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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 Wulff construction ： ウィキペディア英語版 Wulff construction The Wulff construction is a method to determine the equilibrium shape of a droplet or crystal of fixed volume inside a separate phase (usually its saturated solution or vapor). Energy minimization arguments are used to show that certain crystal planes are preferred over others, giving the crystal its shape. ==Theory== In 1878 Josiah Willard Gibbs proposed〔Gibbs, ''Collected Works'', 1928〕 that a droplet or crystal will arrange itself such that its surface Gibbs free energy is minimized by assuming a shape of low surface energy. He defined the quantity :$\backslash Delta\; G\_i=\; \backslash sum\_\backslash gamma\_j\; O\_j~$ Here $\backslash gamma\; \_j$ represents the surface (Gibbs free) energy per unit area of the $j$th crystal face and $O\_j$ is the area of said face. $\backslash Delta\; G\_i$ represents the difference in energy between a real crystal composed of $i$ molecules with a surface and a similar configuration of $i$ molecules located inside an infinitely large crystal. This quantity is therefore the energy associated with the surface. The equilibrium shape of the crystal will then be that which minimizes the value of $\backslash Delta\; G\_i$. In 1901 Wulff stated〔G Wulff, ''Zeitschrift fur Krystallographie und Mineralogie'', 34, 5/6, pp 449-530, 1901.〕 (without proof) that the length of a vector drawn normal to a crystal face $h\_j$ will be proportional to its surface energy $\backslash gamma\_j$: $h\_j=\backslash lambda\; \backslash gamma\_j$. The vector $h\_j$ is the "height" of the $j$th face, drawn from the center of the crystal to the face; for a spherical crystal this is simply the radius. This is known as the Gibbs-Wulff theorem. In 1953 Herring gave a proof of the theorem and a method for determining the equilibrium shape of a crystal, consisting of two main exercises. To begin, a polar plot of surface energy as a function of orientation is made. This is known as the gamma plot and is usually denoted as $\backslash gamma(\backslash hat)$, where $\backslash hat$ denotes the surface normal, e.g., a particular crystal face. The second part is the Wulff construction itself in which the gamma plot is used to determine graphically which crystal faces will be present. It can be determined graphically by drawing lines from the origin to every point on the gamma plot. A plane perpendicular to the normal $\backslash hat$ is drawn at each point where it intersects the gamma plot. The inner envelope of these planes forms the equilibrium shape of the crystal. 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「Wulff construction」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.