Solid-State Growth of Cspbi3 Perovskites: Phases Formation and Stability

Totally inorganic perovskites are playing an increasingly important role for their potential applications in optoelectronics devices. However, a big problem to be solved is the role of the different phases, the presence of which is closely linked to the growth method and to the role of impurities. In this article, we propose a solvent-free, solid-state growth method, which allows to obtain samples free of any organic residues. The analysis of structural (XRD and Raman measurements), optical (absorption, steady-time and time-resolved luminescence) and morphological (HRTEM imaging), permitted to understand the phase evolution during the synthesis as a function of the temporal duration. The dynamic equilibrium process at high temperature between the CsPbI 3 and the starting precursors, CsI and PbI 2 , plays a fundamental role in the final phase. If, from one side, the  and  phases are related to the exact stoichiometry, on the other hand an excess of CsI permits the formation of room temperature stable perovskite  -phase and, with a further excess, the secondary Cs 4 PbI 6


Introduction
Since the 1990s organic-inorganic hybrid halide perovskites have received increasing attention in the optoelectronic context [1] for their intrinsic properties such as ambipolarity, high charge-carrier mobilities, great diffusion lengths and high absorption coefficients [2] [3][4] [5]. As a consequence, they found potential application in many different sectors and devices, from efficient light harvesters to photovoltaics, photodetectors and solar fuels [6] [7][8] [9]. Also, due to their very high photoluminescence quantum yield and narrow-band emission in the whole visible region [10], they are promising materials to exploit for lighting and display applications.
Perovskites are a class of crystalline compounds described by the generic chemical formula AMX3, with A being a large cation, M a smaller metal cation and X an anion, like oxygen or one from the halide series. In the hybrid halides perovskites, the organic cations are small and are typically restricted to methylammonium, ethylammonium and formamidinium; in the all-inorganic halides perovskites the A cation is Caesium or Rubidium. The metal cations are typically divalent metal ions such as Pb 2+ , Ge 2+ , Sn 2+ while the halide anions are I − , Cl − and Br − .
One of the most fascinating characteristics of perovskites is the possibility to tune their optical and electronic properties by varying the composition of halide ion constituents. On the other hand, their application in commercial devices is strongly hampered by low phase stability. The requirements of resistance to various environmental stresses, such as humidity, illumination and high temperatures, being thermodynamically stable under operative conditions should be fully satisfied. Replacing the organic part of perovskites by an inorganic one currently represents a promising way to increase the long-term stability in operating conditions [11] [12]. Indeed, the absence of organic part facilitates the resistance to high temperature and to the interaction with solvents and surrounding atmosphere.
As a general rule, the structural stability of perovskites AMX3 is determined by the Goldschmidt tolerance factor = +

√2( + )
and by the octahedral factor = ⁄ , with rA, rM, rX being the different ionic radii. The ideal cubic structure is not very common and usually occurs in the ranges 0.8<t<1 and 0.4<<0.9 ranges [13].
All the members of the group of lead trihalides undergo phase transitions by varying the temperature, but with the high temperature phase being the cubic perovskite. Indeed, for inorganic for lead-based CsPbX3 (X=Cl, Br, I) four phases are expected: a cubic (), a tetragonal () and two orthorhombic phases (a black  and a non-perovskite yellow  phase). The -phase has a lower band gap as compared to the  phase (in particular, 1.7 eV vs 2.8 eV in CsPbI3, respectively) and displays a different luminescence emission peak (700 nm vs. 550 nm in CsPbI3) and lower emission efficiency.
Since the spherical Cs + ion is not large enough to preserve the PbI6 octahedra, CsPbI3 has relatively smaller t value compared to the hybrid organic-inorganic perovskites. So the cubic phase, which is desirable for optoelectronic applications, is stable only at high temperature and undergoes a phase transition to the thermodynamically favoured orthorhombic  phase when the samples are cooled down to room temperature [14] [15].
Different synthesis techniques were applied to obtain high quality samples, the solution deposition techniques being the most widely utilized, because of their low-cost and easy processing. There are mainly two approaches, based on a one-step or a two-step procedure [16] [17]. In the latter, dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) are used as solvents followed by high temperature annealing process. Solvent properties affect the quality of the film and for this reason, antisolvents engineering or solvent evaporation control are used to promote the crystallization process [18] [19]. Surface passivation strategies are common, the use of hydriodic acid or the so-called hydrogen lead iodide precursor [20][21] [22]. In the former approach, cubic phase is achieved in solution by co-precipitation of monodisperse colloidal nanocrystals, the stability being due to the large contribution of surface energy [23]. These methods require the use of long chain organic capping agents and high boiling point solvents. It was reported that the use of solvents and specific precursors can affect the synthesis, creating organic inclusions in a full inorganic perovskite [24].
Alternatively, other methods allow producing lead halide perovskites without the exploitation of capping ligands or solvents: gas phase deposition, mechanochemical synthesis or synthesis of single crystals [25] [26][27] [28]. In this work, we focalized our studies on CsPbI3 obtained by one step solidstate reaction. This kind of synthesis is relatively simple and, mainly, doesn't need the use of any solvent or ligand. This point is fundamental for clearly assessing the structural parameters that define the stable phase and to define how it is possible to achieve room temperature stable -phase CsPbI3.
Recently it has been proposed that many of the reported fully inorganic perovskite are stabilized by the organic part of the organic precursor utilized during the synthesis (i.e., hydrogen lead iodide), increasing the uncertainty about the real structure of the samples.
On this basis, we investigated the formation of secondary phases by means of XRD, HRTEM, microluminescence and micro-Raman, imaging spectroscopy, time resolved luminescence and optical measurements, pointing out the fundamental role of balancing the stoichiometry between the cations to define which phase will be formed.

