1. Primitive and conventional cells
Structure=Lattice+basis
basis
Primitive cell- parallelepiped
defined by primitive
with one lattice point per cell
Conventional cell may have more than one lattice point
per cell.
Body centered cubic (bcc):
conventional ¹primitive
cell
Fractional coordinates: 000,
100, 010, 001, 110,101, 011,
111, ½ ½ ½
Simple cubic (sc):
primitive cell=
conventional cell
Fractional coordinates of
lattice points: 000, 100,
010, 001, 110,101, 011,
111

2. Primitive and conventional cells
Face centered cubic (fcc):
conventional ¹ primitive cell
Fractional coordinates: 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
Body centered cubic (bcc):
primitive (rombohedron) ¹conventional cell
Fractional coordinates: 000,
100, 101, 110, 110,101, 011,
211, 200

3. Primitive and conventional cells
points of primitive cell
120o
Hexagonal close packed cell (hcp): conventional =primitive cell
Fractional coordinates: 100,
010, 110, 101,011, 111,000,
001

4. Packing B C Close pack A B A Sequence AAAA…- simple cubic
Sequence ABABAB..- hexagonal
close pack
Sequence ABCABCAB..-face
centered cubic

5. Simple Cubic lattice Atomic position projected on a cube face
Crystals: Po 1
height above plane
(in terms of a )
a -lattice parameter
8 corner atoms shared by 8 unit cells
-> one atom per unit cell

6. Body Centred Cubic latticeNa V Cr Fe K Nb Mo Rb Ta W Cs
Atomic position projected
on a cube face 1 1
1/2 1 1
8 corner atoms shared by 8 cells+
one centre atom -> two atoms per cell
(0,0,0) and (½, ½, ½)

7. Face Centred Cubic latticeNi Cu Al Pb Ne Pd Ag Ar Pt Au Kr Xe
Atomic position projected
on a cube face 1 1
0 1 1 1
8 corner atoms shared by 8 cells+
6 face- centred atoms each shared
by two cells -> four atoms per cell
(0,0,0), (0, ½, ½), (½, 0, ½) and
(½, ½, 0)

8. Diamond structure=2FCC lattices
Atomic position projected
on a cube face
FCC lattice +basis of 2 atoms
(2 FCC displaced by ( ¼, ¼, ¼))
Crystals: diamond, Si, Ge, grey Sn,
ZnS, III-V semiconductors
(GaAs, InSb,…) 01
8 atoms per cubic cell
(0,0,0) -> ( ¼, ¼, ¼)
(0, ½, ½) ( ¼, ¾, ¾)
(½, 0, ½) ( ¾, ¼ , ¾)
(½, ½, 0) ( ¾, ¾, ¼) L
tetrad screw axis
(left and right) R

9. NaCl structure Atomic position projected on a cube face
Crystals: LiH, MgO, Mn0,
AgBr, PbS, KCl
Atomic position projected
on a cube face
2 FCC lattices displaced by
( ½ , ½, ½)
0½1
8 ions per cubic cell
Na+ ions
Cl- ions
(0,0,0)
(½,½,½)
(0,½,½)
(½,1,1)
(½,0,½)
(1,½,1)
(½,½,0)
(1,1,½)
Cl-
Na+

10. CsCl structure Atomic position projected on a cube face
Crystals: BeCu, AlNi, CuPd,
CuZn, AgMg
Atomic position projected
on a cube face
2 SC lattices displaced by
( ½ , ½, ½) 01 01
2 ions per cubic cell
Cs+ ions
Cl- ions
(0,0,0)
(½,½,½)
Cl-
Cs+ 01 01

11. Fluorite structure Atomic position projected on a cube face
Crystals: CaF2
Atomic position projected
on a cube face
3 FCC lattices at (0,0,0) and displaced by
( 1/4 ,1/4, 1/4) and (3/4, 3/4, 3/4)
(all 8 tetrahedral sites are occupied) 01 01
¼ ¾
12 ions per cubic cell
¼ ¾
Ca+ ions
F- ions
(0,0,0)
(¼,¼,¼ )
(¾, ¾, ¾)
(0, ½, ½)
(¼, ¾,¾)
(¾, ¼, ¼,)
(½,0, ½)
(¾,¼, ¾)
(¼, ¾, ¼,)
(½,½,0)
(¾, ¾,¼)
(¼, ¼, ¾) 01
¼ ¾
¼ ¾ 01 01