Ch1-Mo Dau & Cau Tao Vat Chat

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CCC PHNG PHC PHNG PHP VP VT LT LPHN TPHN TCH CCH CU TRU TRC VC VT RT RNN

TRONG KHOA HTRONG KHOA HC VC VT LIT LIUU

Dr. NGUYEN ANH TUAN

HANOI-2007

HANOI UNIVERSITY OF TECHNOLOGY

INTERNATIONAL TRAINING INSTITUTE FOR MATERIALS SCIENCE


2/137

MCCH MN HC

1. V mt l thuyt: Nm c cc nguyn l cbn ca mt sphng php/k thut vt l thng dng trong vic phn tch cu trc

bn trong v b mt ca cc vt rn, cng nhmng mng cht rn

trong Khoa hc Vt liu, gm 4 nhm phng php:

+ Cc phng php trn cs nhiu x (XRD, ED, ND)+ Cc phng php hin vi hin vi in t(TEM, STEM, SEM)

+ Cc phng phpphn tch ph (Auger, EPMA, XRF, XPS, EELS,...)

+ Cc hin vi u d qut(SPM: AFM, MFM, STM, SNOM,...)

2. V mt thc hnh: Nm c mt s knng thc hnh, k thut

phn tch cc yu t/thng scbn ca cu trc vt rn thy

c nhng ng dng thng dng ca cc phng php / k thutnu trn. Nm c cc u nhc im v phm vi/gii hn ca

tng phng php phn tch. Bc u c th p dng thc t trong

vic phn tch mu cht rn / vt liu.

NATuan-ITIMS-2007


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NI DUNG BI GING

CHNG 1: CU TRC CA VT RN1.1. Cu trc nguyn t.

1.2. Cht rn v cc lin kt trong cht rn.

1.3. Cu trc tinh th ca cht rn - Mng tinh th v i xng tinh th.

1.4. Cu trc vt rn v nh hnh.

CHNG 2: CC PHNG PHP NHIU X

2.1. Cs ca nhiu x - L thuyt tng qut.

2.2. Nhiu x tia X (XRD).2.3. Nhiu xin t (ED).

2.4. Nhiu xntron (ND).

CHNG 3: CC PHNG PHP HIN VI

3.1. Cs ca HV - Hin vi quang hc (OM).

3.2. Hin vi in t truyn qua (TEM).

3.3. Hin vi in t qut (SEM).

3.4. Cc loi hin vi khc (hin vi laze ng tiu, hin vi tia X, hin vi ntron, ...).

NATuan-ITIMS-2007


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NI DUNG BI GING

CHNG 4: CC PHNG PHP PHN TCH PH4.1. Gii thiu.4.2. Cc phng php phn tch phin t.

4.3. Cc phng php phn tch ph ion.

4.4. Cc phng php phn tch khi ph.

CHNG 5: CC PHNG PHP HIN VIU D QUT (SPM)

5.1. Hin vi lc nguyn t (AFM).

5.2. Hin vi u d qut hiu ng xuyn ngm (STM).

5.3. Hin vi lc t (MFM).5.4. Hin vi quang hc qut trng gn (SNOM).

5.5. Mt s loi hin vi u d qut (SPM) c bit khc.

CHNG 6: CC BI THC HNH

6.1. Phn tch cu trc n tinh th bng nhiu x Lauer.

6.2. Phn tch cu trc a tinh th bng phng php nhiu x bt.

6.3. Phn tch pha nh tnh, nh lng.

6.4. Quan st hnh thi/cu trc b mt bng hin vi in t qut.

6.5. Quan st hnh thi/cu trc b mt bng hin vi lc nguyn t.NATuan-ITIMS-2007


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1. Materials science and technology, Ed. by R.W. Cahn, P. Haasen and E.J.Kramer, Vol. 1&2 A & B, VCH Weinheim, 1993.2. Elemen of X-ray diffraction, B.D. Culity and S.R. Stock; Prentice Hall, 2001.3. Diffraction for Materials Scientists by J.M. Schultz, Prentice-Hall, Inc.,

Englewood Cliffs, New Jersey 1982.

4. Electron Microscopy in Material Science ed. by U. Valdr; Academic PressInc., New York and London 1971.

5. Fundamental of surface and thin film analysis , L.C. Feldman and J.W.Mayer, North Holland, Amsterdam, 1986.

6. Electron Microscopy of thin crystals , P.B. Hirsch, London, 1965.7. Scanning tunneling microscopy and related methods, NATO ASI series E,Vol. 184, 1990.

8. Electron Scattering and Related Spectroscopies, by M. De Crescenzi andM.N. Piancastelli; World Scientific Publishing Co. Pte. Ltd. 1996.

9. Analytical Techniques for Thin films Ed. by K.N. Tu and R. Rosenberg(Treatise on Materials Science and Technology, Vol. 27); Academic Press, Inc.;Hardcourt Brace Jovanovich, Publishers, 1988.

10. Practical surface analysis 2nd ed. by David I. Briggs, John Wiley & Sons

1996.

TI LIU THAM KHO CHNH

NATuan-ITIMS-2007


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CHNG 1: CU TRC CA VT RN

1.1. Cu trc nguyn t

1.1.1. Cu to nguyn t1.1.2. Phn bin t trong nguyn t

1.1.3. Bng tun hon cc nguyn t ha hc

1.2. Cht rn v cc lin kt trong cht rn

1.3. Cu trc tinh th ca cht rn - Mng tinh th v i

xng tinh th1.4. Cu trc vt rn v nh hnh.

NATuan-ITIMS-2007


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1.1.1. Cu to nguyn t Nguyn t: ht nhn (p & n) + e-

in tch: |e| = 1.6 x 10-19C Khi lng: mp mn ~ 1.67 x 10

-27 kg

(~ 1.67 x 10-24

g); me ~ 9.11 x 10-31

kg. SS nguyn tnguyn t: Z= sp trong ht nhn./v nguyn ttrung ha in, Z= sin t. Z ca cc nguyn t trong bng tun hon: t 1 (H) - 94 (Pu).

KhKhi li lng nguyn tng nguyn t: A = mp + mn/v mt nguyn tcho trc: s proton l nhnhau cho cc ng.t,

nhng s neutron (N) c th khc nhau cc ng v khc nhau.A Z + N

n vn v khkhi li lng nguyn tng nguyn t ((amuamu)): Khi lng mi proton (hay ntron) l ~ 1.67 x 10-24g, c quy c l

n vkhi lng ca nguyn t. Khi lng nguyn tcarbon ng v l 12 (6 proton & 6 ntron), (12C),ngha l: A = 12 amu. Nhvy 1 amu = 1/12 .

