This paper discusses the relation between fractal dimension and roughness index for fractal surfaces of solids. The applicability of the relation to fracture of Mode III+Mode I complex loading is shown. The applicability to other rough surfaces is discussed.

Micro-structural characteristics and electrical properties of an n-type GaN epilayer on Al2O3 irradiated by 290-MeV 238U32+ ions to various fluences were investigated using atomic force microscopy (AFM), scanning electron microscopy (SEM), high-resolution X-ray diffraction (HRXRD), and Raman scattering spectroscopy. AFM images show that the nano-hillocks generated, and the diameter and density of the nano-hillocks, increase obviously with increasing ion fluence, accompanied by an increase in surface roughness. SEM images display that the Al, O, and C elements appear on the GaN surface, along with a spiral-like, layered volcanic-cone structure formed at the highest-fluence irradiation. HRXRD reveals that the dislocation density increases, as the lattices gradually expand, and that Ga2O3 was produced with increasing ion fluence. Raman scattering spectra show that no N and Ga vacancies were produced, the free-carrier concentration decreases, while its mobility first increases and then exhibits a significant reduction with increasing ion fluence.

The structure of both low-lying and highly excited states and electromagnetic transitions in Pb-206 and Tl-205 has been studied within the framework of the shell model. The calculation predicts the occurrence of states in Pb-206 With a structure homologous to parent states in Tl-205, a phenomenon experimentally reported in these systems via ((p) over right arrow, alpha) reactions, in analogy with other regions of the mass table. This feature is not restricted to configurations where the two neutron holes are coupled to angular momentum zero, but also applies to higher configurations corresponding to angular momentum recoupling of the two neutron holes. The calculated results, obtained with both a modified surface delta interaction and Kuo-Herling interaction, are in good agreement with the experimental data, further supporting the ability of these interactions to describe nuclear properties in the lead region