清华大学：《材料科学基础》课程教学资源（PPT课件讲稿）Chapter 3. 4 Some Rules Governing the Ionic Compounds

33. 4 Some Rules Governing the Ionic Compounds Pauling's three rules governing the structure of ionic compounds 1. Anion Coordination polyhedron rule Each cation is surrounded by an anion polyhedron, the distance between anion and cation is r=rt tr, while the CN depends on rt

§3.4 Some Rules Governing the Ionic Compounds Pauling’s three rules governing the structure of ionic compounds. 1. Anion Coordination polyhedron rule Each cation is surrounded by an anion polyhedron, the distance between anion and cation is ro ＝r +＋r - , while the CN depends on r +/r-

unstable r>+r r++ stable ionic compound stable there is some covalent bounding

ro＞r +＋r－ ro ＝r +＋r－ stable ionic compound ro＜r +＋r－ there is some covalent bounding stable unstable

Coordination Cation-Anion Coordination Aumber Radins Ratio Geometry 55 3 0.1550.225 0.225-0.414 0.4140.732

anion CN+ polyhedron hexahedron 0.732 octahedron 0.414 tetrahedron 8—6-4—3 0.225 trigonal 0.155

anion polyhedron CN＋ ( )min hexahedron 8 0.732 octahedron 6 0.414 tetrahedron 4 0.225 trigonal 3 0.155 − + r r

2 Valence rule There is a definite relation between valence and CN Let s be the strength of electrostatic bonding between a pair of anion and cation

2. Valence rule There is a definite relation between valence and CN. Let S be the strength of electrostatic bonding between a pair of anion and cation

where, S: bonding strength Zt. number of valence electron CNT: C.N. of cation ion if s=s S. Then Z=CN)×S=(CN)×(zCN+)

CN :C.N. of cation ion : number of valence electron where, : bonding strength CN + + + + = Z S Z S if S1＝S2＝……＝S, Then Z ＝(CN－)×S＝（CN－）×（Z + /CN+）   + − = − = + = = CN 1 CN 1 , i i i Z Si Z S

3. The anion polyhedron prefer to share apex instead of sharing edges or faces Corner-sharing Edge-sharing Face-sharing tetrahedra tetrahedra tetrahedra (a) (b)

3. The anion polyhedron prefer to share apex instead of sharing edges or faces:

33.5 Crystal Structure of Ceramic Materials AB AB, A2B3 ABO3 AB,Oa Ab type N CI 1. NaCl r/r-=0.54 octahedron =>CN+=6 NaCl Z=1=CN(ZCN)=CN×1/6 .CN=6

§3.5 Crystal Structure of Ceramic Materials AB AB2 A2B3 ABO3 AB2O4 ◆Ⅰ. AB type 1. NaCl r + /r－＝0.54 ∴ octahedron ＝> CN+＝6 Z－＝1＝CN－(Z + /CN+ )＝CN－×1/6 ∴ CN－＝6

No L二

2 CsCI r+/r-=0.91 hexahedron=>CN+=8 Z=1=CN(2CN)=CN×1/8 。CN-=8 OCs (CI- CsCl

2. CsCl r + /r－＝0.91 ∴ hexahedron ＝> CN+＝8 Z－＝1＝CN－(Z + /CN+ )＝CN－×1/8 ∴ CN－＝8