# Developments on Perovskite Solar Cells (PSCs): A Critical Review
## 6 Device Challenges
### Perovskite Solar Cell Device Stability
#### 6.1.1 Stability in the Perovskite Crystal Structure (ABX\({}_{3}\))  
The stability of the perovskite crystal structure is determined using the Goldschmidt tolerance factor (t), shown by Equation (1). The cubic (\(\alpha\)) phase is the most stable crystal structure, followed by the tetragonal (\(\beta\)) phase; the least stable crystal structure is the orthorhombic (\(\gamma\)) phase. In any crystal structure, the tolerance factor depends on the ABX\({}_{3}\) constituting organic (e.g., MA\({}^{+}\) = r\({}_{A}\)), inorganic (e.g., Pb\({}^{2+}\) = r\({}_{B}\)) and halogen (e.g., I\({}^{-}\) = r\({}_{0}\)) ionic radius [77]. Further research has revealed that the crystal structure stability is also affected by changes in temperature and pressure. In the study to investigate the effect of temperature on perovskite crystal structure, [PERSON] (2015) reported a MAPbI\({}_{3}\) phase transition from tetragonal to cubic at temperatures greater than 55 \({}^{\circ}\)C. In Figure 13a, the XRD results confirm a tetragonal phase with perovskite characteristic diffraction angles at 14.1\({}^{\circ}\), 28.5\({}^{\circ}\), and 43.3\({}^{\circ}\) associated with the (110), (220), and (330) planes, respectively [78]. An increase in sample temperature affects the crystal shape, as illustrated in Figure 13b-d; the perovskite diffraction peaks shift to lower diffraction angles as the temperature is increased. The observed shift in the XRD peaks suggests the rearrangement of the crystal lattice. Figure 13b-d show the phase transition from a tetragonal phase to a lower diffraction angle cubic phase for samples heated in a temperature range of \(-\)95 to 100 \({}^{\circ}\)C. In another study, [PERSON] (1998) reported the thermal stability of FAPbI\({}_{3}\). The FAPbI\({}_{3}\) has higher thermal stability than MAPbI\({}_{3}\) due to its tetragonal-cubic phase transition occurring at a high temperature of 150 \({}^{\circ}\)C [79]. Therefore, in conclusion, a stable perovskite crystal structure is found at high temperatures and depends on the perovskite material in question. The perovskite crystal structure response mechanism to pressure remains a mystery, as there is an unusual sequence of phase transition with an increase in pressure. For example, phase transitions such as tetragonal-cubic-orthorhombic, orthorhombic-tetragonal-cubic, and vice versa, are observed [80; 81]. [PERSON] (2016) conducted a study to understand MAPbX\({}_{3}\) (X = Br and I) perovskite crystal structure response to compression. Single crystal and powder X-ray diffraction (SCXRD and PXRD) techniques were used to characterize material crystal structure at ambient pressure and during high-pressure conditions [82]. The applied pressure had a significant effect on Pb-X (X = Br and I) bond lengths, volume and \(\alpha\)-\(\beta\) phase transition. Figure 14a,b show MAPbX\({}_{3}\) SCXRD crystal structure model at ambient and high pressure. Figure 14c,d show MAPbX\({}_{3}\) PXRD diffraction patterns under a continuous increase in pressure (compression). At ambient pressure, Pb-X-Pb bond angles are at 180\({}^{\circ}\) as shown in Figure 14a,b, compression results in the Pb-X-Pb bond angle contraction to angles \(<\) 180\({}^{\circ}\), reduces Pb-X bond length, and subsequently \(\alpha\)-\(\beta\) phase transitions at pressures greater than 1.7 and 0.7 GPa for MAPbBr\({}_{3}\) and MAPbI\({}_{3}\) perovskitecrystal structures, respectively. Further compression of the \(\beta\) phase results in further bond length and volume reductions. Strong intermolecular interactions develop due to the tight conformation in the ABX\({}_{3}\) unit cell. The XRD patterns in Figure 14c,d show changes in the MAPbBr\({}_{3}\) and MAPbI\({}_{3}\) crystal structure as pressure is continuously increased up to a maximum pressure of 9 GPa. In both perovskite materials, MAPbX\({}_{3}\) (X = Br and I) normal perovskite behavior is observed at low pressures, as indicated by arrow 1.