Nhvy c 0.6023 x 1024 amu/g S Avogadro l sproton (hay ntron) cn thit to ra mt khi lng l 1 gram.

hay l s nguyn t/phn t c trong 1 mol cht.NATuan-ITIMS-2007


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NATuan-ITIMS-2007

Mu nguyn t Bohr(Mu hnh tinh)

Mu nguyn ttheo chc sng(so snh vi mu Bohr)

Xc sut1

m my

in t

0Khong cchn ht nhn

in tquo Ht nhn

1.1.2. Phn bin t trong nguyn t


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l= 0 l= 1 l= 2

Cc slng t ca in t trong nguyn t:n: Slng t chnh (n = 1, 2, 3, ...), m t kch thc ca quo (hay m my

phn b mt in t: n = 2 > n = 1) v biu th gin tip nng lng ca cc qu

o in t.

l: Slng t gc (l= 0, 1, ... n -1), m t hnh dng ca quo: vi l= 0 hnhcu; l= 1 hnh cc (hnh qu t); l= 2 hnh l ch; v.v... Vi l = 0 chc mt

cch nh hng duy nht trong khng gian (hnh cu); vi cc trng hp l 0

cn c nhng hng khc nhau trong khng gian.

m: Slng t t (m = - l, - (l+ 1), ..., (l+ 1), l), m t snh hng trong khnggian ca mi quo in t ring bit (cn k hiu l ml).

s: Slgn t spin (s = - 1/2; +1/2), m t snh hng spin ca in t trn mi

quo (cn k hiu l ms).


NATuan-ITIMS-2007


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NATuan-ITIMS-2007

....

p orbitals orbital

pzorbitalpyorbitalpxorbital

dz2orbitaldx2-y2orbitaldyzorbitaldxzorbitaldxyorbital


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n=3, l=2, m=0n=2, l=1, m=1n=2, l=1, m=0

n=1, l=0, m=0 n=3, l=2, m=1 n=3, l=2, m=2 n=4, l=2, m=2


NATuan-ITIMS-2007

Mt s dng m my mt in t phn btrong khng gian3D tng ng vi cc t hp khc nhau ca cc slng t


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NATuan-ITIMS-2007


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NATuan-ITIMS-2007

pL2

72P6

50O5

32N4

18M3s

8s

2sK1

Sintti a

cha

trongnguyn

t

Cc lpquo

con

(ng vicc lkhcnhau)

K hiu

lp vquo

chnh

Mc nnglng

(Slng

tchnh)(n)

Electron Capacity = 2n2

: K

: L

: M

: N

: O

: P

K hiu cc lp vin t v sin t ti a cha trong mt nguyn t


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NATuan-ITIMS-2007

1.1.3. Bng tun hon cc nguyn t ha hc

- Nguyn l AUFBAU (tingc, c ngha l BUILDUP trong ting Anh): th hin cch xy

dng bng tun hon cc nguyn t ha hc, da vo cch sp xp cc in tnhth

no trong cc nguyn t.

- C 2 nguyn tc c tun theo:

+ Quy tc Hund

Cc in tc in vo cc quo theo nguyn tc ln lt t cc

mc nng lng thp nht c th.

+ Nguyn l loi trPauli

Hai in t khng th cng chim gi mt trng thi nng lng (ng vi cngmt b cc slng t)

H 1 electron 1s1

He 2 electrons 1s2

Li 3 electrons 1s2

2s1

O 8 electrons 1s22s22p4

Ne 10 electrons 1s22s22p6

Na 11 electrons 1s22s22p63s1

Ar 18 electrons 1s22s22p63s23p6

K 19 electrons 1s22s22p63s23p64s1

Ca 20 electrons 1s22s22p63s23p64s2


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[Ne] 3s2 3p6 = [Ar]Ar18

[Ne] 3s2 3p5Cl17

[Ne] 3s2 3p4S16

[Ne] 3s2 3p3P15

[Ne] 3s2 3p2Si14[Ne] 3s2 3p1Al13

[Ne] 3s2Mg12

[Ne] 3s1Na11

[He] 2s2 2p6 = [Ne]Ne10

[He] 2s2 2p5F9[He] 2s2 2p4O8

[He] 2s2 2p3N7

[He] 2s2 2p2C6

[He] 2s2 2p1B5

[He] 2s2Be4[He] 2s1Li3

1s2 = [He]He2

1s1H1

Electron ConfigurationSymbolAtomicNumber

NATuan-ITIMS-2007

[Ar] 4s2 3d10 4p6 = [Kr]Kr36

[Ar] 4s2 3d10 4p5Br35

[Ar] 4s2 3d10 4p4Se34

[Ar] 4s2 3d10 4p3As33

[Ar] 4s2 3d10 4p2Ge32[Ar] 4s2 3d10 4p1Ga31

[Ar] 4s2 3d10Zn30

[Ar] 4s1 3d10Cu29

[Ar] 4s2 3d8Ni28

[Ar] 4s2 3d7Co27[Ar] 4s2 3d6Fe26

[Ar] 4s2 3d5Mn25

[Ar] 4s1 3d5Cr24

[Ar] 4s2 3d3V23

[Ar] 4s2 3d2Ti22[Ar] 4s2 3d1Sc21

[Ar] 4s2Ca20

[Ar] 4s1K19

Electron ConfigurationSymbolAtomicNumber

The Electron Configurations of the Elements

(1st, 2nd, 3rd, and 4th Row Elements)

THE AUFBAU

PRINCIPLE

THE PERIODIC

TABLE


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mm

NATuan-ITIMS-2007

118Uuo

117Uus

116Uuh

115Uup

114Uuq

113Uut

112Uub

111Rg

110Ds

109Mt

108Hs

107Bh

106Sg

105Db

104Rf2

142-

103Lr214-1

102No2

14--

101Md2

13--

100Fm212--

99Es2

11--

98Cf2

10--

97Bk29--

96Cm271-

95Am

27--

94Pu26--

93Np241-

92U231-

91Pa221-

90Th2-2-

89Ac

2-1-

88Ra2---

87Fr1---

[Rn]+

7s:5f:6d:7p:

86Rn2

14106

85At2

14105

84Po2

14104

83Bi2

14103

82Pb214102

81Tl2

14101

80Hg2

1410-

79Au

11410-

78Pt1

149-

77Ir2147-

76Os2146-

75Re2

145-

74W2144-

73Ta2143-

72Hf2

142-

71Lu2141-

70Yb2

14--

69Tm2

13--

68Er212--

67Ho2

11--

66Dy2

10--

65Tb29--

64Gd271-

63Eu27--

62Sm26--

61Pm25--

60Nd24--

59Pr23--

58Ce211-

57La2-1-

56Ba2---

55Cs1---

[Xe]+

6s:4f:5d:6p:

