Ternary diagrams of the phase, optical bandgap energy and photoluminescence of mixed-halide perovskites

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Ternary diagrams of the phase, optical bandgap energy and photoluminescence of mixed-halide perovskites Se-Yun Kim , Ho-Chang Lee , Yujin Nam , Yeonghun Yun , Si-Hong Lee , Dong Hoe Kim , Jun Hong Noh , Joon-Hyung Lee , Dae-Hwan Kim , Sangwook Lee , Young-Woo Heo PII: DOI: Reference:

S1359-6454(19)30668-8 https://doi.org/10.1016/j.actamat.2019.10.008 AM 15576

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Acta Materialia

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23 May 2019 9 September 2019 9 October 2019

Please cite this article as: Se-Yun Kim , Ho-Chang Lee , Yujin Nam , Yeonghun Yun , Si-Hong Lee , Dong Hoe Kim , Jun Hong Noh , Joon-Hyung Lee , Dae-Hwan Kim , Sangwook Lee , Young-Woo Heo , Ternary diagrams of the phase, optical bandgap energy and photoluminescence of mixed-halide perovskites, Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.10.008

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Ternary diagrams of the phase, optical bandgap energy and photoluminescence of mixedhalide perovskites

Se-Yun Kima,b, Ho-Chang Leea, Yujin Nama, YeonghunYuna, Si-Hong Leeb, Dong Hoe Kimc, Jun Hong Nohd, Joon-Hyung Leea, Dae-Hwan Kimb, Sangwook Leea*, Young-Woo Heoa*

a

School of Materials Science and Engineering, Kyungpook National University, Daegu, 41566,

South Korea b

Division of Energy Technology, Daegu-Gyeongbuk Institute of Science and Technology

(DGIST), Daegu 42988, South Korea c

Department Nanotechnology & Advanced Materials Engineering, Sejong University, Seoul

05006, Republic of Korea d

School of Civil, Environmental and Architectural Engineering, Green School, Korea University,

Seoul 02841, Republic of Korea Corresponding author E-mails: [email protected] (Y. W. Heo), [email protected] (S. Lee)

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Abstract Halide perovskites attract enormous attention as promising light absorption and emission materials for photovoltaics and optoelectronic applications. Here we report ternary diagrams of the phase, optical bandgap energy (Eg) and photoluminescence intensity of methylammonium lead halide (MAPbX3, where X = I, Br and Cl) perovskites, with three vertices of MAPbI3, MAPbBr3 and MAPbCl3. All the compositions were synthesized via a facile mechanochemical reaction at room temperature, to ensure the desired stoichiometries of the final products. Through structural study on MAPbX3, the phase diagram comprising a single phase region and two multiphase regions was obtained. In the single phase region, the a-axis lattice constant increases almost linearly with increasing the average size of the X site ions. Interestingly, Eg decreases almost linearly with increasing the average size of the X site ions, giving negligible deviation from Vegard’s law. As the result, a certain bandgap value, in the range of 1.55 - 2.9 eV, can be easily designed with infinite numbers of compositions. For the last, the ternary diagram of the photoluminescence intensity reveals the effective compositions for red, green and blue light emission. The comprehensive structural and optical information reported in this study is useful for designing halide perovskites for various applications. In addition, our approach for compositional mapping various characteristics using a solid-state reaction is an efficient and robust way to studying halide perovskites.

Keywords: mixed halide perovskite, ternary phase diagram, lattice constant, bandgap energy, photoluminescence

