 500°C. This indicates that the structural distortion range [Δ(c/a − 1)] of 0.6PbTiO3–0.4BiFeO3 is much wider than that of 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3 in the same temperature range. With the increase of temperature, compounds with a slight structural distortion will maintain a large tetragonality, which leads to the zero thermal expansion behavior of 0.6PbTiO3–0.4Bi(Zn1/2Ti1/2)O3. This shows that the degree of structural distortion [Δ(c/a − 1)/ΔT] is closely related to NTE. Therefore, we propose a new method through evaluating the degree of average distortion to determine the NTE of PbTiO3-based compounds.
In addition to the analysis of experimental data, similar conclusions can be drawn from the changes in volume. According to the calculation formula of CTE, we have simplified the formula and obtained the following one. The detailed calculation process can be viewed in the supporting information.
k=\frac{a/c-1}{{T}_{\mathrm{C}}-{T}_{\mathrm{R}}}
(2)
The formula has the same meaning as the degree of average distortion, named average lattice distortion (k). Since the formula of the average lattice distortion is derived from the thermal expansion coefficient (αv) formula, αv and k change synchronously. Thus, we can compare the k values of doped PbTiO3 compounds and PbTiO3 (k = −0.129 × 10−3 °C−1) to predict the enhancement or suppression of NTE. Therefore, in practice, the relative strength of the NTE coefficient of a PbTiO3-based compound can be easily determined only by the room-temperature X-ray diffraction (XRD) to evaluate the lattice constant (a, c) and differential scanning calorimetry (DSC) measurement to access TC.
Under the direction of this method, we have found a possible PbTiO3-based compound, 0.6PbTiO3–0.4Bi(GaxFe1−x)O3, whose NTE behavior is predicted to be enhanced according to the average lattice distortion method. In the literature, 0.6PbTiO3–0.4Bi(GaxFe1−x)O3 possesses a high c/a ratio and a relatively low Curie temperature [19]. According to the data in the reference, the k value of 0.6PbTiO3–0.4Bi(Ga0.05Fe0.95)O3 was calculated to be about −0.166 × 10−3 °C−1, which is even smaller than that of 0.6PbTiO3–0.4BiFeO3 (−0.160 × 10−3 °C−1), whose NTE behavior is already enhanced compared to PbTiO3. Based on the average lattice distortion method, 0.6PbTiO3–0.4Bi(GaxFe1−x)O3 would exhibit an enhanced NTE behavior.
To determine the thermal expansion property, 0.6PbTiO3–0.4Bi(GaxFe1−x)O3 (x = 0, 0.05, and 0.1) were synthesized and then characterized by XRD and DSC. Increasing the doping magnitude, the c/a ratio increases reaching up to 1.12 when x = 0.1 (Fig. 2(a)). Similar to the PbTiO3–BiGaO3 system, the Curie temperature of the 0.6PbTiO3–0.4Bi(GaxFe1−x)O3 system remains constant [14] with various x, which is around 550°C. According to the experimental data, the k values can be calculated as −0.194 × 10−3 °C−1 and −0.203 × 10−3 °C−1 for x = 0 and x = 0.1, respectively, which is much smaller than that of PbTiO3 (−0.129 × 10−3 °C−1). From the perspective of average lattice distortion, the NTE of the system shows an enhanced behavior.
Fig.
2.
(a) a, c axes and the c/a ratio of 0.6PbTiO3–0.4Bi(GaxFe1−x)O3. (b) Temperature dependence of the volume thermal expansion in 0.6PbTiO3–0.4BiFeO3 and 0.6PbTiO3–0.4Bi(Ga0.1Fe0.9)O3 (0.4BF and 0.4BG0.1F0.9, respectively in the figure), and the insets correspond to the charge density distribution.
Temperature-dependent XRD spectra were measured to accurately determine the CTE. The result (Fig. 2(b)) shows that the compounds indeed exhibit an enhanced NTE behavior. The CTE is enhanced from −3.54 × 10−5 °C−1 (25–550°C) of 0.6PbTiO3–0.4BiFeO3 to −3.94 × 10−5 °C−1 (25–550°C) of 0.6PbTiO3–0.4Bi(Ga0.1Fe0.9)O3. The result demonstrates the effectiveness of the proposed method in predicting the enhancement of NTE of PbTiO3-based compounds. In addition, results based on the maximum entropy method also account for the NTE enhancement of the system (see the inserts in Fig. 2(b)). The introduction of BiGaO3 enhances the covalency of Pb/Bi–O, resulting in enhanced NTE behavior in the compound.
To further verify the universality and reliability of the semi-empirical formula, we have calculated the k value of some typical PbTiO3-based compounds with various NTE behaviors and compared the corresponding αv and k in Fig. 3. Statistically, all PbTiO3-based compounds with enhanced NTE are in the blue region and compounds with suppressed NTE are scattered throughout the opposite areas, proving the consistency of αv and k.