54Xe2

106

53I2

105

52Te2

104

51Sb2

103

50Sn2102

49In2

101

48Cd2

10-

47Ag

110-

46Pd-

10-

45Rh18-

44Ru17-

43Tc25-

42Mo15-

41Nb14-

40Zr22-

39Y21-

38Sr2--

37Rb1--

[Kr]+

5s:4d:5p:

36Kr2

106

35Br2

105

34Se2

104

33As

2103

32Ge2102

31Ga2

101

30Zn2

10-

29Cu110-

28Ni28-

27Co27-

26Fe26-

25Mn25-

24Cr15-

23V23-

22Ti22-

21Sc21-

20Ca2--

19K1--

[Ar]+

4s:3d:4p:

18Ar26

17Cl25

16S24

15P23

14Si22

13Al21

12Mg2-

11Na1-

[Ne]+

3s:3p:

10Ne2

6

9F2

5

8O2

4

7N2

3

6C2

2

5B2

1

4Be2

-

3Li1

-

[He]+

2s:

2p:

2He2

1H11s:

Electron configurations of the neutral gaseous atoms in the ground state

THE PERIODIC TABLE OF THE ELEMENTS


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1.1. Cu trc nguyn t


1.2.1. Mu

1.2.2. Cc lin kt trong cht rn1.3. Cu trc tinh th ca cht rn - Mng tinh th v i

xng tinh th


NATuan-ITIMS-2007


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1.2.1. Mu+ Cht rn l mt trng thi ca vt cht mt s ln cc nguyn t(~1023/cm3) lin kt ha hc bn vng vi nhau to ra khi kt tc(ng rn/ ngng t).

+ Bn cht cc lc lin kt l lc tnh in; tng tc t tnh rt yu; tngtc hp dn coi nhkhng c.

+ Bn cht ca lin kt ph thuc vo cu trc in t ca nguyn t.

+ Trng thi in t ca nguyn t c ththu c tchc hc lng t:

Phng trnh Schrodinger trong trng xuyn tm.+ Dng ca lc lin kt quy nh dng ca cht rn v tnh chttng ng.

+ Cc dng thnng tng tcng vai tr chnh trong cc dng lin ktcc nguyn t.

+ Nng lng lin kt tiu biu: ~ 1 - 400 kcal/mol(tng tc t tnh ~1kcal/mol, tng tc hp dn ~ 10-27 kcal/mol).

+ Da trn cs cch sp xp cc nguyn t, c th chia CR lm 3 loi:

CR tinh th, CR a tinh th, vCR v nh hnh (c th c dng t hp).NATuan-ITIMS-2007


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NATuan-ITIMS-2007

S lin kt gia cc nguyn t hnh thnh nn cht rn v cu trc tinh th


20/137


1.2.2. Cc lin kt trong cht rn

Lin kt ion

Lin kt cng ha tr

Lin kt kim loi Lin kt hydro

Lin kt Van der Waals

Xem thm v cc kiu lin kt ny trong Solid State Physics caAshcroft and Mermine

NATuan-ITIMS-2007


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1.1. Cu trc nguyn t


1.3. Cu trc tinh th ca cht rn - Mng tinh th v i

xng tinh th


NATuan-ITIMS-2007


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1.3.1. Cu trc tinh th

NATuan-ITIMS-2007


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Trc tinh th:

n v:

NATuan-ITIMS-2007

Cc vec-tn v:

a theo trc x;

b theo trc y;c theo trc z.

n vc xc lp

theo cc vec tn va, b, c.

Vectcs:

r* = a + b + c

r*

Mt th tch khng gian m

khi tnh tin theo tt c cc

vecttrong mt mng

Bravais, phi lp y hon

ton khng gian m khng,

hoc trng vi chnh n,

hoc li ch trng.


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Vic la chn cc nguyn thy:


NATuan-ITIMS-2007

Trng hp mng 2-D


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Trng hp mng 3-D


NATuan-ITIMS-2007

Vic la chn cc nguyn thy:


26/137

C 7 LOI MNG TINH TH:


NATuan-ITIMS-2007

LP PHNG

T GICTRC THOIMT NGHINGBA NGHING

LC GICTHOI


27/137

.....


NATuan-ITIMS-2007

LP PHNG

T GIC

TRC THOI

N T

TAM T

LC GIC

THOI

Bc ca i xng


28/137

.....


NATuan-ITIMS-2007

16D4h

8D4

8C4v

8D2d

8C4h

4S4

4C4

a=b c

= = = /2Tetragonal

8D2h

4D2

4C2va b c

= = = /2Orthorhombic

4C2h

2C2

2Cs (C1h)

a b c= = /2

Monoclinic

2Ci

1C1a b cTriclinic

Orthographic

projection

OrderPoint

Groups

Conditions


29/137

.....


NATuan-ITIMS-2007

48Oh

24O

24Td

24Th

12T

a = b = c

= = = /2Cubic*

24D6h

12D6

12C6v

12D3h

12C6h

6C6

6C3h

a = b c

= = /2,

=2 /3Hexagonal

12D3d

6D3

6C3v

6S6

3C3

a = b = c

= < 2 /3,/2

Trigonal


30/137


14 mng khng gian - Mng Bravais

NATuan-ITIMS-2007

face-centeredbody-centeredbase-centeredsimple

orthorhombic(trc thoi)

base-centeredsimple

monoclinic(n t)

triclinic(tam t)

LatticesCrystal system


31/137


NATuan-ITIMS-2007

face-centeredbody-centeredsimple

cubic(isometric)

body-centeredsimple

tetragonal(trc thoi)

rhombohedral(trigonal)(thoi)

hexagonal(Lc gic)

LatticesCrystal system

CHNG 1 CU TRC CA VT RN


32/137


NATuan-ITIMS-2007

nguyn thy ca mng

trc thoi tm y:

nguyn thy ca mng

trc thoi n:



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NATuan-ITIMS-2007

nguyn thy ca mngtrc thoi tm khi:

nguyn thy ca mng

trc thoi tm mt:



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nguyn thy Wigner-Seitz:

Wigner-Seitz l vng khng gian bao quanh mt nt mng m vng gn nt mng ny hn bt k nt mng no khc.

Hay: L qu tch cc im trong mt khng gian bao quanh mt nt mng no

v gn n hn bt k nt mng no khc.

NATuan-ITIMS-2007

Cch xy dng WS

- Xc nh nt mng.- Chn nt gc (s l tm ca WS).- Ni nt gc vi tt c cc nt ln cn gn nht.- V cc mt trung trc ca cc on ni giacc nt.- Khng gian c th tch nh nht gii hn bi

cc mt trung trc bao quanh nt gc l WS.

WS trong trng hp mng 2-D



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Bi tp: Xc nh Wigner-Seitz ca 2 mng di y


NATuan-ITIMS-2007



36/137

WS trong trng hp mng 3-D


NATuan-ITIMS-2007



37/137


NATuan-ITIMS-2007

- Mi mng Bravais c t nht 1 Wigner-Seitz.