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1. Introduction Halide perovskites (HPs) have been highlighted during the last decade, due to their superb optical and electrical characteristics, such as high absorption coefficients, direct bandgap, bandgap energy (Eg) tunability, long diffusion length and lifetimes of charge carriers [1-3]. Furthermore, HPs have the advantage of an easy solution-based synthesis process by which highquality crystalline thin films can be grown at a low temperature [4-7]. Therefore, HPs have been actively applied to various devices such as photovoltaics [1], light emitting diodes (LEDs) [8], lasers [9] and photodetectors [10]. Effective control of Eg is essential for diverse applications. For this reason, intensive studies have been conducted on Eg tuning in HPs by substitution of ions occupying each site of the perovskite structure ABX3, where A is occupied by a monovalent cation (methylammonium+ (MA+), formamidinium+ (FA+), Cs+, Rb+, etc.) [11], B by a divalent cation (Pb2+, Sn2+, etc.) [12,13], and X by a halide anion (I-, Br- or Cl-) [14,15]. Based on theoretical studies, in general, an ABX3 HP has a direct bandgap at the gamma point (1/2, 1/2, 1/2), and both the conduction band minimum and the valence band maximum are composed of antibonding orbitals of B np-X ms (where B np = Sn 5p or Pb 6p, and X ms = Cl 3s, Br 4s or I 5s) and B ns-X mp (where B ns = Sn 5s or Pb 6s, and X mp = Cl 3p, Br 4p or I 5p), respectively [16-18]. Therefore, B and X are considered to be directly involved in the configuration of Eg, while A is indirectly involved [17,18]. Through numerous experimental works, the most effective way for Eg tuning has been demonstrated to be halide substitution, in the case of MAPbX3, the most representative perovskite composition. Eg of MAPbX3 can be tuned from 1.54 to 2.97 eV by mixing the X ions [14,15].

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Another important characteristic of an HP is photoluminescence (PL) because the PL efficiency is directly related to performance of photovoltaics and LED [19]. Similar with the case of Eg, the PL efficiency is also greatly affected by the X site anion. Among single components, MAPbBr3 is known to have the highest PL efficiency. Interestingly, in the case of certain compositions, such as MAPb(BryCl1-y)3 [20], FA0.83Cs0.17Pb(IxBr1-x)3 [21] and MAPb0.75Sn0.25(IxBr1-x)3 [22], the best PL efficiency is observed when the halide compositions are mixed. Although bandgap tuning and PL characteristics have been extensively studied in binary mixed-halide component systems, systematic investigation of those characteristic in a threecomponent (i.e. ternary mixed-halide) system, such as MAPb(IxBryClz)3, have not been reported yet. The main reason for the lack of information on the ternary mixed-halide system is that effective solution-based processes for perovskite solar cells have the limitation that the ratio of the source material is not realized in the final thin film because of the unique solution processes [23-26]. In general, perovskite films undergo compositional transformation by heat-treatment with presence of solvents; solvent engineering (i.e. anti-solvent washing) methods use transformation of intermediate phase to desired perovskite phase by a heat-treatment and twostep methods use chemical reaction of PbI2 film with MAI solution followed by heat-treatments. The compositional transformations in polar solvents may lead to non-stoichiometry by retarding crystallization [26,27] and non-stoichiometrical volatilization of source material during the heattreatment process [27]. Also the solution-based thin film systems have another limitation that their material properties are greatly influenced by the film quality which is known to extremely sensitive to various processing variables [28-30].

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In this study, we investigated ternary X site mapping of the phase, lattice constant, optical bandgap and relative PL efficiency. Mechanical chemical reaction methods have been used to minimize the non-stoichiometry and the film quality issues, even though this method cannot be applied for a film fabrication. A ternary phase diagram having vertices of MAPbI3, MAPbBr3 and MAPbCl3 was obtained along with maps of the a-lattice parameter, Eg, and PL intensity. In the single phase region, almost monotonic changes in the lattice constant and optical energy bandgap are found in the ternary mixed system. As a result, the optical energy bandgap was confirmed to have a nearly linear relationship with the average size of the X site ion, regardless of the combination of X site ions. In stark contrast to Eg, the PL intensity varies nonmonotonically with the X site ion combination. We found effective compostions for red, green and blue light emission, along the composition lines with Eg of 1.7, 2.3 and 2.6 eV, respectively.

2. Experimental 2.1. Materials and methods First, perovskite powders of single-component systems, such as MAPbI3, MAPbBr3 and MAPbCl3, were synthesized by the mechanochemical reaction using traditional ball milling. PbI2 (99.999%, Aldrich), PbBr2 (98%, Aldrich), PbCl2 (98%, Aldrich), CH3NH3I (99%, DYESOL), CH3NH3Br (99%, DYESOL) and CH3NH3Cl (99%, ACROS) were used. A mixture of the raw materials, ZrO2 balls and a nonpolar solvent (diethyl ether) was used for mixing and crushing by ball milling for 15 h. Diethyl ether, a nonpolar solvent that does not dissolve the raw materials and the final products, was used to increase the milling yield by preventing adhesion of powders on the surfaces of the balls and the container [31]. After ball milling, the synthesized powders were dried in a drying oven at 40 °C for 4 h to volatilize the solvent. Second, the mixed-halide

