The last decade has witnessed a meteoric rise in the study of lead halide perovskites for optoelectronic applications. The initial 2009 report on CH3NH3PbI3 (MAPI) as a photovoltaic (PV) absorber has led to extensive research on its compositional and structural derivatives. 1,2 Although MAPI-based solar cells have impressive photovoltaic properties (power conversion efficiencies ~25%), the combination of thermal instability (due to the organic methylammonium component), moisture sensitivity, and toxicity concerns (due to Pb 2+ ) have led to a search for alternative materials. 3 The all-inorganic analogue, CsPbI3, has been shown to be more thermally stable than MAPI, but the instability of the perovskite polymorph at room temperature in CsPbI3 limits its usefulness for PV applications. 3 One strategy for eliminating Pb 2+ is creating B-site ordered variants of CsPbX3, such as double perovskites, Cs2M I M III X6 [M I = Na + , Ag + ; M III = In 3+ , Sb 3+ , Bi 3+ ; X = Cl -, Br -]. 4 Studies of double perovskites have resulted in a variety of functional materials that have shown promise for photoluminescent applications. [5][6][7][8] However, the formation of bulk double perovskites containing iodide has been elusive. As a result, the band gaps of double perovskites (roughly 2-5 eV) are too large to be optimal for use in single junction solar cells. To date, the champion double perovskite solar cells show efficiencies of < 2%, observed for both Rb + and S 2-doped Cs2AgBiBr6, far too low for practical applications. 9,10 The absence of A2M I M III I6 double perovskites does not preclude the investigation of ternary and quaternary iodides with alternative structures. Ternary iodides that contain Ag + and trivalent cations like Bi 3+ and Sb 3+ are an obvious alternative. Several ternary compounds can be found in the Ag-Bi-I phase diagram, [11][12][13] including AgBiI4. This compound crystallizes with the CdCl2 structure type, which consists of cubic close packed layers of chloride ions with Cd 2+ filling the octahedral holes in alternating layers. 14 Unfortunately, the thermodynamic instability of AgBiI4 makes synthesis difficult. In fact, AgBiI4 does not appear as a stable phase in the AgI-BiI3 pseudo-binary phase diagram. 15 Bulk powders of AgBiI4 have only been synthesized at high temperatures with long reaction times and quench cooling (≥ 350°C, 144 h), which suggests that while it may be stable at elevated temperatures it is only metastable at room temperature. 14 Searching the literature for ternary M I -M III -I [M I = Na + , Ag + ; M III = In 3+ , Sb 3+ , Bi 3+ ] phases yields few results. NaInI4
is the only such compound in the Inorganic Crystal Structure Database (ICSD), and it contains isolated [InI4] -tetrahedra, and thus would be better described as a salt rather than an extended covalent-network solid. 16 Here we report a new ternary lead free iodide material, AgSbI4 and several AgSb1-xBixI4 compositions, all of which adopt the CdCl2 structure.
A combination of symmetry analysis and ground state energy calculations are used to show why three-dimensional cation ordering is not observed. Variable temperature optical measurements reveal a rather large thermochromic effect, and through a combination of experiment and computation this behavior is shown to originate largely from strong electron-phonon coupling.
The following reagents were commercially purchased and used as received: AgBr (Alfa Aesar, 99.5%), AgI (Alfa Aesar, 99.9%), BiI3 (Sigma Aldrich, 99%), Bi2O3 (Alfa Aesar, 99.99%), CsBr (Alfa Aesar, 99.9%), SbI3 (Fisher Scientific, 99.99%), HBr (Alfa Aesar, 47%), and ethanol (Decon Labs Inc., 200 proof). Polycrystalline samples of AgSbI4 were synthesized via solid state reactions in evacuated silica ampules. For a typical 2.00 g (2.71 mmol) synthesis of AgSbI4, 0.637 g of AgI (2.71 mmol) and 1.363 g of SbI3 (2.71 mmol) were ground in an argon-filled glove box for 20 minutes and then loaded into an alumina crucible (4.78 mm ID × 7.99 mm OD, 102 mm length, AdValue Technology). This crucible was then loaded into a silica ampule (15 mm ID × 19 mm OD, Technical Glass Products) and placed under vacuum on a Schlenk line for 30 minutes at a pressure of ~50 millitorr before sealing. The samples were heated at 125 °C for 18 hours in a muffle furnace with the tubes in a horizontal configuration, with 10 °C/hour ramping rates. One cycle of heating proved sufficient in producing phase pure samples. The synthesis of AgBiI4 was attempted via the same procedure as above, at temperatures from 125-200 °C. AgSb1-xBixI4 [x = 0.25, 0.50, 0.75] samples were synthesized from appropriate molar ratios of AgI, SbI3, and BiI3 following the same synthetic protocol as above, except the synthetic temperature was increased to 175 °C.
