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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 Structure factor ： ウィキペディア英語版 Structure factor In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a particularly useful tool in the interpretation of interference patterns obtained in X-ray, electron and neutron diffraction experiments. The static structure factor is measured without resolving the energy of scattered photons/electrons/neutrons. Energy-resolved measurements yield the dynamic structure factor. ==Derivation== Let us consider a scalar (real) quantity $\backslash phi(\backslash mathbf)$ defined in a volume $V$; it may correspond, for instance, to a mass or charge distribution or to the refractive index of an inhomogeneous medium. If the scalar function is assumed to be integrable, we can define its Fourier transform $\backslash textstyle\; \backslash phi(\backslash mathbf)\; =\; \backslash int\_\; \backslash phi(\backslash mathbf)\; \backslash exp\; (-i\; \backslash mathbf\; \backslash mathbf)\; \backslash ,\; \backslash mathrm\; \backslash mathbf$. Expressing the field $\backslash phi$ in terms of the spatial frequency $\backslash mathbf$ instead of the point position $\backslash mathbf$ is very useful, for instance, when interpreting scattering experiments. Indeed, in the Born approximation (weak interaction between the field and the medium), the amplitude of the signal corresponding to the scattering vector $\backslash mathbf$ is proportional to $\backslash textstyle\; \backslash phi(\backslash mathbf)$. Very often, only the intensity of the scattered signal $\backslash textstyle\; I(\backslash mathbf)$ is detectable, so that $\backslash textstyle\; I(\backslash mathbf)\; \backslash sim\; \backslash left\; |\; \backslash phi(\backslash mathbf)\; \backslash right\; |^2$. If the system under study is composed of a number $N$ of identical constituents (atoms, molecules, colloidal particles, etc.) it is very convenient to explicitly capture the variation in $\backslash phi$ due to the morphology of the individual particles using an auxiliary function $f(\backslash mathbf)$, such that: with $\backslash textstyle\; \backslash mathbf\_,\; j\; =\; 1,\; \backslash ,\; \backslash ldots,\; \backslash ,\; N$ the particle positions. In the second equality, the field is decomposed as the convolution product $\backslash ast$ of the function $f$, describing the "form" of the particles, with a sum of Dirac delta functions depending only on their positions. Using the property that the Fourier transform of a convolution product is simply the product of the Fourier transforms of the two factors, we have $\backslash textstyle\; \backslash phi(\backslash mathbf)\; =\; f(\backslash mathbf)\; \backslash sum\_^\; \backslash exp\; (-i\; \backslash mathbf\; \backslash mathbf\_)$, such that: \right ) \times \left ( \sum_^ \mathrm^_} \right )= \left | f(\mathbf) \right |^2 \sum_ \mathrm^_j - \mathbf_k)}.|}} In general, the particle positions are not fixed and the measurement takes place over a finite exposure time and with a macroscopic sample (much larger than the interparticle distance). The experimentally accessible intensity is thus an averaged one $\backslash textstyle\; \backslash langle\; I(\backslash mathbf)\; \backslash rangle$; we need not specify whether $\backslash langle\; \backslash cdot\; \backslash rangle$ denotes a time or ensemble average. We can finally write: thus defining the structure factor 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「Structure 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.