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perovskites were synthesized using the prepared MAPbI3, MAPbBr3 and MAPbCl3 powders as the raw materials. 2.2. Material characterization The crystal structures of the powders were characterized using X-ray diffractometry (XRD; X' Pert-PRO/MRD, M03XHF) with a Cu Kα X-ray source. The Eg of the powders was obtained by measuring absorbance using a UV-VIS spectrophotometer. PL was measured using a 266 nm diode-pumped solid-state laser (applied power on the sample surface, 310 mW) as an excitation source. A spectrometer (Acton Research Co., Spectrograph 500i) and an intensified CCD (PI-MAX3, Princeton Instrument Co.) were used to collect fluorescence spectra at room temperature.

3. Results and discussion

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Figure 1. Mechanochemical synthesis and crystal structures of MAPbX3. (a) Photographic images and schematic illustration showing the mechanochemical reaction during the ball milling process. See the Supplementary Materials for details. (b) XRD patterns of mechanochemically synthesized MAPbX3 (X = I, Br and Cl) powders, which are the starting materials for synthesizing ternary mixed-HPs (MAPbIxBryClz, where x+y+z=1, x≥0, y≥0 and z≥0). α-Al2O3 was used as the standard powder for calibration of the peaks from perovskites. (c-e) Magnified XRD peaks at approximately 2θ=30°, which correspond to the (c, d) C(002) or (e) T(220) and T(004) planes. The nonsymmetric peak feature, even for the single cubic phase, is due to the usage of both kα1 and the kα2 X-ray beam sources. We did not cut off the kα2 ray to fully collect the diffraction patterns without any attenuation of the intensity. (f) Schematic illustration showing the unit cell of the perovskite crystal structure, where A sites are occupied by monovalent cations, B by divalent cations, and X by monovalent anions. In the case of the ideal cubic phase, the cubic arrays are formed by corner-sharing BX6 octahedrons, and the A sites are located in the cuboctahedral cavities. (g, h) [001] projections of the (g) cubic and (h) tetragonal phases. Gray squares represent the BX6 octahedral cages. The crystal orientation of tetragonal T(110) can be compared with that of cubic C(100).

All the desired compositions were synthesized via the mechanochemical solid-state reaction, i.e., ball milling, at room temperature in a closed system in terms of mass conservation, as shown in Fig. 1a. During ball milling, mechanical energy might be applied through compression, shearing, stroking and impact, resulting in grinding, plastic deformation and localized heating [32,33]. This room temperature process with such a small mechanical energy could induce chemical reactions, such as breaking and rebinding between the organic or metallic and halide ions since the HP materials have a low formation energy [33]. The ternary mixed-HPs were synthesized using pre-synthesized MAPbI3, MAPbBr3 and MAPbCl3 powders as the raw materials, which were also prepared via the room temperature ball milling process (Fig. S1, Supplementary Materials). Fig. 1b-e shows the XRD patterns of the raw materials. All the peaks for each powder are well assigned to its representative phase at room temperature, without any peaks for secondary phases such as PbX2. Fig. 1f-h show schemes of the unit cell and [001]projections of the cubic and the tetragonal phases. Pb2+ with six-fold coordination is surrounded

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by halides located at the face-centered positions of the unit cell, and the MA+ cations are positioned at the corners of the cube with twelve-fold cuboctahedral coordination. Notably, MAPbBr3 and MAPbCl3 have the ideal cubic (named C) phase, while MAPbI3 has a pseudocubic phase, i.e., the tetragonal (named T) phase, in which the c-axis lattice constant is slightly elongated and the PbI6 octahedrons are slightly rotated compared to the ideal C phase [34,35]. Therefore, we carefully analyzed the XRD patterns of the HPs to distinguish the peak separation due to phase transition or segregation from the peak shift due to lattice constant changes, which will be discussed later for the case of peak changes in I-rich systems. Additionally, for the discussion of changes in the lattice constant, we compared the XRD peaks for the (110) plane of the T phase, T(110), and for the (100) plane of the C phase, C(100), because these planes are fundamentally the relevant planes, as shown in Fig. 1g-h. For example, the XRD peaks for C(200) and T(220), the half-spaced planes of C(100) and T(110), are shown in Fig. 1c-e.

