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8.1
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8.2 8.2.1
6
6
6
2
_6
66
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2 2 3 1 1 3
3 3 1 4 1
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8.2.2
2
2
2
1
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8.38.3.1 (A3)
1) ABABAB…
2) : 12( 6 3 )
hexagonal closest packing (hcp)
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P (hP)3)
a = b = 2rc = 1.633ar
1
2
21,
31,
32;0,0,0
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4)
:
4
243,
32,
31;
41,
32,
31
87,
31,
32;
81,
31,
32;
85,0,0;
83,0,0
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1 41/4 1 8
(1331)2
61/6 1 6
(33)1
42
: : =2:2:4=1:1:2
A3
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5) ~A3
001 a=2r=b, c/a=1.633
6) c
c c
3
100%
4 23= 74.05%sin(120 )
r
ab c
3 6hm
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8.3.2 (A1)
1) ABCABC...
2) 12
3) cF
1
4
21,
21,0;
21,0,
21;0,
21,
21;0,0,0 cubic closest packing (ccp)
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4)
: : =4:4:8=1:1:2
8 ( )
4 ( 1 3 )
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5) 74.05%
36) 43
2 2a r
33
33
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A1 A3
12: : =1:1:2
74.05%
A1 A3A1 4 A3A1
A1: Cu Ag Au Ni Pd Pt Al
A3: Mg Zn Nankai University http://struchem.nankai.edu.cn
8.4 8.4.1 (A2)
1) cI
2) : 8+6
body cubic packing (bcp)
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a2
a
3) 68.02%
ar 344)
6 ( 3 3)
12( )
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8.4.2 (A4)1) cF
2
4
2) 4
3) =34.01% 38ra
A4
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A3 hcp A1 ccp A2 bcp A4ABAB... ABCABC...
12 12 8+6 4hP cF cI cF1 4 2 42 4 2 8
2 1 1 24 8 122 4 6
% 74.05 74.05 68.02 34.01
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8.5
A3* La A5 -Sn A6 In A8 -Se
A9 A10 -Hg A11 -Ga A12 -Mn
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A13 -Mn A14 I2 A15
A16 -S A17 P A20 U
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• X•
•
12 8 6 4
1 0.97 0.96 0.88
1212
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X A1a
100
ra 42 42ar
VNZM 0/ (Z M N0
V )
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8.6 8.6.1
1)
Cu-Au
CuAu
Cu3Au
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2) :
>2.0% <0.02%<0.25% >0.6%
8.6.2LaNi5 CaCu5
36
3 atmH0.083g cm-3
(0.089 10-3g cm-3) 1000-253 C
(0.07 g cm-3)Nankai University http://struchem.nankai.edu.cn
8.7
—
A3 A1 A2 A4—
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8.8
NaCl CsCl ZnS
ZnS CaF2
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NaCl •• 2(1 Cl-,1 Na+) • cF• 1 Cl-, 1 Na+
• 4• 6:6• A1 ccp• :• : 4/4=1• : 1, 3• : 1 3• (111) |AcBaCb|Cl-:
Na+: 21
210,
210
21,0
21
21,000
21
21
21,
2100,0
210,00
21
halite 5 3hO Fm m
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CsCl •• 2(1 Cl-,1 Cs+) • cP• 1 Cl-, 1 Cs+
• 1• 8:8•• :• : 1/1=1• : 1• : 1Cl-: 000
Cs+: 21
21
21 1 3hO Pm m
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ZnS •• 2(1 S=,1 Zn++)• cF• 1 S=,1 Zn++
• 4• 4:4• A1 ccp• :• : 4/8=1/2• : 8• : 4• (111) |AaBbCc|S=:
Zn++: 21
210,
210
21,0
21
21,000
43
41
43,
41
43
43,
43
43
41,
41
41
41
2 43dT F m sphalerite
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ZnS •• 4(2 S=,2 Zn++)• P hP• 2 S=,2 Zn++
• 1• 4:4• A3 hcp• :• : 2/4=1/2• 4 ( 2, 2)
1 1• |AaBb|
S=:
Zn++: 21
31
32000
5 2 1 1 3 2 1 700 , 00 ,8 3 3 8 8 3 3 8
or 46 36vC P mc wurtzite
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CaF2•• 3(2 F-, 1 Ca++)• cF• 2 F-,1 Ca++
• 4• 8:4•• :• : 4/8=1/2
81 ( )1 (8 1/8)( )3 (12 1/4) ( )3 (6 1/2) ( )
fluorite
5 3hO Fm m
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4 Ca++:
8 F-: 43
41
43,
41
43
43,
43
43
41,
41
41
41
43
43
43,
41
43
41,
41
41
43,
43
41
41
21
210,
210
21,0
21
21,000
Na2O
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•• 6(4 O=, 2 Ti4+)• tP• 4 O=, 2 Ti4+
• 1• 6:3•• :• : 2/4=1/2• :
1( ) 1( )2( )rutile
144 24hD P mnm
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2 Ti4+:
4 O=:21
