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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bragg plane ： ウィキペディア英語版 Bragg plane In physics, a Bragg plane is a plane in reciprocal space which bisects one reciprocal lattice vector, $\backslash scriptstyle\; \backslash mathbf$.〔 〕 It is relevant to define this plane as part of the definition of the Von Laue condition for diffraction peaks in x-ray diffraction crystallography. Considering the diagram at right, the arriving x-ray plane wave is defined by: :$e^\}\; =\; \backslash cos\; )\}\; +\; i\backslash sin\; )\}$ Where $\backslash scriptstyle\; \backslash mathbf$ is the incident wave vector given by: :$\backslash mathbf\; =\; \backslash frac\backslash hat$ where $\backslash scriptstyle\; \backslash lambda$ is the wavelength of the incident photon. While the Bragg formulation assumes a unique choice of direct lattice planes and specular reflection of the incident X-rays, the Von Laue formula only assumes monochromatic light and that each scattering center acts as a source of secondary wavelets as described by the Huygens principle. Each scattered wave contributes to a new plane wave given by: :$\backslash mathbf\; =\; \backslash frac\backslash hat^\backslash prime$ The condition for constructive interference in the $\backslash scriptstyle\; \backslash hat^\backslash prime$ direction is that the path difference between the photons is an integer multiple (m) of their wavelength. We know then that for constructive interference we have: :$|\backslash mathbf|\backslash cos\; +\; |\backslash mathbf|\backslash cos\; =\; \backslash mathbf\; \backslash cdot\; (\backslash hat\; -\; \backslash hat^\backslash prime)\; =\; m\backslash lambda$ where $\backslash scriptstyle\; m\; ~\backslash in~\; \backslash mathbb$. Multiplying the above by $\backslash scriptstyle\; \backslash frac$ we formulate the condition in terms of the wave vectors, $\backslash scriptstyle\; \backslash mathbf$ and $\backslash scriptstyle\; \backslash mathbf$: :$\backslash mathbf\; \backslash cdot\; (\backslash mathbf\; -\; \backslash mathbf)\; =\; 2\backslash pi\; m$ Now consider that a crystal is an array of scattering centres, each at a point in the Bravais lattice. We can set one of the scattering centres as the origin of an array. Since the lattice points are displaced by the Bravais lattice vectors, $\backslash scriptstyle\; \backslash mathbf$, scattered waves interfere constructively when the above condition holds simultaneously for all values of $\backslash scriptstyle\; \backslash mathbf$ which are Bravais lattice vectors, the condition then becomes: :$\backslash mathbf\; \backslash cdot\; \backslash left(\backslash mathbf\; -\; \backslash mathbf\backslash right)\; =\; 2\backslash pi\; m$ An equivalent statement (see mathematical description of the reciprocal lattice) is to say that: :$e^)\; \backslash cdot\; \backslash mathbf\}\; =\; 1$ By comparing this equation with the definition of a reciprocal lattice vector, we see that constructive interference occurs if $\backslash scriptstyle\; \backslash mathbf\; ~=~\; \backslash mathbf\; \backslash ,-\backslash ,\; \backslash mathbf$ is a vector of the reciprocal lattice. We notice that $\backslash scriptstyle\; \backslash mathbf$ and $\backslash scriptstyle\; \backslash mathbf$ have the same magnitude, we can restate the Von Laue formulation as requiring that the tip of incident wave vector, $\backslash scriptstyle\; \backslash mathbf$, must lie in the plane that is a perpendicular bisector of the reciprocal lattice vector, $\backslash scriptstyle\; \backslash mathbf$. This reciprocal space plane is the ''Bragg plane''. ==See also== * X-ray crystallography * Reciprocal lattice * Bravais lattice * Powder diffraction * Kikuchi line * Brillouin zone 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bragg plane」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.