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Figure 2. XRD analyses of synthesized ternary mixed-HPs. (a) Ternary composition diagram with MAPbI3, MAPbBr3 and MAPbCl3 vertices. Black dots indicate the compositions synthesized for XRD analyses. XRD patterns corresponding to the (b) T(110) and C(100) planes for MAPb(IxBr1-x)3, (c) C(100) plane for MAPb(BryCl1-y)3, and (d) CCl(100) and TI(110) planes for MAPb(ClzI1-z)3 compositions. (e) Evolution of the C(100) XRD peak for the (Br y(Cl0.5I0.5)1y)3 ternary compositions, corresponding to the horizontal arrowed line indicated in (a), with decreasing Br content. (f) XRD peaks corresponding to CI(200) for the compositions of 0.1
Fig. 2a shows a diagram, with three vertices of MAPbI3, MAPbBr3 and MAPbCl3, in which all the compositions examined in this work are indicated. The binary mixed halides are

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designated by (IxBr1-x)3, (BryCl1-y)3 and (ClzI1-z)3 (where 0≤x≤1, 0≤y≤1 and 0≤z≤1), and the ternary mixed halides are designated by (IxBryClz)3 (where x+y+z=1, 0≤x≤1, 0≤y≤1 and 0≤z≤1). First, the binary compositions along the three edges of the diagram were synthesized, and the XRD patterns corresponding to C(100) or T(100) are shown in Fig. 2b-d (see Figs. S2-S4, Supplementary Materials for the XRD patterns over a wider range of diffraction angles). Each binary system shows different peak evolution with varying composition. The (BryCl1-y)3 system shows the simplest trend, with a monotonic shift of the C(100) peak to lower angles with increasing Br content, indicating a homogenous solid solution without any phase transition. The (IxBr1-x)3 system shows not only a shift of the C(100) peak to lower angles with increasing I ion content but also peak separation at high I contents above x = 0.833. We assign each peak as T(002) for the lower angle peak and T(110) for the higher one. The phase transition from the C to T phase is also confirmed by the evolution of the peak at approximately 23.5o corresponding to T(211) (Fig. S2, Supplementary Materials), which can be considered as the indicator peak of the T phase because it is observed only from the T phase. This result is consistent with previous reports that the I-Br binary compound forms a homogeneous solid solution, with a phase transition of approximately x=0.8 [36]. The full width at half maximum (FWHM) of the XRD peaks corresponding to (220)T and (200)C planes of MAPbI3, MAPb(I0.333Br0.667)3, MAPb(I0.667Br0.333)3 and MAPbBr3 is 0.08585, 0.09452, 0.13453 and 0.08963o, respectively. The slightly wider FWHM values for the I-Br mixed compounds can be attributed to the compositional inhomogeneity [37]. However, the peak broadening in our case is not significant as much as the reported result from spin-cast samples where I-Br mixing induces three times increased FWHM. In contrast, more complicatedly, in the ClzI1-z system, the XRD peaks shift insignificantly but decrease or increase in intensity with increasing Cl content. For example, Fig.

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2d shows that the peak at approximately 14° gradually decreases and disappears at z>0.9, whereas a peak at approximately 15.5° appears at z≥0.067 and then gradually increases. Over a wide range from z=0.067 to 0.8, these peaks coexist. For the case of the unmixed perovskites (i.e., z = 0 or 1), the peaks at approximately 14° and 15.5° correspond to T(002) and T(110) of MAPbI3 and to C(100) of MAPbCl3, respectively. Considering that these peaks slightly shift at z≤0.033 and z≥0.8, these peaks for the mixed perovskites (0
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arising from the same contents of large I- and small Cl- ions. In contrast, the separation of the peak at y<0.5 is attributed to phase segregation, not to a phase transition, because the two peaks gradually shift in opposite directions with increasing I and Cl contents and are finally positioned around the diffraction angles corresponding to TI(110) and CCl(100) of the Cl-I binary system (at y=0). Therefore, the lower angle peak is concluded to come from the I-rich phase and the higher angle peak from the Cl-rich phase. Notably, peak separation from C(100) to T(002) and T(110) is not observed for the compositions with 0.1
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(b)