Nu tnh n t l cc trc, c 24 dng khc nhau ca WS.



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S lp y khng gian bi WS


NATuan-ITIMS-2007

- WS tng t mt vin gch hoa- S lp y khng gian bi WStng tnhvic lt nn bng nhngvin gch hoa



39/137

- Mt im bt k trong mng tinh th

khng nm cc v tr nt mng:r = (n + u)a + (p + v)b + (q + w)c

n, p, q l s nguyn;

u; v; w l s khng nguyn

r = (n a +p b + q c) (r')+ (u a + v b + w c) (r')

= r' + r'

r' = vectnt mngr' = vectxut pht t nt mng

r (nh ca vectr)


NATuan-ITIMS-2007

121

112

x

y

z

000

100 110

010

001

111

- Nt mng:

r = ua + vb + wc ; trong u, v, w l nhng s nguyn

rR

r*

c

a

b

u = 1, v = 1, w = 2

r = a + b + 2c

= r* + R = r* + c

Vectxc nh v tr bt k ca mt im trong mng tinh th bng tng ca vectgc cho ca

mt n v vi vectxut pht tnh gc cho

ti mt im bn trong n v v tr u v w

i vi nh gc cho ca n v)

000

0-1



40/137

BBi ti tpp: Xc nh v tr cc nt mng

Hy xc nh cc v tr nt mng ca cc mng Bravais fcc(facecentered cubic) v fco (face centered orthorhombic).


NATuan-ITIMS-2007

000

100a

y

z

010

b

0

00

001c

x110

00

111

- V tr cc nt mng cc gc l: 000, 100, 010, 001, 110, 101, 011, v 111.

- V tr cc nt mng tm mt l: 0, 0, 0, 1, 1, 1.

Cc mng Bravais fccgm:

Cc mng Bravais fco gm:



41/137


NATuan-ITIMS-2007

Hng tinh th:

- Mt hng bt k mtng song song vi n i qua gc mng, sau gn ta ca im bt ktrn ng i qua gc mng . Tt c cc hng tinh th c

th quy v cc hng trong mt n v vi gc c gn nh nt mng.

- Xt mt im bt k v tr u'v'w'(khngnht thit phi l s nguyn) trn ng t

i qua gc ta . ng t si qua tt

c cc im c ta 2u'2v'2w', 3u'3v'3w',

4u'4v'4w',....

- Bt k gi tr no ca u' v' w'u c th chuyn thnh mt b gm cc s nguyn nh

nht bng cch nhn hoc chia lin tc cho cng mt s. V d, nhvy [1], [112],

[224], [448] u chth cng mt hng tinh th. Nhng ngi ta quy c chn b s

gm nhng s nguyn nh nht (nt mng), nhl [112] chhng tinh th ny.

- K hiu [u v w] chhng tinh th hc

ca ng t. Tt c cc ng song song

vi ng ny u c cng chshng

vi ng t ny.

x

y

z

000

100 110

010

001

111

b

c

a

011

101

u'v'w'

t

3u'3v'3w'

2u'2v'2w'



42/137

Nguyn tc xc nh hng tinh th :

Trc tinh th: x y z

Vectn v: a b c

Cc hnh chiu: u'a v'b w'c (to ct cc trc)H s h. chiu: u' v' w'

Rt gn: xn u v w

Chshng: [uvw]


NATuan-ITIMS-2007

Cc hnh chiu: a/3 -1b 0c

H s h. chiu: 1/3 -1 0

Rt gn: x 3 1 -3 0

Chshng: [130]

x

y

z

000

100 110

010

001

111

b

c

a

011

101

V d:

Ct a 1/3

Ct b -1

Ct c 0

[130]



43/137

NATuan-ITIMS-2007

Mt shng tinh th quan trng:

x

y

z

000

100 110

010

001

111

b

c

a

011

101

[110]

[101]

[011]

[111]

[100]

[010]

[001]

[210]

[120]

[201]

10

10

10

0101

11

11

01

[221]

[021]

[012]

[212]

[102]

Gc to bi hai hng tinh th:

Chi vi cc h lp phng: r.r = |r||r'| cos

r = ua + vb + wc r = u a + v b + w c

222222

)'()'()'(

'''cos

wvuwvu

wwvvuu

++++

++==

r'r

r.r'



44/137

x

y

z

000

100 110

010

001

111

b

c

a

011

101

V d mt shng c chs m

NATuan-ITIMS-2007

- Cc hng c ch s m: V d, k hiu l [u v w] hay [u -v w].

c

-b

a

[u v w]

- c

b

a

[u v w]

c

b

- a

[u v w]

- c

-b

- a

[u v w]

[-100]

[0-10]

[00-1]

[110]

[111]

[111]

d dng xc nh cc hng c chs m, cn thit lp bvectn v (xc

nh cs) thch hp, nhng ta no m, trc ca vectcstng

ng cn i chiu ngc li.



45/137

10

NATuan-ITIMS-2007

BBi ti tpp: Xc nh hng trong mng tinh th

Hy xc nh cc hng mng sau y: [123], [-120], [1-4-2] v [-1-3-4].(chv trong gii hn cs)

1- Dng n v.

0

1

2- Vi b ta [u v w] cho (v d [123]),

xc nh s nguyn c gi tr tuyt i lnnht trong b ta (v d 3) - Chia c

ba s cho 3 [123] tr thnh [1].3- Xc nh im 00;

7- Ni gc 000 vi im 1 c hng [123].

4- Xc nh im 00;5- Xc nh c im 0;

6- Tnh tin im 0 theo chiu trc c mton 1 n v c im 1.

Vi cch lm tng t, ta c cc hng [-120], [1-4-2], [-1-3-4].

Lu : trong trng hp c chs m, cn xoay h ta ca n v mt

cch thch hp xc nh cc ta trong phm vi mt cs.

000

-a

b[-120]

000

a

-b

c

[1-42]1

000

-a

-b

-c1

[-1-3-4]

000

a

b

c

00

00



46/137

Hng ca mt lp (hnh thi) - H ca hng:

- l cc hng lin quan n tnh i xng ca chng.

- Quy c chn mt trong cc hng i din cho mt tp hp cc

hng c tnh cht nhvy v k hiu bng du ...: uuu i dincho mt h gm cc hng [uuu], [-uuu], [u-uu], [uu-u], [-u-uu], [-u-u-u]...

NATuan-ITIMS-2007[1-1-1]

[1-11]

000

a

b

c

V d: 111i din cho mt h cc

hng ng cho trong mng lp

phng: [111], [1-11], [-1-11], [-1-1-1],...

[111]

[-1-11][-111]

[11-1]

[-11-1][-1-1-1]

Nhn xt: Cc hng ngc nhau c cc

chs ta i du nhau. [111] >< [-1-1-1].