Powder X-ray diffraction (PXRD) data were collected on a Bruker D8 Advance powder diffractometer (40 kV, 40 mA, sealed Cu X-ray tube) equipped with an incident beam monochromator (Johansson type SiO2-crystal) and Lynxeye XE-T position sensitive detector. Variable temperature powder X-ray diffraction (VT-PXRD) was performed on a Bruker D8 Advance powder diffractometer in Bragg-Brentano geometry (Cu-Kα radiation), equipped with an Anton Paar HTK 1200 N High-Temperature Oven-Chamber. Rietveld refinements of PXRD data were carried out using the TOPAS-Academic (Version 6) software package. 17 A Rigaku MiniFlex II benchtop powder X-ray diffractometer (30 kV, 15 mA, sealed Cu X-ray tube, with a NaI scintillation detector) was used for initial phase identification and monitoring material stability to atmospheric conditions. UV-visible diffuse reflectance spectra (DRS) were collected from 178 nm to 890 nm with an Ocean Optics USB4000 spectrometer equipped with a Toshiba TCD1304AP (3648-element linear silicon CCD array) detector. The spectrometer features an Ocean Optics DH-2000-BAL deuterium and halogen UV-vis-NIR light source and a 400 μm R400-7-ANGLE-VIS reflectance probe. The spectrometer was calibrated using a Spectralon Diffuse Reflectance Standard. Variable temperature DRS (VT-DRS) studies were obtained using a Fisher Scientific Isotemp Hot Plate (Model: SP88854205) as the heat source. An oil bath and alcohol thermometer were used to determine the sample temperature during the trials. Measurements were taken at 25 °C increments, with the sample held at each temperature for 15 minutes before data was collected. The temperature range over which DRS and PXRD experiments were conducted was determined via thermogravimetric analysis (TGA), collected on a Thermogravimetric Analyzer TGA Q50. For TGA, the samples were heated under a nitrogen stream of 50 mL/min with a heating rate of 10 °C/min between 25 °C and 425 °C.
Possible ordered arrangements of Ag + /M 3+ metal cations were determined via symmetry analysis using ISODISTORT. 18,19 The ISODISTORT program was used to identify the space groups that arise from the occupational distortion in the Cd 2+ site. The distortion modes and irreducible representations were analyzed across all commensurate k-points following the second methodology of the program. The k-points studied were Γ, F, L, and T. Ordered structures were also obtained by manually generating all possible patterns of Ag + /M 3+ ordering in a 2 × 2 × 2 supercell of the rhombohedral CdCl2 structure. These ordered structures were compared with those that arose from the symmetry analysis to make sure no simple pattern of cation ordering was overlooked. Structures were visualized using VESTA. 20 Hexagonal cells with 12 AgSbI4 formula units (a 2 × 2 × 2 supercell of the CdCl2 structure) containing the cation ordering patterns found using ISODISTORT were fully relaxed with respect to lattice and atomic positions using the Vienna Ab initio Simulation Package (VASP) 21,22 within the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) 23 functionals. A plane-wave cut-off of 250 eV and Γ-point centered 3 × 3 × 3 k-point mesh were used for integration. 24 After relaxation, the structures were converted to primitive cells using SeeK-path, 25 and final energy, density of states, and band gap were calculated with the HSE06 hybrid functional including spin-orbit coupling and Blöchl's tetrahedron method 26 for k-point integration.