(a) MAPbI3 1.0

MAPbI3 6.27 Å

0.9

ɑ-axis lattice constant (Å)

0.8 0.1

0.7 0.6

0.2

0.5 0.4

0.3

0.2

0.4

0.1

C

CI+CCl

TI+CCl

0.5

MAPbBr3

0.3

5.93 Å

MAPbBr3 1.0

6.27

0.9

0.6

0.8

6.05

0.5 0.4

5.98

0.3

0.9

MAPbCl3

6.12

0.6

0.8

1.0

6.20

0.7

0.7

5.90

0.2

0.1

5.68 Å

5.83

MAPbCl3

5.76 5.68

Figure 3. Ternary diagrams of the phase and a-axis lattice constant. (a) Ternary phase diagram with vertices of MAPbI3, MAPbBr3 and MAPbCl3. The pink area is the single phase region, and the gray and black areas are multiphase regions. Solid dots represent that the composition has the single phase of C or T, half-solid dots represent the multiphase of CI+CCl, and open dots represent the multiphase of TI+CCl. The boundaries between the single phase and multiphase regions are left empty as a buffer zone because whether such compositions are in the single phase or multiphase region is unclear based on the XRD results. Further studies are needed to define a more accurate boundary. (b) Ternary diagram of the a-axis lattice constant, which was determined from the XRD patterns using Bragg’s law. Only the single phase region is shown. The lattice constant of each composition is represented by color. Gray dots indicate the examined compositions.

Based on the XRD analyses, a ternary phase diagram of MAPb(IxBryClz)3 at room temperature was obtained, as shown in Fig. 3a. To determine the boundaries of the single phase and multiphase regions, XRD was taken at closer intervals around the boundaries (Fig. S8, Supplementary Materials). Solid, half-solid and open dots indicate the examined compositions that stabilize as the single phase of C (or T, only for binary IxBr1-x with x<~0.2), the multiphase of CI and CCl, and the multiphase of TI and CCl, respectively. The distribution of the dots clearly shows three different regions. We classify the regions as one single phase region and two 13

multiphase regions. The boundaries between the single phase and multiphase regions are left empty as a buffer zone because we did not investigate finer compositions in these zones; some of solid dots are still placed in the white buffer area because small amount of residue (PbCl2 or PbI2) is observed. The single phase region develops around the MAPbBr3 vertex and extends sharply along the I-Br and Br-Cl edges, which can be explained by the low solid solution limits of the Cl-I system and the homogeneous solid solution nature of the I-Br and Br-Cl systems, as discussed above. Since the ionic radius of Br- (196 pm) is close to the average of those of I- (220 pm) and Cl- (181 pm) [42], reasonably, the tolerance for containing both I and Cl is enhanced with increasing Br content. Bragg’s law gives the lattice constants of each phase with varying composition in the single phase region and even in the multiphase regions, as summarized in Tables S1 and S2 (Supplementary Materials), respectively. In general, a multiphase film or powder is considered unsuitable for substantive applications, such as optoelectronic devices, due to its complexity and, more importantly, its low optoelectronic performance [43,44]. For this reason, we focused further investigations on the single phase region. Fig. 3b shows a ternary diagram of the a-axis lattice constant (a) in the single phase region. a varies from 5.68 to 6.27 Å, as expressed with color; kα1 peaks were used to calculate the a-lattice parameter. Each color forms a parallel line, almost horizontal and with a gentle slope, indicating that all the compositions having identical average ionic radii have similar lattice constants. In addition, the lattice constant increases almost linearly with the ionic radius of X-. A plot of a versus RX-, where RX- is equal to the linearly averaged ionic radius according to the I, Br and Cl composition, has a high r2, the coefficient of determination of simple linear regression, as high as 0.9991 (Fig. S9, Supplementary Materials). This linearity provides predictability, hence making it simple to design a desired composition.

