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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 Debye-Waller factor ： ウィキペディア英語版 Debye–Waller factor The Debye–Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x-ray scattering or coherent neutron scattering caused by thermal motion. It has also been called the B factor or the temperature factor. Often, "Debye-Waller factor" is used as a generic term that comprises the Lamb-Mössbauer factor of incoherent neutron scattering and Mössbauer spectroscopy. The DWF depends on the scattering vector q. For a given q, DWF(q) gives the fraction of elastic scattering; 1 - DWF(q) correspondingly gives the fraction of inelastic scattering. (Strictly speaking, this probability interpretation is not true in general.) In diffraction studies, only the elastic scattering is useful; in crystals, it gives rise to distinct Bragg peaks. Inelastic scattering events are undesirable as they cause a diffuse background — unless the energies of scattered particles are analysed, in which case they carry valuable information (for instance in inelastic neutron scattering or electron energy loss spectroscopy). The basic expression for the DWF is given by :$\backslash text\; =\; \backslash left\backslash langle\; \backslash exp\backslash left(i\; \backslash mathbf\backslash cdot\; \backslash mathbf\backslash right)\; \backslash right\backslash rangle^2$ where u is the displacement of a scattering center, and <...> denotes either thermal or time averaging. Assuming harmonicity of the scattering centers in the material under study, the Boltzmann distribution implies that $\backslash mathbf\backslash cdot\; \backslash mathbf$ is normally distributed with zero mean. Then, using for example the expression of the corresponding characteristic function, the DWF takes the form :$\backslash text\; =\; \backslash exp\backslash left(\; -\backslash langle\; (\backslash mathbf)^2\; \backslash rangle\; \backslash right)$ Note that although the above reasoning is classical, the same holds in quantum mechanics. Assuming also isotropy of the harmonic potential, one may write :$\backslash text\; =\; \backslash exp\backslash left(\; -q^2\; \backslash langle\; u^2\; \backslash rangle\; /\; 3\; \backslash right)$ where ''q'', ''u'' are the magnitudes (or absolute values) of the vectors q, u respectively, and $\backslash langle\; u^2\; \backslash rangle$ is the mean squared displacement. In crystallographic publications, values of $U$ are often given where $U\; =\; \backslash langle\; u^2\; \backslash rangle$. Note that if the incident wave has wavelength $\backslash lambda$, and it is elastically scattered by an angle of $2\backslash theta$, then :$q\; =\; \backslash frac$ In the context of protein structures, the term B-factor is used. The B-factor is defined as: :$B\; =\; 8\backslash pi^2\; \backslash langle\; u^2\; \backslash rangle$ It is measured in units of Å2. The B-factors can be taken as indicating the relative vibrational motion of different parts of the structure. Atoms with low B-factors belong to a part of the structure that is well-ordered. Atoms with large B-factors generally belong to part of the structure that is very flexible. Each ATOM record (PDB file format) of a crystal structure deposited with the Protein Data Bank contains a B-factor for that atom. ==References== 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「Debye–Waller factor」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.