It should be pointed out that k and αv are not equivalent. Owing to the omission of some terms relative to the intrinsic CTE (αv), k has two disadvantages in describing the process of NTE. (i) The average lattice distortion formula is not applicable for some PbTiO3-based compounds with a very small ratio of c/a. Because the formula assumes that all tetragonal to cubic phase transitions would induce NTE behavior. However, this was not the case. It is not suitable for PbTiO3-based compounds with zero thermal expansion like 0.8PbTiO3–0.2Bi(Ni1/2Ti1/2)O3. (ii) k is derived from αv and reduces a little bit of αv (the reduced part is schematically shown by the shaded area in Fig. S1), so there is an intrinsic error in the results.
Fig.
3.
Statistical chart of αv and k of some typical PbTiO3-based compounds.
According to a previous study, ωS in the SVFS theory is represented as the contribution of ferroelectric polarization to NTE, which could explain the mechanism of enhanced NTE in PbTiO3-based compounds but could not predict it. In fact, ωS is closely related to the c/a ratio. The result of Fig. 4 demonstrates a strong linear relationship between the tetragonal distortion (c/a − 1) and ωS in 0.6PbTiO3–0.4Bi(Ga0.1Fe0.9)O3. This also indicates that ωS cannot accurately estimate the magnitude of the NTE property because the NTE cannot be estimated merely from the point of c/a. At present, all NTE enhanced systems based on PbTiO3 have a higher c/a than PbTiO3, but the reverse is not necessarily true. There are some tetragonality-enhanced PbTiO3-based systems with weakened NTE, like PbTiO3–BiInO3 [11] and PbTiO3–Bi(Cu0.5Ti0.5)O3 [20]. In practice, the magnitude of the thermal expansion coefficient is the average rate of the change of volume with respect to temperature, while the average rate in the change of c/a with temperature also shows a similar meaning, explaining the rationale for the average lattice distortion.
Fig.
4.
Linear correlation between c/a − 1 and ωS for 0.6PbTiO3–0.4Bi(Ga0.1Fe0.9)O3 from 25 to 550°C.
In summary, a semi-empirical formula was developed to understand and obtain new enhanced NTE compounds based on PbTiO3. A new parameter, average lattice distortion (k), was proposed to evaluate and further predict NTE behaviors. By this method, a new enhanced NTE system, 0.6PbTiO3–0.4Bi(GaxFe1−x)O3, was found. We can quickly determine the magnitude of NTE relative to PbTiO3 through room-temperature XRD and DSC measurements. Also, the experimental data showed that it is reasonable to use k to estimate the strength of NTE. Overall, the average lattice distortion is of predictive significance for finding new enhanced NTE systems in PbTiO3-based compounds.
Acknowledgements
This research was financially supported by the National Key R&D Program of China (No. 2020YFA0406202) and the National Natural Science Foundation of China (Nos. 22090042 and 21731001).
Conflict of Interest
The authors declare no competing financial interest.
G. Shirane, S. Hoshino, and K. Suzuki, X-ray study of the phase transition in lead titanate, Phys. Rev., 80(1950), No. 6, p. 1105. DOI: 10.1103/PhysRev.80.1105
[2]
J. Chen, L. Hu, J. Deng, and X. Xing, Negative thermal expansion in functional materials: Controllable thermal expansion by chemical modifications, Chem. Soc. Rev., 44(2015), No. 11, p. 3522. DOI: 10.1039/C4CS00461B
[3]
J. Chen, X.R. Xing, R.B. Yu, and G.R. Liu, Thermal expansion properties of lanthanum-substituted lead titanate ceramics, J. Am. Ceram. Soc., 88(2005), No. 5, p. 1356. DOI: 10.1111/j.1551-2916.2005.00314.x
[4]
A. Chandra, D. Pandey, M.D. Mathews, and A.K. Tyagi, Large negative thermal expansion and phase transition in (Pb1–xCax)TiO3 (0.30 ≤ x ≤ 0.45) ceramics, J. Mater. Res., 20(2005), No. 2, p. 350. DOI: 10.1557/JMR.2005.0062
[5]
X.R. Xing, J.X. Deng, Z.Q. Zhu, and G.R. Liu, Solid solution Ba1−xPbxTiO3 and its thermal expansion, J. Alloys Compd., 353(2003), No. 1-2, p. 1. DOI: 10.1016/S0925-8388(02)01178-7
