Brillouin Zones Face-centered cubic

Label Γ L X W K

Coordinates (g1,g2,g3) 000 1 1 1 2 2 2 1 1 2 2

0

1 1 3 2 4 4 3 3 3 8 8 4

Brillouin Zones

Body-centered cubic

Label Γ H P N

Coordinates (g1,g2,g3) 000



1 1 1 2 2 2 1 1 1 4 4 4 1 2

00

-

2

-

Brillouin Zones

Simple cubic

Label Γ X M R

Coordinates (g1,g2,g3) 000 0 12 0 1 1 0 2 2 1 1 1 2 2 2

-

3

-

Brillouin Zones

Hexagonal

Label Γ A M L K

Coordinates (g1,g2,g3) 000 0 0 12 0 12 0 0 12 12  13 23 0

H

 13

-

4

-

2 1 3 2

Brillouin Zones

Rhombohedral for

Label Γ Z L F

2c a

Coordinates (g1,g2,g3) 000 1 1 1 2 2 2 1 2 1 1 2 2

0 0 0

-

5

-

Brillouin Zones

Rhombohedral for

Label Γ Z L F

2c a

Coordinates (g1,g2,g3) 000 1 1 1 2 2 2 1 2

0 0 1 1 0 2 2

-

6

-

Brillouin Zones

Body centered tetragonal c < a

Label Γ N X Z P

Coordinates (g1,g2,g3) 000 0 12 0 0 0 12

 12

1 1 2 2 1 1 1 4 4 4

-

7

-

Brillouin Zones

Body centered tetragonal c > a

Label Γ N X Z P

Coordinates (g1,g2,g3) 000 0 12 0 0 0 12



1 1 1 2 2 2 1 1 1 4 4 4

-

8

-

Brillouin Zones

Simple tetragonal

Label Γ M Z A R X

Coordinates (g1,g2,g3) 000 1 1 0 2 2 0 0 12 1 1 1 2 2 2 1 1 2 2 1 2

0 0 0

-

9

-

Brillouin Zones

Face-centered orthorhombic

1 1 1 1 1 1 1 1 1   ,   , and   a2 b2 c2 b2 c2 a2 c2 a2 b2

Label Γ Y X Z L

Coordinates (g1,g2,g3) 000 0  12  12 1 1 202 1 1 0 2 2 1 20 0

-

10

-

Brillouin Zones

Face-centered orthorhombic with

1 1 1   c2 a2 b2

(b)

Label Γ Y X Z L

Coordinates (g1,g2,g3) 000 0 12 12 1 1 20 2 1 10 2 2 1 20 0

-

11

-

Brillouin Zones

Face-centered orthorhombic with

1 1 1   b2 a2 c2

(c)

Label Γ Y X Z L

Coordinates (g1,g2,g3) 000 1 12 12 1 1 202 1 1 0 2 2 1 20 0

-

12

-

Brillouin Zones

Face-centered orthorhombic with

(d)

Label Γ Y X Z L

Coordinates (g1,g2,g3) 000 0  12  12 1 1 2 0 2 1 1 0 2 2 1 20 0

-

13

-

1 1 1   a2 b2 c2

Brillouin Zones

Body-centered orthorhombic for a > b > c or a > c > b

Label Γ X R S T W

Coordinates (g1,g2,g3) 000 1 2

 12

1 2 1 2

1 2 3 4

-

14

-

1 2

00 0  12  12 0

 14  14

Brillouin Zones

Body-centered orthorhombic for b > a > c or b > c > a

Label Γ X R S T W

Coordinates (g1,g2,g3) 000 1 2

1 2 1 2

1 2 3 4

-

15

-

 12  12 00 0  12  12 0

 14  14

Brillouin Zones

Body-centered orthorhombic for c > b > a or c > a > b

Label Γ X R S T W

Coordinates (g1,g2,g3) 000 1 1 2 2 1 2 1 2 1 2 3 4

-

16

-

 12

00 0  12  12 0

 14  14

Brillouin Zones

Base centered orthorhombic a > b

Label Γ Y Z T S R

Coordinates (g1,g2,g3) 000 1 1 0 2 2 0 0 12 1 1 1 2 2 2 1 2 1 1 2 2

0 0

-

17

-

0

Brillouin Zones

Base-centered orthorhombic b > a

Label Γ Y Z T S R

Coordinates (g1,g2,g3) 000  12 12 0 0 0 12 1 1 1 2 2 2 1 2 1 1 2 2

0 0

-

18

-

0

Brillouin Zones

Simple orthorhombic

Label Γ Y X Z U T S R

Coordinates (g1,g2,g3) 000  12 0 0 0 12 0 0 0 12 0 12 12  12 0 12  12 12 0

 12

-

19

-

1 1 2 2

Brillouin Zones

Base centered monoclinic

Label Γ A Z M L V

Coordinates (g1,g2,g3) 000  12 0 0 0  12 12

 12  12 12  12 0 12 0 0 12

-

20

-

Brillouin Zones

Simple monoclinic

Label Γ B Y Z C D A E

Coordinates (g1,g2,g3) 000  12 0 0 0 12 0 0 0 12 0 12 12  12 0 12  12 12 0 ,  12  12 0, or 12 12 0  12 12 12 ,  12  12 12 , or 12 12 12

-

21

-

Brillouin Zones

Triclinic

Label Γ B F G

Coordinates (g1,g2,g3) 000 1 20 0 0 12 0 0 0 12

-

22

-