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BIT team makes important progress in strain gradient engineering research

Recently, the team of Academician Fang Daining and Professor Hong Jiawang of Beijing Institute of Technology has made important progress in the research of strain gradient engineering and discovered a new physical mechanism driving the asymmetric mechanical properties in ferroelectrics --the Flexo-deformation effect. Related results were published as "Asymmetric Mechanical Properties in Ferroelectrics Driven by Flexo-deformation Effect" in  Journal of the Mechanics and Physics of Solids, the top journal in the field of solid mechanics. The first author of the article is a PhD student Lun Yingzhuo .

Multi-field coupling mechanical behavior in advanced functional materials is a hot research topic in the field of solid mechanics in recent years. The flexoelectric effect is a new type of electromechanical coupling effect that has attracted much attention in this field after the piezoelectric effect, which refers to the physical phenomenon of dielectric materials generating electric polarization under the action of strain gradients. Since the strain gradients are significantly enhanced with the decrease of the structure size, the flexoelectric effect has important effects on the physical-mechanical properties of materials such as force, electricity, heat, magnetism and light on the micro-nano scale, and induces various novel physical effects. In addition to the flexoelectric effect arising from the coupling of strain gradients and electric quantity, the coupling effects of strain gradients with other physical quantities have emerged in recent years, such as flexomagnetic effect, flexophotovoltaic effect, flexopyroelectric effects, etc. (as shown in Figure 1) and have important application prospects.

Figure 1. Novel multi-physical field coupling phenomena induced by strain gradients.

Compared with the research on the flexoelectric effect in the coupling behavior of electrical properties of materials, its effect on the mechanical properties of materials still lacks in-depth exploration and understanding, especially for the study of the mechanical behavior of materials and structures on the micro-nano scale. It has been found that the flexoelectric effects often induce abnormal asymmetric mechanical properties in ferroelectric materials, such as asymmetric contact stiffness and asymmetric crack propagation, which have important implications for the application of microelectromechanical systems based on flexoelectric effects. However, at present, the physical mechanical mechanisms of these asymmetric mechanical properties are still unclear, which affects the application of microelectronic devices based on flexoelectric effects.

To address the scientific problems above, the research team established a theoretical model based on the framework of electromechanical coupling between flexoelectric and piezoelectric effects, took self-supporting ferroelectric oxide thin films as the research object, and quantitatively investigated the novel bending expansion/shrinkage behavior in the bending ferroelectric oxide thin films (as shown in Figure 2). They revealed the key role of strong coupling interaction between flexoelectric and inverse piezoelectric effects in the asymmetric bending mechanical behavior, and found the abnormal asymmetric bending rigidity driven by this mechanism (i.e., the bending rigidity of the ferroelectric material is not the same when bending in the opposite direction). As a result, a universal physical-mechanical mechanism is further extended as the flexo-deformation effect. This mechanism qualitatively explains the asymmetric mechanical behaviors in the ferroelectric materials before, such as asymmetric contact stiffness and asymmetric crack propagation. Based on this, the research team predicted the possible asymmetric bending expansion/shrinkage behavior and asymmetric bending stiffness in ferroelectric materials (shown in Figure 3). These findings provide scientific basis for an in-depth study of the asymmetric mechanical properties of ferroelectrics and the development of novel devices with asymmetric mechanical functional properties.

Figure 2. (a,b) Mechanical behavior of asymmetric bending thickness expansion/shrinkage in ferroelectric films dependent on spontaneous polar orientation. (c) Thickness dependent on film bending curvature. (d) Dimensional effect of asymmetric bending stiffness.

The flexo-deformation effect, which builds on the flexo-diffusion effect proposed earlier by the team for strain gradient engineering (Nanoscale, 12, 15175 (2020)), investigates the coupling effect between strain gradients and asymmetric mechanical properties, and further enriches the physical blueprint for the study of multi-field coupling in the strain gradient in advanced materials  (as shown in Figure 1).

Figure 3. In ferroelectrics, Flexo-deformation effect induces (a,b) asymmetric nanoindentation, asymmetric crack propagation phenomena(c,d), and predicted (e,f) asymmetric bending mechanical behavior.

This research was sponsored by the National Natural Science Foundation of China, the key project of Beijing Natural Science Foundation, and the Science and Technology Innovation Project for Graduate Students of BIT.