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
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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.
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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, ...).
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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
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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.
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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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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).
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....
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
CHNG 1: CU TRC CA VT RN
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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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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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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
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[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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CHNG 1: CU TRC CA VT RN
mm
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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. Cht rn v cc lin kt trong cht rn
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
1.4. Cu trc vt rn v nh hnh.
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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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S lin kt gia cc nguyn t hnh thnh nn cht rn v cu trc tinh th
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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
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1.1. 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.
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1.3.1. Cu trc tinh th
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Trc tinh th:
n v:
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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:
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Trng hp mng 2-D
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Trng hp mng 3-D
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Vic la chn cc nguyn thy:
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C 7 LOI MNG TINH TH:
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LP PHNG
T GICTRC THOIMT NGHINGBA NGHING
LC GICTHOI
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.....
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LP PHNG
T GIC
TRC THOI
N T
TAM T
LC GIC
THOI
Bc ca i xng
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.....
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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
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.....
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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
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14 mng khng gian - Mng Bravais
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face-centeredbody-centeredbase-centeredsimple
orthorhombic(trc thoi)
base-centeredsimple
monoclinic(n t)
triclinic(tam t)
LatticesCrystal system
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face-centeredbody-centeredsimple
cubic(isometric)
body-centeredsimple
tetragonal(trc thoi)
rhombohedral(trigonal)(thoi)
hexagonal(Lc gic)
LatticesCrystal system
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nguyn thy ca mng
trc thoi tm y:
nguyn thy ca mng
trc thoi n:
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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.
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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
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WS trong trng hp mng 3-D
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- 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
CHNG 1: CU TRC CA VT RN
NATuan-ITIMS-2007
- WS tng t mt vin gch hoa- S lp y khng gian bi WStng tnhvic lt nn bng nhngvin gch hoa
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- 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)
CHNG 1: CU TRC CA VT RN
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
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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).
CHNG 1: CU TRC CA VT RN
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:
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CHNG 1: CU TRC CA VT RN
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'
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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]
CHNG 1: CU TRC CA VT RN
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]
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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'
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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.
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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
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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].
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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)
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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.
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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
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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.
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NATuan-ITIMS-2007
Cc mt phng quan trng tng ng khc
H mt phng {100}
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H mt phng {110}
NATuan-ITIMS-2007
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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
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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
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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
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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
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Bi tp: Xc nh cc mt phng song song di y
NATuan-ITIMS-2007
c
a
b
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(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)
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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
CHNG 1: CU TRC CA VT RN
V i h th h k i khi i t
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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
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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
CHNG 1: CU TRC CA VT RN
M ti h th & C t ti h th
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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.
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
S t
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NATuan-ITIMS-2007
S sp xp cc nguyn t
lp
lp
lp
lp
lp
lp
lp
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NATuan-ITIMS-2007
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
Mt ti h th ti bi
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NATuan-ITIMS-2007
Mt s tinh th tiu biu
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NATuan-ITIMS-2007
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NATuan-ITIMS-2007
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NATuan-ITIMS-2007
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NATuan-ITIMS-2007
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
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NATuan-ITIMS-2007
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
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NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
1.3.2.i xng tinh th v cc nhm i xng
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NATuan-ITIMS-2007
g g
CHNG 1: CU TRC CA VT RN
1.3.2.i xng tinh th v cc nhm i xng
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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:
CHNG 1: CU TRC CA VT RN
i xng tinh th v cc nhm i xng
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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:
CHNG 1: CU TRC CA VT RN
1) Nhm im:
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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 :
CHNG 1: CU TRC CA VT RN
M' A & M = nt mng A', M' = nt mng
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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)
CHNG 1: CU TRC CA VT RN
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C1
C2
C3
CHNG 1: CU TRC CA VT RN
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C4
C6
CHNG 1: CU TRC CA VT RN
V d v php quay bc n = 4 (900) ca mng lp phng 2-D
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CHNG 1: CU TRC CA VT RN
- Php phn chiu (php i xng gng):
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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
CHNG 1: CU TRC CA VT RN
K hiu nhm im
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CHNG 1: CU TRC CA VT RN
Hnh chiu ni
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Biu din cc hng tinh th trong KG bng cc im trn mt phng
Th hin tnh i xng ca tinh th
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CHNG 1: CU TRC CA VT RN
Cc php i xng thuc nhm im (khng
h t h ti ) b h
K hiuN php i xng gng
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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)
CHNG 1: CU TRC CA VT RN
Ghi ch:
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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.
