SOLID STATE PHYSICS - PowerPoint by nzoRiV

VIEWS: 12 PAGES: 11

• pg 1
```									SOLID STATE PHYSICS

Course Coordinator
Dr. Dana A. Tahir
Unit Cell in 3D

Crystal Structure   2
Unit Cell in 3D

Crystal Structure   3
Three common Unit Cell in 3D

Crystal Structure   4
UNIT CELL

Primitive                          Conventional & Non-primitive

 Single lattice point per cell
 Smallest area in 2D, or                      More than one lattice point per cell
Smallest volume in 3D                         Integral multibles of the area of
primitive cell

Simple cubic(sc)                          Body centered cubic(bcc)
Conventional = Primitive cell                 Conventional ≠ Primitive cell
Crystal Structure                             5
The Conventional Unit Cell

   A unit cell just fills space when
translated through a subset of
Bravais lattice vectors.
   The conventional unit cell is
chosen to be larger than the
primitive cell, but with the full
symmetry of the Bravais lattice.
   The size of the conventional cell
is given by the lattice constant
a.

Crystal Structure              6
Primitive and conventional cells of FCC

Crystal Structure        7
Primitive and conventional cells of BCC

Primitive Translation Vectors:
1
a1  ( x  y  z )
ˆ ˆ ˆ
2
1
a2  ( x  y  z )
ˆ ˆ ˆ
2
1
a3  ( x  y  z )
ˆ ˆ ˆ
2
Primitive and conventional cells
Body centered cubic (bcc):
conventional primitive cell
b   c
Fractional coordinates of lattice points in
a       conventional cell:
000,100, 010, 001, 110,101, 011, 111, ½ ½ ½

Simple cubic (sc):
primitive cell=conventional cell
b       c          Fractional coordinates of lattice points:
000, 100, 010, 001, 110,101, 011, 111
a
Crystal Structure                   9
Primitive and conventional cells

Body centered cubic (bcc):
b
c
primitive (rombohedron) conventional cell

a       Fractional coordinates:
000, 100, 101, 110, 110,101, 011, 211, 200

Face centered cubic (fcc):
conventional primitive cell

b                    Fractional coordinates:
c               000,100, 010, 001, 110,101, 011,111, ½ ½ 0, ½
0 ½, 0 ½ ½ ,½1 ½ , 1 ½ ½ , ½ ½ 1
a
Crystal Structure                        10
Primitive and conventional cells-hcp
points of primitive cell

Hexagonal close packed cell (hcp):
conventional primitive cell

Fractional coordinates:
c
100, 010, 110, 101,011, 111,000, 001

b

a

Crystal Structure                    11

```
To top