材料科学基础
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson nine
§ 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-.
ro＞ r+＋ r－
ro＝ r+＋ r－
stable ionic compound
ro＜ r+＋ r－
there is some covalent bounding
stable
unstable
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
i onc a t i onof.N.C:CN
e l e c t r onv a l e n c eofn u m be r:
s t r e n g t hbo n di n g:,w h e r e
CN
?
?
?
?
?
Z
S
Z
S
if S1＝ S2＝ …… ＝ S,Then
Z ＝ (CN－ )× S＝（ CN－ ） × （ Z+/CN+）
??
??
?
?
?
? ?? CN
1
CN
1
,
i
i
i
i SZSZ
3,The anion polyhedron prefer to share apex
instead of sharing edges or faces:
§ 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
2,CsCl
r+/r－ ＝ 0.91
∴ hexahedron ＝ > CN+＝ 8
Z－ ＝ 1＝ CN－ (Z+/CN+)＝ CN－ × 1/8
∴ CN－ ＝ 8
3,Zinc blende ( ZnS )
CN－ ＝ 4 CN+ ＝ 4
4,Wurtzite ( ZnS,ZnO )
S(O)＝ 1/2＋ 1/2＋ 1
＝ 2
Zn＝ 1/4× 4＋ 1
＝ 2
8
1
2
1
8
3
)O(,S
Zn:
?120
? Ⅱ,AB 2 type
1,Fluorspar (CaF2)
Li2O Na2O
75.0??
?
r
r
CN+ ＝ 8
CN- ＝ 4
2,Rutile (TiO2)
48.0??
?
r
r
3CN)
3
2
(CN2
3
2
6
4
6CN
???
???
?
??
?
S
? Ⅲ, A2B3 type ( )
32 OAl??
4CN
)
2
1
(CN2
2
1
6
3
6CN
??
?
???
?
?
?
S
? Ⅳ,ABO 3 type ( BaTiO3,CaTiO3 )
)(2
2
1
2
2
OBOA
OB
OA
rrrr
arr
arr
????
??
??
? Ⅴ, AB2O4 type (spinel,MgAl2O4 )
Mg,4＋ 4＝ 8
Al,4× 4＝ 16 8(MgAl2O4)
O,4× 8＝ 32
Examples and Discussions
Exercise
Thank you !
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