English

• 1. INTRODUCTION

  Hybrid organic-inorganic perovskites (HOIPs) have been studied intensively in physics, chemistry, and materials science because of their rich physical properties^[1-3], such as photovoltaic and optoelectronic^[4], dielectricity^[5], magnetism^[6], ferroelectricity^[7], ferroelasticity^[8], and multiferroicity^[9]. For example, semiconducting HOIPs (CH₃NH₃PbX₃, X = I, Br, or Cl) have been recognized as promising light-harvesting materials for future high-performance and ultralow-cost-per-watt photovoltaic devices^[10-12]. Over the past decade, great efforts have been made in developing new types of hybrid perovskite materials and exploring their unique functionalities. In addition, low-cost and simple one-pot synthesis, solution processability and ease for scale-up make them promising candidates in various fields. Nevertheless, halides based HOIPs are largely dominated by toxic lead compounds, while other halides have not been well explored until a recent study about the successful synthesis of a few hybrid perovskite chlorides using the organic diamine cation templates^[13]. To further extend this possibility, a new HOIP bromide, [C₆H₁₄N₂]KBr₃, was synthesized and structurally characterized. The elastic properties and acoustic velocity behavior of this new HOIP were systematically studied via the density functional theory (DFT) calculations and further validated by recourse to nanoindentation.

  2. EXPERIMENTAL

  2.1 Materials and methods

  All chemicals and solvents were of reagent grade and used as received. Infrared spectra were collected over the range of 4000~400 cm^-1 on a Bruker VERTEX-70 ATR spectrometer. Elemental analysis of the sample was performed on a German Vario Micro cube Elementar instrument.

  2.2 Synthesis

  All chemicals and solvents used in this study were of reagent grade or higher purity, purchased from commercial vendors and used as received. Single crystals of [C₆H₁₄N₂]KBr₃ were prepared from stoichiometric 1:2:1 mixtures of aqueous solutions of potassium bromide (KBr), hydrobromic acid (HBr) and triethylenediamine hexahydrate C₆H₁₂N₂⋅6H₂O. The resulting colorless solution (PH = 1~2) was left in Petri dishes at 20 ℃ for several days, during which time faceted colorless blocks of the products grew. They were harvested by filtration and rinsed with acetone. The asymmetric unit can be observed in Fig. S1, while the purity of the compounds was confirmed by powder X-ray diffraction (Fig. S2), infrared spectra (Fig. S3) and elemental analysis. The elemental analysis for [C₆H₁₄N₂]KBr₃: calcd. (%) (M_r = 392.99): C, 18.34; N, 7.13; H, 3.59. Found (%): C, 18.31; N, 7.10; H, 3.409. FT-IR(KBr/cm^–1) for [C₆H₁₄N₂]KBr₃: = 3448(s), 3005(vs), 2913(vs), 2881(vs), 2778(vs), 2706(vs), 2597(vs), 2569(vs), 2532(vs), 2458(s), 1637(w), 1470(m), 1436(s), 1410(s), 1384(vs), 1318(m), 1280(m), 1195(s), 1053(vs), 1002(w), 891(m), 852(m), 806(w), 793(w), 557(w), 409(w).

  2.3 Single-crystal X-ray diffraction

  Single-crystal X-ray diffraction was executed on an Oxford Diffraction Rigaku XtaLAB mini^TM diffractometer with graphite-monochromated Mo-Kα radiation (λ = 0.71073 Å) at 293 K under ambient pressure using an empirical absorption correction through CrysAlis^Pro (version 1.171.39.6a) software for data collection. The program Olex2-1.2 was employed as an interface to invoke program SHELXS and SHELXL executables, where direct methods were applied to resolve crystal structure in solution program SHELXS, and used full-matrix least squares on F² to refine anisotropic atomic displacement parameters of all non-hydrogen atoms in refinement program SHELXL^[14]. Eventually, a riding model was applied to refine hydrogen atoms of [C₆H₁₄ N₂]²⁺ ligand.

