Journal of Mechanical Science and Technology 29 (2) (2015) 715~721 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-015-0131-0 X-ray diffraction measurement of residual stress in sol-gel grown lead zirconate titanate thick films on nickel-based super alloy substrate † Hamidreza Hoshyarmanesh 1 , Naser Nehzat 1 , Mehdi Salehi 2 and Mojtaba Ghodsi 3,* 1 Dep. of Mechanical Engineering, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran 2 Dep. of Materials Engineering, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran 3 Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat 123, Oman (Manuscript Received December 22, 2013; Revised October 5, 2014; Accepted November 1, 2014) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Residual compressive stress of Pb(Zr 0.52 Ti 0.48 )O 3 thick films was investigated using residual strains derived from X-ray diffraction pat- terns. Sin 2 ψ method was applied for the 5, 10 and 15 µm sol-gel derived thick films annealed at 700°C for 1 hr as high frequency struc- tural health monitoring square-shape transducers of 10×10 mm, deposited onto the curved nickel-based super alloy substrates. A triaxial model was proposed based on piezoelectric constitutive equations, and Bragg’s law at a large diffraction angle (~89º) was utilized con- sidering the electromechanical coupling factor as well as elastic, dielectric and piezoelectric constants. Thickness variations led to a sig- nificant change in residual stress magnitudes delineated from more-accurate triaxial model compared to small angle plane-stress results not considering the piezoelectric coupling effects. Keywords: PZT thick film; Triaxial residual stress; Sol-gel deposition; Supper alloy substrate; X-ray diffraction ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction The optimum performance of Pb(Zr 0.52 Ti 0.48 )O 3 (PZT) thick films in micro-electro-mechanical systems, actuators, struc- tural health monitoring transducers, energy harvesting mod- ules, etc. is extremely influenced by residual stresses and strains [1]. To improve the electromechanical properties, re- sidual stresses should be controlled during the film fabrication. Although residual stress in piezoceramic thin films is often neglected due to a lack of adequate stress measuring capabili- ties [2], it has great effects on the properties of thin and thick films [1, 3]. Tensile or compressive stresses are introduced dependent on the processing technique and properties of the substrate/bottom electrode [4]. The influence of residual stress on preferred domain orientation, dielectric and piezoelectric behaviors associated with the non-180° domain wall motions and clamping effects has been studied by several authors [5- 10]. Berfield et al. [2] investigated the influence of residual stress on sol-gel derived Pb(Zr 0.53 Ti 0.47 )O 3 thin films of vary- ing thicknesses integrated onto Pt/Ti/SiO 2 /Si substrates. Park et al. [11] described a new structure to measure the residual strain of multi-layer piezoelectric thin films prepared by sol- gel method consisting of SiO x /Pt/PZT/Pt on SiN x substrate. Zheng et al. [12] grew Pb(Zr 0.52 Ti 0.48 )O 3 thin films of thick- nesses 0.05, 0.5, and 1.0 µm on Pt/Ti/Si by pulsed laser depo- sition (PLD) and proposed an extended model, in which the piezoelectric coupling factor determined by the elastic, dielec- tric and piezoelectric constants to evaluate the residual stress with X-ray diffraction (XRD). This study has a major concentration on the residual stress of 5, 10 and 15 µm PZT thick films deposited by sol-gel tech- nique onto the curved surface of IN738 nickel-based supper alloy substrate using GAXRD patterns at relatively large dif- fraction angle (~89º), and a proposed triaxial model consider- ing the piezoelectric coupling factor. Most literature works refer to stress/strain analysis of thin films on Si, Pt, or other laboratory substrates using plane-stress method, not consider- ing the piezoelectric coupling factor and dielectric permittivity [2, 4, 10], which are the fundamental terms in piezoelectric constitutive equations. Although few studies [12] focus on a two-dimensional extended model to evaluate the residual stress in small angles regarding coupling factor, they never present a comprehensive analysis for thick films. Larger dif- fraction angles noticeably enhance the measurement accuracy. Sol-gel deposition is popular among a variety of coating methods to fabricate ferroelectric films, particularly on the free-shape industrial parts. The main origin of residual stress was chiefly recognized as being thermal stress due to suppres- sion of phase transformation and intrinsic stresses in porous * Corresponding author. Tel.: +968 24142675, Fax.: +968 24141316 E-mail address: ghodsi@squ.edu.om † Recommended by Associate Editor Jun-Ho Jeong © KSME & Springer 2015