CHNG 1: CU TRC CA VT RN
Ghi ch:
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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).
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CHNG 1: CU TRC CA VT RN
Mt s v d vi xng trong khng gian
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-i xng gng trong khng gian 2D:
CHNG 1: CU TRC CA VT RN
-i xng xuyn tm trong khng gian 3D
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CHNG 1: CU TRC CA VT RN
Combinations of Symmetry Operations 32 Crystal Classes
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CHNG 1: CU TRC CA VT RN
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CHNG 1: CU TRC CA VT RN
TmkhiTmmtTm yNguynthy
Kiu mng
H tinh th
14 mng Bravais
- Cc mng tinh th kh d,m c to nn bng php
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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
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S8S6S4S2
C6h
C5h/S5
C4h
C3h/S3
C2h
C1h/S1
C6vC5vC4vC3vC2v
C6C5C4C3C2C1
CHNG 1: CU TRC CA VT RN
Hnh chiu ni ca cc phn t nhm i xng im v cc k hiu Schnflies tng ng
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D6hD5hD4hD3hD2h
D6dD5dD4dD3dD2d
D6
D5D4
D3
D2
CHNG 1: CU TRC CA VT RN
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]
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*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 ) ]
CHNG 1: CU TRC CA VT RN
2x4S4tetragonal-disphenoidial10
444
C4tetragonal-pyramidal9
TetragonalBn phng
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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
CHNG 1: CU TRC CA VT RN
3*6C3htrigonal-dipyramidal22
666
C6hexagonal-pyramidal21
HexagonalSu phng
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*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
CHNG 1: CU TRC CA VT RN
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.
CHNG 1: CU TRC CA VT RN
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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.
NATuan-ITIMS-2007
CHNG 1: CU TRC CA VT RN
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M M
M
CHNG 1: CU TRC CA VT RN
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
CHNG 1: CU TRC CA VT RN
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
CHNG 1: CU TRC CA VT RN
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
CHNG 1: CU TRC CA VT RN
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
CHNG 1: CU TRC CA VT RN
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
CHNG 1: CU TRC CA VT RN
Mt s v d:
3. P1 2 1
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Monoclinic
CHNG 1: CU TRC CA VT RN
Mt s v d:
28. P m a 2
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Orthorhombic
CHNG 1: CU TRC CA VT RN
Mt s v d:
100. P4 b m
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Tetragonal
CHNG 1: CU TRC CA VT RN
Mt s v d:
159. P3 1 c
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Trigonal
CHNG 1: CU TRC CA VT RN
Mt s v d:
168. P6
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Hexagonal
CHNG 1: CU TRC CA VT RN
Mt s v d:
195. P2 3
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Cubic
CHNG 1: CU TRC CA VT RN
1.1. Cu trc nguyn t
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1.2. Cht rn v cc lin kt trong cht rn
1.3. Cu trc tinh th ca cht rn - Mng tinh th v ixng tinh th
1.4. Cu trc vt rn v nh hnh.
CHNG 1: CU TRC CA VT RN
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CHNG 1: CU TRC CA VT RN
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CHNG 1: CU TRC CA VT RN
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(32 nhm im)
CHNG 1: CU TRC CA VT RN
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CHNG 1: CU TRC CA VT RN
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Crystal Structure
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