Unraveling the Elastic Properties of (Quasi)Two-Dimensional Hybrid Perovskites: A Joint Experimental and Theoretical Study.

The unique properties of hybrid organic-inorganic perovskites (HOIPs) promise to open doors to next-generation flexible optoelectronic devices. Before such advances are realized, a fundamental understanding of the mechanical properties of HOIPs is required. Here, we combine density functional theory (DFT) modeling with a diverse set of experiments to study the elastic properties of (quasi)2D HOIPs. Specifically, we focus on (quasi)2D single crystals of phenethylammonium methylammonium lead iodide, (PEA)PbI(MAPbI), and their 3D counterpart, MAPbI. We used nanoindentation (both Hertzian and Oliver-Pharr analyses) in combination with elastic buckling instability experiments to establish the out-of-plane and in-plane elastic moduli. The effect of Van der Waals (vdW) forces, different interlayer interactions, and finite temperature are combined with DFT calculations to accurately model the system. Our results reveal a nonmonotonic dependence of both the in-plane and out-of plane elastic moduli on the number of inorganic layers () rationalized by first-principles calculations. We discuss how the presence of defects in as-grown crystals and macroscopic interlayer deformations affect the mechanical response of (quasi)2D HOIPs. Comparing the in- and out-of-plane experimental results with the theory reveals that perturbations to the covalent and ionic bonds (which hold a 2D layer together) is responsible for the relative out-of-plane stiffness of these materials. In contrast, we conjecture that the in-plane softness originates from macroscopic or mesoscopic motions between 2D layers during buckling experiments. Additionally, we learn how dispersion and π interactions in organic bilayers can have a determining role in the elastic response of the materials, especially in the out-of-plane direction. The understanding gained by comparing and experimental techniques paves the way for rational design of layered HOIPs with mechanical properties favorable for strain-intensive applications. Combined with filters for other favorable criteria, e.g., thermal or moisture stability, one can systematically screen viable (quasi)2D HOIPs for a variety of flexible optoelectronic applications.