npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

New Phys.: Sae Mulli 2024; 74: 545-550

Published online June 28, 2024

Copyright © New Physics: Sae Mulli.

Room Temperature Elasticity of Mixed Halide Perovskite Single Crystals Studied by Brillouin Spectroscopy

Furqanul Hassan Naqvi, Syed Bilal Junaid, Jae Hyeon Ko*

School of Nano Convergence Technology, Nano Convergence Technology Center, Hallym University, Chuncheon 24252, Korea

Correspondence to:*

Received: April 1, 2024; Revised: April 19, 2024; Accepted: May 1, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

The mechanical properties of halide perovskites play an important role in the design and application of these materials in photovoltaic devices. The data of two elastic constants, C11 and C44, of 14 halide perovskites with respect to lattice constant and the density have been collected and investigated. The C11 showed a decreasing trend with increasing lattice constant, regardless of the type and composition of cations and anions in the perovskites. This indicated that smaller lattice constants are associated with shorter bond lengths on average and thus steeper interatomic potentials. The shear elastic constant C44 showed low values below 4 GPa, with the exception of a few compositions. In particular, the FA-included perovskites had extremely low C44 below 3 GPa. The low shear stiffness seems to be a common feature of halide perovskites, which may be attributed to the pliable octahedral tilting/rotation of the corner-sharing octahedra.

Keywords: Halide Perovskite, Elastic Constant, Brillouin spectroscopy

Halide perovskites are characterized by their ABX3 structure, where A is either an organic or inorganic cation, B is a metal cation (Pb or Sn) and X is a halide anion. These materials have emerged as a fascinating class of materials with remarkable optoelectronic properties[1]. They have an extraordinary potential in a wide range of photovoltaic and optoelectronic applications, including solar cells, light emitting diodes (LEDs) and photodetectors etc[2-4]. The efficiency of perovskite solar cells has progressed rapidly over the past decade, with power conversion efficiencies now exceeding 25%[5]. This rapid improvement in efficiency is attributed to their high absorption coefficients, tunable band gaps, and long carrier diffusion lengths[6-8].

Elastic properties are an essential part for the mechanical stability of materials and can provide valuable information about the material’s resistance to deformation under stress. Therefore, understanding the elastic properties is important for fabricating durable perovskite-based devices. The elastic stiffness coefficient, abbreviated as the elastic constant, is one of the fundamental physical constants of condensed matter. The set of elastic constants is related to the interatomic potential and has been a research target of theoretical calculations[9-15]. Moreover, elastic constants play an important role in determining thermal expansion behavior of materials used. This is beneficial for devices that experience temperature fluctuations. In addition, it is one of the design parameters of optoelectronic devices that usually operate under harsh conditions, such as solar cells. Moreover, elastic constants also play a pivotal role in determining the thermal expansion behavior of materials. Materials with high elastic moduli (indicating stiffer materials) generally have lower thermal expansion coefficients[16]. Furthermore, in microelectromechanical systems (MEMS), precise control over elastic properties allows fine tuning of device response. This enhances their sensitivity in applications such as sensors and actuators[17].

The number of independent elastic constants is determined by the symmetry of the crystal. There are a few experimental methods to determine the elastic constants, the Brillouin spectroscopy being one of them. This spectroscopic technique probes the elastic properties in the hypersonic range, typically on the order of a few or a few tens of GHz. Because it is a non-destructive method, it has been widely used to study the elasticity of various solids and liquids including halide perovskites[13, 18-20].

It is well known that the halide perovskites are generally very soft in terms of elasticity. While the optoelectronic properties are much studied[21], the literature focused on the elasticity of these materials is still limited, specially under device operating conditions such as room temperature. In this study, we aim to fill this literature gap by measuring the room temperature elastic constants of a variety of halide perovskites using Brillouin spectroscopy. We have systematically investigated the elastic properties of various halide perovskite single crystals. This study is a general summary of our previous work[22, 23] , some new results, and previous studies by other groups[18]. In particular, the relationship between the elastic constants and the lattice constant or density is presented.