In order to study the effect of temperature on the band gap, first the influence of thermal expansion was studied by fixing the lattice constants to the experimental values for the different temperatures and solely relaxing the atomic positions, before calculating the band structure with the above hybrid-functional settings. In order to study the coupling between atomic motion and band gap, molecular dynamics (MD) simulations for 288-atom hexagonal supercells with 6 layers were performed within the canonical ensemble using PBE potentials, Γ-point only k-point sampling, an energy cutoff of 187 eV, a time step of 2 fs, and a Nosé thermostat with a Nosé-mass corresponding to a period of 40 time steps.
Experimental lattice constants for the respective temperatures were used.
Synthesis of AgSbI4 provided a phase pure product with a dark red color. While a single-phase product can be obtained by heating at the relatively modest temperature of 125 °C, figure S2 shows no evidence of mechanochemical reaction between SbI3 and AgI upon grinding at room temperature. A satisfactory fit to the PXRD data can be obtained with a starting model based on the CdCl2 structure with R3 ̅ m space group symmetry, as previously reported for AgBiI4. 14 The lattice parameters of AgSbI4 are a = 4.32257(3) Å and c = 20.6796(2) Å, which are comparable to the values of a = 4.311 Å and c = 21.12 Å reported for AgBiI4. 14 Additional structural details are provided in Table S1. Both compounds adopt the CdCl2 structure type (see Figure 1), which consists of a cubic close packed array of anions with cations filling the octahedral holes in alternating layers. The Ag + and Sb 3+ cations are disordered over a single crystallographic site, Wyckoff site 3a. It should be mentioned that a preferred orientation correction is necessary to obtain a satisfactory fit to the PXRD data.
Attempts to synthesize of AgBiI4 at reaction temperatures between 125 °C and 200 °C were not successful, instead producing a mixture of Ag2BiI5 and BiI3, even for those reactions where samples were quench cooled (Figure S1). 14,15 Samples of AgSb1-xBixI4 [x = 0.25, 0.50, 0.75] were prepared by heating to 175 °C for 18 hours. These samples were shown to be phase pure by subsequent PXRD analysis. Representative Rietveld refinements are provided in Figures S3 andS4. The higher reaction temperature was necessary for these three samples, as syntheses carried out at 125 °C resulted in samples containing clear signs of unreacted starting materials. All compounds in the solid solution have R3 ̅ m symmetry like the end members. It should be noted that the powder data can also be fit to a larger Fd3 ̅ m cell (the 3D Rudorffite polymorph). However, prior analysis using single crystal data of AgBiI4 conclusively shows that AgBiI4 is best described as having the layered CdCl2 structure-type. 14 We assume the same is true for AgSb1-xBixI4 studied here.
The lattice parameters for the solid solution follow a Vegard's Law type behavior (Figure 1). The incorporation of antimony apparently stabilizes the AgSb1-xBixI4 solid solution against phase segregation into Ag2BiI5 and BiI3, while at the same time lowering the synthetic temperature. This is advantageous in comparison to the more extreme synthetic conditions needed to synthesize polycrystalline AgBiI4 (T ≥ 350°C with annealing times of 144 h). AgSbI4 tends to absorb atmospheric moisture if left exposed to ambient air for longer than a few days. Consequently, all samples were stored in a desiccator. The stability of AgSb0.25Bi0.75I4 upon exposure to light and humidity was studied over a 14-day span (~70% humidity and direct sunlight). Some changes are visible via PXRD and UV-vis DRS, but these effects are reversible upon reheating (Figures S5,S6). TGA was utilized to determine decomposition temperatures of the material. The decomposition pathway involves the sublimation of MI3 [M = Sb 3+ , Bi 3+ ], as determined by the mass loss percentages from TGA, as shown in Figure S7. The solid solution compounds are stable to ~175 °C, while the antimony end member starts to decompose at ~150 °C.
In halide double perovskites, like Cs2AgBiBr6 and Cs2AgSbCl6, the Ag + and Sb 3+ /Bi 3+ ions adopt an ordered arrangement, whereas no sign of cation ordering is evident in the PXRD data of any AgSb1-xBixI4 composition. To explore this attribute in more detail, we used the ISODISTORT program 18,19 to obtain crystallographic descriptions of structures that could arise from a hypothetical 1:1 ordering of cations on the octahedral sites of the rhombohedral CdCl2 structure.
