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Laue equations : ウィキペディア英語版
Laue equations

In crystallography, the Laue equations give three conditions for incident waves to be diffracted by a crystal lattice. They are named after physicist Max von Laue (1879–1960). They reduce to Bragg's law.
==Equations==

Take \mathbf_i to be the wavevector for the incoming (incident) beam and \mathbf_o to be the wavevector for the outgoing (diffracted) beam. \mathbf_o - \mathbf_i = \mathbf is the scattering vector (also called transferred wavevector) and measures the change between the two wavevectors.
Take \mathbf\, ,\mathbf\, ,\mathbf to be the primitive vectors of the crystal lattice. The three Laue conditions for the scattering vector, or the Laue equations, for integer values of a reflection's reciprocal lattice indices (h,k,l) are as follows:
: \mathbf\cdot\mathbf=2\pi h
: \mathbf\cdot\mathbf=2\pi k
: \mathbf\cdot\mathbf=2\pi l
These conditions say that the scattering vector must be oriented in a specific direction in relation to the primitive vectors of the crystal lattice.

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