Irreducible Representations of Diperiodic Groups

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a generalized translational group and an axial point group. The results are presented in the form of the tables, containing the matrices of the irreducible representations of the generators of the groups. General properties and some physical applications (degeneracy and topology of the energy bands, selection rules, etc.) are discussed.Comment: 30 pages, 5 figures, 28 tables, 18 refs, LaTex2.0

Surface Characteristics of Nanocrystalline Apatites: Effect of Mg Surface Enrichment on Morphology, Surface Hydration Species, and Cationic Environments

The incorporation of foreign ions, such as Mg2+, exhibiting a biological activity for bone regeneration is presently considered as a promising route for increasing the bioactivity of bone-engineering scaffolds. In this work, the morphology, structure, and surface hydration of biomimetic nanocrystalline apatites were investigated before and after surface exchange with suchMg2+ ions, by combining chemical alterations (ion exchange,H2OD2O exchanges) and physical examinations (Fourier transform infrared spectroscopy (FTIR) and highresolution transmission electron microscopy (HRTEM)). HRTEM data suggested that the Mg2+/Ca2+ exchange process did not affect the morphology and surface topology of the apatite nanocrystals significantly, while a new phase, likely a hydrated calcium and/or magnesium phosphate, was formed in small amount for high Mg concentrations. Near-infrared (NIR) and medium-infrared (MIR) spectroscopies indicated that the samples enriched withMg2+ were found to retain more water at their surface than the Mg-free sample, both at the level of H2O coordinated to cations and adsorbed in the form of multilayers. Additionally, the H-bonding network in defective subsurface layers was also noticeably modified, indicating that the Mg2+/Ca2+ exchange involved was not limited to the surface. This work is intended to widen the present knowledge on Mg-enriched calcium phosphate-based bioactive materials intended for bone repair applications