Looking across the commensurate k-points (Γ, F, L, and T), 12 subgroups of the R3 ̅ m parent structure were found. Two of these can be dismissed: Γ 1+ P1 returns the parent structure with no ordering and F 1+ P3 results in a structure with multiplicities of the two cation sites that are incompatible with 1:1 ordering of Ag + and M 3+ cations. Each of the 10 remaining structures can be divided into one of three groups based on the types of layers that are present. The highest symmetry structure in each of these groups was chosen to be representative of the group. Structure 1 consists of alternating AgI2 -and MI2 + layers. This structure, which belongs to the T 1+ irreducible representation (irrep.), maintains the R3 ̅ m symmetry of the parent structure while doubling the length of the c-axis. Structure 2 consists of alternating silverrich and M 3+ -rich layers. Within each layer the minority cation is surrounded by octahedra containing the opposite cation in a pattern that maintains a 3-fold rotation axis. To maintain this symmetry the layer composition alternates between AgM3I8 2+ and Ag3MI8 2-. This structure results from the L 1+ irrep and has R3 ̅ m symmetry, like structure 1, but with a unit cell where both the a-and c-axes are doubled. Consequently, the unit cell volume is four times larger than structure 1. Structure 3 can be described as a striped ordering of cations, with the stripes running parallel to one another from one layer to the next. Unlike structures 1 and 2, structure 3 maintains the charge balanced AgMI4 stoichiometry within each layer. In total, 6 of the 10 subgroups (F 1+ P1, F 1+ C2, F 1+ S1, L 1+ P1, L 1+ P2, and L 1+ C1) are made up of similar AMI4 layers with striped ordering of cations, but each differs from the others in the way those layers are stacked. F 1+ P1 was chosen to be the best representative of this group, due to it having the cell with smallest volume and highest symmetry (P2/m). To determine the impact of layer stacking on the overall stability of the structure, subgroups that are variants of structures 2 and 3 were investigated. Structure 4 has the same layers as structure 3, however, the layers are rotated so that the stripes run parallel to the a-axis in one layer and parallel to the b-axis in the next layer. Only one subgroup allows for this stacking: L 1+ S1, with P1 ̅ symmetry. This subgroup has 8 unique octahedral sites and therefore many patterns of ordering are consistent with this symmetry, but for the energy modeling that follows the ordered pattern shown in Figure 2 was adopted. Finally, structure 5 can be described as a lower symmetry version of structure 2 where the AgM3I8 2+ and Ag3MI8 2-layers are offset in a way that breaks the 3-fold rotation axis. Generated from the L 1+ C2 subgroup, structure 5 has C2/m space group symmetry. A summary of the ISODISTORT results for these five structures is given in Table 1. Further details can be found in the Supplemental Information (Table S2). Density functional theory (DFT) calculations were used to assess the energetics of the cation ordered structures 1-5, and the results are shown in Table 1. The analysis shows that the energies are largely determined by the structure and composition of the layers. Structure 1 with alternating AgI2 -and MI2 + layers possesses the highest energy. Structures 2 and 5, where the charge imbalance between layers is smaller, but not zero, are the next highest in energy. Finally, structures 3 and 4, both of which have charge-balanced layers and stripe ordering have the lowest energy. The calculations show the energy of the structure depends very little on how the layers are stacked. For example, the striped structures (3 and 4) both have ground state energies of -14.69 eV/formula unit. In a similar vein structures 2 and 5 have very similar energies. Given this result we would expect that even if cation ordering was maintained within the layers, a high concentration of stacking faults would result. Thus, three-dimensional, long range order of cations seems unlikely in ABX4 compositions with the CdCl2 structure type. along with the unit cell vectors (in terms of the hexagonal setting of the parent CdCl2 unit cell), space group symmetry and calculated ground state energies. The origin is (0,0,0) for all structures.
The optical absorption properties of AgSb1-xBixI4 were measured with UV-vis DRS. The DRS data was transformed using the Kubelka-Munk (KM) function to extract estimated band gaps. This is given by Equation 1:
where F(R) is the optical absorption coefficient and R is the reflectance. This equation allows the absorbance of a material to be expressed as a function of the reflectance. 27 All compounds are semiconductors, with band gaps at room temperature that vary from 1.68 eV (x = 0.75) to 1.92 eV (x = 0).