Synthesis
CsPbI3 and Cs4PbI6 samples were synthesized by a solid-state reaction of CsI and PbI2. Stoichiometric raw materials were weighed, ground in an agate mortar, and then sintered in a furnace.
Different synthesis processes were performed.
First, the samples were slowly heated at 10 °C/min, up to 400 °C and treated at constant temperature for 10 minutes. Then, the samples were slowly cooled to room temperature.
The same process was carried out multiple times treating the samples at 400 °C for 1 hour, 5 and 10 hours, 17 hours and 24 hours, respectively, to study the effect of the synthesis duration on the final products. Hereinafter, the samples are called CPI3-10m, CPI3-1h, CPI3-5h, CPI3-10h, CPI3-17h, CPI3-24h. In order to discriminate the features of CsPbI3 from those of secondary phases, we synthesized pure Cs4PbI6. We repeated the previous procedure, treating the sample at 400 °C for 5 hours. The resulting sample will be indicated as C4PI6 in the following. As stated above, the stability is affected by oxygen and moisture, so the syntheses were performed in continuous vacuum (~8•10 -5 mbar).

Characterization
X-ray patterns were collected at room temperature by using a Rigaku Miniflex II diffractometer with θ-2θ Bragg-Brentano geometry with Cu Kα (λ = 1.54059 Å) radiation. The powder patterns were recorded in the 5° ≤2θ ≤ 45° range. High temperature measurements were performed with a Bruker calculating planar and angular relationships between diffraction spots and comparing them with the diffraction cards previously adopted for X-ray diffraction analysis.

