Experimental evidence is presented for an electron-liquid to electron-crystal phase transition in a sheet of electrons on a liquid-He surface. The phase transition has been studied for electron areal densities from 3xl0 8 cm" 2 to 9xl0 8 cm" 2 and has yielded melting temperatures between 0.35 and 0.65 K. The phase transition occurs at r = 137 ± 15, where r is a measure of the ratio of potential energy to kinetic energy per electron.We report the first experimental determination of a portion of the phase boundary for the electron-liquid to electron-crystal phase transition in a classical, two-dimensional (2D) Coulomb system 0 The 2D system that we have studied consists of a monolayer of electrons trapped on the surface of liquid helium. This electron layer is a nearly ideal 2D Coulomb system for such a study because the areal density of electrons can be varied over several orders of magnitude and the He surface is inherently clean (i.e., free of traps and scattering centers).Historically, Wigner first calculated in 1934 that an electron-liquid to electron-solid phase transition should occur in the 3D Fermi system at low densities. 1 Crandall and Williams noted that the analogous phase transition should occur in the classical 2D electron system at sufficiently high electron areal densities,, 2 The thermodynamic state of a classical Coulomb system is determined by the quantity T which is a measure of the ratio of Coulomb potential energy to kinetic energy per particle. For the classical 2D electron system this ratio becomes T =ir l/2 N s l/2 e 2 /k B T, where N s is the electron areal density and T is the system temperature. For T< 1 the kinetic energy predominates and the system behaves like an electron gas. At intermediate densities 1 ^ T £ 100, the electron motions become highly correlated or liquidlike. At high densities Tz 100, the Coulomb potential energy predominates and the electrons are expected to undergo a phase transition to form a periodic crystalline array. An experimental determination of this phase boundary is of interest to provide guidance for the difficult calculations and numerical experiments that are emerging for the melting transition in the classical 2D Coulomb solid.In this Letter we briefly describe our experimental technique and apparatus. We then summarize our experimental results and compare our phase boundary with the results of computer experiments by others.An excess electron outside a free surface of liquid helium can be bound just above the surface in a potential well formed by the combination of the long-range classical image potential and the short-range repulsive barrier to penetration into the liquid. While the electron is bound in the direction normal to the surface with a binding energy of 0.7 meV, it remains free to move parallel to the surface. For a bound electron the spatial extent of its wave function normal to the ( surface is «10" 6 cm while the interelectron spacing is typically 5xl0" 5 cm; so the electrons interact like point charges. The experimentally accessible ran...

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