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Complete electromechanical tensors of PMN-PT

The full set of mechanical compliances, dielectric permittivities and piezoelectric charge coefficients of Mn doped 0.65Pb(Mg1/3Nb2/3) O3-0.35PbTiO3 (0.65PMN-0.35PT:Mn) at the morphotropic phase boundary (MPB) has been obtained in complex form. A method based on the use of four piezoelectric resonances for three sample geometries has been used.

These are length resonance of a bar poled and excited along its length, shear resonance of a plate poled across and excited along its thickness, thickness resonance of a disk poled and excited along its thickness and radial resonance of a disk poled and excited along its thickness. The procedure provides the real and imaginary parts of the coefficients, and therefore the different losses. Piezoelectric losses are responsible for heat generation and hysteresis in actuators. Bars and discs presented well defined single piezoelectric length, thickness and radial resonances, respectively, from which a number of coefficients was obtained.

Plates presented double piezoelectric shear resonances. The methods of analysis of this resonance were modified for addressing these double resonances. Their physical origin was investigated and found to be associated with the presence of a perovskite phase gradient (tetragonal and rhombohedral) across the thickness of the plates originated during (side) poling. This gradient seems to be characteristic of the composition. The resonance associated with the well poled material was identified and analysed for obtaining the rest of coefficients.

The full set is: s11E=13.5-i0.04 x10-12 m2 N-1, s12E=-4.8+i0.02 x10-12 m2 N-1, s13E=-5.6+i0.08 x10-12 m2 N-1, s33E=14.6-i0.14 x10-12 m2 N-1, s55E=31.0-i0.63 x10-12 m2 N-1, e11T=(3740-i38) eo, e33T=(4047-i41) eo, d33=488-i7 x10-12 C N-1, d31=-219+i2 x10-12 C N-1 and d15=554-i22 x10-12 C N-1.

A number of coefficients were also obtained as a function of temperature up to 100oC. The set of coefficients for MPB PMN-PT:Mn can be compared with those of a Navy type II PZT based piezoelectric ceramic, which have been reported together with the description of the method (M. Algueró, C. Alemany, L. Pardo and A.M. González, “Method for obtaining the full set of linear electric, mechanical and electromechanical coefficients and all related losses of a piezoelectric ceramic”. Journal of the American Ceramic Society 87 209-215 (2004)).

Results for MPB PMN-PT:Mn have already been partially published ((M. Algueró, B. Jiménez, C. Alemany and L. Pardo, “Temperature dependence of the electrical, mechanical and electromechanical properties of high sensitivity novel piezoceramics”. Boletín de la Sociedad Española de Cerámica y Vidrio 43:2 540-543 (2004)), and a second article enclosing the complete results have been submitted to to Journal of the American Ceramic Society (M. Algueró, C. Alemany, L. Pardo and M. Pham-Thi, “Piezoelectric resonances, linear coefficients and losses of morphotropic phase boundary Pb(Mg1/3Nb2/3)O3-PbTiO3 ceramics”).

Full sets of coefficients for the available piezoelectric ceramics are required for exploiting all the possibilities of finite element analysis, both in fundamental research (mechanisms of degradation) and development (element design). This numerical technique is necessary to explore the countless shapes provided by solid free form fabrication technologies.

Reported by

Instituto de Ciencia de Materiales de Madrid - CSIC
28049 Madrid
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