CERAMICS INTERNATIONAL Available online at www.sciencedirect.com Ceramics International ] (]]]]) ]]]–]]] A simple thermal wave method for the evaluation of the polarization state of embedded piezoceramics Gunnar Suchaneck a,n , Agnes Eydam a , Matthias Ru¨ bner b , Matthias Schwankl b , Gerald Gerlach a a Solid State Electronics Lab, TU Dresden–Helmholtzstrasse 18, 01062 Dresden, Germany b Chair of Metals Science and Technology, Friedrich-Alexander-Universit ¨ at Erlangen-Nuremberg-Martensstrasse 5, 91058 Erlangen, Germany Abstract In this work, we demonstrate that the thermal wave method is a promising approach for non-destructive evaluation of polarization state of embedded piezoelectrics in integrated sensor–actuator modules. The embedded piezoceramics are subjected to periodic heating by a square wave-modulated laser array through the top layers. A transient thermal analysis was performed using the finite element modeling package ANSYS. The ANSYS simulation reveals the presence of a transient heating-up period before reaching steady state. Inside the PZT piezoceramics, the thermal excitation becomes nearly sinusoidal and shifted in phase as known for harmonic excitation. At low modulation frequencies, the pyroelectric response of the embedded Pb(Zr,Ti)O 3 plates is governed by thermal losses to the embedding layers. Here, the sample behavior can be described by a harmonically heated piezoelectric plate exhibiting heat losses to the environment characterized by a single thermal relaxation time enabling an estimation of the thermal conductance at the interfaces of the embedded piezoelectric. & 2012 Elsevier Ltd and Techna Group S.r.l. All rights reserved. Keywords: B. Non-destructive evaluation; D. PZT; E. Actuators 1. Introduction Transient methods for the determination of the thermal or pyroelectric properties of thin films by pulse or periodic heating the film have been known for more than 140 years [1–6]. Fouriers law and the law of energy conservation result in a parabolic heat diffusion equation which yields for a homogeneous and isotropic material in the absence of internal heat sources DY 1 a @Y @t ¼ 0 ð1Þ where D is the Laplace operator, Y=T  T 0 , T 0 the temperature of the environment and a the thermal diffu- sivity.The solution of this equation for a slab with periodic surface temperature is a temperature oscillation which is attenuated and retarded in phase with increasing depth [1]. Such a temperature oscillation can be regarded as a highly damped wave exhibiting a complex wave vector [7] k ¼ ffiffiffiffiffi io a r ¼ 1 þ i ð Þ ffiffiffiffiffi o 2a r ð2Þ which is determined by the circular frequency of heat modulation o. Note, that following Fouriers law, the time average of the heat flux taken over a period is zero. Therefore, thermal waves are not traveling waves carrying energy, but just an oscillation of the temperature field [8]. According to eq. (2), these oscillations are damped already within one period (the ‘‘wavelength’’ of the temperature oscillations amounts to l ¼ 2p  d p , where d p ¼ (2a/o) 1/2 is the penetration depth of the temperature oscillation). Consequently, by recording a heating-rate-dependent phy- sical property such as the pyroelectric coefficient [4,5], the depth profile of this property may be determined from spectral measurements employing the frequency-dependent penetration depth d p . This was demonstrated by the laser intensity modulation method (LIMM) which is suitable to www.elsevier.com/locate/ceramint 0272-8842/$ - see front matter & 2012 Elsevier Ltd and Techna Group S.r.l. All rights reserved. http://dx.doi.org/10.1016/j.ceramint.2012.10.141 n Corresponding author. Tel.: þ 49 351 463 35281; fax: þ 49 351 463 32320. E-mail address: Gunnar.Suchaneck@tu-dresden.de (G. Suchaneck). Please cite this article as: G. Suchaneck, et al., A simple thermal wave method for the evaluation of the polarization state of embedded piezoceramics, Ceramics International (2012), http://dx.doi.org/10.1016/j.ceramint.2012.10.141