X-ray diffraction measurements
The phase stability of CPI3 samples at different temperatures is underlined in Figure 1. CPI3-10m sample was obtained by solid state reaction with the correct stoichiometric amount of the precursors. Figure 1A reports the XRD pattern obtained at 400 °C in continuous vacuum, confirming the presence of -CsPbI3, with lattice parameter a = 6.218(1) Å (ICSD 161481). The sample was kept at 400 °C degree for 10 minutes and cooled down to RT, hence the XRD pattern was collected again ( Figure   1B). The sample turns in color from black to yellow and the Rietveld refinement on the X-ray diffraction pattern confirms the formation of the -CsPbI3 structure: the peaks are relatives to the orthorhombic -CsPbI3 (ICSD 27979), with crystal structure Pmnb (space group N. 62) and lattice parameters a=4.7993(2) Å, b=10.4521(6) Å, c=17.7456(9) Å, with Rwp=10.5 % and RB=8 %. This result shows the possibility of rapidly synthesizing lead halide perovskites by solid state reaction in the -CsPbI3 phase, which only at high temperature converts to -phase, as already reported in previous study [29].
Comparing these patterns with the one from CPI3-10m, the secondary phase Cs4PbI6 with crystal structure R-3c:H (Space group N. 167) is clearly observable in addition to the -CsPbI3 phase. The percentages of these two phases have been calculated by Rietveld refinement using the software MAUD [30] and highlighting that the percentage of Cs4PbI6 increases proportionally to the synthesis duration (Table 1).     The local properties were therefore analysed by optical microscope imaging coupled with a Raman and luminescence system. The samples appear constituted by black spots, surrounded by a white phase, mixed to a yellow phase.
The Raman spectrum, collected on the black spots, shows the presence of Cs4PbI6 (65 and 90 cm -1 ) and -CsPbI3 (55, 107 cm -1 ). The yellow part of the sample appears to be -CsPbI3 ( Figure 5) [29]. Focusing our attention on the PL at 715 nm, we performed a luminescence map. Figure 6 shows the intensity of the emission as function of the position, compared to the image collected by optical microscope. It's possible to notice as the emission is more intense in correspondence of the black spots.  The quantum efficiency of the samples calculated at 715 nm, obtained with an integration sphere with a de-focalized beam, gives a general overview on the emission properties of the different samples (Table 2). In addition, considering that this red emission is related to a -phase and it is well known that the quantum efficiency of this phase is close to the unity [34], it is possible to obtain an indirect rough estimation on the amount of -phase in the synthetized samples. The values in Table 2 confirm the low amount of -CsPbI3 deduced by X-Ray diffraction measurements, below the 1% detection limit [34][35].
In Figure 8,    Table 3. The average lifetime has been calculated using the following relation [36]: Figure 9: Time resolved luminescence measurement on two different points of CPI3-10h sample;  exc =500 nm. Faster decay times from the same emitting centres are related to the presence of non-radiative path: where obs is the decay time experimentally measured by time resolved luminescence, R and R (NR and NR) are the decay time and transition rate for a radiative (non-radiative) process. The faster the observed decay, the higher the presence of non-radiative path often related to structural defects.
In this case it is possible to argue that defective matrix non-homogeneously generates non radiative path for the emission from the phase of CsPbI3, as can be evinced from the punctual Raman/luminescence analysis and from HRTEM images.  Moreover, the well-defined, straight interface between the and -phases of CsPbI3 reported in These symmetry relationships were used to calculate the actual lattice mismatch (m) occurring between average lattice spacings of the two phases along a given direction (table 4). In general terms, the mismatch parameter m between the average lattice spacings of two different phases (indicated as d1 and d2, respectively) can be defined as: The direction. The relevant epitaxially-related lattice planes are presented in Figure 11, along with the corresponding diffraction spots in the 2D-FFTs. A slight angular distortion can be observed between the 2 -1 1 spots of -CsPbI3 and the 1-3-1 spots of CsPbI3 in comparison to their theoretical value, which could be attributed to local deformations in the crystalline frameworks in proximity to the interface. A general model on the phase formation in the solid-state synthesis is proposed in Figure 12. In the first step, -CsPbI3 is obtained from the precursors, CsI and PbI2 for temperature below 300 °C. Then, as the temperature increases, the transition between the  and  phase occurs in a relatively fast period (observed in 10 minutes). The -phase is a cubic CsPbI3 perovskite structure, consisting in I−ions corner-shared by two [PbI6] 4octahedra, with the Cs cation occupying the 12-fold coordination site formed in the middle of the cube of eight octahedra. The -phase requires the correct stoichiometry in the perovskite structure and high temperature (above 320 °C) to remain stable.
As time goes on, at 400 °C, the CsPbI3 phase partially undergoes a dynamic equilibrium consisting in its reverse dissociation into the starting precursors, CsI and PbI2.
PbI2 partially evaporates, leaving behind most/all the CsI and creating an amorphous layer around -CsPbI3. As already reported in literature, an excess of CsI in CsPbI3 helps the formation and the stabilization of the distorted perovskite  phase [37]. The  phase is orthorhombic, belonging to the Pbnm space group, and it remains stable at RT in a non-stoichiometric relationship CsI/PbI2>1. On the other hand, the  phase converts to the  phase at RT [14,15].
So, upon returning to RT after a variable amount of time spent at 400 °C, local variations in the CsI/PbI2 ratio caused by the evaporation rates of PbI2, determine which stable phases will form in the samples.  phase crystals will form in regions with an optimal CsI/PbI2 ratio (i.e.=1) at high temperature, and they will transform to  phase at RT. Whenever the ratio is higher than 1, the creation of -CsPbI3 is favoured over the . Finally, when the CsI/PbI2 ratio >>1, the formation of crystalline domains of secondary phase Cs4PbI6 is most likely, since the temporal increase of the thermal treatment generates a stronger excess of CsI, which prevents the formation of the perovskite phase and facilitates the formation of Cs4PbI6 (CsI/PbI2 about 4:1).
In this sense, structural analysis performed by HRTEM shows that domains of the different phases can be observed in close proximity, which confirms the heterogeneity in sample composition that was previously indicated by optical microscopy, luminescence and Raman maps. Also, the presence of epitaxial relationships at the interface between  and  phase domains suggest that the structural   rearranging caused by local variations in the PbI2 ratio does not imply a drastic rearrangement of the atomic positions, so that a smooth structural transition between  and  phases can be maintained even with a sharp interface.

