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On the Points of Melting

David G. Grier

March 11, 1996

Although melting and freezing are two of the most common structural phase transitions in everyday experience, surprisingly little is known regarding their microscopic mechanisms. Part of the difficulty in crafting a complete understanding of such fundamental transformations is that experiments on conventional materials such as copper or water can tell us very little about what happens on the atomic scale as a crystal transforms itself into a fluid. Not only are atoms small and rapidly moving, but comparatively few of them take part in the process at any time. Even computer simulations are hard-pressed to accomodate the enormous sample sizes and range of time scales involved in converting a chunk of ice into a puddle of water. The plasma crystal described by Thomas and Morfill [1] is a new model system in which some of the mysteries of structural phase transitions can be played out on a stage which scientists can watch with standard video cameras.

The plasma crystal works on the fairly straightforward principle that like-charged particles repel each other. The particles in Thomas and Morfill's experiments are micrometer scale polymer spheres which acquire their charges through immersion in an ionized gas known as a plasma. Each sphere is roughly a tenth of the diameter of a human hair. Because their container prevents them from moving apart indefinitely, the spheres adopt a configuration which minimizes their total energy given their temperature and density. If the charge-mediated interaction among the spheres is great enough to overcome the randomizing buffeting of the surrounding gas, then they form into regularly spaced arrays which are analogous to the orderly ranks of atoms in crystals. If the thermal energy of the gas wins, the plasma crystal melts to a dynamic and disordered state reminiscent of a fluid. This is the sense in which the ensemble of spheres in the ``dusty plasma'' serves as a model for atoms in simple materials undergoing phase transitions. Unlike atoms, however, plasma crystal spheres are large enough to see with the unaided eye and their motions can be tracked through computerized image processing. The hope is that detailed observations on such an experimentally accessible model system will provide insights germane to the widest class of condensed matter systems.

Similar hopes have been pursued through investigations on other model systems in recent decades [2]. Microscopic spheres colloidally suspended in a fluid solvent also undergo a variety of phase transitions depending on their density, their chemical environment, and the temperature. Even so-called hard spheres which interact only on contact undergo an entropically driven freezing transition to a crystalline state. Colloidal spheres with charged groups chemically grafted to their surfaces form crystals of different symmetries as well as fluids and glasses. Mixing spheres of two or more different sizes leads to even greater complexity which has yet to be explored fully.

Thermal equilibrium in a conventional material's ensemble of atoms is maintained by interatomic collisions. These are energy- and momentum-conserving processes mediated by interactions with strong quantum mechanical contributions. In a colloidal suspension, the temperature is set by the surrounding fluid. Viscous drag with the fluid means that energy and momentum need not be conserved in colloidal collisions and represents a major difference in the microscopic dynamics between colloidal and conventional phase transitions. The mechanism of thermalization and microscopic dynamics appear even more interesting in plasma crystals.

The plasma in a plasma crystal is maintained by a radio-frequency discharge which deposits energy into and partially ionizes a low pressure gas. The radio-frequency source also exerts forces on the charged microspheres, and the resulting excess energy is transferred through collisions to the background of neutral gas molecules at roughly room temperature. Lowering the pressure of the buffer gas lowers the rate at which energy is removed from the ensemble of spheres and thus allows its equilibrium temperature to rise. As in colloidal suspensions, thermal equilibrium is maintained by (classical) collisions among the spheres. Unlike fluid suspensions, however, collisions in a plasma crystal should be very nearly elastic since the low-pressure gas provides comparatively little viscous damping. By adjusting the pressure of buffer gas, Thomas and Morfill can effectively control the temperature of the ensemble of spheres and literally watch the plasma crystal melt at ``atomic'' resolution.

Some aspects of the melting process they see are familiar to everyone; others have been discussed in the technical literature; still others appear strange and novel. The plasma crystal consists of a stack of a dozen or so horizontal layers with harged spheres arranged in lattice that have six-fold symmetry in each layer. The particles vibrate about their lattice positions much as thermal phonons set atoms vibrating in conventional materials. The crystal is subject to the same types of topological lattice defects which crop up in conventional and colloidal crystals.

As Thomas and Morfill raise the effective temperature, the plasma crystal melts. Near the melting transition, residual crystallites coexist with the resulting fluid much like ice cubes floating in water. The fluid at this stage has unusual properties. Rather than engaging in random Brownian motion like atoms in conventional fluids at equilibruim, the ``plasma fluid'' has strongly correlated flows in the plane and little exchange of particles between planes. Layering in dense fluids is well known in colloidal suspensions [3] and has been observed using the surface force apparatus in conventional fluids [4]. If the strongly correlated in-plane motion is the plasma crystal equivalent of conventional convection, how is it driven? If not, then what is it? Answering these questions will require a deeper understanding of the local energetics in plasma crystals than is currently available.

When they raise the temperature still further, the ``floe and flow'' morphology gives way to a uniformly disordered fluid which still retains a degree of layering and has a surprising amount of orientational order in the plane, the particles arranging themselves into patterns with local six-fold symmetry. This strange state of matter has been likened to the orientationally ordered hexatic fluid, although the hexatic phase is predicted to occur only in two dimensions, not three [5]. Although the oriented fluid state might be peculiar to the plasma crystal, it could be a sign of a new intermediate stage of melting in a wide range of materials.

Finally, at the lowest gas pressures and highest temperatures, the oriented layered fluid crosses over to a more familiar isotropic homogeneous gas-like phase.

Plasma crystals also display intriguing non-thermal properties. Rather than jostling randomly, spheres in a plasma crystal trace out elliptical trajectories under some conditions. Presumably the response of the spheres to the driving field, these motions may provide a means to measure the interactions among the spheres as well as between the spheres and the field.

Studying this interplay may lead to an understanding of the startling nonuniform behavior observed in the fluid under some conditions. Are the observed fluctuations examples of equilibrium phase separation or or do they represent a crossover to nonequilibrium behavior?

Answers to such questions will deepen our understanding of this exciting new state of matter. They also will enable researchers to apply results from plasma crystal experiments to resolving fundamental problems in condensed matter physics such as the mechanisms and pathways of structural phase transitions.




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David G. Grier
Mon Mar 11 11:17:58 CST 1996