Commensurate Melting and Domain Walls in Surface Phases

Summary

Certain adsorbed surface systems display commensurate ordered phases which, as temperature T, or chemical potential, ζ, (controlled by the vapor pressure) vary, may melt via a continuous transition. Examples of particular interest are the √3 x √3 hexagonal phases of helium on graphite¹ and krypton on graphite² and the 3 x 1 rectangular phase of atomic hydrogen on the (110) surface of iron^3,4. Both these types of ordered phase exhibit p = 3 distinct but fully equivalent types of domain, say, A, B and C. This fact can be represented by an internal, global symmetry, Yp, which, for p = 3, is the same as that of the Potts model. On this basis it has been suggested^5,6 that the melting of such phases should be in the universality class of the 3-state Potts model with, in particular, a specific heat exponent α =. 1/3 as, indeed, is confirmed for one coverage of helium on graphite¹. However, the real physical symmetry is lower than the product,Yp x L, of the internal symmetry and the lattice symmetry,L, which describes the simple Potts model^7,8. This reduced symmetry can be seen in a physically intructive way^8,9 by examining the structure of the walls separating domains in various relative arrangements : thus in the rectangular 3 x 1 phases one finds that the [+] walls, A∣B, B∣C and C∣A (oriented normal to the direction in which the absorbate lattice constant is 3 times the substrate lattice constant) are all equivalent but Differ in structure from the complementary [-] walls A ∥ C, C ∥ B and B ∥ A; like wise in the hexagonal phases one finds two physically distinct types of wall⁸.