|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)|
|1D-chain||spacing a||set of parallel planes||1 + 2 = 3|
|2D-array||spacings a, b angle α||set of parallel lines||2 + 1 = 3|
|3D-crystal||spacings a, b, c
angles α, β, γ
|3D lattice of points||3 + 0 = 3|
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Birkbeck College, University of London.