  2.4 Powder X-ray diffraction

  Room temperature powder X-ray diffraction (PXRD) was carried out on apparatus (X´Pert PRO, PANalytical B. V.) with a Cu radiation (λ = 1.5418 Å, operating at 40 KV and 30 mA) for confirming the phase purity. The sample was prepared by fully grinding the single crystals and the diffraction data were collected in the range of 5~70^o at a rate of 3°/min. The cell parameters were refined with the Le Bail method by using TOPAS-Academic v5 software (Fig. S2), and yielded a = 9.4756(1), b = 9.4756(1), c = 23.1371(2) Å, V = 1799.08(3) ų (Rp = 2.8%, Rwp = 3.7% and GOF = 1.141), which were consistent with the results of single crystal X-ray diffraction.

  2.5 The first-principles calculation

  The first principles calculations were made to obtain the elastic anisotropy of material by using CASTEP, a total energy package based on plane-wave pseudo-potential density functional theory^[15]. The functions developed in local density approximation (LDA)^{[16, 17]} were used to indicate the exchange-correlation energy. Optimized ultrasoft pseudo-potentials^[18] were adopted to model the effective interaction between the valance electrons and atomic cores, which allowed us to use a set of relatively small plane-wave basis without compromising the computational accuracy. The kinetic energy cut-off was set as 400 eV and Monkhorst-Pack^[19], k-point mesh spanning was less than 0.04 Å^-1.

  2.6 Nanoindentation experiment

  Nanoindentation experiments were implemented at room temperature using a Hysitron Nanoindenter (Hysitron Corp. USA) with a pyramidal sharp Berkovich diamond indenter tip (end radius is 100 nm)^[20]. The indenter sequentially recorded the load (P) and depth (h) under conditions of a loading and unloading rates of 0.5 mNs^-1 and indenter tip was held for 10 s in the largest displacement 620 nm. A fused silica standard with an elastic modulus of 72 GPa and hardness of 9 GPa was adopted for calibration in the experiment. In addition, the elastic modulus of the diamond indenter (1141 GPa) and Poisson's ratio (0.07) were applied for calculation^[21]. Individual untwined single crystals with fine (1-1-2) and (1-12) surfaces were faced-indexed via single-crystal X-ray diffraction. The data from the P-h curves of the sample were analyzed by using a standard Oliver-Pharr method^[22].

  3. RESULTS AND DISCUSSION

  3.1 Crystal structure

  [C₆H₁₄N₂]KBr₃ adopts a perovskite arrangement (in this case the crystal symmetry is trigonal; enantiomorphous space group P3₁21 (No. 152)), which is a chiral perovskite (Fig. 1a). The crystal chirality originates from a helical motif of the non-chiral structural units and the bulk sample must consist of an equal number of crystals of both chiralities (i.e. space groups P3₁21 and P3₂21). By using the Goldschmidt's Tolerance Factor concept we estimate tolerance factor (0.831) of [C₆H₁₄N₂]KBr₃ which is in good agreement with stable perovskite structure value (0.80~1.0)^[23]. Crystal data of [C₆H₁₄N₂]KBr₃ are listed in Table S1: a = b = 9.4756(1) Å, c = 23.1371(2) Å, V = 1799.08(3) ų, and Z = 6. In the structure (Fig. S1), two potassium and three bromine ions along with one "dabconium" dication (all atoms on general positions) build an asymmetric unit. The topology of the corner-sharing KBr₆ octahedra is the same as that of ABO₃ cubic perovskite (Fig. 1a), while the dabconium cation occupies the A cation site and bonds to the KBr₃ network via hydrogen bonding (N(1)H···Br(1) = 2.3857 Å and N(2)H···Br(3) = 2.3863 Å, as shown in Fig. 1b, which is totally different from its chloride analogue [C₆H₁₄N₂]KCl₃ for which face-sharing undistorted KCl₆ octahedra have strong hydrogen bonding (NH···Cl = 2.1419 Å) that connects the KCl₃ network in three-dimensions^[13]. The bridging angles at hydrogen bonded bromines (K(1)‒Br(1)‒ K(2) = 167.865° and K(1)‒Br(3)‒K(2) = 164.889°) for [C₆H₁₄N₂]KBr₃ are more than double to those (K‒Cl(1)‒K = 71.993° and K‒Cl(2)‒K = 72.788°) for [C₆H₁₄N₂]KCl₃, showing higher order of distortion in KBr₆ octahedra, as compared to KCl₆ octahedra.