The single crystals used in our study were synthesized using the solvent evaporation method. The choice of solvent was based on solute solubility and the required product. The solutes were dissolved in equimolar concentrations in solvents such as N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), N-methylformamide (NMF), and gamma-butyrolactone (GBL). The solute-solvent mixture was continuously stirred at 40 C until fully dissolved. The resulting solution was then filtered through a 0.22 μm syringe filter into a crystallization dish. The dish was then covered with aluminum foil to facilitate slow evaporation and left undisturbed for 2–4 days at a constant temperature between 85–105 C, depending on the sample being prepared. Subsequently, the obtained single crystals were washed with dichloromethane and dried in a vacuum oven at 60 C for 12 hours to obtain the final crystals.

Brillouin spectra were measured by using a conventional tandem multi-pass Fabry-Perot interferometer (TFP-2, JRS Co., Zürich, Switzerland) at a wavelength of 532 nm. For backscattering measurement, a modified microscope (BH-2, Olympus, Tokyo, Japan) was used. A conventional photon-counting system was combined with a multichannel analyzer to detect and average the signal (1024 channels). The typical free spectral range was set to be ±33 GHz, which is enough to probe both the longitudinal acoustic (LA) and the transverse acoustic (TA) modes. The phonon propagation direction was [100] in the cubic phase, thus, the obtainable elastic constants were mainly C11 and C44. The sound velocity and the elastic constant were calculated from the mode frequency by considering the reported refractive index of each sample.

Figures 1(a)–(d) show typical Brillouin spectra of three selected halide perovskite single crystals, MAPbCl3, MAPbBr1.5Cl1.5, and MA0.9Cs0.1PbCl3 along with fitting lines. All spectra consist of two Brillouin doublets, the LA and the TA modes in the high frequency and the low frequency ranges, respectively. Each Brillouin spectrum was fitted by using the Voigt function, which is a convolution between the instrumental Gaussian and the Lorentzian functions, the latter being the response function of acoustic phonons. Table 1 lists the halide perovskites studied and their elastic constants along with the lattice constant, the density, and the method by which the elastic properties were probed. Some of the data were cited from our previous works[22, 23] and other references[18] as shown in the table. Among the listed samples, MAPbI3 and CsPbCl3 are not cubic at room temperature. However, the elastic data of MAPbI3 and CsPbCl3 in the table were obtained from their cubic phases at 340 K and 320 K, respectively[18].

Figure 1. (Color online) Room temperature Brillouin spectra of MAPbCl3, MAPbCl1.5Br1.5, MA0.9Cs0.1PbCl3 single crystals (a) along with their individual spectrum and the fitting line (b–d).

Table 1 . Summary of the lattice constants, the density, the two elastic constants, and the experimental method for all studied single crystals. Some data were taken from our previous work[22, 23] and another report[18].

CompositionLattice constant (\AA)Density (kg/m3)C11 (GPa)C44 (GPa)MethodReference
MAPbCl35.67314940.73.71BrillouinOur work[22]
MAPbBr0.5Cl2.55.71327839.13.73BrillouinOur work[22]
MAPbBrCl25.75332637.13.68BrillouinOur work[22]
MAPbBr1.5Cl1.55.8350635.73.63BrillouinOur work[22]
MA0.87FA0.13PbCl35.68314738.73.08BrillouinOur work[22]
MA0.77FA0.23PbCl35.69314237.92.9BrillouinOur work[22]
FAPbBr1.5Cl1.55.83345737.71.63BrillouinThis work
CsPbCl3b)5.55445842.97.05BrillouinThis work
MA0.9Cs0.1PbCl35.65326842.14.0BrillouinThis work
MA0.7Cs0.3PbCl35.64347845.74.39BrillouinThis work

INS: Inelastic neutron scattering

a measured at 340 K in the cubic phase

b measured at 320 K in the cubic phase

Figures 2(a) and (b) show the two elastic constants C11 and C44, respectively, as a function of the lattice constant. Figures 3(a) and (b) are the same plots, i.e., the C11 and C44, respectively, as a function of the density. The inset of Fig. 2 shows an extended view of C11 for MAPbBr1-xClx and MA1-xFAxPbCl3 mixed crystals. The C11 and C44 values are distributed in the approximate range of 11 to 46 GPa and 1.5 to 7.3 GPa, respectively. The C11 seems to be correlated with the lattice constant but not with the density. The correlation between C44 and either the lattice constant or the density is not clearly seen. That is natural, considering that C11 involves the volume-changing stress-strain relationship while C44 does not. Several interesting aspects can be deduced from these plots.

