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一、内容简介

     自2002年以来,共发表国际学术论文60余篇;论文内容主要涉及:①在铁电材料非线性行为方面,发现了均匀电致蠕变现象,电畴翻转引起裂纹/电极尖端的声发射,裂纹/电极/孔洞/缺陷的非均匀电致蠕变及其电畴成核,长大和聚合等物理新现象,并给出了材料在单向应变状态(均匀蠕变)和复杂应变状态(非均匀蠕变)下服从相同的动力学演化方程;②在生物材料和细胞的电化学传感器检测应用方面,发现了人牙的釉质-牙本质界面的纳米微结构导致的负热阻的物理新现象。③基于生物材料特异性显色效应的电化学传感器设计;④铁电材料的非线性介电的瑞利效应,电卡和热卡等效应及其储能应用。截至2018年为止在国际期刊上发表的SCI论文36篇,在Web of Science核心合集中共被引用595次,单篇最高被引66次;SCI期刊JCR影响因子最高达9.518。其中,铁电材料的电致蠕变行为研究领域为国内外首创,是铁电材料的电致蠕变行为研究的奠基之作,为内变量理论在多场耦合下的时效应/率效应研究提供了实验和理论解决方案。部分成果获得2015年陕西科学技术奖一等奖2014年陕西高等学校科学技术一等奖(第三完成人)。

 

    在教学方面,主持教改项目《大数据时代下材料力学开放实验与学生动手能力的评价体系建设》, 项目编号:1619Y, 2016年;发表教改论文3篇; 获得了全国第六届基础力学青年教师讲课比赛优胜奖(2016);指导学生完成的《云智能珠宝管理系统》项目,获得了西安交通大学第四届"互联网+"创新创业大赛银奖(第一参与人,2016)和西安交通大学第四届"互联网+"创新创业大赛银奖(第一参与人,2017);该项目于2017年实现了在深圳落地,详情请见第12届RFID世界应用创新大会——特邀报告《云智能珠宝管理系统》

 

二、代表性论文(铁电材料在宏观和电畴尺度下的电致蠕变行为及其实验表征方法和模型构建)

  1. Liu Qd,Chen Yh. Experimental Observation and Measurement for Domain Switching Emission Wave and its Average Velocity Emitted from the Near Tip Zone of a Static Crack in PLZT. EXPERIMENTAL MECHANICS, 2012, 52(6): 619-627.
  2. Liu Qd,Huber Je. Electrical creep around a circular hole in PLZT 8/65/35. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2012, 32(1): 195-202.
  3. Liu Qd,Huber Je. Electrical creep induced ferroelectric domain wall motion in BaTiO3 single crystal. APPLIED PHYSICS LETTERS, 2011, 99(25290325).
  4. Liu Qd,Fleck Na,Huber Je,Chu Dp. Birefringence measurements of creep near an electrode tip in transparent PLZT. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2009, 29(11): 2289-2296.
  5. Liu Qd,Huber Je. State dependent linear moduli in ferroelectrics. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2007, 44(17): 5635-5650.
  6. Liu Qd,Huber Je. Creep in ferroelectrics due to unipolar electrical loading. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2006, 26(13): 2799-2806.

 

 