  Figure 1

  

  Figure 1.  3D framework structure of [C₆H₁₄N₂]KBr₃. Color codes: N, blue; C, black; H, white; K, blue gray; Br, dark yellow; KBr₆ octahedra, turquoise. Hydrogen bonds are indicated by black dashed lines

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  3.2 Mechanical properties

  Mechanical properties of the material are crucial for successful technological applications. Particularly, their anisotropy is very important for evaluating the long term functioning reliability. To fully understand the mechanics of [C₆H₁₄N₂]KBr₃, we have performed comprehensive DFT calculations to obtain the full elastic constants of [C₆H₁₄N₂]KBr₃, which gave the extracted Young's moduli (E), Shear moduli (G), Poisson's ratios (ν), anisotropy indexes (A) and bulk moduli (B) (Table 1). Fig. 2 represents the E values graphically as 3D and sectional 2D diagrams, indicating the crystal is stiffest along < 03-1 > , which may be due to hydrogen bonding, as this direction is just normal to hydrogen bonding, but most complaint along < 011 > and this direction is just parallel to hydrogen bonding. The anisotropic index of elastic modulus^[24] is A_E = E_max/E_min = 14.08/11.54 = 1.22, which indicates a medium anisotropy in E. To testify the calculated values of E, we conducted nanoindentation experiments using single-crystals of [C₆H₁₄N₂]KBr₃. Representative load-indentation depth (P-h) curves obtained on the (1-12) and (1-1-2) faces are shown in Fig. 3 and Fig. S7. The experimental based values of E and H for (1-12) and (1-1-2) faces are 14.20(3), 13.80(7) GPa, and 0.96(6), 0.28(3) GPa, respectively, which may have attributed to the presence of hydrogen bonding^[25-27]. The experimental values are in good agreement with DFT results E_(1-12) = 11.72 GPa, E_(1-1-2) = 12.37 GPa, indicating the validity of our first principles approach. The calculated anisotropy in E (A_E = E_max/E_min) is 1.22, showing an insignificant anisotropy. The shear modulus, G (i.e. ratio of shear stress to shear strain), is a measure of the stiffness of a material or structure when subjected to (opposing) shear forces acting parallel to the surfaces. Variations of G, extracted from the DFT calculations, in a 3D and a 2D polar plots projected normal to the (100) plane, are displayed in Fig. S4a and Fig. S4b, respectively. The calculated anisotropy in G of [C₆H₁₄N₂]KBr₃ is the ratio of its maximum and minimum values as A_G = G_max/G_min = 5.68/4.56 = 1.24, showing the same anisotropy as A_E. The experimental E values are 29~37% larger than those from the widely used photovoltaic CH₃NH₃PbI₃ (10.4~10.7 GPa) though the density of [C₆H₁₄N₂]KBr₃ is only about 52% of that of CH₃NH₃PbI₃^[28]. But the comparison of E_min (11.54 GPa) to G_min (4.56) implies that [C₆H₁₄N₂]KBr₃ is more vulnerable to shearing. This observation is particularly important in the context of manufacturing, as it demands special attention for aspects such as shear-induced plasticity, amorphization and rapture^[28]. Poisson's ratios (ν) are the ratio of transverse strains (ɛ_j) to the axial strains (ɛ_i), ν = –ɛ_j/ɛ_i. The graphical presentations as 3D and sectional 2D diagrams are given in Fig. S5a and Fig. S5b, respectively. The calculated values of ν ranges from 0.18 to 0.32, showing more flexible nature of [C₆H₁₄N₂]KBr₃, as compared to brittle (typically for brittle materials (ν > 0.26)^[29]. The anisotropy index A_ν = ν_max/ν_min = 1.77 is relatively higher than other two anisotropy indexes (A_E and A_G). The bulk modulus (B) (i.e. the inverse of compressibility) is a measure of volumetric elasticity and signifies the mechanical resistance of a material against volumetric changes (strains) under uniform hydrostatic pressure. Our DFT calculations for bulk modulus (B = 8.51 GPa) also reveal the soft nature^[30] of [C₆H₁₄N₂]KBr₃, indicating higher volume compressibility under hydrostatic stress.

