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Piezoelectricity in three‐phase systems: Effect of the boundary phase

 

作者: Hiroyoshi Ueda,   Eiichi Fukada,   Frank E. Karasz,  

 

期刊: Journal of Applied Physics  (AIP Available online 1986)
卷期: Volume 60, issue 8  

页码: 2672-2677

 

ISSN:0021-8979

 

年代: 1986

 

DOI:10.1063/1.337094

 

出版商: AIP

 

数据来源: AIP

 

摘要:

The influence of electrical conductivity on the piezoelectricity of polymers was studied using a three‐phase model. The model consists of a continuous nonpiezoelectric phase (phase 1) surrounding a spherical piezoelectric phase (phase 2), which is itself bounded by an electrically conductive shell (phase 3). The piezoelectric constants for the system can be expressed asd=d2KPKTande=e2KPKS, whered2ande2are the piezoelectric strain and stress constants of phase 2, respectively, andKPis a function of the dielectric constants of phases 1, 2, and 3.KTandKSare expressed as functions of the elastic constant of each phase. The piezoelectric constantsdandedecrease with decreasing elastic constant of phase 3 and with increasing dielectric constant of phase 3. The three‐phase system shows a Maxwell–Wagner piezoelectric relaxation with a relaxation time given by &tgr;=(2&egr;1+&egr;2+&eegr;&egr;3)/(2&sgr;1+&sgr;2+&eegr;&sgr;3), where &eegr;=2&dgr;/a. In these expressions &egr;iand &sgr;iare the dielectric constant and the electrical conductivity of phasei, respectively,ais the radius of the sphere (piezoelectric phase), and &dgr; is the thickness of the electrically conductive shell around the piezoelectric phase. When &tgr;1(=&egr;1/&sgr;1)>&tgr;2[=(&egr;2+&eegr;&egr;3)/(&sgr;2+&eegr;&sgr;3)], the functional dependence ofKPon frequency implies the occurrence of a relaxation process. Conversely, when &tgr;1<&tgr;2, a retardation process is observed.

 

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