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The effects of the dimensional reduction from three-dimensional (3-D) to two-dimensional (2-D) and one-dimensional (1-D) on stiffness/compliance and piezoelectric coefficients are understood by deriving the 2-D and 1-D constitutive equations from the 3-D equations. Two modified coefficients are proposed that have enabled understanding the effects of the dimensional reduction and effects on the design and analysis of sensors and actuators.

The electrocaloric (EC) effect in ferroelectric/antiferroelectric thin films has been widely investigated due to its potential applications in solid state cooling devices. It is demonstrated that the EC effect of the Pb0.78Ba0.2La0.02ZrO3 (PBLZ) relaxor thin films prepared by using a sol–gel method strongly depends on the substrates. The maximum ΔT of PBLZ thin films deposited on Pt(111)/TiOx/SiO2/Si(100) (Pt), LaNiO3/Pt(111)/TiOx/SiO2/Si(100) (LaNiO3/Pt), LaNiO3/n-type GaN (LaNiO3/n-GaN) and LaNiO3/p-type GaN (LaNiO3/p-GaN) substrates is ∼13.08 K, 16.46 K, 18.70 K, and 14.64 K, respectively. Moreover, negative EC effects in a broad temperature range (∼340 K to 440 K) could be obtained in the thin films deposited on LaNiO3/n-GaN and LaNiO3/p-GaN substrates, which is ascribed to higher proportions of orthorhombic antiferroelectric phase to rhombohedral ferroelectric phase induced by the GaN substrates. These results indicate that tailoring the EC effects by changing the substrates could provide a new strategy in designing an EC cooling device with high cooling efficiency. [ABSTRACT FROM AUTHOR]

Accurate performance evaluation is crucial to the design and development of macro/micro-sized piezoelectric devices, and key to this is the proper use of the stiffness/ compliance and piezoelectric coefficients of the piezoelectric ceramics involved. Although the literature points out effective piezoelectric coefficients e(31,f) and d(33,f) for thin film materials and reduced dimensionality of equations for bulk material, the elastic and piezoelectric coefficients remain unchanged from the 3-D equations in most reported 1-D and 2-D analyses of the macro/micro-sized devices involving the e form of the constitutive equations. The use of unchanged coefficients leads to variations between numerically predicted and experimental results in most devices. To understand effects of the dimensional reduction from 3-D to 2-D and 1-D on stiffness/compliance and piezoelectric coefficients, this paper derives the 2-D and 1-D constitutive equations from the 3-D equations, focusing on the discussion of often-required device configurations for sensor and actuator design and analysis. Two modified coefficients are proposed, termed reduced and enhanced, which enable better understanding of effects of the dimensional reduction and also effects on the design and analysis of sensors and actuators.