CsPbX₃ perovskite nanocrystals (X = Cl, Br, I) undergo rapid, reversible anion exchange: halide ions hop between adjacent corner-shared PbX₆ octahedra faster than the cation lattice can rearrange, so mixing two nanocrystal populations — or adding fresh halide precursor — continuously re-tunes the whole ensemble's bandgap without changing crystal structure or particle size.
Composition axis: t ∈ [0,1] maps Cl → Br → I
t ≤ 0.5: y = 2t mixes Cl(1-y)/Br(y), bowing b₁ = 0.5 eV
t > 0.5: y = 2t-1 mixes Br(1-y)/I(y), bowing b₂ = 0.33 eV
Eg(y) = (1-y)·Eg_A + y·Eg_B − b·y·(1-y) [eV, Vegard's law + bowing]
Exchange kinetics (first-order, ligand-assisted):
dx/dt = k · (x_target − x)
Quantum-confinement correction (particle-in-a-box, strong confinement):
ΔE_conf ≈ C / L² (blueshift as edge length L shrinks)
Emission wavelength: λ (nm) = 1240 / Eg (eV)
- Target mix slider / preset buttons — sets the equilibrium halide composition the ensemble is driven toward (pure CsPbCl₃ ≈ 405 nm violet, CsPbBr₃ ≈ 520 nm green, CsPbI₃ ≈ 680 nm red).
- Exchange rate k — how fast ligand-assisted anion diffusion pulls the ensemble's real composition x toward the target; higher k means the color snaps over in under a second, lower k shows a slow multi-second drift exactly as seen in stopped-flow spectroscopy of real CsPbX₃ exchange reactions.
- Edge length L — below ~10 nm, quantum confinement adds an extra blueshift on top of the composition-set bandgap, shown live in Eg and λ.
- Inject precursor — simulates dosing the flask with a new halide source: the target composition is nudged and the exchange kinetics restart, visible as every nanocrystal's color sweeping toward the new equilibrium in real time.
Real-world relevance: this halide-exchange tunability is what lets a single perovskite-QD ink be color-tuned post-synthesis for display backlights and LEDs, without growing a new batch of nanocrystals for every wavelength.