A Dimensional Summary 
A Dimensional Summary
Crystallographers work mainly in 3 dimensions. However, en route to deriving the Structure Factor equation, we passed through cases of lower dimension. The essentials are summarised in the following table; note that if we attribute 0, 1, 2 and 3 dimensions to points, lines, planes, and solids (respectively) we find a dimensional connection between a crystal and its reciprocal lattice (fourth column).
1. Real Space Crystal  Defining Parameters  2. Reciprocal Space  Dimension (1)+(2) 

1Dchain  spacing a  set of parallel planes  1 + 2 = 3 
2Darray  spacings a, b angle α  set of parallel lines  2 + 1 = 3 
3Dcrystal  spacings a, b, c angles α, β, γ 
3D lattice of points  3 + 0 = 3 
© Copyright 19972006.
Birkbeck College, University of London.

Author(s):
Paul Barnes Martin Vickers 