三、国际期刊论文发表情况

  1. Shi P.,  et al.  Tailoring ferroelectric polarization and relaxation of BNT-based lead-free relaxors for superior energy storage properties. Chemical Engineering Journal, Vol. 428, 2022. Accession Number: WOS:000727799800005 DOI: 10.1016/j.cej.2021.132612.
  2. Yuan Y., et al.  Antiferroelectric-ferroelectric phase transition and negative electrocaloric effect in alkaline-earth element doped PbZrO3 thin films. Journal of Alloys and Compounds, Vol. 899, 2022. Accession Number: WOS:000749614600005 DOI: 10.1016/j.jallcom.2021.163165.
  3. Shi P, et al.  Enhancement of energy storage properties of Bi0.5Na0.5TiO3-based relaxor ferroelectric under moderate electric field. APPLIED PHYSICS LETTERS 120 (13), 2022. DOI:  https://doi.org/10.1063/5.0086042.
  4. Gao YF, et al. Grain size modulated (Na0.5Bi0.5)(0.65)Sr0.35TiO3-based ceramics with enhanced energy storage properties. CHEMICAL ENGINEERING JOURNAl, Vol. 433(2), 2022. DOI:  https://doi.org/10.1016/j.cej.2021.133584.
  5. Yang B., et al.  Insights into the tribo-/pyro-catalysis using Sr-doped BaTiO3 ferroelectric nanocrystals for efficient water remediation [J]. Chemical Engineering Journal 416, 128986, 2021. doi: https://doi.org/10.1016/j.cej.2021.128986 
  6. Guo X.D., Shi P. , Lou X.J., Liu Q.D. and Zuo H.  Superior energy storage properties in (1-x)(0.65Bi0.5Na0.5TiO3-0.35Bi0.2Sr0.7TiO3)-xCaZrO3 ceramics with excellent temperature stability [J]. Journal of Alloys and Compounds 2021 (876). doi: https://doi.org/10.1016/j.jallcom.2021.160101
  7. Zhu, X., et al.  Enhanced energy storage density of Sr0.7BixTiO3 lead-free relaxor ceramics via A-site defect and grain size tuning [J]. Chemical Engineering Journal. Vol. 420, 2021. doi: https://doi.org/10.1016/j.cej.2021.129808
  8. Shi P., et al. Significantly enhanced energy storage properties of Nd3+ doped AgNbO3 lead-free antiferroelectric ceramics [J]. Journal of Alloys and Compounds. Vol. 877, 2021(160162). doi: https://doi.org/10.1016/j.jallcom.2021.160162
  9. Zhu X.P.,  et al. Enhanced energy storage density of Sr0.7BixTiO3 lead-free relaxor ceramics via A-site defect and grain size tuning [J]. Chemical Engineering Journal. Vol. 420 (1), 129808, 2021. doi: https://doi.org/10.1016/j.cej.2021.129808
  10. Li S.Y., et al.  Enhanced energy storage properties in lead-free NaNbO3–Sr0.7Bi0.2TiO3–BaSnO3 ternary ceramic [J]. Journal of Materials Science, Vol. 56(1), 2021. doi: https://doi.org/10.1007/s10853-021-06075-x
  11. Shi P., et al.  Bi0.5Na0.5TiO3-based lead-free ceramics with superior energy storage properties at high temperatures [J]. Composites Part B Engineering, Vol.  215, (108815), 2021. doi: https://doi.org/10.1016/j.compositesb.2021.108815
  12. Shi P, Li TY, Lou, XJ, Yu ZH, Zhu XP, Zhou C, Liu QD, He LQ, Zhang XX, Yang S. Large electric-field-induced strain and energy storage properties in Bi0.5Na0.5TiO3-(0.5Ba0.7Ca0.3TiO3-0.5BaTi0.8Zr0.2O3) lead-free relaxor ferroelectric ceramics [J]. JOURNAL OF ALLOYS AND COMPOUNDS. Vol. 860, Issue 15, (158369), 2021. doi: https://doi.org/10.1016/j.jallcom.2020.158369
  13. Zhang YB, Liu QD, Hou JL, Jaubert JJ, Yu YJ, Jaubert JN, et al. Experimental study on micro-crack initiation in photovoltaic polycrystalline silicon wafer [J]. MATERIALS SCIENCE IN SEMICONDUCTOR PROCESSING.  Volume 123, (105539), 2021. doi: https://doi.org/10.1016/j.mssp.2020.105539
  14. Gao Y., et al. Grain size modulated (Na0.5Bi0.5)0.65Sr0.35TiO3-based ceramics with enhanced energy storage properties. Chemical Engineering Journal 433(47):133584, 2021. DOI: https://doi.org/10.1016/j.cej.2021.133584
