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

Abstract

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 ab initio 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)2PbI4(MAPbI3) n−1, and their 3D counterpart, MAPbI3. 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 (n) 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 ab initio 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.

In-Plane Mechanical Properties of Two-Dimensional Hybrid Organic–Inorganic Perovskite Nanosheets: Structure–Property Relationships

“…C8PbI shows almost identical E ∥ (0.7 ± 0.1 GPa) to C6PbI. These E ∥ values are comparable to the modulus of polymeric elastomers and fall in the lower end of the modulus range of some organic semiconductor materials . This shows that when the chain length reaches to C6, the in-plane elastic properties of 2D lead iodide HOIPs are close to those of organic materials.…”

“…To the best of our knowledge, there are no direct measurements of υ for 2D HOIPs. Theoretical calculations predict that C4PbI has an in-plane υ = 0.23, and υ is largely independent of halide species , and the relative fraction of the organic vs inorganic components in the crystals for n ≤ 4. , Given that the spacer molecules investigated here are all linear alkylammoniums similar to butylammoniums in C4PbI, we set υ = 0.23 for our data analysis.…”

“…3D HOIP crystals are considered “soft” in nature, with much lower elastic moduli compared to conventional inorganic semiconductors, , exhibiting mechanical behaviors closer to metal–organic framework materials. , Such “soft” nature leads to a much lower energy penalty in structural changes and is believed to give rise to many unusual properties in HOIPs, including self-healing, , high ion migration, , and low thermal conductivity . The inorganic metal halide octahedral framework [MX 6 ] 4– and the organic A-site cation play dominant and secondary roles in determining the mechanical properties of HOIPs, respectively. ,,− The 2D structure endows HOIPs with even lower stiffness in the out-of-plane direction than the 3D ones because the organic layers and the van der Waals (vdW) interfaces between adjacent organic layers are soft links in the out-of-plane directions. − Instrument nanoindentation studies of 2D HOIP crystals reveal that the out-of-plane mechanical performance of 2D HOIPs can be tuned over a wide range by controlling the metal halide framework, the organic spacer molecules, and the interfaces between 2D layers …”

Mechanical Properties of a 2D Lead-Halide Perovskite, (C6H5CH2NH3)2PbCl4, by Nanoindentation and First-Principles Calculations

“…This is because of the thicker inorganic layers of corner shared [PbI 6 ] 2– octahedron along with the methylammonium cations reside into the cavities . Interestingly, the out-of-plane E and H values of triclinic (C 6 H 5 CH 2 CH 2 NH 3 ) 2 PbI 4 are slightly larger than the (C 6 H 5 CH 2 NH 3 ) 2 PbCl 4 , probably ascribed to the symmetry, the CH···π interactions, and the phenyl–phenyl interface. , In comparison with the homologous (CH 3 (CH 2 ) m NH 3 ) 2 PbX 4 (X = Cl, Br and I), which has a narrower distance of inorganic layers and similar hydrogen bonding between the amine cations and [PbI 6 ] 2– octahedrons, the E and H values of (C 6 H 5 CH 2 NH 3 ) 2 PbCl 4 are higher about 5–6.3 and 0.02–0.19 GPa, respectively, than (CH 3 (CH 2 ) m NH 3 ) 2 PbI 4 . Although (CH 3 (CH 2 ) 11 NH 3 ) 2 PbI 4 has uniform interlamellar spacing (1.7 nm) and larger atomic density, the softer alkyl long chain essentially reduces the mechanical stability.…”

Mechanical response of butylamine based Ruddlesden Popper organic-inorganic lead halide perovskites

“…al. have published an extensive experimental and theoretical study on out of plane and in-plane mechanical properties of phenylethylammonium methylammonium lead iodide single crystals PEA 2 MA n−1 Pb n I n−1 [12] and reported a non-monotonic variation in elastic moduli for these crystals with varying number of inorganic layers (n). Li et.…”