Conclusions
The paper is focalized on the solid-state synthesis of pure inorganic Lead Halide perovskites of the class CsPbI3.
We have shown that a pure  phase can be obtained with a brief treatment (in the order of minutes) at 400 °C without any solvent, and that it quickly passes to a stable  phase at room temperature.
XRD analysis evidences that the increase of treatment time at steady temperature generates the formation of the secondary phase Cs4PbI6, while micro-Raman and micro-luminescence measurements underline the presence of the luminescent-phase.
The analysis of the collected data, time resolved measurements and HRTEM imaging permitted to understand the phase behaviour during the synthesis as a function of the temporal duration. After few minutes at high temperature, the CsPbI3 phase partially undergoes a dynamic equilibrium process consisting in the reverse dissociation to its starting precursors, CsI and PbI2. Lead iodide quickly evaporates at 400 °C, creating an excess of CsI and the consequent formation of stable perovskite phase at room temperature and, in a longer temporal step, the secondary phase Cs4PbI6.
The samples are not uniform and present amorphous phases and defectivity in the crystals structure but remain stable at room temperature.
Beyond the importance of base studies on this important class of materials, in this work, we have shown the possibility to easily obtain bulk CsPbI3 and we indicate the mechanism for future development and control of the phase formation of Lead halide perovskites.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request

Acknowledgements
Funding: This work was supported by the "Fondazione di Sardegna" within the project L.R 7. CUP F74I19000930007 "NG-Light: a new generation of phosphors". Figure 1 Rietveld re nement of the sample CPI3-10m at 400 °C a) and at room temperature b).

Figure 3
Rietveld re nement of C4PI6 sample. Absorption and steady-state luminescence spectra of CPI3-10m a) and steady-state luminescence spectrum of CPI3-1h b). In the inset, a zoom of the range 400-670 nm.

Figure 5
Raman spectra of CPI3-10h sample, λexc = 785 nm. a) Spectrum collected on a black spot, pointed out in the inset, with peaks of Cs4PbI6 (*) and CsPbI3δ phase. b)Spectrum gathered on the yellow part of the sample, pointed out in the inset. The images were obtained with optical microscope imaging. Luminescence map of the emission at 715 nm of the sample CPI3-10h: in a) a 2D map and in the inset the image by optical microscope. In b) a 3D map and in the inset the PL emission spectrum.

Figure 7
Raman and luminescence measurements on seven points in the CPI3-10h sample. a) Raman spectra, b) luminescence spectra (b) and 715 nm PL intensity (c). The spectra were collected on spatial point indicated in the inset of panel (c).  Time resolved luminescence measurement on two different points of CPI3-10h sample; λexc=500 nm.

Figure 10
Representative HRTEM images of the CPI3-10h sample. Lattice planes of γ-CsPbI3, δ-CsPbI3, and Cs4PbI6 are indicated in red, green and white, respectively. The 2D-FFT diffractograms used to calculate the orientations of each domain are reported in the central column.

Figure 11
Epitaxy study on the interface between γ-CsPbI3 and δ-CsPbI3, previously reported in Figure 10. γ-CsPbI3 and δ-CsPbI3 crystal domains in the HRTEM image (left) are depicted in red and green, respectively. The diffraction spots in the 2D-FFT diffractograms corresponding to the lattice planes used for the mismatch calculations are indicated according to the same color-coding.

Figure 12
Model of the phase transition during the synthesis process and image of the sample after the synthesis.