47/137

Xc nh cc mt phng trong mng tinh th - Ch s Miller:

- Quy nh s dng h thng chs Miller tinh th hc ca Anh

- Hng ca cc mt phng mng c gn vi cc trc tinh th hc;

- Vic xc nh mt mt phng mng c da trn cc khong cch thc(tnh t gc mng) m n ct 3 trc tinh th: lnhng on ct ca cc

trc: a/h; b/k; c/l.

NATuan-ITIMS-2007

c

b

a0a/h

c/l

b/k

(hkl)

- Chs Miller xc nh mt mt phng l b s nghch o ca cc phn

on 1/h; 1/k; 1/l, ngha l h; k; l, v c vit trong ngoc n (h k l).

Nguyn tc xc nh hng tinh th :

Trc tinh th: x y z

Vectn v: a b cCc hnh chiu: a/h b/k c/l

H s h. chiu: 1/h 1/k 1/l

Nghch o: h k l

Chshng: (hkl)



48/137

NATuan-ITIMS-2007

0

c

0 1 2 3 4

b

a

(421)

02

46 8

1

2

3

V d:

di cc trc: 4 8 3

di cc on ct: 1 4 3Phn s cc on ct: 1/4 1/2 1

Cc chs Miller: 4 2 1

Lu : - Khi mt phng ct cc trc pha m, cc chMiller tng ng

cng l cc s m. K hiu l, v d: (h k l), (h k l), hoc dng du "-".

- Trng hp cc mt phng khng ct mt trc no , ngha l

song song vi trc , hoc cha trc

c coi l ct nhau

Phn on tng ng s l 1/ Trong trng hp ny quy

c chs Miller l 0.



49/137

Ct -1b

Ct c

Ct a

NATuan-ITIMS-2007

Bi tp: Xc nh chs Miller ca cc mt phng trong hnh di y:

a) Mt mu vng:

- Cc on ct: a, 1b , c- Cc phn on: , 1, - Nghch o: 2 1 0- Chs Miller (hkl): (210)

0

c

b

a

(210)

b) Mt mu hng:- Cc on ct: a , -1b, c- Cc phn on: , -1 , - Nghch o: 2 -1 0

- Chs Miller (hkl): (210)c) Mt mu xanh:- Cc on ct: 1a, b, 2c- Cc phn on: 1, , 2- Nghch o: 1, 0, 1/2 2 , 0, 1

- Chs Miller (hkl): (201)

Tr li

(201)

(210)

Ct 2c

Ct b Ct a 1

Ct a

Ct 1b

Ct c



50/137

NATuan-ITIMS-2007

Mt s mt phng quan trng nht ca mng tinh th

Nhn xt:

Trong h lp phng, [uvw]chnh l vectphp tuyn

ca mt (hkl)

Lu :i vi cc h khc

iu ny khng ng.



51/137

NATuan-ITIMS-2007

Cc mt phng quan trng tng ng khc

H mt phng {100}



52/137

H mt phng {110}

NATuan-ITIMS-2007



53/137

NATuan-ITIMS-2007

Cc mt mng song song

- Cc mt phng (nh nk nl) song song vi mt (h k l) v cch nhau

mt khong d= 1/n.

(200)

(100)

d200d100

a

c

b



54/137

Lu :

- Tp hp cc mt song song khc nhau trong mng c cc khong cchdgia cc mt khc nhau: Cc mt c khong cch cng ln chs Millercng nh v c mt nt mng cng ln.

NATuan-ITIMS-2007

a

b

(11)

(10)

(31)(12)(41)

(13)

Lu :iu ny cng ng cho mng 3-D



55/137

NATuan-ITIMS-2007

Khong cch gia cc mt phng

Mng Lp phng:(Cubic)

Mng T gic:(Tetragonal)

Mng Trc thoi:(Orthorombic)

Mngn nghing(n t):(Monoclinic)

Mng Ba nghing (tam t):(Triclinic)

Mng Su cnh (lc gic):

(Hexagonal)

( )2/1

222

2

1

++= lkha

d

2/1

2

2

2

22

+

+

c

l

a

kh

2/1

2

2

2

2

2

2

++c

l

b

k

a

h

2/1

2

2

2

2

2

2

2

sin

cos2

++

b

kac

hl

c

l

a

h

2/1

222

2

2

22

2

22

2

2

coscoscos2coscoscos1

)coscos(cos2

)coscos(cos2

)coscos(cos2

sinsinsin

+

+++++

ca

lh

bc

kl

ab

hk

c

l

b

k

a

h

( )2/1

2

222

2

3

4

+++

c

lkhkh

a

Cho mng lc gic n

Cho mng thoi (Rhombohedral)( ) ( )( )

2/1

23

22222

2

cos3cos21

coscos2sin1

+

+++++

lhklhklkha



56/137

Gc gia hai mt phng

NATuan-ITIMS-2007

37.681.981.937.611.4711

35.278.978.935.215.8511

31.472.472.431.425.2311

30.065.965.930.035.221135.354.754.735.354.7111

60.045.045.060.090.0011

45.090.090.045.00.00100

101001010110100ANGLE



57/137

Bi tp: Xc nh cc mt phng song song di y

NATuan-ITIMS-2007

c

a

b



58/137

(0001)

NATuan-ITIMS-2007

Trng hp mng lc gic

- H lc gic khc hn vi cc h khc

do c i xng su cnh, trong

mt shng tinh thtng ng

nhau li khng c cng b chs.- thun li, ngi ta s dng h ta

BravaisBravais--MillerMiller, l mt h 4-trc,

trong 3 trc nm trong mt phngxy,

a1, a2, v a3, to vi nhau gc 1200v trc tht, trc c, hng theo trc z.

n v(cs)

l lng try thoi

a1

a2

c

1200

a3

z

- n vc thit lp trn cs3vectn v a1, a2, v c.

- Cc mt phng trong cc h lc gic cnhn din bng b 4 chs Miller-Bravais:

(hkil), trong chs i l nghch o ca

phn on ct trc a3.

a1/h

a2/k

a3/i

a1

a2

a3

a3

(hki0)

(1210)

(1011)

(1100)



59/137

NATuan-ITIMS-2007

Trng hp mng lc gicLu :

- 3 chsu trong b chs Miller-Bravais thuc mt phngxy(chac3 vectng phng a1, a2, v a3).

- Chs i lun l chs ph thuc cc

chs h v k, v mt mt phng ct

cc on trn cc trc a1 v a2 cnglun xc nh on ct ca n trntrc a3:

h + k = - i

hay: h + k + i = 0

Hy chng minh iu ny !