  15. Zhang BY, Lou, XJ, Zheng K, Xie XF, Shi P, Guo MY, Zhu XP, Gao YF, Liu, QD, Kang RR. Enhanced electrocaloric effect in the Sm and Hf co-doped BaTiO3 ceramics [J]. CERAMICS INTERNATIONAL (2021), Vol. 47 Issue 1 Pages 1101-1108. doi: Accession Number: WOS:000589662900001 DOI: https://doi.org/10.1016/j.ceramint.2020.08.226
  16. Guo MY, Sun BW, Wu M, Sun HN, Zhang L, Liu QD, Wang DY, Lou, XJ. Effect of polarization fatigue on the electrocaloric effect of relaxor Pb0.92La0.08Zr0.65Ti0.35O3 thin film [J]. APPLIED PHYSICS LETTERS, 2020 Vol. 117 Issue 20. Accession Number: WOS:000595261700001 DOI:  https://doi.org/10.1063/5.0018741
  17. Yang, BA; Chen, HB; Guo, XD; Wang, L; Xu, T; Bian, JH; Yang, YD; Liu, QD; Du, YP; Lou, XJ. Enhanced tribocatalytic degradation using piezoelectric CdS nanowires for efficient water remediation [J]. JOURNAL OF MATERIALS CHEMISTRY, 2020 Vol. 8 Issue 42 Pages 14845-14854. Accession Number: WOS:000586316600018 DOI: https://doi.org/10.1039/d0tc03519j
  18. Zhu X, Shi P, Lou X, Gao Y, Guo X, Sun H, Liu Q, Ren Z, Remarkably enhanced energy storage properties of lead-free Ba0.53Sr0.47TiO3 thin films capacitors by optimizing bottom electrode thickness [J]. JOURNAL THE EUROPEAN CERAMICS SOCIETY (2020), doi: https://doi.org/10.1016/j.jeurceramsoc.2020.06.038
  19. Ma Z, Li G, Sun BW, He LQ, Gao WW, Sun QZ, Liu QD, Lou XJ. Enhanced electric-field-induced strain in 0.7Bi(1-x)SmxFeO3-0.3BaTiO3 lead-free ceramics[J]. Journal of Materials Science, 2020, 55(6): 1–11. https://doi.org/10.1007/s10853-020-04613-7
  20. Sun HN, Wang XJ, Sun QZ, Zhang XX, Ma Z, Guo MY, Sun BW, Zhu XP, Liu QD, Lou XJ. Large energy storage density in BiFeO3-BaTiO3-AgNbO3 lead-free relaxor ceramics [J]. JOURNAL THE EUROPEAN CERAMICS SOCIETY, 2020, 40(8): 2929-2935. https://doi.org/10.1016/j.jeurceramsoc.2020.03.012
  21. Zhu XP, Guo MY, Sun BW, Shi P, Wu M, Ma Z, Gao YF, Sun HN, Zhang BY, Liu QD(*CA), Lou XJ. Significantly enhanced energy storage density of epitaxial Ba0. 53Sr0. 47TiO3 thin films by optimizing bottom electrode material[J]. CERAMICS INTERNATIONAL, Vol 46(9), 13900-1390615, 2020. https://doi.org/10.1016/j.ceramint.2020.02.184
  22. Pan Suxin, Li Qun, Liu Qida. Ferroelectric creep associated with domain switching emission in the cracked ferroelectrics[J]. COMPUTATIONAL MATERIALS SCIENCE, 2017, 140: 244-252. https://doi.org/10.1016/j.commatsci.2017.08.048
  23. Wang Rong,Niu Lin,Li Qun,Liu Qida,Zuo Hong. The peritubular reinforcement effect of porous dentine microstructure[J]. PLOS ONE, 2017, 12(8):1-15. https://doi.org/10.1371/journal.pone.0183982
  24.  Zou Rui,Zhou Qin, Liu Qida,Li Quanli,Chen Zhiqing,Niu Lin. Temperature Affects the Hydroxyapatite Crystal Arrangement on Silk Fibroin Surfaces[J]. POLYMERS & POLYMER COMPOSITES, 2017, 25(9): 689-694. https://doi.org/10.1177/096739111702500907
  25. Niu Lin, Dong Shao-jie, Kong Ting-ting, Wang Rong, Zou Rui, Liu Qi-da. Heat Transfer Behavior across the Dentino-Enamel Junction in the Human Tooth[J]. PLOS ONE, 2016, 11(9):1-14. https://doi.org/10.1371/journal.pone.0158233
  26.  Li Qun, Pan Suxin, Liu Qida, Wang Jie. Domain switching emission from the mixed-mode crack in ferroelectrics by birefringence measurement and phase field modeling[J]. SMART MATERIALS AND STRUCTURES, 2016, 25(07LT017). https://doi.org/10.1088%2F0964-1726%2F25%2F7%2F07lt01
  27.  Wang Xianhui, Yang Hao, Liang Shuhua, Liu Mabao, Liu Qida. Effect of TiB2 Particle Size on Erosion Behavior of Ag-4wt% TiB2 Composite[J]. RARE METAL MATERIALS AND ENGINEERING, 2015, 44(11): 2612-2617. https://doi.org/10.1016/S1875-5372(16)60004-8
