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▪결정 (crystal) : 3차원공간에서원자가주기적으로같은모양으로 배열을하고있는고체
▪비결정(amorphous): 원자의규칙배열이없다. (예: 유리)
▪단위세포, 단위격자(unit cell) : 결정을만들수있는점들의가장간단한배열.
▪격자상수(lattice parameter, lattice constant) : 축의길이 a, b, c축사이의각 a, b, g
2.6 결정계
a
b
c
ab
g
≠
≠ ≠ g
입방a b g
a b g
a b g
정방
사방
단순
체심면심
저심
≠
≠
≠ ≠ ≠
≠ ≠ ≠ ≠ ≠
g
g
g
g
a b
a b
a g b
a b
능면체마름모
육방
단사
삼사
단사
monoclinicmonoclinic
대칭요소(symmetry elements)
Simple or Primitive-P – 000 - multiplicity = 1
(Atoms/Unit Cell or Lattice point per cell)
[8 x (1/8) =1]
Base Centering
– C - Lattice Points at 000 and 0½½- Lattice Points at 000 and ½0½ -Lattice Points at 000 and ½½0
• multiplicity = 2 [8 x (1/8) + 2 x (1/2) =2]
Body Centering- I - 000 and ½½½• multiplicity = 2 [8 x (1/8) +1 =2]
Face Centering– F - 000, ½½0, ½0½ and0½½• multiplicity = 4 [8 x (1/8) + 6 x (1/2) =4]
Rhombohedral Centering– R - 000, 2/31/31/3, and1/32/32/3– multiplicity = 3–Trigonal
[8 x (1/8) + 1 + 1 =3]
세개의입방 결정계(cubic) 단위 세포와 그 격자
=√2ad (2r)
V
Multiplicity
2=√2a
a a a
d (2r)
CN
d
a = d (a/2)2 + (a/2)2= d2(a/2)2 + (√2a/2)2= d2
dd
2
a2 + (√2a)2 = (2d)2
D = g/cm3
m à 4 atoms (face centered)
MW = 207.20g Pb/1mol Pb
Avogadro’s number = 1molPb/(6.02 x1023Pb atoms)
V = a3 (cubic)
r = √2a/4 (face centered)
m à 4 atoms (face centered)
MW = 207.20g Pb/1mol Pb
Avogadro’s number = 1molPb/(6.02 x1023Pb atoms)
V = a3 (cubic)
r = √2a/4 (face centered)
입방
정방
능면체
사방
부록A3-2단위포 부피
육방
단사
삼사
계산 d006 =
부록A3-1면간거리
입방
정방
능면체
사방
육방
단사
삼사
7 결정계 : 결정의대칭성에 따라정의.단위세포의모서리와각사이에관련성에따라결정.
14 Bravais Lattice(동일환경격자점조건 )
P(Simple, Primitive)I(Body-Centered)F(Face-Centered)
P(Simple, Primitive)I(Body-Centered)
P(Simple, Primitive)I(Body-Centered)F(Face-Centered)C(Base-Centered)
32 Point Group(한점에대한대칭조작)
대칭요소ReflectionRotationInversion
73Space Group
32 Point Group
+14BravaisLattice 73
Space Group+
11Screw Axis+
5 GlidePlane
230Space Group
230UniqueCombi-nation
P(Simple, Primitive)I(Body-Centered)F(Face-Centered)C(Base-Centered)
R(RhombohedralCentered)
P(Simple, Primitive)
P(Simple, Primitive)C(Base-Centered)
P(Simple, Primitive)
SchoenfliesSymbol쉔플리스C3v
(E,C33sv)&Hermann-MauguinSymbol
3m
32 Point Group
+14BravaisLattice 73
Space Group+
11Screw Axis+
5 GlidePlane
As reported previously, Fig. 1 shows the anion-ordered Sr3AlO4F oxyfluoride structure,
which is a tetragonal phase with space group I4/mcm; it is arranged by stacking
alternating Sr(2)2F3+ and Sr(1)AlO4
3− layers along the c axis [8]. There are 10-fold-
coordinated Sr(1), 8-foldcoordinated Sr(2), and 4-fold-coordinated Al3+ cation sites in
the host structure.
7 결정계 : 결정의대칭성에 따라정의.단위세포의모서리와각사이에관련성에따라결정.
14 Bravais Lattice(동일환경격자점조건 )
P(Simple, Primitive)I(Body-Centered)F(Face-Centered)
P(Simple, Primitive)I(Body-Centered)
P(Simple, Primitive)I(Body-Centered)F(Face-Centered)C(Base-Centered)
32 Point Group(한점에대한대칭조작)
대칭요소ReflectionRotationInversion
73Space Group
32 Point Group
+14BravaisLattice 73
Space Group+
11Screw Axis+
5 GlidePlane
230Space Group
230UniqueCombi-nation
P(Simple, Primitive)I(Body-Centered)F(Face-Centered)C(Base-Centered)
R(RhombohedralCentered)
P(Simple, Primitive)
P(Simple, Primitive)C(Base-Centered)
P(Simple, Primitive)
SchoenfliesSymbol쉔플리스C3v
(E,C33sv)&Hermann-MauguinSymbol
3m
32 Point Group
+14BravaisLattice 73
Space Group+
11Screw Axis+
5 GlidePlane
