Research progress of the investigation of intrinsic and extrinsic origin of piezoelectric materials by X-ray diffraction

Zhang Guan-Jie; Yang Hao; Zhang Nan

doi:10.7498/aps.69.20200301

Abstract

Ferroelectric/piezoelectric perovskites are an important class of functional material and have broad application prospects in commercial, industrial, military and other areas because of their high dielectric constants, high piezoelectric coefficients, and high electromechanical coupling coefficients. Their structures, applications, and physical mechanisms have been intensively studied in condensed matter physics and material science. The piezoelectric properties of ferroelectric materials mainly originate from the intrinsic field-induced lattice distortion and extrinsic domain inversion and domain wall motion. Therefore, the understanding of and the distinguishing between these mechanisms are important for ascertaining the origin of the high-piezoelectric properties and developing new functional materials. In this article, we review the research progress of technical means and methodology of analyzing the changes of crystal lattices and magnetic domains of materials under the action of an externally applied electric field through the high-energy synchrotron X-ray diffraction experiments. The techniques and analysis methods involved in the review cover the time-resolved X-ray diffraction, single/double-peak analysis, full-pattern refinement, center-of-mass calculation, and field-induced phase transformation analysis, which are used to study the intrinsic and extrinsic contributions to sample’s macroscopic properties. It is expected to provide the research methods, which fulfill the individual experimental requirements, and the technical support for the mechanism analysis of various piezoelectric materials through the introduction and review of various methods.

Keywords:

Authors and contacts

Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: Zhang Nan, nzhang1@xjtu.edu.cn

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Cited By

图 1 频闪数据收集原理

Figure 1. Principle of stroboscopic data-acquisition

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图 2 (a) Choe等^[40]的数据采集系统; (b) Choe等^[40]的系统中信号同步过程; (c) Daniels等^[41]的数据采集系统; (d) Daniels等的系统中数据采集的时间序列; (e)频闪技术中样品所施加电场与时间的关系, 以及相关衍射强度随电场变化趋势^[40]

Figure 2. (a) Data acquisition system by Choe et al.^[40]; (b) signal synchronization process in the system of Choe et al.^[40]; (c) data acquisition system by Daniels et al.^[41]; (d) timing sequences for data acquisition processes in the system of Daniels et al.; (e) time dependence of the AC electric field and the collected intensity of diffraction wings, showing the field-induced intensity exchange between the two wings^[40]. (a) (b) (e) Copyright © 2017 International Union of Crystallography. Reproduced with permission of the International Union of Crystallography.

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图 3 NBT单晶{00h}衍射峰X-ray衍射峰强度　(a) {002}衍射峰的静态ω-2θ二维衍射图像; (b)外加电场(沿[001]方向)与时间的关系; (c)−(e)使用频闪技术收集到的{004}衍射峰的ω-2θ二维衍射图像, 分别对应不同的时间通道与电场^[33]

Figure 3. Diffraction intensity of the X-ray around the {00h} family of reflections of NBT single crystal: (a) Static ω versus 2θ mesh of the {002} reflections family; (b) the time-dependence of the applied external electric field (along [001]); (c)−(e) stroboscopically collected versus 2θ meshes of the {004} family of reflections, corresponding to different time channels and electric fields^[33]

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图 4 NBT单晶中不同{hkl}_pc衍射峰的ω-2θ二维衍射图像, 其中从上到下的白线表示三方相, 单斜相C_c和三方-四方混合相可能的分峰$ 2\theta $位置　 (a) {222}; (b) {114}^[46]

Figure 4. Two ω versus 2θ maps for different {hkl}_pc of NBT single crystal collected on the high-resolution diffractometer. The lines indicate the simulated position of the scattering angle: from top to bottom, rhombohedral, monoclinic, and a combination of rhombohedral and tetragonal: (a) {222}; (b) {114}^[46] (Copyright © 2010 International Union of Crystallography. Reproduced with permission of the International Union of Crystallography)

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图 5 时间分辨高能X射线衍射装置以及德拜环不同区域分别对应晶粒方向与电场不同夹角的衍射图谱^[49]

Figure 5. Experimental set-up for time-resolved high-energy X-ray diffraction. Different sections in the Debye ring correspond to grains with specific angles respect to the applied E field^[49] (Copyright © 2011 John Wiley and Sons).

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图 6 La掺杂PZT陶瓷中002畴体积分数与电场不同夹角的关系(底图分别显示与电场呈0°与90°条件下(002)与(200)衍射峰体积分数的变化)^[49]

Figure 6. η₀₀₂ as a function of the field amplitude as well as orientation with respect to the direction of applied field, for an unpoled La-doped tetragonal PZT ceramic under the application of static electric fields. The measured and fitted (002)-type diffraction peaks corresponding to the particular values of η₀₀₂ (marked by circles and indicated by arrows) are shown in the bottom section of the figure. For the fitted diffraction patterns, the deconvoluted (200) and (002) peaks are shown in black solid lines. The integration of individual (002) and (200) peaks are terminated beyond the peak position of the adjacent peak, as indicated by the color-shaded areas^[49] (Copyright © 2011 John Wiley and Sons).