Figure 3 shows extracted band gaps from temperature-dependent diffuse reflectance measurements. The values red-shift as the temperature increases; this is a trend seen in most semiconductors. 28 The extent of the band gap change with temperature is approximately 3× larger than typical diamond-like semiconductors like Si and GaAs, which have ΔEg/T of ~0.27 and 0.45 meV/K between 300 and 400 K. 29 In an attempt to assess whether the cause of the increase is due to the layered crystal structure or the increased ionicity of the bonds, VT-DRS measurements were taken on a cubic halide double perovskite (Cs2AgBiBr6) and the titular solid solution. Cs2AgBiBr6 was synthesized using previously described methods and the phase purity of the resulting product was verified using PXRD (Figure S8). The diffuse reflectance data and the resulting KM plots for AgSbI4, AgSb0.25Bi0.75I4, Cs2AgBiBr6, and BiI3 are shown in Figures S9-S12 and the resulting band gaps are summarized in Table S3. Measurements were not performed on SbI3 due to its hygroscopicity and volatility; however, a red-shift in color is observed when SbI3 is heated. To understand why the thermochromic shift for CdCl2-type compounds is greater than diamond-like semiconductors, we examine the roles of thermal lattice expansion and electron-phonon coupling, i.e. the influence of atomic motion on the band gap. Temperature-dependent lattice dilation is a consideration in the Varshni equation 30 , which is an empirical model for band gap changes with temperature in semiconductors. For most semiconductors, temperature increase causes the lattice to expand and the band gap to decrease. Therefore, it is reasonable to think that a larger thermal expansion of the lattice would cause an increased thermochromic effect. Thermal expansion coefficients indicate the extent to which characteristics of a material, such as the bond lengths and the volume, change as a function of temperature. To determine these values, Equation 2 is used:
where Vi and Vf are the initial and final volume, Ti and Tf are the initial and final temperature in K, and αV is the voluthermal expansion coefficient. 31 If the volumes are replaced with M-X bond lengths, we can calculate the bond thermal expansion parameters (αM-X). The resulting expansion coefficients are listed in Table 2 Due to the layered nature of the compound and the relatively weak polar covalent M-I bonds [M = Sb 3+ , Bi 3+ ],
AgSbI4 and AgSb0.25Bi0.75I4 show relatively large thermal expansion, which is anisotropic and is ~30% larger in the cdirection than within the ab-plane (Table 2). VT-PXRD was used to determine the thermal expansion coefficients of these materials. A representative set of diffraction patterns for AgSbI4 is shown in S4). A comparison with the literature provides context for the observed values. As a point of comparison, the thermal expansion of CoMnCl4, which is a mixed metal compound that shares the CdCl2 structure type with AgSb1-xBixI4, has been studied. While the axial thermal expansion coefficients (αa = 18.6 vs. αc = 30.4) 33 are much smaller than those seen here for AgSbI4 and AgSb0.25Bi0.75I4, in both cases the expansion along the c-axis (perpendicular to the layers) is significantly larger than it is in the ab-plane. The diamond-like semiconductors CdTe and copper-indium-gallium-selenide (CIGS) have smaller thermal expansion coefficients of αV = 14 and αV = 27, respectively. 34,35 This is to the strong three dimensional covalent bonding network that limits increases in interatomic spacing in these compounds. In contrast, the lower valence of the bonds in the CdCl2 structure (1/3 in CdCl2 vs. 1/2 in CdTe) leads to weaker bonding than seen diamond-like semiconductors with tetrahedral coordination, and in turn the weaker bonds lead to greater thermal expansion. That's not to say that the change in crystal structure doesn't also play a role. The cubic double perovskite Cs2AgBiBr6 contains a pseudo-octahedral environment for the anion (linear if we ignore Cs-Br bonds) that contrasts with the trigonal pyramidal anion environment in AgSb1-xBixI4. This change in anion environment may help to explain the volumetric expansion coefficient αv that is significantly smaller than for AgSb1-xBixI4. 32 Table 2 shows that the layered phases, AgSbI4, AgSb0.25Bi0.75I4, and BiI3 all have αM-X values that are nearly twice that of Cs2AgBiBr6 (see also Fig-
). These layered structures contain halide ions in an anisotropic bonding environment (Figure 5), which seems to facilitate M-X bond expansion. S3). This thermochromic shift in band gap is consistent with literature studies on single crystals and thin films of Cs2Ag-BiBr6. 32 The differences in thermal expansion and thermochromism likely are due to the differences in halide bonding environments in the two systems. In the double perovskites, the halide is in a linear environment with 3-D connectivity, whereas the halide ions in the CdCl2 structure have an asymmetric trigonal pyramidal environment. Upon heating facile metal-halide bond expansion into the van der Waals gap can take place in the CdCl2 structure, driving the larger αM-X and resulting a larger temperature dependence of the band gap shift. The αM-X values seem to be a better predictor of band gap shifts than αV. This is demonstrated by BiI3, which has ΔEg and αM-X values that are similar to AgSb1-xBixI4, but a smaller αV due to differences in filling of octahedral holes.
