1b 91 ¬ 0 - struchem.nankai.edu.cn · Nankai University E5 º L F1b 91 ¬ 0.v

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7.1 7.1.1

1.

-Long-range-order


Crystalline Solid Glass(Amorphous Solid)


c b+c a+b+c 1:2:4

NaCl


2.

F+V=E+2

(F: V: E: )

NaCl 6 128

3.

4. X

5.


7.1.2 (lattice)


A

B

C

X


1. (one-dimensional lattice)

a

a m = 0, 1, 2, … amT m

a


bnamT nm,

2.

ab

a

b


( )( )

( )Nankai University http://struchem.nankai.edu.cn

ab

a

ba

b

a

b

ab

a=b a^b=90

a b a^b=90

a=b a^b=120

a b a^b 90


ab

1.2.

ab


4.

6 1414 (Bravias)

(m, n, p = 0, 1, 2, …)

cpbnamT pnm ,,


a

b

c

a, b, ca,

b, c

= b ^ c = c ^ a =a ^ b

a, b, c,


cubic a = b = c, = ß = = 90o

P- (Primitive) I- (Body centred) F- (All-face centred)

Phexagonal (P)

a = b c, = ß = 90o,

= 120o

a aa

a aa

cP cI cF

hP

Rhexagonal (R)

a = b c, = ß = 90o,

= 120ohR


a

a

a

Rhombohedral (R)a = b = c, = ß = 90o

Rhexagonal (R)

a = b c, = ß = 90o,

= 120o

hR


orthorhombic a b c, = ß = = 90o

C- (C-face centred)

tetragonal (P I) a = b c,= ß = = 90o

a

c

b

a a

c

tP tI

oP oI oC oF


anorthic (P)(triclinic)

a b c, 90o

monoclinic (P C) a b c, = = 90o, 90o

a b

c

a b

c

mP mC

aPNankai University http://struchem.nankai.edu.cn

c

120

a ba a

a

a a

c

a

c

b a b

c

a b

c

a

a

a


1.

()

——

7.1.3


1 ——

a a = 2r

2.

a


2

CH2n

?



6 2 C 4 H

1 1 1 1 1 1 1

2 2 2 2 2 2 2

3 3 3 3 3 3 34 4 4 4 4 4 4

5 5 5 5 5 5 56 6 6 6 6 6 6



C

a

2C 4H

a

—


2 C

2

3


4 NaCl

1Cl-, 1Na+

F cF

4Cl- 4Na+

:

:

:


5 CsCl

1Cl-, 1Cs+

P cP

1Cl- 1Cs+

:

:

:


1S=, 1Zn++

4S=, 4Zn++

6. ZnS

F cF

:

:

:


7. ZnS

2S=, 2Zn++

2S=, 2Zn++

P hP

:

:

:


8. CaF2

1Ca++, 2F-

4Ca++ 8F-

F cF

:

:

:


9.

2C

8C

F cF

:

:

:


3.

6 6 *14 14


7.1.4


a, b, c, , ,

( )


OP= xa+yb+zc

•

••

O

P

ab

c

xa yb

zc

Y

Z

P XY Z zc

P YZ X xaP XZ Y yb

Nankai University http://struchem.nankai.edu.cna

b

Cl-: 0,0,0; 1/2,1/2,0; 0,1/2,1/2; 1/2,0,1/2

Na+: 1/2,0,0; 0,1/2,0; 0,0,1/2; 1/2,1/2,1/2

S= : 0,0,0; 2/3,1/3,1/2;

Zn++: 0,0,5/8; 2/3,1/3,1/8

Cl 4 Na+ 4 S 2 Zn: 2


S2 :

Zn2+:

S 4 Zn: 4S: +Zn: 1/8

0,0,0; 1/2,1/2,0; 0,1/2,1/2; 1/2,0,1/2

1/4,1/4,1/4;3/4,3/4,1/4; 3/4,1/4,3/4;1/4,3/4,3/4;

ZnS


F8

F : 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;

CaF2


•

•

• 1/8 ( )


F1/4,1/4,1/4 0,0,03/4,3/4,1/4 1/2,1/2,03/4,1/4,3/4 1/2,0,1/21/4,3/4,3/4 0,1/2,1/23/4,3/4,3/4 1/2,1/2,1/23/4,1/4,1/4 1/2,0,01/4,3/4,1/4 0,1/2,01/4,1/4,3/4 0,0,1/2

Ca0,0,0 3/4,3/4,3/4 (-1/4,-1/4,-1/4)1/2,1/2,0 1/4,1/4,3/41/2,0,1/2 1/4,3/4,1/4 0,1/2,1/2 3/4,1/4,1/4


x, y, z 1/2

CaTiO3


7.1.5

( )

=1/3:1/2:1 =2:3:6=h*:k*:l*

a b

c

a

b

c

O

A

B

C

( ) (h*k*l*)

(236)OA/a = 3 OB/b = 2 OC/c = 1


(100) (110)

(111) (h*k*l*)( )

—

a b

ca b

c

a b

c


ab

(110) (210)

(100)

(120)-


2*2*2*)( ***

lkhad

lkh

2*2*2*)( )()()(

1***

clbkahd

lkh

2*22*2*)(

)()(

1***

clakhd

lkh

2

2*

2

2***2*)(

3)(4

1***

cl

akkhh

dlkh


(hkl))( lkh


7.2 327.2.1

1.

Cn ˆnC n n L( =2 /n)

ˆ m M i i I

Sn ˆnS n L( )Ii


2.

