Theoretical investigations of pressure- and temperature-induced phase transitions under quantum confinement have revealed significant deviations from bulk behavior, particularly in materials like metal halide perovskites and vanadium dioxide (VO2) nanoparticles. Quantum confinement effects, which become prominent at nanoscale dimensions, alter the electronic structure, phonon dispersion, and thermodynamic stability of these materials, leading to unique phase transition pathways not observed in their bulk counterparts. Ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT) calculations have been instrumental in predicting these phenomena, providing insights into size-dependent structural stability and transition mechanisms.
In bulk metal halide perovskites, such as CsPbI3, phase transitions between cubic, tetragonal, and orthorhombic structures are well-documented and driven by temperature changes. However, under quantum confinement, the phase stability landscape shifts dramatically. AIMD simulations of CsPbI3 nanoparticles with diameters below 10 nm demonstrate that the cubic phase, which is metastable in bulk at room temperature, becomes stabilized at smaller sizes due to surface energy contributions and reduced octahedral tilting. The energy barrier for phase transitions increases as particle size decreases, leading to hysteresis in temperature-dependent transitions. For example, while bulk CsPbI3 undergoes a cubic-to-tetragonal transition near 310 K, nanoparticles below 5 nm retain cubic symmetry up to 350 K, with the transition temperature scaling inversely with size.
Pressure-induced phase transitions in perovskites also exhibit confinement effects. Bulk CsPbI3 transforms from a perovskite to a non-perovskite phase above 0.3 GPa, but nanoparticles resist this transition until higher pressures. DFT calculations show that the critical pressure for phase transition increases by approximately 0.1 GPa per nanometer reduction in particle size below 10 nm. This is attributed to the increased surface-to-volume ratio, which enhances the contribution of surface tension to the total free energy, thereby stabilizing the perovskite phase. Similar trends are observed in hybrid organic-inorganic perovskites like MAPbI3, where quantum confinement suppresses the formation of intermediate phases observed in bulk under pressure.
Vanadium dioxide (VO2) provides another compelling case for size-dependent phase transitions. Bulk VO2 exhibits a well-known insulator-to-metal transition (IMT) near 340 K, accompanied by a structural change from monoclinic to tetragonal rutile. In VO2 nanoparticles, AIMD simulations predict a suppression of the IMT temperature (T_IMT) as particle size decreases. For particles below 20 nm, T_IMT drops by 5–10 K per nanometer, with the transition becoming increasingly diffuse due to surface disorder and finite-size effects. The monoclinic phase is stabilized at smaller sizes, with the energy difference between monoclinic and rutile phases decreasing by 2–3 meV per atom for every nanometer reduction in diameter.
Pressure responses of VO2 nanoparticles also diverge from bulk behavior. Bulk VO2 undergoes a series of high-pressure phase transitions, including a monoclinic-to-rutile transition above 10 GPa. In contrast, nanoparticles exhibit a delayed transition onset, with the critical pressure increasing by 1–2 GPa for particles below 15 nm. This is linked to the dominance of surface energy contributions, which alter the relative stability of competing phases. AIMD simulations reveal that the coordination environment of vanadium atoms in nanoparticles remains distorted under pressure, delaying the formation of the high-pressure rutile phase.
The contrasting phase diagrams of bulk and confined systems can be summarized as follows:
Bulk CsPbI3:
- Cubic to tetragonal transition: ~310 K
- Perovskite to non-perovskite transition: ~0.3 GPa
Nanoparticle CsPbI3 (5 nm):
- Cubic phase stable up to ~350 K
- Perovskite phase stable up to ~0.8 GPa
Bulk VO2:
- IMT at ~340 K
- Monoclinic to rutile transition above 10 GPa
Nanoparticle VO2 (10 nm):
- IMT at ~290 K
- Monoclinic to rutile transition above 12 GPa
These predictions are supported by computational studies employing hybrid functionals and van der Waals corrections, which accurately capture the electronic and structural changes under confinement. The size-dependent shift in phase boundaries is primarily driven by three factors: surface energy, which becomes increasingly significant at smaller sizes; phonon confinement, which alters the vibrational entropy; and electronic confinement, which modifies the density of states near the Fermi level.
In metal halide perovskites, quantum confinement leads to bandgap widening, which further stabilizes certain phases. For instance, the optical bandgap of CsPbI3 nanoparticles increases by 0.1–0.2 eV per nanometer below 10 nm, shifting the relative stability of phases with different bandgaps. This effect is less pronounced in VO2, where electron correlation plays a dominant role in the phase transition.
Theoretical frameworks also predict kinetic effects in confined systems. Nucleation barriers for phase transitions increase in nanoparticles due to the reduced volume available for domain formation. In VO2, the energy barrier for monoclinic-to-rutile transition rises by 10–15% for 10 nm particles compared to bulk, leading to slower transition kinetics. Similarly, perovskite nanoparticles exhibit delayed nucleation of non-perovskite phases under pressure due to the high energy cost of creating new interfaces in confined geometries.
Comparative studies of bulk and nanoscale phase diagrams highlight the importance of finite-size effects in materials design. For applications requiring stable phases over wide temperature or pressure ranges, such as perovskite solar cells or VO2-based switches, nanoparticle systems offer tunable transition thresholds through size control. Computational models continue to refine these predictions, incorporating advanced techniques like machine learning potentials to bridge length and time scales in simulations of confined systems. The insights gained from these studies guide experimental synthesis and characterization efforts, enabling the rational design of nanomaterials with tailored phase transition properties.