Journal of Materials Science

, Volume 41, Issue 1, pp 53–63 | Cite as

Flexoelectric effects: Charge separation in insulating solids subjected to elastic strain gradients

  • L. Eric Cross


After a brief historical introduction this article will present a summary of experimental work carried through at Penn State to explore the flexoelectric coefficients μ ijkl in ferroelectric, incipient ferroelectric and relaxor ferroelectric perovskites. The initial objective was to understand the magnitude of flexoelectricity in these systems to see whether it would be possible to develop a piezoelectric composite containing no piezoelectric element, which nonetheless could have practically useful properties. Recent discussions of the thermodynamic converse effect, ie. the generation of elastic strain by an electric field gradient, now suggest that such composites might be designed to have unique properties such as a direct but no converse effect, or vice-versa, and materials with this character could have important practical application. Present data already suggest that the direct effect may make an important contribution to the properties of epitaxial thin films where mismatch can give rise to very steep elastic strain gradients. Clearly, more work is needed to fully quantify the flexoelectric behavior. It will be important to measure single crystals in the ceramic systems which have been studied and to characterize the converse effect as a check of the measured values.


Dielectric Permittivity Barium Titanate Strontium Titanate Barium Strontium Titanate Converse Effect 
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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • L. Eric Cross
    • 1
  1. 1.Evan Pugh Professor Emeritus of Electrical Engineering, The Materials Research InstitutePennsylvania State UniversityUniversity ParkUSA

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