  Table 1

  

  Table 1.  DFT Calculation Results for Elastic Constants, Young's Modulus, Shear Modulus, Poisson's Ratios, Bulk Modulus and Anisotropy Indexes

  DownLoad: CSV

  Properties		Quantities		[C6H14N2]KBr3
  Stiffness coefficient Cij (GPa)		C11		16.2498
  		C33		14.3127
  		C44		4.8262
  		C12		5.4112
  		C13		4.8324
  		C14		0.4694
  		C15		0.0561
  Young's modulus E (GPa)		Emax		E(03-1) = 14.0763
  		Emin		E(011) = 11.5444
  Shear modulus G (GPa)		Gmax		G(021) < -100 > = 5.6804
  		Gmin		G(01-2) < -100 > = 4.5648
  Poisson's ratios ν		νmax		ν < -100 > < 0-2-1 > = 0.3179
  		νmin		ν < 214 > < -2-11 > = 0.1795
  Bulk modulus B (GPa)		8.506
  Anisotropy measure		AE		1.219
  		AG		1.244
  		Aν		1.771

  Figure 2

  

  Figure 2.  Young's modulus (E) representation surfaces extracted from DFT calculations. (a) 3D surface, (b) 2D polar plots of E projected normal to the (100) plane

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  Figure 3

  

  Figure 3.  Representative load-indentation depth (P-h) curves for (1-1-2) and (1-12) oriented facets of [C₆H₁₄N₂]KBr₃ single crystal measured by a Berkovich tip

  DownLoad: Full-Size Img PowerPoint

  3.3 Acoustic velocity

  The velocities of acoustic waves in solids are closely related to the elastic properties of the material. The general relation is:

  $ \rho \frac{\partial^{2} u_{i}(r, t)}{\partial t^{2}}=\sum\limits_{j, k, l=1}^{3} C_{i j k l} \frac{\partial^{2} u_{l}(r, t)}{\partial x_{j} \partial x_{k}},(i, j, k, l=1,2,3) $

  where ρ is the density of material, u is the displacement (the small displacement of adjacent atoms), and C_ijkl is the matrix of the elastic stiffness constants. Another equation (Christoffel's equation) relates acoustic velocities to crystallographic direction and elastic moduli as:

  $ \operatorname{det}\left|\Gamma-\rho v^{2}\right|=0 $

  where v is the speed of acoustic velocity and Г is the Kelvin-Christoffel matrix. From these two relations, we can calculate the sound velocities in various crystallographic directions by using elastic stiffness constants C_ijkl, but Christoffel's equation has three roots for sound velocities which correspond to a longitudinal and two transverse modes. Generally, the intensities of longitudinal wave peaks are greater than those of the transverse waves, and are directly related to the elastic moduli for different crystallographic directions^[31]. A graphical representation of 'v' in all directions is given in Fig. 4a-b as 3D and sectional 2D diagrams. The calculated maximum and minimum speeds of longitudinal waves by DFT using C_ijkl along < 03-1 > and < 011 > are v_max = 2.74 and v_min = 2.57 kms^-1, respectively. The maximum speed along (03-1) plane indicates higher (maximum) value of elastic modulus (14.07 GPa). As in this direction the atoms are in dense connection mode while for (011) plane, they are not densely connected and the speed in this direction is minimum showing lower (minimum) value of elastic modulus (11.54 GPa).