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Moreover, expansion of the phase diagram, from the previously reported binary compositions to the ternary compositions with a wide range of the single phase region, enables the use of infinite (x,y,z) combinations to obtain a certain lattice constant, which will be discussed later along with Eg and RYPL. The high linearity indicates that Vegard’s law is obeyed with a very small deviation, i.e., a small bowing parameter. The bowing parameters of the a-axis lattice constant of the IxBr1x-zClz

ternary composition (aI-Br-Cl) are determined using Equation (1) [45-47].

aI-Br-Cl = (1-x-z)·aBr + x·aI + z·aCl – x(1–x)·bI-Br – z(1–z)·bBr-Cl – xz·bxz

(1)

where aX is the a-axis lattice constant of each X system, bX is the binary bowing parameter of each X system, and bxz is the ternary bowing parameter. Through a second-order polynomial fitting (Fig. S9, Supplementary Materials), the binary parameters, bI-Br and bBr-Cl, are determined to be -0.02 and -0.08 Å, respectively. Then, using the binary parameters and Equation (1), the ternary parameter bxz is determined to be 0.05 Å, for the first time to the best of our knowledge. In addition, the remaining binary parameter bI-Cl, which has been difficult to experimentally obtain for the Cl-I binary system due to the low solubility, is determined using the relation bxy = bI-Cl – bBr-I – bBr-Cl under a quadratic approximation [46]. Our experimentally obtained bI-Cl is 0.15 Å.

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Figure 4. Optical bandgap energy of ternary compositions. (a) Ternary phase diagram showing the points at which F(r) were measured. The horizontal blue and vertical red lines indicate the (Bry(Cl0.5I0.5)1-y)3 and (Br0.5ClzI0.5-z)3 compositions, respectively. (b) F(r) of the single binary compositions along the edges of the I-Br and Br-Cl systems in the ternary map. F(r) of (c) the (Br0.5ClzI0.5-z)3 compositions and (d) the (Bry(Cl0.5I0.5)1-y)3 compositions. (e) Ternary diagram of optical Eg, determined from the F(r) using the Tauc plot (Fig. S11, Supplementary Materials). Only the single phase region is shown. Eg is represented by color. Gray dots indicate the examined compositions. (f) Optical Eg of the compositions in the single composition region as a function of the a-lattice constant. r2 denotes the coefficient of determination of simple linear regression.

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For photovoltaic, optical and optoelectronic applications, effective control of Eg is essential. Therefore, diffuse reflectance UV-Vis spectra F(r) were measured to obtain the optical Eg in the single phase region of the ternary composition diagram, as shown in Fig. 4a. All the examined compositions are indicated in the diagram as solid dots, and all the F(r) of these compositions are shown in Fig. S10 (Supplementary Materials). Among them, the F(r) of the binary compositions along the I-Br and Br-Cl edges are shown in Fig. 4b, and those of the ternary compositions along the horizontal and vertical lines indicated in Fig. 4a, i.e., (Bry(Cl0.5I0.5)1-y)3 and (Br0.5ClzI0.5-z)3, are shown in Fig. 4c and d, respectively. The F(r) intensities do not greatly deviate from each other. The absorption edge of the binary composition gradually increases over a wide range as the ionic radius of the X site decreases, which agrees well with previous reports. This trend is also observed in the ternary system. The absorption edge of the (Bry(Cl0.5I0.5)1-y)3 compositions with almost the same ionic radii varies in a narrow range from ~2.0 to ~2.2 eV, while that of the (Br0.5ClzI0.5-z)3 compositions with largely changing ionic radii varies in a wide range from ~1.8 to 2.6 eV. Using the spectra, the optical Eg are determined by extrapolation of the Tauc plots, as shown in Fig. S11 (Supplementary Materials). Fig. 4e shows a ternary diagram of the optical Eg in the single phase region. The Eg of MAPbI3, MAPbBr3 and MAPbCl3 is determined to be 1.54, 2.25 and 2.97 eV, respectively, and all the other compositions have Eg values between 1.54 and 2.97 eV. Experimental and theoretical studies have shown that in binary systems, Eg varies over a wide range with X site substitution [14,15, 16-18]. Our results confirm that the ternary system agrees well with the trend that Eg gradually increases with decreasing RX-. Therefore, this ternary Eg diagram implies that a certain Eg in the range of 1.55 - 2.9 eV can be obtained for various combinatorial compositions of MAPb(IxBryClz)3. For example, to obtain an Eg of 2.25 eV, one

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can design the composition to be MAPb(I0.25Br0.5Cl0.25)3 or another ternary composition, such as MAPb(I0.08Br0.8Cl0.12)3 or MAPb(I0.17Br0.6Cl0.23)3, as well as the simple MAPbBr3. This result is very important in the sense of extension of the composition map, which may lead to the development of more suitable physical properties for desired applications. Another interesting point is that each color forms a parallel line with a slope slightly greater than that of the lattice diagram (Fig. 3b). This result indicates that the compositions with identical RX- have similar Eg, similar to the trend of the a-axis lattice constant; hence, Eg also obeys Vegard’s law with a very small deviation. We determine the bowing parameters of the Eg of the IxBr1-x-zClz ternary composition (EI-Br-Cl) using Equation (2) [45-47].

