Compositional engineering in perovskite materials has emerged as a powerful strategy for tailoring their structural, electronic, and optical properties. By systematically varying cations, halides, or metal ions, researchers can fine-tune bandgaps, phase stability, and charge transport characteristics. This approach enables the optimization of perovskites for a wide range of applications, from photovoltaics to light-emitting devices, without requiring device-specific architectures. The key to successful compositional engineering lies in understanding the interplay between different ions, their miscibility, and the resulting effects on material behavior.

Mixed-cation perovskites combine organic or inorganic cations to enhance stability and performance. Common cations include methylammonium (MA), formamidinium (FA), and cesium (Cs). The incorporation of multiple cations can suppress phase segregation, improve thermal stability, and modify the crystal lattice. For example, mixing MA and FA in lead iodide perovskites results in a more stable structure than pure FAPbI3, which exhibits an undesirable yellow phase at room temperature. The addition of Cs further stabilizes the black perovskite phase by reducing lattice strain. The phase behavior of these mixtures can be mapped using pseudo-ternary diagrams, revealing regions of single-phase solid solutions and miscibility gaps. A well-known system is Csx(MA0.17FA0.83)(1-x)PbI3, where x ≈ 0.1 yields optimal phase stability and photovoltaic performance. The bandgap in such systems follows a near-linear trend with composition, though deviations occur due to local structural distortions.

Mixed-halide perovskites, typically combining iodine (I) and bromine (Br), allow continuous bandgap tuning from about 1.5 eV (pure I) to 2.3 eV (pure Br). This tunability is crucial for tandem solar cells and light-emitting diodes. However, halide segregation under illumination remains a challenge, driven by lattice strain and halide migration. The miscibility of I and Br depends on the A-site cation; CsPb(I1-xBrx)3 shows better halide homogeneity than MAPb(I1-xBrx)3 due to reduced lattice distortion. Phase diagrams for mixed-halide perovskites often exhibit a miscibility gap at intermediate compositions, leading to phase separation into I-rich and Br-rich domains. Bandgap bowing is observed in these systems, where the bandgap deviates from a linear interpolation between the endpoints. The bowing parameter, typically around 0.3 eV for MAPb(I1-xBrx)3, arises from the nonlinear variation in Pb-X bond lengths and octahedral tilting.

Mixed-metal perovskites, such as those incorporating both lead (Pb) and tin (Sn), enable bandgap reduction below 1.3 eV, extending light absorption into the near-infrared. The Pb-Sn system exhibits a smaller bandgap bowing effect compared to halide-mixed perovskites, with a bowing parameter near 0.1 eV. However, Sn2+ oxidation to Sn4+ introduces p-type doping and increases carrier recombination. Phase stability in Pb-Sn perovskites is sensitive to composition; Sn-rich alloys (x > 0.5 in MASn1-xPbxI3) are prone to rapid degradation. The miscibility of Pb and Sn is generally high due to their similar ionic radii, but local inhomogeneities can still occur. Other mixed-metal systems, such as partial substitution of Pb with germanium (Ge) or bismuth (Bi), have been explored to reduce toxicity or modify electronic structure, though these often introduce new challenges in phase purity and defect tolerance.

The phase behavior of compositionally engineered perovskites is governed by thermodynamic and kinetic factors. Solid-solution formation depends on the tolerance factor, ionic radii mismatch, and bond enthalpy differences. Systems with small differences in ionic radii, such as I and Br, tend to form complete solid solutions, while larger mismatches, such as between MA and Cs, can lead to phase segregation or ordered phases. The Goldschmidt tolerance factor provides a rough guide for predicting stability, but local distortions and entropy effects complicate the picture. High-entropy compositions, where multiple cations or anions are randomly distributed, can stabilize metastable phases by increasing configurational entropy.

Bandgap engineering in mixed perovskites is influenced by several factors. For mixed-cation systems, the bandgap shifts are primarily due to changes in lattice constants and octahedral tilting. In mixed-halide perovskites, the bandgap varies with the halide electronegativity and Pb-X bond covalency. Mixed-metal systems exhibit bandgap changes due to alterations in the metal s- and p-orbital contributions to the conduction band minimum. The bowing effect in these systems arises from nonlinear variations in bond lengths, orbital hybridization, and local strain. Empirical models, such as the quadratic bowing equation, can describe these trends but require experimental validation for each composition.

Defect chemistry plays a critical role in compositionally engineered perovskites. Mixed compositions can passivate defects by reducing vacancy formation energies or introducing compensating impurities. For example, Br incorporation in I-based perovskites suppresses iodine vacancy formation, while Sn substitution in Pb perovskites alters the charge neutrality point. However, mixed systems can also introduce new defect states, such as halide vacancies acting as recombination centers or Sn2+ oxidation creating deep traps. The defect tolerance of a perovskite is thus highly composition-dependent, requiring careful optimization to minimize non-radiative losses.

Stability considerations are paramount in compositional engineering. Mixed-cation perovskites often show improved thermal stability compared to single-cation analogs due to reduced phase transition energies. Mixed-halide systems face challenges from photoinduced segregation, though certain compositions (e.g., high Br content) exhibit greater resistance. Mixed-metal perovskites, particularly Pb-Sn alloys, require encapsulation to prevent oxidation. Accelerated aging tests and phase diagram analysis help identify stable compositions, but long-term degradation mechanisms remain an active area of research.

Future directions in compositional engineering include high-throughput screening of novel mixtures, machine learning-assisted phase prediction, and exploration of non-traditional ions such as chalcogens or transition metals. The development of metastable phases through kinetic control, such as low-temperature processing or strain engineering, offers additional opportunities for property tuning. Understanding the fundamental relationships between composition, structure, and properties will continue to drive advances in perovskite materials science.

In summary, compositional engineering provides a versatile toolkit for designing perovskites with tailored properties. By carefully selecting and balancing cations, halides, and metal ions, researchers can achieve precise control over bandgap, stability, and defect behavior. The interplay between thermodynamics, kinetics, and electronic structure determines the success of these mixed systems, requiring a multidisciplinary approach to material design. Continued exploration of new compositions and deeper mechanistic insights will further expand the potential of engineered perovskites.