V cc trc a1, a2, v a3 bng nhau, sau khi nhnp/t vi hki, v n im B lun pha m caa3 nu C v D pha dng, nn:

a1

a2

a3

a3

(hki0)

A

C

O

D

B

AB

OAOC

AB

AC

OD

OC ==

ia

iaha

ka

ha

/

//

/

/

3

31

2

1 =

0111

=++== ikhhikkihkhi


V i h th h k i khi i t


60/137

NATuan-ITIMS-2007

- V i ph thuc h v k, nn i khi ngi ta s dng k hiu mt phng l

(h k l), thm ch b c du '' n gin nhbiu din cc h khc (hkl).

a1

a2

c

a3

z

[110]

[010]

[001]

[100]

[210]

[011]

- Hng trong h lc gic n tt nhtc biu din trong khun kh ca 3vectcsa1,a2 vc, ngha l ly n

v l lng try thoi- Trong cc h lc gic khc c th phibiu din y c 4 thng s trong bchs Miller-Bravais, ngha l s dng

cc on ct trong c 4 vectcsa1,a2, a3 vc (ly n v l lc lng y lcgic). Lu : Trong trng hp lunnh phi ly chs th ba l m catng hai chsu: h + k= -i.

( ) ( ) ( ) nwlkhiuvn

kvun

h =+=== ;;2

3

;2

3

- Chuyn i t h thng 3-ch s sangh thng 4-ch s: [ ] [ ]hkiluvw

T ti h th



61/137

Trc vng v vng tinh th:

NATuan-ITIMS-2007

- Mt vng (zone) bao gm cc mt tinh th ct nhau sao cho cc cnh giao nhau

song song vi nhau to thnh vng tinh th (crystallography zone).

- Hng c xc nh bi cc cnh song song to thnh trc vng (zone axis).

zone axis

crystallography zonecrystallography zone


M ti h th & C t ti h th


62/137

NATuan-ITIMS-2007

Mng tinh th & Cu trc tinh th:

- mng, nt mng.- Cc nguyn t hay nhm nguyn t.

- S sp xp cc nguyn t theo mt trt t nht nh.

Mng tinh th

- Kiu sp xp Cu trc tinh th.



63/137

NATuan-ITIMS-2007


S t


64/137

NATuan-ITIMS-2007

S sp xp cc nguyn t

lp

lp

lp

lp

lp

lp

lp



65/137

NATuan-ITIMS-2007



66/137

NATuan-ITIMS-2007


Mt ti h th ti bi


67/137

NATuan-ITIMS-2007

Mt s tinh th tiu biu



68/137

NATuan-ITIMS-2007



69/137

NATuan-ITIMS-2007



70/137

NATuan-ITIMS-2007



71/137

NATuan-ITIMS-2007



72/137

NATuan-ITIMS-2007



73/137

NATuan-ITIMS-2007



74/137

NATuan-ITIMS-2007



75/137

NATuan-ITIMS-2007



76/137

NATuan-ITIMS-2007



77/137

NATuan-ITIMS-2007


1.3.2.i xng tinh th v cc nhm i xng


78/137

NATuan-ITIMS-2007

g g


1.3.2.i xng tinh th v cc nhm i xng


79/137

NATuan-ITIMS-2007

- Khi thc hin mt php bin i R no ln tinh th, vdlm quaytinh th quanhmt trc, hay tnh tin n,... c c mt tinh th trng vi tinh thban u gi

l php bin i i xng.

- V d: Vic tnh tin vectcs r* = a + b + c c ththu c cc nt mng TR

TR= (n a +p b + q c), vi n, p, q l cc s nguyn.TRc gi l php tnh tin.

- Nhm i xng l tp hp cc phn t l cc php bin i i xng, trong bao

gm c php ng nht E, c coi l phn tn v ca nhm (L thuyt nhm).

- Mi cu trc tinh thc c trng bng nhm i xng ca n.

Nhc li mt s khi nim cbn:


i xng tinh th v cc nhm i xng


80/137

NATuan-ITIMS-2007

- Php tnh tin TR c thc thc hin bt k tinh th no Tp hp cc php

tnh tin to thnh nhm tnh tin R = {TR}.

Lu : R l nhm c s phn t v hn, v l nhm giao hon (khng ph

thuc th t khi thc hin tch ca hai php tnh tin).

- Nhm i xng trong chcha ccphp quay,php phn chiu, v t hp ca

hai php bin i ny (nhquay-phn chiu, nghch o), khng k php tnh tin,

gi l nhm im (P).Cc nhm im to ra cc lp tinh th: c 32 nhm im 32 lp tinh th.

Nhc li mt s khi nim cbn:


1) Nhm im:


81/137

NATuan-ITIMS-2007

Cc phn t ca nhm i xng im

Phn t K hiu Quc t

Trc (quay) n

Trc (quay o) n

Mt phng (phn chiu) m ()

Nghch o I

Tm i xng (ngh/o)

ng nht 1 (E)

Nhm im:

P = {n, m, 1, I, (n, m, 1, I)}

I l php bin i nghch o (VD: n

n); l php bin i t hp (VD: nm).

- Php quay:+ Mt php quay c xc nh bi trc quay C v gc quay .+ Do tnh cht tun hon ca mng tinh th php quay l php bin i i

xng, gc quay chc th c mt s gi tr no :


M' A & M = nt mng A', M' = nt mng


82/137

NATuan-ITIMS-2007

a

A

M

A'

AM' = m.MA' = m.a (m =1, 2, 3,...)

Mt khc:

AM' = MA + 2a.cos(-)

= a.[1 + 2cos(-)]= a.(1 - 2cos)

1 - 2cos = m 3600 1800 1200 900 600

(2) () (2/3) (/2) (/3)

n 1 2 3 4 6

= 2/

a a

a

n l bc ca trc quay.Khng c n = 5 & > 6

K hiu php quay: Cn(K hiu Schnflies)



83/137

NATuan-ITIMS-2007

C1

C2

C3



84/137

NATuan-ITIMS-2007

C4

C6


V d v php quay bc n = 4 (900) ca mng lp phng 2-D


85/137

NATuan-ITIMS-2007


- Php phn chiu (php i xng gng):


86/137

NATuan-ITIMS-2007

Php phn chiu l php ly i xng qua mt mt phng, k hiu l m.- Php ng nht E: Hai ln phn chiu qua mt mt phng s tr v chnh n

mm = m2= E

- Php quay-phn chiu: Trong mt nhm im c th c c php bin i quay (trc

i xng n) v php phn chiu (i xng gng m). Trong trng hp mt phn chiu

trc i xng (k hiu l mh) nmh = n (k hiu quc t) Sn (k hiu Schnflies).

+ C th thy rng: S2 I Php nghch o chnh l php ly i xng qua tm I,

l giao im ca trc quay bc 2 vi mt phn chiu.

T hp cc php quay & i xng gng nm (theo cch k hiu Schnflies l

Cnm) 12 php bin i i xng cho php trong tinh th hc.