In order to check these speculations and differentiate the effect of thermal expansion from the effect of thermal motion, the structures with charge balanced layers (3 and 4) were explored further computationally. We first calculated the effect of thermal expansion on the band gap of AgSbI4 for relaxed cells with DFT for the two lowest energy structures. Within the HSE hybrid functional, the change in the band gap from thermal expansion is very small, for structure 3 from 1.798 eV at 298 K to 1.796 eV at 373 K, and for structure 4, from 1.843 eV at 298 K to 1.835 eV at 373 K. These changes are much smaller than the observed thermochromic shift in AgSbI4, from which we conclude that thermal expansion itself is not the major contributing factor. To understand the effect of dynamic thermal motion of the atoms on the band gap, we then performed ab-initio MD simulations for 288-atom cells of structure 3 of AgSbI4 at 298 K and 373 K for ~8 ps, where the burn-in phase ends after 3-4 ps. Since these simulations are computationally demanding, no hybrid functional calculations were performed, resulting in significantly decreased band gaps (~1 eV). However, the trends and overall effects can still be analyzed. Figure 6 shows the results for the band gap, which shows an increase of oscillation amplitude at higher temperature, indicative of significant electron-phonon coupling. Using PBE, the band gaps for structure 3 at 298 K and 373 K are quite similar with values of 1.059 eV and 1.054 eV respectively. The effect of electron-phonon coupling is an order of magnitude larger, with dynamic band gaps of 0.94(6) eV and 0.88 (8) eV for 298 and 373 K, respectively. Thus, the temperature increase reduces the band gap by 60 meV or 6.8%, values that are much larger than the effect calculated solely from thermal expansion (5 meV or 0.5% using PBE) and rather similar to the experimental band gap decrease of 100 meV (5.4%) for AgSbI4. The shrinking of the band gap can be directly related to the amplitude of the atomic vibrations as measured through their mean square displacements, which at 298 K has an average value of 0.33(7) Å 2 , taken over the ~5 ps after the burn-in phase of the MD simulations where the displacements level out (Figure S16). However, this value increases to 1.9(1) Å 2 at 373 K, leading to much stronger oscillations of the band gap. This significant electron-phonon coupling is likely the primary cause of the observed thermochromic effect.
The novel ternary phase AgSbI4 and several samples within the AgSb1-xBixI4 solid solution have been synthesized via low temperature (< 200 °C) solid state routes and subsequently characterized. AgSbI4 and AgBiI4 both adopt the rhombohedral CdCl2 structure type and form a complete solid solution, although pure AgBiI4 appears to be metastable at room temperature. Symmetry analysis and DFT calculations show that structures with charge balanced layers are strongly favored, but there is little driving force for coherent ordering of cations from one layer to the next. All materials are semiconductors, with room temperature band gaps ranging from 1.92 eV (x = 0) to 1.68 eV (x = 0.75). The band gaps show a large red shift with increasing temperature, over 1 meV/K. This effect is driven largely by significant electron-phonon coupling in the system.