Electroelastic equations describing slow hysteresis in polarized ferroelectric ceramic plates

Journal of Applied Physics

Volumn 83, Issue 11, 1998, Pages 6126-6139

  Huang, L ^a,b   Tiersten, H F ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b TEXAS INSTRUMENTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442670027     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.367482     Document Type: Article

References (21)

1. H. F. Tiersten, Int. J. Eng. Sci. 9, 587 (1971).
2. J. C. Baumhauer and H. F. Tiersten, J. Acoust. Soc. Am. 54, 1017 (1973).
3. E. Fatuzzo and W. J. Merz, Ferroelectricity (Wiley, New York, 1967).
4. B. Jaffe, W. R. Cook, Jr., and H. Jaffe, Piezoelectric Ceramics (Academic, London, 1971).
5. B. D. Coleman and M. Gurtin, J. Chem. Phys. 47, 597 (1967).
6. It would be desirable to have it done at zero frequency, but this is not possible because the material would change temperature from Joule heating, which would cause the coefficients to change drastically.
7. R. A. Toupin, Journal of Rational Mechanics and Analysis 5, 849 (1956).
8. LM. In other works it is stated that measurements verify the symmetry. Alternatively, Coleman's formulation of thermodynamics can be used to demonstrate the symmetry. It should also be noted that if in the four-dimensional vector space the material coefficients arising when (2.36) and (2.37) are substituted in (2.34) are written as a symmetric matrix plus an antisymmetric matrix, the rate of entropy production arising from the quadratic terms containing the antisymmetric matrix vanishes. Since terms of this nature usually arise as gyroscopic terms, which have nothing to do with thermodynamics, it can be argued that such terms should not arise unless there is some well-defined physical reason for their existence, such as superposed magnetic fields or angular momentum.
9. The conditions that arise when a material surface abuts either free space or a conductor, in which case surface charge can arise, are discussed in detail in H. F. Tiersten, J. Acoust. Soc. Am. 57, 660 (1975).
10. 1.
11. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1953), Eq. (7.25).
12. 3 is positive or negative, respectively.
13. This is consistent with our qualitative physical reasoning based on domain switching and would certainly be required for more complicated shapes of hysteresis loops than those considered in this work.
14. IEEE Standard on Piezoelectricity, IEEE Std. 176-1978 (IEEE, New York, 1978), Table 2.
15. 6v (6 mm).
16. A. J. M. Spencer, in Continuum Physics, edited by A. C. Eringen (Academic, New York, 1972), Vol. 1, Part III.
17. H. F. Tiersten, J. Appl. Phys. 74, 3389 (1993).
18. R. D. Mindlin, An Introduction to the Mathematical Theory of the Vibration of Elastic Plates (U.S. Army Signal Corps Engineering Laboratory, Fort Monmouth, New Jersey, 1955), Sec. 6.04.
19. The three-dimensional linear piezoelectric constants are given in Table II. They were calculated from data provided by the manufacturer, American Piezo Ceramics, for PZT type 8-50, which is equivalent to Navy type II or Piezoelectric Products type G-1195. Relations in Eqs. (43) of Ref. 14 were used in the calculation.
20. When actuators are used on the top and bottom of plates and beams in the case of flexure, one polarization loop is always outside the initial saturation polarization-electric-field curve and the other, inside. As the inside loop moves down towards depolarization under repeated operation, the outside loop moves up towards the completely switched condition. Since the distance from the starting saturation loop at zero electric field to the completely switched state is usually less than the distance to the depolarized state, it is likely that the fully switched state is reached in one actuator before the depolarized state is reached in the other. Furthermore, when the hysteretic behavior is caused by the amplitude of the driving voltage employed, if the power can be turned off at an appropriate point in the cycle, the depolarized (or completely switched) state can be avoided for a considerably longer operating period. Since the polarization-electric-field loops must be traversed in a counterclockwise direction, the loops in Fig. 5 indicate that the appropriate point in the cycle is just after the turning points when each loop will return to zero field at a value of polarization nearest the value on the initial saturation polarization-electric-field curve.
21. We used the word loop to refer to a single curve of a loop, which is actually composed of two connected curves, because this terminology is convenient in this context.