I

m

C2

2

2m

E

m

C3

3S2

600


K hiu nhm im


87/137

NATuan-ITIMS-2007


Hnh chiu ni


88/137

NATuan-ITIMS-2007

Biu din cc hng tinh th trong KG bng cc im trn mt phng

Th hin tnh i xng ca tinh th



89/137

NATuan-ITIMS-2007



90/137

NATuan-ITIMS-2007


Cc php i xng thuc nhm im (khng

h t h ti ) b h

K hiuN php i xng gng


91/137

NATuan-ITIMS-2007

m

m

1 2 43 6

1 2 3 64

c php tnh tin) bao gm cc php quay vphp phn chiu gng: Cnm

- 1 (hay n) l php quay 1 (hay 1/n) vngquanh trc i xng.- 1 (hay n) l cc php quay trn, sau lyi xng qua tm.

(= I m)( 3

m)


Ghi ch:


92/137

NATuan-ITIMS-2007

Trong k hiu ca Schnflies:

- O(octahedron) k hiu nhm c i xng ca mt hnh tm mt (hay cn

gi l hnh lp phng), c cc php bin i thch hp nhc mt phnx vung gc vi trc quay (Oh) hay khng c mt phn x ny (O).

- T(tetrahedron) k hiu nhm c i xng ca mt hnh bn mt (t din).

- Tdbao gm c cc php bin i thch hp,- Tkhng bao gm cc php bin i thch hp,

- Th l Tc thm php nghc o.

- Cn (cyclic) biu th nhm c mt trc quay bc n (n-fold) rotation axis.- Cnh l Cn c thm mt phn x vung gc vi trc quay n.

- Cnv l Cn c thm mt phn x song song vi trc quay n.


Ghi ch:


93/137

NATuan-ITIMS-2007

Trong k hiu ca Schnflies:

- Sn (Spiegel, ting German l gng) k hiu nhm chcha mt trc quay-

phn x bc n.

- Dn (Dihedral, hoc hai mt) k hiu nhm c mt trc quay bc n v c thm

mt trc quay bc 2 vung gc vi trc quay bc n.

- Dnh l Dn c thm mt mt phn x vung gc vi trc quay bc n.

- Dnv l Dn c thm mt phn x song song vi trc quay bc n.

(Lu :/l tinh th hc gii hn chc n = 1, 2, 3, 4, hoc 6).



94/137

NATuan-ITIMS-2007



95/137

NATuan-ITIMS-2007


Mt s v d vi xng trong khng gian


96/137

NATuan-ITIMS-2007

-i xng gng trong khng gian 2D:


-i xng xuyn tm trong khng gian 3D


97/137

NATuan-ITIMS-2007


Combinations of Symmetry Operations 32 Crystal Classes


98/137

NATuan-ITIMS-2007



99/137

NATuan-ITIMS-2007


TmkhiTmmtTm yNguynthy

Kiu mng

H tinh th

14 mng Bravais

- Cc mng tinh th kh d,m c to nn bng php


100/137

I

I

I

F

F

A hoc C

A, B, hoc C

P

P

P

P

P

(P) = R

P

BA NGHING

MT NGHING

TRC THOI

T GIC

LC GIC

THOI

LP PHNG

NATuan-ITIMS-2007

P:

A:

B:

C:

I:

F:

.321

v321

,321

,321

321v

321

321v

321

321v

321

321v

321

321

2ba

cba2

cacba

2cb

cbacba

2cba

cbacba

2ba

cbacba

2ca

cbacba

2cbcbacba

cba

++++++++

++++++

+++++++

++++++

++++++

++++++

++

mmmmmm

mmmmmm

mmmmmm

mmmmmm

mmmmmm

mmmmmm

mmm

Cc vecttnh tin ca mng

c o b g p ptnh tin n v trong mih tinh th, c m tbng 14 mng Bravais.

mi = 1, 2, 3,

CHNG 1: CU TRC CA VT RNHnh chiu ni ca cc phn t nhm i xng im v cc k hiu Schnflies tng ng


101/137

NATuan-ITIMS-2007

S8S6S4S2

C6h

C5h/S5

C4h

C3h/S3

C2h

C1h/S1

C6vC5vC4vC3vC2v

C6C5C4C3C2C1


Hnh chiu ni ca cc phn t nhm i xng im v cc k hiu Schnflies tng ng


102/137

NATuan-ITIMS-2007

D6hD5hD4hD3hD2h

D6dD5dD4dD3dD2d

D6

D5D4

D3

D2


Bng tng hp cc nhm im ca h tinh th [s dng c k hiu quc

t (hay k hiu ca Hermann-Mauguin) v c k hiu ca Schnflies]


103/137

NATuan-ITIMS-2007

*2228

D2horthorhombic-bipyramidal8

*224

C2vorthorhombic-pyramidal7

2224

D2orthorhombic-sphenoidal6

OrthorhombicH trc thoi

2*4

C2hmonoclinic-prismatic5

1*2

Csmonoclinic-domatic4

222

C2monoclinic-sphenoidal3

MonoclinicMt nghing

1x2

Citriclinic-pinacoidal2

111C

1triclinic-pedial1

TriclinicBa nghing

Nhng phn ti xng

nggp

(orbifold)(S phn t)

H quc t(Hermann-Mauguin)

HSchnflies

Nhm im / Lptinh th

(S TT = Nhm im)

H tinh th

( y g ) ]


2x4S4tetragonal-disphenoidial10

444

C4tetragonal-pyramidal9

TetragonalBn phng


104/137

NATuan-ITIMS-2007

2*312

or orD3dditrigonal-scalahedral20

*336

or orC3vditrigonal-pyramidal19

3226

or orD3trigonal-trapezoidal18

3x6

S6(C3i)

rhombohedral17

333

C3trigonal-pyramidal16

Rhombohedral(trigonal)H Mt Thoi(hay HBaphng)

*422

16

D4hditetragonal-dipyramidal

15

2*28

orD2dtetragonal-scalenoidal14

*448

C4vditetragonal-pyramidal13

4228

D4tetragonal-trapezoidal12

4*8

C4htetragonal-dipyramidal11


3*6C3htrigonal-dipyramidal22

666

C6hexagonal-pyramidal21

HexagonalSu phng


105/137

NATuan-ITIMS-2007

*43248

Ohhexoctahedral32

*33224

Tdtetrahedral31

43224Ogyroidal30

3*224

Thdiploidal29

33212

Ttetartoidal28

CubicLp phng

*622

24

D6hdihexagonal-dipyramidal

27

*32212

orD3hditrigonal-dipyramidal26

*6612

C6vdihexagonal-pyramidal25

62212

D6hexagonal-trapezoidal24

6*12

C6hhexagonal-dipyramidal23


Cc nhm im c th tn ti trong mt khng gian Euclid c s chiu bt k . Cv s cc nhm im ring bit trong mi chiu khng gian Tuy nhin trong tinh

Lu :


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v s cc nhm im ring bit trong mi chiu khng gian. Tuy nhin, trong tinh

th hc, chc mt s hu hn cc nhm im l tng thch vi i xng tnh tin.

