Using the Wigner–Ibach surmise to analyze terrace-width distributions: history,user’s guide,and advances

A history is given of the applications of the simple expression generalized from the surmise by Wigner and also by Ibach to extract the strength of the interaction between steps on a vicinal surface, via the terrace width distribution (TWD). A concise guide for use with experiments and a summary of some recent extensions is provided. PACS 68.35.Md; 05.40.-a; 68.37.Ef     

Temperature-dependent nucleation and capture-zone scaling of C60 on silicon oxide

Submonolayer films of C₆₀ have been deposited on ultrathin SiO₂ films for the purpose of characterizing the initial stages of nucleation and growth as a function of temperature. Capture zones extracted from the initial film morphology were analyzed using both the gamma and generalized Wigner distributions. The calculated critical nucleus size i of the C₆₀ islands was observed to change over the temperature range 298 K to 483 K. All fitted values of i were found to be between 0 and 1, representing stable monomers and stable dimers, respectively. With increasing temperature of film preparation, we observed i first increasing through this range and then decreasing. We discuss possible explanations of this reentrant-like behavior.     

Properties of intersecting families of ordered sets

The first part of this paper deals with families of ordered k-tuples having a common element in different position. A quite general theorem is given and special cases are considered. The second part deals with t families of sets with some intersection properties, and generalizes results by Bollobás, Frankl, Lovász and Füredi to this case.