Rippled crystal surfaces

KINETIC RATE LAW ISSUES IN THE MORPHOLOGICAL RELAXATION OF RIPPLED CRYSTAL SURFACES... 

Crystals are often associated with their unique polyhedral shapes. Their smooth, shining facets provide a constant source of fascination to ancient, arid modem beings alike. Advances in microscopy have not, tainted the myth a bit interesting surface stmctures are found down to the atomic level, be it surface reconstmction, surface ripples and dimples, or snow-flakish fractals... 

In solutions of water and surfactant, the surfactant monolayers can join, tail side against tail side, to form bilayers, which form lamellar liquid crystals whose bilayers are planar and are arrayed periodically in the direction normal to the bilayer surface. The bilayer thickens upon addition of oil, and the distance between bilayers can be changed by adding salts or other solutes. In the oil-free case, the hydrocarbon tails can be fluidlike (La) lamellar liquid crystal or can be solidlike (Lp) lamellar liquid crystal. There also occurs another phase, Pp, called the modulated or rippled phase, in which the bilayer thickness varies chaotically in place of the lamellae. Assuming lamellar liquid crystalline symmetry, Goldstein and Leibler [19] have constructed a Hamiltonian in which (1) the intrabilayer energy is calculated... 

Although scientists talk about the dual wave and particle properties of electrons, many nonscientists still believe that electrons are only tiny particles. Rooted as we are in the macroscopic world, it can be difficult for some to picture a particle as also being a wave. One look at the accompanying picture, however, should help change that. What looks like ripples surrounding two barely submerged pebbles in a pool of water is really the surface of a copper crystal. 

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