  28.  Geng Wenping, Liu Yang, Lou Xiaojie, Zhang Fuping, Liu Qida, Dkhil Brahim, Zhang Ming, Ren Xiaobing, He Hongliang, Jiang Anquan. Polarization fatigue in antiferroelectric (Pb,La)(Zr,Ti)O3 thin films: The role of the effective strength of driving waveform[J]. CERAMICS INTERNATIONAL, 2015, 411: S289-S295. https://doi.org/10.1016/j.ceramint.2015.03.265
  29.  Li Wei,Xin Lipeng,Xu Xin, Liu Qida,Zhang Ming,Ding Shujiang,Zhao Mingshu,Lou Xiaojie. Facile synthesis of three-dimensional structured carbon fiber-NiCo2O4-Ni(OH)2 high-performance electrode for pseudocapacitors[J]. SCIENTIFIC REPORTS, 2015, 5(9277). https://doi.org/10.1038/srep09277
  30.  Lou Xj,Zhang Hj,Luo Zd,Zhang Fp,Liu Y,Liu Qd,Fang Ap,Dkhil B,Zhang M,Ren Xb,He Hl. Effect of polarization fatigue on the Rayleigh coefficients of ferroelectric lead zirconate titanate thin films: Experimental evidence and implications[J]. APPLIED PHYSICS LETTERS, 2014, 105(10290710). https://doi.org/10.1063/1.4895616
  31.  Luo Zhengdong, Lou Xiaojie, Zhang Fuping, Liu Yang, Chang Dingding, Liu Chenqi, Liu Qida, Dkhil Brahim, Zhang Ming, Ren Xiaobing, He Hongliang. Rayleigh-like nonlinear dielectric response and its evolution during electrical fatigue in antiferroelectric (Pb,La)(Zr,Ti)O3 thin film[J]. APPLIED PHYSICS LETTERS, 2014, 104(14290414). https://doi.org/10.1063/1.4870992
  32.  Liu Qd, Chen Yh. Experimental Observation and Measurement for Domain Switching Emission Wave and its Average Velocity Emitted from the Near Tip Zone of a Static Crack in PLZT[J]. EXPERIMENTAL MECHANICS, 2012, 52(6): 619-627. https://doi.org/10.1007/s11340-011-9527-7
  33.  Liu Qd, Wang Xh, Liu Mb. Inhomogeneous Creep of Polarization and Strain Around a Circular Hole in Ferroelectrics Under Electric Field: Experiments and Modeling[J]. FERROELECTRICS LETTERS SECTION, 2012, 39(1-3): 8-14. https://doi.org/10.1080/07315171.2012.707023
  34.  Lin Zhenyu, Chen Lifen, Zhang Guiyun, Liu Qida, Qiu Bin, Cai Zongwei, Chen Guonan. Label-free aptamer-based electrochemical impedance biosensor for 17 beta-estradiol[J]. ANALYST, 2012, 137(4): 819-822. https://doi.org/10.1039/c1an15856b
  35.  Liu Qd, Huber Je. Electrical creep around a circular hole in PLZT 8/65/35[J]. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2012, 32(1): 195-202. https://doi.org/10.1016/j.jeurceramsoc.2011.08.008
  36.  Liu Qd, Huber Je. Electrical creep induced ferroelectric domain wall motion in BaTiO3 single crystal[J]. APPLIED PHYSICS LETTERS, 2011, 99(25290325). https://doi.org/10.1063/1.3671327
  37.  Qiu Suyan, Xie Lidan, Gao Sen, Liu Qida, Lin Zhenyu, Qiu Bin, Chen Guonan. Determination of copper(II) in the dairy product by an electrochemical sensor based on click chemistry[J]. ANALYTICA CHIMICA ACTA, 2011, 707(1): 57-61. https://doi.org/10.1016/j.aca.2011.09.013
  38.  Liu Qd. Huber Je. Investigation into the creeping polarization and strain in PZT-855 under combined mechanical and electrical loadings[J]. ACTA MECHANICA, 2011, 220(1-4): 1-14. https://doi.org/10.1007/s00707-011-0462-6
  39.  Qiu Suyan,Gao Sen,Liu Qida,Lin Zhenyu,Qiu Bin,Chen Guonan. Electrochemical impedance spectroscopy sensor for ascorbic acid based on copper(I) catalyzed click chemistry[J]. BIOSENSORS & BIOELECTRONICS, 2011, 26(11): 4326-4330.  https://doi.org/10.1016/j.bios.2011.04.029
  40.  Zhu Xi,Zhang Yashan,Yang Weiqiang,Liu Qida,Lin Zhenyu,Qiu Bin,Chen Guonan. Highly sensitive electrochemiluminescent biosensor for adenosine based on structure-switching of aptamer[J]. ANALYTICA CHIMICA ACTA, 2011, 684(1-2): 121-125. https://doi.org/10.1016/j.aca.2010.10.038