Figure 2. (Color online) (a) C11 and (b) C44 elastic constants as a function of the lattice constant for all studied single crystals. The inset shows an extended view of the C11 for MAPbBr1-xClx and MA1-xFAxPbCl3 mixed crystals.

Figure 3. (Color online) (a) C11 and (b) C44 elastic constants as a function of the density for all studied single crystals.

First, the C11 tends to decrease as the lattice constant increases, which is especially true for a particular system such as MAPbBr1-xClx. The C11 of MAPbBr1-xClx decreases monotonically with increasing Br content and thus the lattice constant (See the inset of Fig. 2). The C11 was reduced by 12.3% by changing the Br content from x=0 to x=1.5 in MAPbBr1-xClx. The effect of the lattice constant on C11 is more pronounced for the MA1-xFAxPbCl3 mixed crystals compared to MAPbBr1-xClx as can be seen from the inset of Fig. 2. In the same context, the C11 of MAPbX3 decreases significantly as the X-site anion changes from Cl (40.7 GPa) to Br (32.2 GPa) and then to I (21.8 GPa). This trend is applicable to the FAPbX3 where the C11 decreases from Br1.5Cl1.5 (37.7 GPa) to Br (31.2 GPa) and then to I (11.1 GPa). It should be noted that the elastic constant may depend on the experimental technique and its characteristic probe frequency if there is a substantial acoustic dispersion. The overall correlation between the lattice constant and C11 is generally justified because smaller lattice constants indicate shorter bond lengths and thus steeper interatomic potentials. A linear relationship between the bulk modulus and the average (shortest) bond distance (or a bond strength) has been confirmed in previous studies where the nanoindentation method was used[24, 25]. The halide perovskite may exhibit a structural instability when the lattice constant becomes larger than ∼6.4 \AA which is the lattice constant of FAPbI3 as shown in Fig. 2[18].

Second, the shear modulus C44 in Fig. 2(b) does not show a clear correlation with the lattice constant. The overall C44 values of the halide perovskites are surprisingly small below 6 GPa except for MAPbI3 and CsPbCl3 which show values above 7 GPa. This kind of low shear rigidity seems to be a common feature of halide perovskites. The pliant tilting and rotation of corner-sharing octahedra and the rotation-translation coupling were proposed to be the origin of the shear softness (extremely low C44) and the large elastic anisotropy[9, 18, 26]. In particular, the C44’s of the FA-included compositions are significantly small below 3 GPa. The substitution of MA with FA results in small change in the lattice constant. The FA cation has a larger ionic radius and is less symmetric compared to the MA cation, thus, the larger elastic constant of MAPbX3 was attributed to the steric effect of the MA molecules[18].

Despite the active research on the elastic properties of various halide perovskites, several issues remain to be investigated. First, the role of octahedral tilting/rotation in the formation of low shear rigidity needs to be scrutinized in more detail. In particular, the contribution of the tilting/rotation and the hydrogen bonding of A-site cations with the octahedra to the elastic constants and the elastic anisotropy should be further investigated. Second, although theoretical calculations of the elastic constants show reasonably good agreement with experimental values for some compositions and can reveal qualitative relationships with other physical parameters, there are still noticeable differences between experiment and theoretical calculations[10, 20]. It indicates that the approximations and model potentials used in the calculation need to be refined to improve the agreement between experiment and theory. Finally, the present approach should be revisited in terms of other physical properties such as the tolerance factor, the electronegativity, and the chemical bond length (or the bond strength), which will be the focus of our further investigation.

The mechanical properties of halide perovskites are important from both fundamental and application perspectives. They are one of the design parameters when they are manufactured and applied to devices such as solar cells, which are typically operated under harsh conditions. In addition, elastic properties are closely associated with the charge-carrier and thermal transport dynamics. The present study integrated two important elastic constants, C11 and C44, for a wide range of mixed halide perovskites in their cubic phases. The dependence of the two elastic constants on the cation and/or anion composition revealed interesting and important elastic properties, such as the correlation of C11 with the lattice constant and the unusually low shear C44. These properties may indicate flexibility and ductility of these materials when used as absorption layer in solar cells. In addition, the present data can serve as important parameters for refining theoretical models for halide perovskites.

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00219703).

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