This view puts actual atoms in the picture instead of an energy chart. A simple-cubic lattice of instanced spheres fills a sphere of radius R — the nanocrystal itself — and a translucent point cloud marks where a confined electron is most likely to be found, drawn from the same particle-in-a-sphere ground state used to derive the bandgap in the 2D energy-level view.
P(r) ∝ sin²(πr/R) (radial probability density, ground state)
surface fraction ≈ 1 − (1 − a/R)³ (a = one atomic shell)
E_gap(R) = E_bulk + ħ²π²/2μR² · λ = 1240/E_gap [nm]
Shrink the radius and two things happen at once, both visible directly: the lattice loses atoms fast (volume shrinks as R³) while the fraction sitting in the outermost shell — highlighted in a different colour — climbs sharply, because surface area only shrinks as R². That rising surface-to-volume ratio is what makes nanoparticles so much more chemically reactive than bulk material. At the same time the electron cloud contracts and brightens near the centre, and the emission colour shown here (computed from the same confinement formula as the 2D simulation) blue-shifts.
- Crystal radius — physical size of the modelled nanocrystal; atom count scales roughly with R³, surface fraction rises as R shrinks.
- Material — sets the bulk bandgap/effective mass feeding the same confinement formula as the 2D energy-level simulation.
- Electron cloud — toggles the ground-state probability-density point cloud, sampled from P(r) ∝ sin²(πr/R).
- Surface atoms — toggles the colour highlight marking atoms in the outermost lattice shell.
Note: atom density is reduced from real lattice spacing (~0.3 nm) for smooth real-time rendering — the R³/R² scaling laws shown are physically accurate even though the absolute atom count is illustrative.