Mechanically Tunable Elastic Modulus of Freestanding Ba_1−xSr_xTiO₃ Membranes via Phase-field Simulation

The freestanding ferroelectric membranes with super-elasticity show promising applications in flexible electronic devices such as transducers, memories, etc. While there have been recent studies on the effect of mechanical bending on the domain structure evolutions and phase transitions in ferroelectric membranes, its influence on Young's modulus of these freestanding membranes is less explored, which is crucial for the design and application of flexible electronics. Here, a phase-field model is developed to simulate the tunability of Young's modulus of freestanding Ba₁₋_<i>x</i>Sr_<i>x</i>TiO₃ membranes under mechanical bending. It is demonstrated that the bent membrane shows a uniform Young's modulus compared with the unbent membrane. By increasing the bending angle, Young's modulus tunability is enhanced, which can be attributed to the vortex-like domain structures induced by mechanical bending. These vortex-like domains with large domain wall energy inhibit the subsequent domain switching under externally applied tensile strain and reduce the eigenstrain variation, which leads to a large Young's modulus. In addition, the formation of vortex domain structure is suppressed with increasing Sr²⁺ content in Ba₁₋_<i>x</i>Sr_<i>x</i>TiO₃ membranes at the same bending degree, resulting in a decrease in Young's modulus tunability. Our work reveals that the tunability of Young's modulus of freestanding ferroelectric membranes can be achieved by mechanical bending, which provides guidance for designing flexible electronic devices.