Dominant factors influencing the nanoindentation response of piezoelectric materials: a case study in relaxor ferroelectrics

The nanoindentation response of a piezoelectric material is, in general, influenced in a complex manner by its elastic, dielectric and piezoelectric properties. The present study is focused on obtaining a comprehensive understanding of the dominant material factors influencing the force–depth mechanical indentation response and the charge–depth electrical indentation response of piezoelectric materials. From a large number of three-dimensional finite element simulations of the indentation of simple and complex piezoelectric materials (such as PZT-5A and relaxor ferroelectrics), the following principal conclusions are obtained: (1) For indentations with both conducting and insulating indenters, the mechanical indentation stiffness is influenced more by the elastic properties, while the electrical indentation stiffness is influenced largely by the piezoelectric properties of the indented materials. (2) For longitudinal indentations using a conducting indenter, the elastic constants, C ₃₃ and C ₁₃, and piezoelectric constants, e₃₃ and e₁₅, are, respectively, the first and second most dominant material constants that influence the mechanical indentation stiffness and the electrical indentation stiffness. (3) For transverse indentations using a conducting indenter, the elastic constants, C ₁₁ and C ₁₂, are, respectively, the first and second most dominant material constants that influence the mechanical indentation stiffness. (4) In the indentation of relaxor ferroelectrics based on PMN-xPT and PZN-xPT, which exhibit a range of elastic, dielectric and piezoelectric properties, it is generally observed that materials with higher normal elastic and piezoelectric constants, i.e., C ₃₃ and e₃₃, respectively, exhibit higher mechanical and electrical indentation stiffnesses.