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The 1979 experiment of C. C. Grimes and colleagues studied a two-dimensional sheet of electrons above liquid helium. It reported crystallization at densities $3\times 10^8$ to $9\times 10^8{\mathrm{cm}}^{-2}$, with melting temperatures $0.35$ to $0.65\mathrm{K}$. The sheet was classical: Coulomb energy competed with thermal motion, unlike the kinetic-energy comparison used for a zero-temperature degenerate Wigner crystal. It supplies evidence for electron ordering while keeping these two physical regimes distinct.^[ref]

A Wigner crystal is an ordered electron arrangement favored when repulsion overwhelms the kinetic cost of localization. In a three-dimensional electron gas with a neutralizing background, define a mean spacing $a=(3/4\pi n{)}^{1/3}$ and effective Bohr radius $a_B^{\ast }=4\pi \epsilon {\hslash }^2/(m^{\ast }{e}^2)$. The Coulomb-to-kinetic energy ratio of an electron gas scales asThus low density favors the crystal in the degenerate quantum model. Translational symmetry is broken, and excitations include collective lattice vibrations. The melting criterion depends on dimension, screening, disorder and quantum fluctuations, so this scaling argument does not supply a universal numerical transition density.

The electron crystallization on liquid helium experiment provides an important related observation: a dilute two-dimensional electron sheet above liquid helium crystallized on cooling. It was a classical electron system, with thermal rather than Fermi motion competing with Coulomb energy; its coupling parameter is $\Gamma =E_C/(k_{B}T)$. It therefore illustrates Coulomb ordering without being a direct measurement of the zero-temperature three-dimensional quantum transition.^[ref]