MAE438-538 Notes electrostrictive behavior

MAE438-538 Notes electrostrictive behavior - University at...

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University at Buffalo Department of Mechanical and Aerospace Engineering MAE 438/538 Prof. D.D.L. Chung April 8, 2003 Electrostrictive behavior Electrostrictive behavior (or electrostriction) is a phenomenon in which the dimension changes in response to an applied electric field, due to the energy increase associated with the polarization induced by the electric field in the material. The polarization may be due to atoms becoming egg-shaped rather than spheres, bonds between ions changing in length, or orientation of the permanent electric dipoles in the material. An electrostrictive material is centrosymmetrical in crystal structure, in contrast to piezoelectric or ferroelectric materials, which are noncentrosymmetrical. The dimensional changes can be in all directions, in contrast to the directional dimensional change in piezoelectricity or ferroelectricity. Also in contrast to piezoelectric or ferroelectric behavior, no voltage of field is created by electrostriction and an applied stress does not cause an electric field (i.e., no converse effect). Thus, electrostriction can be used for actuation, but not sensing. Electrostriction is a second-order effect, i.e., the strain is proportional to the square of the electric field, or S = M 2 (1) where S is the strain, is the electric field and M is the electrostrictive coefficient. The second-order effect is due to the anharmonicity of the “springs” that connect the adjacent ions. The anharmonicity is associated with an asymmetric potential well (Fig. 1), so that a spring tends to extend more easily than contracting. Thus, upon increase in energy, the average bond distance increases. In contrast, piezoelectricity or ferroelectricity is a first order effect. The strain due to electrostriction is small compared to that due to piezoelectricity or ferroelectricity. For example, a field of 10 4 V/m produces 23 nm per meter in quartz, but electrostrictive glass produces only 1 nm per meter. However, electrostrictive materials exhibit essentially no hysteresis upon cycling the electric field, whereas piezoelectric/ferroelectric materials exhibit hysteresis due to non-linearity between strain and electric field at high fields (> 100 V/mm), as shown in Fig. 2. The most important electrostrictive materials are ceramics based on Pb(Mg 1/3 Nb 2/3 )O 3 , i.e., PMN or lead magnesium niobate, which exhibits strains as high as 0.1% (i.e., 10 ? m per centimeter) at moderate fields ( 10 6 V/m). The phenomenon is called giant electrostriction. These materials are also relaxor ferroelectrics. They are ferroelectrics below the Curie temperature, but electrostrictive above the Curie temperature. No poling treatment is needed for electrostrictive materials and these materials do not age (depole). Example problem
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This note was uploaded on 07/09/2011 for the course MAE 438 taught by Professor Chung during the Spring '09 term at SUNY Buffalo.

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MAE438-538 Notes electrostrictive behavior - University at...

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