Eg,I-Br-Cl = (1-x-z)·Eg,Br + x·Eg,I + z·Eg,Cl – x(1–x)·bI-Br – z(1–z)·bBr-Cl – xz·bxz

(2)

where EX is the Eg of each X system, bX is the binary bowing parameter of each X system, and bxz is the ternary bowing parameter. The binary parameters, bI-Br and bBr-Cl, are determined to be 0.20 and 0.15 eV (Fig. S12, Supplementary Materials), similar to the previously reported experimental values of 0.33 and 0.30 eV, respectively [36,48-50]. Using the binary parameters and Equation (2), the ternary parameter bxz is determined to be 0.5 eV, for the first time to the best of our knowledge. In addition, the remaining binary parameter bI-Cl, which has been difficult to experimentally obtain for the Cl-I binary system due to the low solubility, is determined using the relation bxy = bI-Cl – bBr-I – bBr-Cl under a quadratic approximation [46]. Our experimentally obtained bI-Cl is 0.85 eV, which agrees well with previous first-principles calculation (0.873 eV) [51]. Strictly speaking, this does not mean that the electronic Eg does not deviate from the Vegard rule. However, the electronic Eg bowing would not different significantly from the

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optical Eg bowing obtained in this study, when considering the low excitonic binding energy (0.02-0.05 eV) of MAPbX3 films [52-55] and the small variation by mixing halides [52, 56], as well as the large particle size (micrometer scale) of our powders in which the excitonic binding energy would be much smaller compared to thin films, nanoparticles and quantum dots [55, 5759]. Uniquely, the optical bowing observed for MAPbX3 is very small. The deviation from Vegard’s law is small when the ion size and electronegativity differences between substituted and original atoms are small [60-62]. Considering the differences in ion size and electronegativity, the HP solid solution has one of the smallest bowing parameters compared to other semiconductor systems, such as II-IV and III-V compounds, as shown in Fig. S13 (Supplementary Materials). Such small optical bowing is extraordinary; hence, further study to reveal the origin of the low optical bowing of HPs is ongoing in our group. Regardless of the understanding of the low bowing phenomenon, one can easily obtain a specific Eg by designing ternary halide compositions using the experimentally obtained small optical bowing parameters. Furthermore, the composition design becomes much easier by utilizing the dependence of Eg on the a-axis lattice constant (Fig. 4f). Notably, all the compositions, i.e., not only the binary but also the ternary compositions, lie on a line with a high r2 of 0.9855, indicating an almost linear relationship between Eg and the lattice constant.

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Figure 5. Relative PL yields of ternary compositions. (a) Ternary phase diagram showing the points at which PL was measured. The horizontal blue and vertical red lines indicate the (Bry(Cl0.5I0.5)1-y)3 and (Br0.5ClzI0.5-z)3 compositions, respectively. (b) Normalized PL as a function of the photon energy of the single binary compositions along the edges of the I-Br and Br-Cl systems in the ternary map. (c) PL intensity versus Rx- of the binary compositions. PL of (d) the 20

(Br0.5ClzI0.5-z)3 compositions and (e) the (Bry(Cl0.5I0.5)1-y)3 compositions. (f) Ternary diagram of the PL intensity. Only the single phase region is shown. The PL intensity is represented by color. Gray dots indicate the examined compositions. (g) Ternary diagram of the Urbach energy, which was determined from the exponential tail of F(r) near the absorption edge.

