Bubble Raft
A bubble raft is a single layer of soap bubbles floating on water, first used by Lawrence Bragg and John Nye in 1947 to model the atomic structure of metals. Each bubble acts like an atom — attracted at long range, repelled at short range. Watch them self-organize into hexagonal close-packing, then poke the raft to create grain boundaries, dislocations, and vacancies. Voronoi cells reveal the crystal structure: six neighbors means perfection; five or seven means a defect.
V(r) = ε[(σ/r)12 − 2(σ/r)6] · Equilibrium at r = σ
Bragg and Nye’s bubble model
In 1947, Sir Lawrence Bragg and John Nye published a landmark paper using rafts of uniform soap bubbles as a two-dimensional analogue of metallic crystal structure. By floating hundreds of small bubbles on a water surface, they could directly observe phenomena like grain boundaries, dislocations, and vacancies — defects that profoundly affect the mechanical properties of real metals but were impossible to image directly at the atomic scale at that time.
Lennard-Jones potential
Each bubble pair interacts via a potential similar to the Lennard-Jones potential: V(r) = ε[(σ/r)12 − 2(σ/r)6]. The r−12 term models short-range repulsion (bubbles resist overlap), while the r−6 term models the longer-range attraction from surface tension. The equilibrium separation occurs at r = σ, where the force is zero and the potential is at its minimum. This creates a natural tendency for bubbles to space themselves evenly.
Hexagonal close-packing
In two dimensions, the densest packing of equal circles is the hexagonal lattice, where each circle touches six neighbors. This arrangement maximizes the packing fraction at π/(2√3) ≈ 0.9069. The bubble raft naturally finds this configuration because it minimizes the total potential energy. The Voronoi diagram (dual of the Delaunay triangulation) reveals the local order: each Voronoi cell with six sides indicates a bubble with six neighbors in a locally perfect crystal.
Crystal defects
When you disturb the raft, you create defects — regions where the hexagonal order breaks down. A vacancy is a missing bubble, causing its neighbors to have fewer than six contacts. A dislocation is a 5-7 pair: one bubble with five neighbors adjacent to one with seven, forming the end of an extra half-row of bubbles. Grain boundaries are lines of dislocations separating regions (grains) with different orientations of the hexagonal lattice. These defects are exactly analogous to those found in real crystalline metals.