Given the primitive vectors of an arbitrary Bravais lattice and the Miller indices of a set of lattice planes in it, it is shown how to construct an alternative set of primitive vectors that are adapted to the lattice planes in the following sense: all but one of these alternative vectors serve as a basis for the points in one of the lattice planes, and the remaining vector serves to shift any of these lattice planes into a neighboring one. This construction is described for a three-dimensional Bravais lattice and then generalized to arbitrary d-dimensional lattices. This construction can be used to generate computer images of lattice points in a succession of crystal lattice planes, which could be useful for instructional purposes.

Topics
Condensed matter physics, Crystal lattices, Crystal structure, Mathematical crystallography, Sphere packings, Quasicrystals, Relativistic four vector, Euclidean geometries, Projective geometries, Educational assessment
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A listing of many sources of crystallographic software is maintained by NetSci at ⟨http://www.netsci.org/Resources/Software/Struct/xray.html⟩⁠. Descriptions of many software packages are given. One such package is available from CaRine Crystallography ⟨http://pro.wanadoo.fr/carine.crystallography/⟩⁠.
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2006
American Association of Physics Teachers
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