GRAIN BOUNDARY CRYSTALLOGRAPHY. D. Romeu, L. Beltrán, J.L. Aragón, A. Gómez. Instituto de Física. UNAM, Apartado Postal 20-364, D.F. 01000 México

In this work we present a mathematical model capable of describing in detail the atomic structure of arbitrary grain boundaries (GB) in metals and other materials and constitutes the first step towards a complete crystallographic description of GBs. Due to its evident technological implications, GB have been intensely studied in the past with limited success, due, mostly, to the absence of a complete model accounting for the structure of arbitrary GB. This has hampered the establishment of a correlation between boundary structure and properties.

Using tools closely related to those used in Quasicrystals, the present model describes in detail the atomic structure of arbitrary GB, not being restricted to those known as "special" and establishes a link between the fields of quasicrystals and GB, permitting a better understanding of both. The model replaces the notion of "coincidence sites" by "best possible fit" and it is continuous (as the O-lattice) over all the angular range.

Our results show that the value of Sigma alone is not enough to characterize special boundaries. In particular, it has been found that some low Sigma GB in FCC metals have a very poor fit (Sigma 17) while others with higher Sigma are surprisingly good (Sigma 41), thus explaining previous experimental results indicating that Sigma 41 is a special boundary.