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图 7 NBT-BT陶瓷在施加最大电场E_max = 4 kV/mm下的实验(a)和模拟(b)所得的取向相关衍射图样^[60]

Figure 7. Measured (a) and modelled (b) orientation dependent diffraction patterns of NBT-BT at maximum field E_max = 4 kV/mm^[60] (Copyright © 2015 AIP Publishing).

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图 8 La掺杂的PbZr_0.52Ti_0.48O₃陶瓷中晶格应变与畴壁运动对宏观压电常数及非线性压电常数的贡献^[49]

Figure 8. Contributions of lattice strain and domain wall motion to macroscopic piezoelectric coefficient and non-linear piezoelectric coefficient in La-doped PbZr_0.52Ti_0.48O₃ ceramics^[49] (Copyright © 2011 John Wiley and Sons)

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图 9 (1–x)(K_1–yNa_y)(Nb_1–zSb_z)O₃-xBi_0.5(Na_1–wK_w)_0.5HfO₃ (x = 0.035, y = 0.52, z = 0.05, w = 0.18)陶瓷　(a), (b) (100)和(220)衍射峰随电场的演变过程; (c) (100)和(220)衍射峰中低角度衍射峰与高角度衍射峰的强度之比(I₁/I₂)随电场的变化^[64]

Figure 9. (1–x)(K_1–yNa_y)(Nb_1–zSb_z)O₃-xBi_0.5(Na_1–wK_w)_0.5HfO₃ ceramic with x = 0.035, y = 0.52, z = 0.05 and w = 0.18: (a), (b) Evolution of the (100) and (220) pseudocubic reflections as a function of the electric field; (c) ratio of low angle peak intensity to high angle intensity (I₁/I₂) for (100) and (220) pseudocubic reflections as a function of the electric field^[64] (Copyright © 2017 The Royal Society of Chemistry)

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图 10 NN-BT陶瓷{200}衍射峰在电场作用下的重新分布现象^[68]

Figure 10. {200} reflections and their redistributions under electric field for NN-BT^[68] (Copyright © 2017 AIP Publishing)

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图 11 (a) {111}衍射峰的衍射强度(沿YZ方向积分)与X的关系曲线, 垂直的红蓝线分别对应$ {E}_{+}\backslash {E}_{-} $状态下的质心位置; (b), (c)沿不同X范围积分的二维衍射强度分布图, 分别对应图(a)中的Group 1和Group 2; (d), (e)一个YZ Box范围内积分的衍射强度与X的关系曲线, 其中(d), (e)分别对应Group 1中的Box 2和Group 2中的Box 2 ^[70]

Figure 11. (a) The X dependence of the diffraction intensity around {111} reflections, integrated within the full YZ range. The vertical red and blue lines mark the center of mass positions corresponding to the E₊ and ${E_ - } $ states. (b), (c) YZ dependence of the diffraction intensity integrated within two ranges of X, corresponding to Group 1 and Group 2 in panel (a). Several boxes are marked to show the positions of Bragg peak sub-components. (d), (e) Integrated intensities within one YZ box against X under four states of field. (d) Corresponds to Box 2 in Group 1 and (e) to Box 2 in Group 2^[70] (Copyright © 2018 International Union of Crystallography. Reproduced with permission of the International Union of Crystallography)

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图 12 三方相-四方相相变中可能的极化矢量旋转路径^[18,76]

Figure 12. The two possible paths for the polarization direction to change from [111] in the rhombohedral (R) phase to [001] in the tetragonal (T) phase^[18,76] (Copyright © 2001 American Physical Society)

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图 13 KNN基陶瓷中的三方相-单斜相-正交相的极化旋转路径

Figure 13. Polarization rotation path of rhombohedral-monoclinic-orthorhombic phase in KNN-based ceramic

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图 14 对于0.94NBT-0.06BT陶瓷　(a) 在25, 50, 75和100 ℃下的单极电场-应变曲线; (b) 可恢复应变(S_max – S_rem)的温度依赖关系 ^[80]

Figure 14. For 0.94NBT-0.06BT ceramic, (a) unipolar strain hysteresis at 25, 50, 75, and 100 ℃; (b) temperature-dependence of recoverable strain (S_max – S_rem)^[80] (Copyright © 2013 AIP Publishing)

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图 15 对BF-0.3 BT-0.03 NLN陶瓷在 ± 60 kV/cm的电场下进行了两个电场循环观察到的{111}, {200}和{220}峰的等高线图 (a)平行电场方向; (b)垂直电场方向^[82]

Figure 15. Contour plots of the {111}, {200} and {220} peak profiles for (a) $ \beta $ = 0° and (b) $ \beta $ = 90° obtained from the in situ X-ray diffraction experiment for BF-0.3 BT-0.03 NLN, with two cycles of electric field poling under ± 60 kV/cm^[82] (Copyright © 2019 The Royal Society of Chemistry)

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