X-ray diffraction measurement of residual stress in sol-gel grown lead zirconate titanate thick films on nickel-based super alloy substrate

Residual compressive stress of Pb(Zr_0.52Ti_0.48)O₃ thick films was investigated using residual strains derived from X-ray diffraction patterns. Sin²ψ 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 structural 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 considering the electromechanical coupling factor as well as elastic, dielectric and piezoelectric constants. Thickness variations led to a significant change in residual stress magnitudes delineated from more-accurate triaxial model compared to small angle plane-stress results not considering the piezoelectric coupling effects.