( =2 /n)L( ) I or I L( )

n

4'

3'

2'

1'

L( /2) I

1"2"

3"

4"1

2

3

4

4- 4- 4-


21 Si

633 Si

44 S

336 Sm

12 Sm


3. nn=1, 2, 3, 4, 6


4. , i , :

i —i —


5. m


7.2.2

c 3 a=b=c = = = 90

h

6 a=b c = = 90 = 120

3

a=b c = =90 = 120

a=b=c = = 90

t 4 a = b c = = = 90o m

2a b c = = = 90

m 2 m a b c = = 90a i a b c 90

6

3

4


34

43O

T

OhO

i

ThTdT

i4-

CsCi

im

DnhDndDn

mhmdn2 n

n

4-S4

D2h( ) D3h(* ) D4h( ) D6h( )D2d(* ) D3d( )D2( ) D3( ) D4( ) D6( )

n

mhmv

C3+i

Cnh

Cnv

C3iCn

C2h( ) C3h(* ) C4h( ) C6h( )C2v( ) C3v( ) C4v( ) C6v( )C3i( )C1( ), C2( ), C3( ), C4( ), C6( )

C3h, D3h 6D2d 4

__

7.2.3 (32 )


1. (Schöflies Symbol)2. (Hermann-Mauguin Symbol)

32

•( );

•

7.2.4 32


c 4 3 // 4 a, b, c a, a + b + c, a + b

c // 6( 6) a, b // 2 m a, b c c, a, 2a + b

c // 3( 3) a, b // 2 m a, b c c, a h

a, b, c 3 3( 3) a + b + c, a - b

t c // 4( 4) a, b // 2 m a, b c c, a, a + b

o a, b, c // 2 m a, b, c m b // 2 ( m), a, c c b a a, b, c 3 a



1.2.3.

a 4

a+b+c 3a+b mTd m43


m

D2h

b ca2

m2

m2

Oh

a a+b+c a+b

m4 3 m

2

4 23m m

ac

a

b

c


baac ,,

C4 C4v C4h D4 D4h D2d

42m 4 4mm 4/m 422 4 2 2 _

_ _ _mmmc

a a+b


32

Maximal subgroups and minimal supergroups of the three-dimensional crystallographic point groups. Solidlines indicate maximal normal subgroups; double or triple solid lines mean that there are two or three maximalnormal subgroups with the same symbol. Dashed lines refer to sets of maximal conjugate subgroups. Thegroup orders are given on the left

1

2

3

4

6

8

12

16

24

484 2m m3

mmm4 2 2

432 43m 32 m

23

mmm6 2 2

622 62m 6mm m6 3 2

m

6 6 32 3m 3

3

4 222 mm2 m 2

2 m 1

1

422 42m 4mm 4m

2 2 2mmm

4


N

S

AB

CD

A'B' C'D'

A'

B'

C'D'

7.2.5

S4


7.2.6

Oh mm234

CaF2( )

3m m


Td m34

ZnS( )


O 432

NH4Cl -Mn(A13)

Th

FeS2

32m

T 23

FeSi

3m


C6 6

KAlSiO4( )

C3h

AgH2PO4

C6h

Ca5(PO4)3OH

6

m6


- (SiO2)D6 622

C6v 6mm ZnO ( )

D3h 6 2m BaTiSi3O9( )

D6h mmm226 Be3Al2(SiO3)6( )

MoS2( )

Zn (H2O)6/mmm


mmm224

TiO2( ) D4h

CuFeS2( )

D2d

NiSO4·6H2O

D4 422

m24

4/mmm


m4C4h

BaTiO3C4v 4mm

4S4

C4 4PbMoO4( )

BPO4

CaWO4( )


D3d m23

C3 3

C3i 3

D3 32

C3v 3mKAl3(SO4)2(OH)6( )

CaCO3( )Al2O3( )

HgS( ) -SiO2( )

CaMg(CO3)2( )FeTiO3( )

Pb9As4S15( )

3m


D2hmmm222

(S)

D2 222

C2v 2mm(mm2)

MgSO4·7H2O( )

Na2Al2Si3O10·2H2O( )

(mmm)


m2 Na2B4O7·10H2O( )

CaSO4·2H2O( )

C2 2

Cs m

C2h

Ca2Zn2Si2O7(OH)2·H2O( )

C4H6O8( )


1

C1 1

CiNaAlSi3O8( )CuSO4·5H2O( )

Al2Si2O5(OH)4( )CaS2SO3·6H2O


1. ()

n m i n

2.

7. 3 230

7.3.1


t Tnm

)()2( anmT

nL

NaCl

42

1

23

4

5

1'

a

a/4

41 42 43 4


(T) (TM) ()

o

o

o

o

aa/2

o

o

o

o

o

o

o

o

M T

A

A A

a. a(b c) a(b c) a/2(b/2 c/2)


42 21


NaCl 42 NaCl c


• no

o o

o o

o

oo o

o o

ooa

b

222,

22,

22,

22cbacbcaba

• d( )

o

o o

o o

o

oo o

o

oa

b44

,44

,44

cacbba


41



1

2 3 4 6

3

4

6

21

31 32

41 42 43

61 62 63 64 65

+

2/m 21/m

4/m 42/m

6/m 63/m

i ( 1 )

m( 2 )

a b c ------ .........

n - - - - -

d · · · · · ·


7.3.2 230

cCC

cPC

cPC

mCC

mPC

mPC

mC

h

h

h

h

h

h

h

2

2

2

2

2

2

2

62

152

42

32

122

12

2

C2h 6

P14

21 b, b21 , b

c


7.3.3

• ( )

( )

5 12

2hC P

c

y=1/4 c

21

41

a

c

0 b 0


zyx ,,1 1, ,2 2

x y z

, ,x y z 1 1, ,2 2

x y z

+

_

+

__12

_12

+

_ _

+

+

_

+_12

__12

41

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1b 91 ¬ 0 - struchem.nankai.edu.cn · Nankai University E5 º L F1b 91 ¬ 0.v