The PL spectra of the samples were measured to obtain the PL intensity, which can be considered as the relative PL yield (RYPL) because identical pumping source and power were used for the measurements. Fig. 5a shows the measured compositions in the single phase region of the ternary composition diagram. All PL spectra are shown in Fig. S14 (Supplementary Materials). All binary and ternary systems show PL peak positions consistent with the F(r) absorption edges, indicating mainly band-to-band transition-induced radiation. The PL of the binary compositions along the I-Br and Br-Cl edges are shown in Fig. 5b. Interestingly, the PL intensities vary in a nonmonotonic manner with decreasing RX- (Fig. 5c), i.e., the maximum PL intensity occurs at (Br0.8Cl0.2)3. This phenomenon is also observed in the ternary system. Fig. 5d and e shows the PL spectra of (Bry(Cl0.5I0.5)1-y)3 and (Br0.5ClzI0.5-z)3, which correspond to the horizontal and vertical lines in Fig. 5a, respectively. The (Bry(Cl0.5I0.5)1-y)3 system exhibits a gradual increase in the PL intensity with increasing y. In contrast, the (Br0.5ClzI0.5-z)3 system shows higher PL intensities at both ends of the composition line and lower PL intensities in the middle. These tendencies are easier to observe in Fig. 5f, which represents the ternary diagram of the PL intensity. This diagram clearly shows that the compositions of (Br0.5I0.5)3, (Br1)3 ~ (Br0.8Cl0.2)3 and (Br0.5Cl0.5)3 have higher PL intensities than the peripheral compositions. We deduce based on the Urbach energy that the large differences in the PL intensity among the compositions do not originate from different degrees of structural disorder or imperfections in the stoichiometry of the synthesized powders [63, 64]. The Urbach energies of the ternary compositions were compared, as shown in Fig. 5g, by fitting the absorption tails shown in Fig.

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S15 (Supplementary Materials). The Urbach energy varies over a large range from ~20 to ~90 meV. However, most of the compositions have low Urbach energies from ~20 to ~30 meV, except in the region close to the MAPbCl3 vertex. The high RYPL compositions are all positioned in the low Urbach energy region, and the neighboring compositions have similar Urbach energies. To the best of our knowledge, this ternary PL map is presented here for the first time. This map is not yet perfect since wide intervals occur between each examined point; a PL map with a narrower interval may reveal other compositions with higher intensities. Nevertheless, it is meaningful to confirm that certain compositions with relatively high PL yields compared to other compositions with identical Eg can be obtained. For example, the mixed-halide compositions exhibit higher PL intensities than any peripheral compositions for the cases of Eg of approximately 1.7 eV, 2.3 eV and 2.6 eV, which correspond to red, green and blue light, respectively. Therefore, one can easily find the optimal compositions for red, green and blue light emission. More interestingly, the trend of RYPL along the I-Br [65] and Cl-Br [20] binary systems is similar to the trends of the photocurrent PL intensity and PL decay time, which have been previously reported. Among the I-Br binary compositions, the longest PL decay time and the highest photocurrents were obtained for MAPb(IxBr1-x)3 at x=0.667 [65]. Additionally, among the Cl-Br binary compositions, the highest PL intensity and longest average recombination lifetime were obtained for MAPb(BryCl1-y)3 at y=0.8 [20]. Our PL results also show the highest RYPL at y=0.8 for MAPb(BryCl1-y)3. Considering that efficient PL is required for the high performance of optoelectronics [19], our findings have profound implications for identifying effective compositions for applications.

4. Conclusions

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Our study focuses on the exploration of the MAPb(IxBryClz)3 ternary mixed system by synthesizing materials via a facile mechanochemical method that can minimize the nonstoichiometric problem. The ternary phase diagram with vertices of MAPbI3, MAPbBr3 and MAPbCl3 was obtained along with maps of the a-lattice parameter, energy bandgap, and relative quantum yield. Certain Eg and a-lattice parameter, in the ranges of 1.55 - 2.9 eV and 5.58 - 6.27 Å, respectively, can be obtained for various combinatorial compositions, and the Eg of MAPbX3 perovskites can be approximated due to the small Eg deviation from Vegard’s. Additionally, the PL yield varies greatly with the X site ion combination, even for the same bandgap and the same lattice constant. Through this work, we extended the structural and optical information of the ternary mixed-halide perovskites. In addition, we demonstrated that the compositional mapping using a solid-state reaction is an efficient and robust way to studying basic properties of halide perovskites.

Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) [NRF-2017R1A4A1015022] and the Technology Development Program to Solve Climate Change of the National Research Foundation (NRF) funded by the Ministry of Science and ICT, Republic of Korea (2016M1A2A2936781).

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Graphical abstract

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