  Figure 4

  

  Figure 4.  Acoustic velocity (v) representation surfaces extracted from DFT calculations. (a) 3D surface. (b) 2D polar plots of 'v' projected normal to (100) plane

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  Table 2

  

  Table 2.  Select Bond Lengths (Å) and Bond Angles (°) for [C₆H₁₄N₂]KBr₃

  DownLoad: CSV

  Bond		Dist.
  K(1)–Br(1)		3.4133(18)
  K(1)–Br(3)		3.3704(15)
  K(1)–Br(2)		3.3161(22)
  K(2)–Br(2)		3.4444(18)
  Angle		(°)
  Br(1)–K(1)–Br(2)		77.81(17)
  Br(2)–K(1)–Br(3)		145.15(16)
  Br(1)–K(1)–Br(3)		91.56(16)
  K(1)–Br(2)–K(2)		87.00(15)

  4. CONCLUSION

  In conclusion, a new hybrid organic-inorganic perovskite has been hydrothermally synthesized and structurally characterized. [C₆H₁₄N₂]KBr₃ crystallizes in the chiral trigonal space group P3₁21 with a good thermal stability up to 550 K. We have systematically explored the fundamental elastic properties of [C₆H₁₄N₂]KBr₃ via combined DFT calculations and nanoindentation experiments. The elastic moduli, shear moduli, Poisson's ratios and sound velocity properties along all crystallographic directions are thoroughly mapped through the full elastic coefficients. Moreover, our nanoindentation experiments are consistent with the theoretical results, indicating the reliability of our DFT calculations. Its higher stiffness and thermal stability as compared to the well-known photovoltaic CH₃NH₃PbI₃ makes it a possible candidate for exploring optoelectronic properties.

  
  
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• 

  Figure 1  3D framework structure of [C₆H₁₄N₂]KBr₃. Color codes: N, blue; C, black; H, white; K, blue gray; Br, dark yellow; KBr₆ octahedra, turquoise. Hydrogen bonds are indicated by black dashed lines

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  Figure 2  Young's modulus (E) representation surfaces extracted from DFT calculations. (a) 3D surface, (b) 2D polar plots of E projected normal to the (100) plane

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  Figure 3  Representative load-indentation depth (P-h) curves for (1-1-2) and (1-12) oriented facets of [C₆H₁₄N₂]KBr₃ single crystal measured by a Berkovich tip

  下载: 全尺寸图片 幻灯片
  

  Figure 4  Acoustic velocity (v) representation surfaces extracted from DFT calculations. (a) 3D surface. (b) 2D polar plots of 'v' projected normal to (100) plane

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  Table 1.  DFT Calculation Results for Elastic Constants, Young's Modulus, Shear Modulus, Poisson's Ratios, Bulk Modulus and Anisotropy Indexes

  Properties		Quantities		[C6H14N2]KBr3
  Stiffness coefficient Cij (GPa)		C11		16.2498
  		C33		14.3127
  		C44		4.8262
  		C12		5.4112
  		C13		4.8324
  		C14		0.4694
  		C15		0.0561
  Young's modulus E (GPa)		Emax		E(03-1) = 14.0763
  		Emin		E(011) = 11.5444
  Shear modulus G (GPa)		Gmax		G(021) < -100 > = 5.6804
  		Gmin		G(01-2) < -100 > = 4.5648
  Poisson's ratios ν		νmax		ν < -100 > < 0-2-1 > = 0.3179
  		νmin		ν < 214 > < -2-11 > = 0.1795
  Bulk modulus B (GPa)		8.506
  Anisotropy measure		AE		1.219
  		AG		1.244
  		Aν		1.771

  下载: 导出CSV

  Table 2.  Select Bond Lengths (Å) and Bond Angles (°) for [C₆H₁₄N₂]KBr₃

  Bond		Dist.
  K(1)–Br(1)		3.4133(18)
  K(1)–Br(3)		3.3704(15)
  K(1)–Br(2)		3.3161(22)
  K(2)–Br(2)		3.4444(18)
  Angle		(°)
  Br(1)–K(1)–Br(2)		77.81(17)
  Br(2)–K(1)–Br(3)		145.15(16)
  Br(1)–K(1)–Br(3)		91.56(16)
  K(1)–Br(2)–K(2)		87.00(15)

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