Trong KG 1-D chc 2 nhm, trong KG 2-D c 10 nhm v trong KG 3-D c 32

nhm nhvy, c gi l nhm im tinh th hc.

Khng gian tha mn 5 tin ca Euclid:

1- Tin vim & ng thng: ng ni gia 2 im bt ktrong KG l mt ng thng.

2- Tin von thng & ng thng: Bt kon thng no cng c thc ko dithnh ng thng v hn.

3- Tin von thng & ng trn: Tmt on thng bt kc thxy dng c ngtrn ly on thng l bn knh.

4- Tin v Gc vung: Tt c cc gc vung ng dng vi nhau.5- Tin vng thng song song: Nu hai ng thng cng ct ng thba sao chotng ca cc gc trong cng pha nhhn hai gc vung, th hai ng thng chc chn phi

ct mi ng khc trn pha nu ko di.



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- Cc nhm khng gian trong 3-D c to nn t vic t hp 32 nhm

im tinh th hc vi 14 mng Bravaistng ng vi 7 h tinh th.



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S t hp ca tt c php bin i i xng ny s to ra tng cng

230 nhm khng gian duy nht m t tt c cc khnng i xng

tinh th c th c.

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M M

M


Monoclinic

2. P-11. P1

Triclinic2) Nhm khng gian

MT NGHING

BA NGHING


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74. I m m a73. I b c a72. I b a m71. I m m m

70. F d d d69. F m m m68. C c c a67. C m m a66. C c c m

65. C m m m64. C m c a63. C m c m62. P n m a61. P b c a

60. P b c n59. P m m n58. P n n m57. P b c m56. P c c n55. P b a m54. P c c a53. P m n a52. P n n a51. P m m a

50. P b a n49. P c c m48. P n n n47. P m m m46. I m a 2

45. I b a 244. I m m 243. F d d242. F m m 241.A b a 2

40.A m a 239.A b m 238.A m m 237. C c c236. C m c21

35. C m m 234. P n n 233. P n a 2132. P b a 231. P m n 21

30. P n c229. P c a 2128. P m a 227. P c c226. P m c21

25. P m m 224. I21 21 2 123. I2 2 222. F2 2 221. C2 2 2

20. C2 2 2119. P21 21 2 118. P21 21 217. P2 2 2116. P2 2 2

Orthorhombic

15. C1 2 / c114. P1 21 / c113. P1 2 / c1

12. C1 2 / m 111. P1 21 / m 110. P1 2 / m 19. C1 c18. C1 m 1

7. P1 c16. P1 m 15. C1 2 14. P1 21 13. P1 2 1

TRC THOI


Tetragonal T GIC


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142. I41 / a c d141. I41 / a m d140. I4 / m c m

139. I4 / m m m138. P42 / n c m137. P42 / n m c136. P42 / m n m135. P42 / m b c134. P42 / n n m133. P42 / n b c132. P42 / m c m131. P42 / m m c130. P4 / n c c

129. P4 / n m m128. P4 / m n c127. P4 / m b m126. P4 / n n c125. P4 / n b m

124. P4 / m c c123. P4 / m m m122. I-4 2 d121. I-4 2 m120. I-4 c2

119. I-4 m 2118. P-4 n 2117. P-4 b 2116. P-4 c2115. P-4 m 2

114. P-4 21 c113. P-4 21 m112. P-4 2 c111. P-4 2 m110. I41 c d

109. I41 m d108. I4 c m107. I4 m m106. P42 b c105. P42 m c

104. P4 n c103. P4 c c102. P42 n m101. P42 c m100. P4 b m

99. P4 m m98. I41 2 297. I4 2 296. P43 21 295. P43 2 2

94. P42 21 293. P42 2 292. P41 21 291. P41 2 290. P4 21 289. P4 2 288. I41 / a87. I4 / m86. P42 / n85. P4 / n

84. P42 / m83. P4 / m82. I-481. P-480. I41

79. I478. P4377. P4276. P4175. P4


Trigonal THOI


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194. P63 / m m c193. P63 / m c m

192. P6 / m c c191. P6 / m m m190. P-6 2 c189. P-6 2 m188. P-6 c2

187. P-6 m 2186. P63 m c185. P63 c m184. P6 c c183. P6 m m

182. P63 2 2181. P64 2 2180. P62 2 2179. P65 2 2178. P61 2 2

177. P6 2 2176. P63 / m175. P6 / m174. P-6173. P63172. P64171. P62170. P65169. P61168. P6

Hexagonal

167. R-3 c166. R-3 m165. P-3 c1164. P-3 m 1163. P-3 1 c

162. P-3 1 m161. R3 c160. R3 m159. P3 1 c158. P3 c1157. P3 1 m156. P3 m 1155. R3 2154. P32 2 1153. P32 1 2

152. P31 2 1151. P31 1 2150. P3 2 1149. P3 1 2148. R-3

147. P-3146. R3145. P32144. P31143. P3

LC GIC


199 I 2 3198 P 2 3197 I 2 3196 F 2 3195 P 2 3

Cubic LP PHNG


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230. I a -3 d

229. I m -3 m228. F d-3 c227. F d-3 m226. F m -3 c225. F m -3 m

224. P n -3 m223. P m -3 n222. P n -3 n221. P m -3 m220. I-4 3 d

219. F-4 3 c218. P-4 3 n217. I-4 3 m216. F-4 3 m215. P-4 3 m

214. I41 3 2213. P41 3 2212. P43 3 2211. I4 3 2210. F41 3 2

209. F4 3 2208. P42 3 2207. P4 3 2206. I a -3205. P a -3

204. I m -3203. F d-3202. F m -3201. P n -3200. P m -3

199. I21 3198. P21 3197. I2 3196. F2 3195. P2 3

http://img.chem.ucl.ac.uk/sgp/mainmenu.htm


Mt s v d:

1. P1

C th tra cu trong: http://img.chem.ucl.ac.uk/sgp/mainmenu.htm


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Triclinic


Mt s v d:

3. P1 2 1


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Monoclinic


Mt s v d:

28. P m a 2


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Orthorhombic


Mt s v d:

100. P4 b m


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Tetragonal


Mt s v d:

159. P3 1 c


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Trigonal


Mt s v d:

168. P6


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Hexagonal


Mt s v d:

195. P2 3


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Cubic


1.1. Cu trc nguyn t


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1.3. Cu trc tinh th ca cht rn - Mng tinh th v ixng tinh th




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(32 nhm im)



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Crystal Structure


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Documents

Ch1-Mo Dau & Cau Tao Vat Chat