Hybrid perovskite materials with the general formula ABX₃ have garnered significant attention due to their unique structural properties and phase stability. The prototypical example, methylammonium lead iodide (CH₃NH₃PbI₃), exhibits a versatile crystal structure that can accommodate various compositional modifications, leading to tunable optoelectronic properties. The stability and structural dynamics of these materials are governed by the interplay between the A-site cation, B-site metal, and X-site halide, as well as external factors such as temperature and pressure.

The ABX₃ perovskite structure consists of a three-dimensional framework where the B-site cation (typically Pb²⁺ or Sn²⁺) is octahedrally coordinated by six X-site halide anions (I⁻, Br⁻, or Cl⁻), forming [BX₆]⁴⁻ octahedra. These octahedra share corners, creating a network with cuboctahedral voids occupied by the A-site cation (e.g., CH₃NH₃⁺, Cs⁺, or formamidinium (FA⁺)). The stability of the perovskite phase is highly sensitive to the ionic radii of the constituent ions, as described by the Goldschmidt tolerance factor (t) and octahedral factor (μ). The tolerance factor is given by t = (r_A + r_X) / [√2 (r_B + r_X)], where r_A, r_B, and r_X are the ionic radii of the A, B, and X ions, respectively. For stable perovskite formation, t should ideally lie between 0.8 and 1.0, while the octahedral factor μ = r_B / r_X should be between 0.4 and 0.9.

The A-site cation plays a critical role in stabilizing the perovskite structure. Organic cations such as methylammonium (MA⁺) and formamidinium (FA⁺) introduce dynamic disorder due to their rotational freedom, which can stabilize high-symmetry phases at higher temperatures. In contrast, inorganic cations like Cs⁺ are rigid and favor lower-symmetry phases. The size of the A-site cation also affects the lattice dimensions and phase stability. For instance, MA⁺ (∼2.17 Å) and FA⁺ (∼2.53 Å) are larger than Cs⁺ (∼1.81 Å), leading to different lattice distortions and phase transition behaviors. Mixed A-site compositions (e.g., MA/FA or MA/Cs) can enhance phase stability by balancing steric and electronic effects.

The B-site metal, predominantly Pb²⁺ or Sn²⁺, influences the electronic structure and structural stability. Pb²⁺-based perovskites are more stable than their Sn²⁺ counterparts due to the higher electronegativity and lower tendency of Pb²⁺ to oxidize to Pb⁴⁺. However, Sn²⁺ perovskites exhibit narrower bandgaps, making them attractive for certain applications. The ionic radius of the B-site cation also affects the [BX₆]⁴⁻ octahedral geometry, with smaller cations (e.g., Sn²⁺) leading to more distorted structures.

The X-site halide determines the bond strength and lattice rigidity. Iodide (I⁻) perovskites are the most stable due to the larger ionic radius of I⁻, which accommodates greater lattice flexibility. Bromide (Br⁻) and chloride (Cl⁻) perovskites exhibit higher structural rigidity but are prone to phase segregation under illumination or thermal stress. Mixed halide compositions (e.g., I/Br or Br/Cl) can stabilize intermediate phases but may suffer from halide migration and phase separation.

Phase transitions in hybrid perovskites are strongly temperature-dependent. CH₃NH₃PbI₃ undergoes a series of phase transitions from cubic (Pm-3m, >330 K) to tetragonal (I4/mcm, 160–330 K) to orthorhombic (Pnma, <160 K) as temperature decreases. These transitions are driven by the ordering of the A-site cation and tilting of the [BX₆]⁴⁻ octahedra. The cubic phase is characterized by ideal perovskite symmetry, while the tetragonal and orthorhombic phases exhibit octahedral tilting and cation ordering, reducing symmetry. The phase transition temperatures can be modulated by compositional engineering. For example, replacing MA⁺ with FA⁺ raises the cubic-to-tetragonal transition temperature, while Cs⁺ substitution suppresses the tetragonal phase entirely in some cases.

Lattice distortions, such as octahedral tilting and A-site cation displacement, significantly impact phase stability. Octahedral tilting reduces the lattice symmetry and can stabilize lower-symmetry phases. The magnitude of tilting is quantified by the tilt angles, which increase with decreasing temperature. A-site cation disorder can also stabilize high-symmetry phases by dynamically averaging out local distortions. In contrast, ordered A-site cations favor lower-symmetry phases with distinct structural motifs.

Pressure-induced phase transitions further illustrate the structural flexibility of hybrid perovskits. Under hydrostatic pressure, CH₃NH₃PbI₃ undergoes a series of phase transitions, including amorphization at high pressures (>3 GPa). The compressibility of the lattice is anisotropic, with the organic cation layer being more compressible than the inorganic [PbI₆]⁴⁻ framework. Pressure can also induce irreversible phase segregation in mixed halide perovskites.

The stability of hybrid perovskites is also affected by environmental factors such as humidity and light. Hydration can lead to the formation of hydrated phases (e.g., CH₃NH₃PbI₃·H₂O), which disrupt the perovskite structure. Light-induced degradation can cause phase segregation in mixed halide perovskites or decomposition in iodide-rich compositions. These degradation pathways are often initiated by lattice defects or strain.

Defects in hybrid perovskites, such as vacancies, interstitials, and antisite defects, play a dual role in structural stability. While some defects (e.g., halide vacancies) can facilitate ion migration and degradation, others (e.g., A-site vacancies) may stabilize certain phases by relieving strain. Defect tolerance is a hallmark of hybrid perovskites, as the electronic structure is less sensitive to defects than in conventional semiconductors.

In summary, the crystal structure and phase stability of hybrid perovskites are governed by a delicate balance of ionic radii, bonding interactions, and external conditions. The A-site cation dictates dynamic disorder and lattice dimensions, the B-site metal influences electronic structure and octahedral geometry, and the X-site halide determines bond strength and phase segregation tendencies. Temperature, pressure, and environmental factors further modulate the structural dynamics, making hybrid perovskites a rich system for fundamental studies of phase transitions and stability mechanisms. Understanding these relationships is essential for designing stable perovskite materials with tailored properties.