  41.  Qiu Suyan,Gao Sen,Xie Lidan,Chen Hongqin,Liu Qida,Lin Zhenyu,Qiu Bin,Chen Guonan. An ultra-sensitive electrochemical sensor for ascorbic acid based on click chemistry[J]. ANALYST, 2011, 136(19): 3962-3966. https://doi.org/10.1039/c1an15316a
  42.  Yang Weiqiang,Zhu Xi, Liu Qida, Lin Zhenyu,Qiu Bin,Chen Guonan. Label-free detection of telomerase activity in HeLa cells using electrochemical impedance spectroscopy[J]. CHEMICAL COMMUNICATIONS, 2011, 47(11): 3129-3131. https://doi.org/10.1039/c0cc05230b
  43.  Zhu Xi,Gao Xiaoyao,Liu Qida,Lin Zhenyu,Qiu Bin,Chen Guonan. Pb2+-introduced activation of horseradish peroxidase (HRP)-mimicking DNAzyme[J]. CHEMICAL COMMUNICATIONS, 2011, 47(26): 7437-7439. https://doi.org/10.1039/C1CC11349F
  44.  Lin Zhenyu,Luo Fang,Liu Qida,Chen Lifen,Qiu Bin,Cai Zongwei,Chen Guonan. Signal-on electrochemiluminescent biosensor for ATP based on the recombination of aptamer chip[J]. CHEMICAL COMMUNICATIONS, 2011, 47(28): 8064-8066. https://doi.org/10.1039/C1CC12080H
  45.  Lin Zhenyu,Yang Weiqiang,Zhang Guiyun,Liu Qida,Qiu Bin,Cai Zongwei,Chen Guonan. An ultrasensitive colorimeter assay strategy for p53 mutation assisted by nicking endonuclease signal amplification[J]. CHEMICAL COMMUNICATIONS, 2011, 47(32): 9069-9071. https://doi.org/10.1039/c1cc13146j
  46.  Zhu Xi,Xu Huifeng,Gao Xiaoyao,Li Xianghui,Liu Qida,Lin Zhenyu,Qiu Bin,Chen Guonan. Design of a DNA electronic logic gate (INHIBIT gate) with an assaying application for Ag+ and cysteine[J]. CHEMICAL COMMUNICATIONS, 2011, 47(32): 9080-9082. https://doi.org/10.1039/C1CC12734A
  47.  Lin M, Liu Qd, Kim T, Xu F, Bai Bf, Lu Tj. A new method for characterization of thermal properties of human enamel and dentine: Influence of microstructure[J]. INFRARED PHYSICS & TECHNOLOGY, 2010, 53(6): 457-463. https://doi.org/10.1016/j.infrared.2010.09.004
  48.  Niu Lin, Zou Rui, Liu Qida, Li Quanli, Chen Xinmin,Chen Zhiqing. A Novel Nanocomposite Particle of Hydroxyapatite and Silk Fibroin: Biomimetic Synthesis and Its Biocompatibility[J]. JOURNAL OF NANOMATERIALS, 2010(729457). https://doi.org/10.1155/2010/729457
  49.  Liu Qd,Fleck Na,Huber Je,Chu Dp. Birefringence measurements of creep near an electrode tip in transparent PLZT[J]. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2009, 29(11): 2289-2296. https://doi.org/10.1016/j.jeurceramsoc.2009.01.008
  50.  Liu Qd,Huber Je. State dependent linear moduli in ferroelectrics[J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2007, 44(17): 5635-5650. https://doi.org/10.1016/j.ijsolstr.2007.01.014
  51.  Liu Qd,Huber Je. Creep in ferroelectrics due to unipolar electrical loading[J]. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2006, 26(13): 2799-2806. https://doi.org/10.1016/j.jeurceramsoc.2005.07.051
  52. Liu Qd, Chen Yh. Application of path-independent integral to cracked piezoelectric materials[B]. BOOK SECTION in "Mechanics of Electromagnetic Material Systems and Structures", Edited by Y. Shindo, WIT press, Southampton, Boston, 2003. ISBN: 978-1-85312-920-9, Pages 137-152.
  53.  Liu Qd. On J(k)-integral vector for bi-piezoelectric materials[J]. INTERNATIONAL JOURNAL OF FRACTURE, 2002, 118(4): 83-88.  https://link.springer.com/article/10.1023/A%3A1023364907804 
  54.  Liu Qd,Chen Yh. Energy analysis for permeable and impermeable cracks in piezoelectric materials[J]. INTERNATIONAL JOURNAL OF FRACTURE, 2002, 116(1): L15-L20. https://doi.org/10.1023/A:1022606212516

