MATERIALS & CRYSTALLOGRAPHY

reciprocal lattice basis

constructs a reciprocal space basis dual to the real space basis vector.

b1=2πa2×a3a1⋅(a2×a3)\mathbf b_1=2\pi\frac{\mathbf a_2\times\mathbf a_3}{\mathbf a_1\cdot(\mathbf a_2\times\mathbf a_3)}

symbols, variables and units

a_i: real space basis vector (m); b_i: m⁻¹; the remaining basis vectors are cyclically replaced.

applicable conditions and boundaries

The primitive cell volume is non-zero; the physics convention including 2π is used.

formula source code

The following is a copyable LaTeX expression.

\mathbf b_1=2\pi\frac{\mathbf a_2\times\mathbf a_3}{\mathbf a_1\cdot(\mathbf a_2\times\mathbf a_3)}

Reference and Extended Learning

DoITPoMS · University of Cambridge ↗

is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.

reciprocal latticereciprocal space

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