CCP4 web logo Basic Maths for Protein Crystallographers
Lattice geometry
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Diffraction from a crystal lattice is visible at discrete points conveniently indexed as an integer triple (h,k,l), or in vector notation as ha*+kb*+lc*, relative to the reciprocal lattice vectors a*,b*,c*. These are defined to have the properties

a*· a = b*· b = c*· c = 1
a*· b = a*· c = b*· c = 0

i.e. a* is perpendicular to b and c, and therefore parallel to b×c. E.g. in P31:

P31 geometry

where c and c* lie vertically in the plane of the drawing, and a* comes perpendicularly out of the plane of the drawing.