 

四、国际会议论文发表情况

 

1. Liu Mb,Wang Xh, Liu Qd,Gao H, Application of smart coating sensor in crack detection for aircraft, in Applied Mechanics and Materials. 2012. p. 554. DOI: https://www.scientific.net/AMM.152-154.554

2. Liu Mb, Liu Qd,Wang Xh,Gao H, Environmental Effect on Fatigue Properties of Die-cast Magnesium Alloys, in Applied Mechanics and Materials. 2012. p. 548. DOI: https://www.scientific.net/AMM.152-154.548

3. Liu Qd, Time Dependent Polarization and Strain Evolution Around A Circular Hole In Ferroelectrics, in Proceedings of the ASME Conference on Smart Materials Adaptive Structures and Intelligent Systems. 2012. p. 47-51. DOI: https://doi.org/10.1115/SMASIS2012-7949.

4. Lin M, Liu Qd, Xu F, Bai Bf, Lu Tj, In Vitro investigation of heat transfer in human tooth, in Proceedings of SPIE,Volume 7522, Fourth International Conference on Experimental Mechanics; 75222N (2010) DOI: https://doi.org/10.1117/12.851623.

5. Liu Qd, Huber Je, Measurement of strain and polarization concentration field around an electrode tip in PLZT8/65/35, in JSAEM STUDIES IN APPLIED ELECTROMAGNETICS AND MECHANICS, Z.M. Chen, J. Jiang and X. Ma, Z.M. Chen, J. Jiang and X. Ma Editors. 2009. p. 329.

6. Liu Qd, Huber Je, Inhomogeneous creep fields in PLZT: an experimental study. Proc. SPIE. 6929, Behavior and Mechanics of Multifunctional and Composite Materials 2008.  DOI: https://doi.org/10.1117/12.774385.

7. Liu Qd, Huber Je, Creeping polarization and remanent strain in ferroelectrics under uniaxial electromechanical loading. Proc. SPIE. 6526, Behavior and Mechanics of Multifunctional and Composite Materials 2007. DOI: https://doi.org/10.1117/12.713608.

8. Liu Qd, Huber Je, Evolution of elastic, dielectric, and piezoelectric coefficients of PZT under electro-mechanical loading. Proc. SPIE. 6526, Behavior and Mechanics of Multifunctional and Composite Materials 2007. DOI: https://doi.org/10.1117/12.713606.

9. Liu Qd, Huber Je, Time dependent evolution of polarization in PZT. Proc. SPIE. 6170, Smart Structures and Materials 2006: Active Materials: Behavior and Mechanics. DOI: https://doi.org/10.1117/12.657405.