14 bravais lattices and Screw axes - دانشگاه کاشان · 14 bravais lattices and Screw...
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14 bravais lattices and Screw axes
Transcript of 14 bravais lattices and Screw axes - دانشگاه کاشان · 14 bravais lattices and Screw...
14 bravais lattices and Screw axes
Point and Space Groups
• 7 crystal systems
• 14 Bravais lattices
• 230 non-Bravais lattices
• 32 point symmetries
– 2 triclinic
– 3 monoclinic
– 3 orthorhombic
– 7 tetragonal
– 5 cubic
– 5 trigonal
– 7 hexagonal
Space Groups
Combining translations and point groups
Plane Group Symmetry
p211
Plane Group Symmetry
17-plane groups
When the three symmetry elements, mirrors, rotation axis and glide planes are shown on the five nets, 17-plane groups are derived.
17-plane groups
17-plane groups
17-plane groups
17-plane groups
17-plane groups
17-plane groups
17-plane groups
17-plane groups
17-plane groups
t
1
17-plane groups
t
2
t
1
17-plane groups
t
2
t
1
17-plane groups
t
2
t
1
17-plane groups
t
2
t
1
17-plane groups
t
2
t
1
17-plane groups
t
2
t
1
17-plane groups
t
2
t
1
17-plane groups
Symmetry 2 (00z)
Symmetry 2(.5 .5 z)
نقاط توپر الیه اول، نقاط تو خالی الیه دوم
تقارنهای صفحه ای و نقطه ای
Symmetry 2
Monoclinic
(00z) R (.5 .5 z) R
Symmetry 222
(.5 .5 z) R
222 symmetry in Diamond
222 symmetry in Diamond
Crystal Structure 37
ORTHORHOMBIC SYSTEM
Orthorhombic (Simple) a = ß = g = 90o
a b c
Orthorhombic (Base-centred)
a = ß = g = 90o
a b c
Orthorhombic (BC) a = ß = g = 90o
a b c
Orthorhombic (FC) a = ß = g = 90o
a b c
Symmetry 4
Symmetry 4
Crystal Structure 40
– TETRAGONAL SYSTEM
Tetragonal (P) a = ß = g = 90o
a = b c
Tetragonal (BC) a = ß = g = 90o
a = b c
Symmetry 3
Symmetry 3
Symmetry 6
Crystal Structure 51
1-CUBIC
Crystal Structure 52
a- Simple Cubic (SC)
Crystal Structure 54
Face Centered Cubic (FCC)
اتم در سلول واحدش وجود دارد 4•
•(Cu,Ni,Pb..etc) ساختارfcc. دارند
Crystal Structure 55
3 - Face Centered Cubıc
Atoms are all same.
Crystal Structure 56
2 - HEXAGONAL SYSTEM
دارد وجود واحدش سلول در اتم سه.
Crystal Structure 57
2 - HEXAGONAL SYSTEM
Atoms are all same.
Crystal Structure 58
a
b
c
P Monoclinic
a= g =90 o b a b c
a
b
c
I = C a
b
P Triclinic a b g a b c
c
c
a P
Orthorhombic a= b = g =90 o a b c
C F I b
3-D Symmetry
3-D Symmetry
3-D Symmetry
Contrasting glide and screw
screw axes
screw axes
monoclinic
Orthorhombic
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Symbols for Symmetry Elements (2)
International Tables for Crystallography, Volume A, Table 1.4.5, p. 9 (2002)
90
Symbols for Symmetry Elements (3)
International Tables for Crystallography, Volume A, Table 1.4.2, p. 7 (2002)
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