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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 Pauling's rules ： ウィキペディア英語版 Pauling's rules :''This article is about Pauling's rules on crystal structures. For Pauling's rules on oxoacid strengths, see Acid dissociation constant.'' Pauling's rules are five rules published by Linus Pauling in 1929 for predicting and rationalizing the crystal structures of ionic compounds.〔 〕 ==First rule: the radius ratio rule== For typical ionic solids, the cations are smaller than the anions, and each cation is surrounded by coordinated anions which form a polyhedron. The sum of the ionic radii determines the cation-anion distance, while the cation-anion radius ratio $r\_+\; /\; r\_-$ (or $r\_c\; /\; r\_a$) determines the coordination number (C.N.) of the cation, as well as the shape of the coordinated polyhedron of anions.〔Pauling (1960) p.524〕〔Housecroft C.E. and Sharpe A.G. ''Inorganic Chemistry'' (2nd ed., Pearson Prentice-Hall 2005) p.145 ISBN 0130-39913-2〕 For the coordination numbers and corresponding polyhedra in the table below, Pauling mathematically derived the ''minimum'' radius ratio for which the cation is in contact with the given number of anions (considering the ions as rigid spheres). If the cation is smaller, it will not be in contact with the anions which results in instability leading to a lower coordination number. The three diagrams at right correspond to octahedral coordination with a coordination number of six: four anions in the plane of the diagrams, and two (not shown) above and below this plane. The central diagram shows the minimal radius ratio. The cation and any two anions form a right triangle, with $2r\_-\; =\; \backslash sqrt\; 2(r\_-\; +\; r\_+)$, or $\backslash sqrt\; 2\; r\_-\; =\; r\_-\; +\; r\_+$. Then $r\_+\; =\; (\backslash sqrt\; 2\; -\; 1)r\_-\; =\; 0.414\; r\_-$. Similar geometrical proofs yield the minimum radius ratios for the highly symmetrical cases C.N. = 3, 4 and 8.〔Toofan J. (1994) J. Chem. Educ. 71 (9), 147 (and Erratum p.749) ''A Simple Expression between Critical Radius Ratio and Coordination Numbers''〕 For C.N. = 6 and a radius ratio greater than the minimum, the crystal is more stable since the cation is still in contact with six anions, but the anions are further from each other so that their mutual repulsion is reduced. An octahedron may then form with a radius ratio greater than or equal to .414, but as the ratio rises above .732, a cubic geometry becomes more stable. This explains why Na+ in NaCl with a radius ratio of 0.55 has octahedral coordination, whereas Cs+ in CsCl with a radius ratio of 0.93 has cubic coordination.〔R.H. Petrucci, W.S. Harwood and F.G. Herring, General Chemistry (8th ed., Prentice-Hall 2002) p.518 ISBN 0-13-014329-4〕 If the radius ratio is less than the minimum, two anions will tend to depart and the remaining four will rearrange into a tetrahedral geometry where they are all in contact with the cation. The radius ratio rules are a first approximation which have some success in predicting coordination numbers, but many exceptions do exist.〔 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「Pauling's rules」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.