[6]
J. Chen, X.R. Xing, J.X. Deng, and G.R. Liu, Thermal expansions of ceramics in the system Pb1−x(La1/2K1/2)xTiO3, J. Alloys Compd., 372(2004), No. 1-2, p. 259. DOI: 10.1016/j.jallcom.2003.09.137
[7]
P.H. Hu, Z.M. Cao, J. Chen, J.X. Deng, C. Sun, R.B. Yu, and X.R. Xing, Structure and negative thermal expansion of Pb1−xBixTiO3, Mater. Lett., 62(2008), No. 30, p. 4585. DOI: 10.1016/j.matlet.2008.08.028
[8]
P.H. Hu, J. Chen, X.Y. Sun, J.X. Deng, X. Chen, R.B. Yu, L.J. Qiao, and X.R. Xing, Zero thermal expansion in (1–x)PbTiO3–xBi(Mg, Ti)1/2O3 piezoceramics, J. Mater. Chem., 19(2009), No. 11, art. No. 1648. DOI: 10.1039/b816822a
[9]
P.H. Hu, J. Chen, J.X. Deng, and X.R. Xing, Thermal expansion, ferroelectric and magnetic properties in (1–x)PbTiO3–xBi(Ni1/2Ti1/2)O3, J. Am. Chem. Soc., 132(2010), No. 6, p. 1925. DOI: 10.1021/ja908014u
[10]
J. Chen, X.R. Xing, C. Sun, P.H. Hu, R.B. Yu, X.W. Wang, and L.H. Li, Zero thermal expansion in PbTiO3-based perovskites, J. Am. Chem. Soc., 130(2008), No. 4, p. 1144. DOI: 10.1021/ja7100278
[11]
P.H. Hu, J. Chen, C. Sun, J.X. Deng, and X.R. Xing, B-site dopant effect on the thermal expansion in the (1−x)PbTiO3–xBiMeO3 Solid solution (Me = Fe, In, Sc), J. Am. Ceram. Soc., 94(2011), No. 10, p. 3600. DOI: 10.1111/j.1551-2916.2011.04632.x
[12]
J. Chen, X.R. Xing, R.B. Yu, and G.R. Liu, Structure and enhancement of negative thermal expansion in the PbTiO3–CdTiO3 system, Appl. Phys. Lett., 87(2005), No. 23, art. No. 231915. DOI: 10.1063/1.2140486
[13]
J. Chen, X.R. Xing, G.R. Liu, J.H. Li, and Y.T. Liu, Structure and negative thermal expansion in the PbTiO3–BiFeO3 system, Appl. Phys. Lett., 89(2006), No. 10, art. No. 101914. DOI: 10.1063/1.2347279
[14]
T. Yang, Y.L. Wang, L.L. Fan, N. Wang, K. Lin, J. Chen, and X.R. Xing, Strong covalent bonding for enhanced negative thermal expansion in (1−x)PbTiO3–xBiGaO3, J. Phys. Chem. C, 124(2020), No. 37, p. 20445. DOI: 10.1021/acs.jpcc.0c05948
[15]
J.S.O. Evans, Negative thermal expansion materials , J. Chem. Soc., Dalton Trans., 1999, No. 19, p. 3317.
[16]
A.W. Sleight, Compounds that contract on heating, Inorg. Chem., 37(1998), No. 12, p. 2854. DOI: 10.1021/ic980253h
[17]
K. Takenaka, Progress of research in negative thermal expansion materials: Paradigm shift in the control of thermal expansion, Front. Chem., 6(2018), p. 267. DOI: 10.3389/fchem.2018.00267
[18]
J. Chen, F.F. Wang, Q.Z. Huang, L. Hu, X.P. Song, J.X. Deng, R.B. Yu, and X.R. Xing, Effectively control negative thermal expansion of single-phase ferroelectrics of PbTiO3–(Bi,La)FeO3 over a giant range, Sci. Rep., 3(2013), art. No. 2458. DOI: 10.1038/srep02458
[19]
J.R. Cheng, N. Li, and L.E. Cross, Structural and dielectric properties of Ga-modified BiFeO3–PbTiO3 crystalline solutions, J. Appl. Phys., 94(2003), No. 8, p. 5153. DOI: 10.1063/1.1609655
[20]
L.L. Fan, Q. Li, L.X. Zhang, N.K. Shi, H. Liu, Y. Ren, J. Chen, and X.R. Xing, Negative thermal expansion and the role of hybridization in perovskite-type PbTiO3–Bi(Cu0.5Ti0.5)O3, Inorg. Chem. Front., 7(2020), No. 5, p. 1190. DOI: 10.1039/C9QI01546A
Kexin Jiang, Qi Shao, Zijie Song, et al. Structure and thermal expansion in Cu2-Co P2O7. Ceramics International, 2024.
DOI:10.1016/j.ceramint.2024.12.208
2.
Huabin Yang, Xueting Wang, Xinyi Yang, et al. Revealing high temperature structural behavior behind the enhanced piezoelectric properties of lead-free 0.7BiFeO3-0.3BaTiO3 ceramics by in-situ process. Journal of the European Ceramic Society, 2024, 44(5): 3247.
DOI:10.1016/j.jeurceramsoc.2023.12.058
3.
Chengyi Yu, Kun Lin, Yili Cao, et al. Two-dimensional zero thermal expansion in low-cost MnxFe5−xSi3 alloys via integrating crystallographic texture and magneto-volume effect. Science China Materials, 2022, 65(7): 1912.
DOI:10.1007/s40843-021-1996-2
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