21
21,000
0uu21
21
21 uu
21
21
21 uuuu0,
u
u
u
u
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A1 ccp
A2 bcp
A3 hcp
A4
NaCl
CaF2
ZnS
ZnS
TiO2
CsCl
NiAs
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AB CsCl 2(1Cl-,1Cs+) cP 1 1Cl-,1Cs+ 0,0,0 1/2,1/2,1/2
NaCl( ) 2(1Cl-,1Na+) cF 4 1Cl-,1Na+ 0,0,0; 1/2,1/2,0;
0,1/2,1/2; 1/2,0,1/21/2,1/2,1/2; 1/2,0,0; 0,1/2,0; 0,0,1/2
ZnS( ) 4(2S=,2Zn++) hP 1 2S=,2Zn++ 0,0,0; 2/3,1/3,1/2 0,0,5/8; 2/3,1/3,1/8
ZnS( ) 2(1S=,1Zn++) cF 4 1S=,1Zn++ 0,0,0; 1/2,1/2,0;
1/2,0,1/2; 0,1/2,1/21/4,1/4,1/4; 3/4,3/4,1/4;3/4,1/4,3/4; 1/4,3/4,3/4
AB2 CaF2( ) 3(2F-,1Ca++) cF 4 2F-,1Ca++
1/4,1/4,1/4; 3/4,3/4,1/4;3/4,1/4,3/4; 1/4,3/4,3/4; 3/4,3/4,3/4; 3/4,1/4,1/4;1/4,3/4,1/4; 1/4,1/4,3/4
0,0,0; 1/2,1/2,0; 1/2,0,1/2;0,1/2,1/2
(TiO2)6(4O=,2Ti++) tP 1 4O=,2Ti++ 0,0,0; 1/2,1/2,1/2
1 1 1, ,0; , ,2 2 21 1 1, ,0; , ,2 2 2
u u u u
u u u u
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CsCl 8 8 1/1=1 1NaCl( ) 6 6 A1 (ccp) 4/4=1 4 ,
1, 31 3
ZnS( ) 4 4 A3 (hcp) 2/4=1/2 4 ,
2, 211
ZnS( ) 4 4 A1 (ccp) 4/8=1/2 8
8
CaF2( ) 8 4 4/8=1/2
8 11 (8 1/8)
3 (12 1/4)3 (6 1/2)
13
(TiO2)6 3 2/4=1/2
4 11 (4 1/4)2 (4 1/2)
11
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• —
• ,
• Lande( ) NaCl
8.9 1. (Goldschmidt)
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NaCl
ra 42 ra 42a=2(r+ + r-)
a=2(r+ + r-)
(a) (c)(a)
(c)
+
+
+
+
+
+
+
+ +
+ +
+
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MgO MnO CaO MgS MnS CaS
a/Å 4.21 4.44 4.80 5.19 5.21 5.68
CaMnMg rrrOSrr
MgS MnS MgS MnS(a)
Sra 42 ÅrS 84.14
20.52
NaCl ,
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MnS CaSCaS (c)
2/68.584.1CaSCa rrr
ÅrCa 00.1
MgO MnO CaOMnO CaO (c)
280.400.1OOCarrr ÅrO 40.1
ÅrMn 82.0244.440.1MnOMn rrr
MgO (a)(b) 1.4142*4.21=5.95 1.40*4=5.60MgO (c)
71.0Mgr221.440.1MgOMg rrr
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(Landé) 1920
1923 (Wasastjerna)
1926
F (1.33Å) O2 (1.32Å)80 ( )
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*zC
zC
r nn Cnn
1927 Pauling
2. Pauling ( )
3. (Shannon )1969 Shannon Prewitt
(effective ionic radii)1976 Shannon —
— — —
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1.
8.10
A
B C
D
r-
2r- + 2r+
rAB 2 )2(22)(2 rABrrAC
rrr 2 414.012rr
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0.414 r+/r- <0.732 60.225 r+/r- < 0.414
4
2 3 4(ZnS)
6(NaCl)
8(CsCl, CaF2)
12
r+/r- 0.155 0.225 0.414 0.732 1
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2. ( )
WW
CNCN
nn
n+:n- CN+ CN- W+:W-
CsCl 1:1 8 8 1:1NaCl 1:1 6 6 1:1
ZnS 1:1 4 4 2:2ZnS 1:1 4 4 2:2
CaF2 1:2 8 4 2:11:2 6 3 4:2
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3.
AgF AgCl AgBr AgIrAg+ 1.13r 1.33 1.81 1.96 2.20
r+ + r 2.46 2.94 3.09 3.332.46 2.77 2.88 2.99
r+ / r 0.85 0.62 0.58 0.51CsCl NaCl NaCl NaClNaCl NaCl NaCl ZnS
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AB
8 6 4 3 2CsCl NaCl ZnS
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( )() (
)
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8.11 Pauling
1928 Pauling:
—
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12 9 8 81.0 0.732 0.732 0.645
7 6 40.592 0.414 0.225
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— ( )
:S=W+/CN+
:CN
iiSW
1
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Cl- 1
NaCl
Na+ : 6
Na+-Cl- :SNa+-Cl-=1/6
Cl- : 6
16616
1iiS
CN
iiSW
1
1
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Ca2+ Ti4+
CaTiO3
Ti4+ 6
STi4+-O2-=4/6=2/3
Ca2+ 12
SCa2+-O2-=2/12=1/6
O2- Ti4+ :Ca2+ :
24 24
612
3242
1iiO SW
2
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:(CN-)
( )( )
—
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1 0.58 0.33
1 0.71 0.58
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4.
5.
( )
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8.12
8.12.1
SiC BN
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-BN SiC
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8.12.2
CdI2
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8.12.3
: CO2 CO2P
4 CO2 P
I2
2 I24 I2
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ZnS Zn S O1/3 H