Mathematics – Metric Geometry
Scientific paper
2006-05-18
J. Phys.: Conf. Ser. 30 (2006), 163-167
Mathematics
Metric Geometry
4 pages, SSPCM (31 August - 7 September 2005, Myczkowce, Poland)
Scientific paper
10.1088/1742-6596/30/1/019
Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of a lattice $\Gamma$ with a rotated copy $R\Gamma$ of itself. They are useful for classifying grain boundaries and have been studied extensively since the mid sixties. Recently the interests turned to so-called multiple CSLs, i.e. intersections of $n$ rotated copies of a given lattice $\Gamma$, in particular in connection with lattice quantizers. Here we consider multiple CSLs for the 3-dimensional body centered cubic lattice. We discuss the spectrum of coincidence indices and their multiplicity, in particular we show that the latter is a multiplicative function and give an explicit expression of it for some special cases.
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