EAN: 9780939950195

MATHEMATICAL CRYSTALLOGRAPHY KARTONIERT (TB)

Volume 15 of Reviews in Mineralogy is written with two goals in mind. The first is to derive
the 32 crystallographic point groups  the 14 Bravais lattice types and the 230 crystallographic
space group types. The second is to develop the mathematical tools necessary for these
derivations in such a manner as to lay the mathematical foundation needed to solve numerous
basic problems in crystallography and to avoid extraneous discourses. To demonstrate how these
tools can be employed  a large number of examples are solved and problems are given. The book
is  by and large  self-contained. In particular  topics usually omitted from the traditional
courses in mathematics that are essential to the study of crystallography are discussed. For
example  the techniques needed to work in vector spaces with noncartesian bases are developed.
Unlike the traditional group-theoretical approach  isomorphism is not the essential ingredient
in crystallographic classification schemes. Because alternative classification schemes must be
used  the notions of equivalence relations and classes which are fundamental to such schemes
are defined  discussed and illustrated. For example  we will find that the classification of
the crystallographic space groups into the traditional 230 types is defined in terms of their
matrix representations. Therefore  the derivation of these groups from the point groups will be
conducted using the 37 distinct matrix groups rather than the 32 point groups they represent.

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