Important Formulas: Solid State

 Page 1


  
SOLID STATE
? Classification of Crystal into Seven System
Crystal System Unit Cell Dimensions Bravais Example
and Angles Lattices
Cubic a = b = c ; ? = ? = ? = 90° SC, BCC, FCC    NaCl
Orthorhombic a ? b ? c ; ? = ? = ? = 90° SC, BCC, end
centred & FCC      S
R
Tetragonal a = b ? c ; ? = ? = ? = 90° SC, BCC  Sn, ZnO
2
Monoclinic a ? b ? c ; ? = ? = 90° ? ? SC, end centred      S
M
Rhombohedral a = b = c ; ? = ? = ? ? 90° SC   Quartz
Triclinic a ? b ? c ; ? ? ? ? ? ? 90° SC    H
3
BO
3
Hexagonal a = b ? c ; ? = ? = 90°;? = 120° SC   Graphite
? ANALYSIS OF CUBICAL SYSTEM
Property SC BCC FCC
(i) atomic radius (r)
2
a
3
a
4 2 2
a
a = edge length
(ii) No. of atoms per
unit cell (Z) 1 2 4
(iii) C.No. 6 8 12
(iv) Packing efficiency 52% 68% 74%
(v) No. voids
(a) octahedral (Z) __ __ 4
(b) Tetrahderal (2Z) __ __ 8
? NEIGHBOUR HOOD OF A PARTICLE :
(I) Simple Cubic (SC) Structure :
Type of neighbour Distance no.of neighbours
nearest     a 6 (shared by 4 cubes)
(next)
1
  
2 a
12 (shared by 2 cubes)
(next)
2
  
3 a
8  (unshared)
Page 2


  
SOLID STATE
? Classification of Crystal into Seven System
Crystal System Unit Cell Dimensions Bravais Example
and Angles Lattices
Cubic a = b = c ; ? = ? = ? = 90° SC, BCC, FCC    NaCl
Orthorhombic a ? b ? c ; ? = ? = ? = 90° SC, BCC, end
centred & FCC      S
R
Tetragonal a = b ? c ; ? = ? = ? = 90° SC, BCC  Sn, ZnO
2
Monoclinic a ? b ? c ; ? = ? = 90° ? ? SC, end centred      S
M
Rhombohedral a = b = c ; ? = ? = ? ? 90° SC   Quartz
Triclinic a ? b ? c ; ? ? ? ? ? ? 90° SC    H
3
BO
3
Hexagonal a = b ? c ; ? = ? = 90°;? = 120° SC   Graphite
? ANALYSIS OF CUBICAL SYSTEM
Property SC BCC FCC
(i) atomic radius (r)
2
a
3
a
4 2 2
a
a = edge length
(ii) No. of atoms per
unit cell (Z) 1 2 4
(iii) C.No. 6 8 12
(iv) Packing efficiency 52% 68% 74%
(v) No. voids
(a) octahedral (Z) __ __ 4
(b) Tetrahderal (2Z) __ __ 8
? NEIGHBOUR HOOD OF A PARTICLE :
(I) Simple Cubic (SC) Structure :
Type of neighbour Distance no.of neighbours
nearest     a 6 (shared by 4 cubes)
(next)
1
  
2 a
12 (shared by 2 cubes)
(next)
2
  
3 a
8  (unshared)
  
(II) Body Centered Cubic (BCC) Structure :
Type of neighbour Distance no.of neighbours
nearest 2r = 
2
3
a 8
(next)
1
= a 6
(next)
2
= 
2 a
12
(III) Face Centered Cubic (FCC) Structure :
Type of neighbour Distance no. of neighbours
nearest
2
a
     12 = 
?
?
?
?
?
? ?
2
8 3
(next)
1
 a     6 = 
?
?
?
?
?
? ?
4
8 3
(next)
2
2
3
a
24
? DENSITY OF LATTICE MATTER (d) = 
A
N
Z
 
?
?
?
?
?
?
?
?
3
a
M
where N
A
 = Avogadro?s No. M = atomic mass or molecular mass.
? IONIC CRYSTALS
C.No. Limiting radius ratio 
?
?
?
?
?
?
?
?
?
?
r
r
  3 0.155 ? 0.225 (Triangular)
  4 0.225 ? 0.414 (Tetrahedral)
  6 0.414 ? 0.732 (Octahedral)
  8 0.732 ? 0.999 (Cubic).
? EXAMPLES OF A IONIC CRYSTAL
(a) Rock Salt (NaCl) Coordination number (6 : 6)
(b) CsCl  C.No. (8 : 8)
Edge length of unit cell :-
a
sc
 = 
) r r (
3
2
?
?
?
(c) Zinc Blende (ZnS) C.No. (4 : 4)       a
fcc
 = 
3
4
 
) r r ( 2 2
s Zn
? ? ?
(d) Fluorite structure (CaF
2
) C.No. (8 : 4)     a
fcc
 = 
) r r ( 
3
4
? 2
F Ca
? ?
Page 3


  
SOLID STATE
? Classification of Crystal into Seven System
Crystal System Unit Cell Dimensions Bravais Example
and Angles Lattices
Cubic a = b = c ; ? = ? = ? = 90° SC, BCC, FCC    NaCl
Orthorhombic a ? b ? c ; ? = ? = ? = 90° SC, BCC, end
centred & FCC      S
R
Tetragonal a = b ? c ; ? = ? = ? = 90° SC, BCC  Sn, ZnO
2
Monoclinic a ? b ? c ; ? = ? = 90° ? ? SC, end centred      S
M
Rhombohedral a = b = c ; ? = ? = ? ? 90° SC   Quartz
Triclinic a ? b ? c ; ? ? ? ? ? ? 90° SC    H
3
BO
3
Hexagonal a = b ? c ; ? = ? = 90°;? = 120° SC   Graphite
? ANALYSIS OF CUBICAL SYSTEM
Property SC BCC FCC
(i) atomic radius (r)
2
a
3
a
4 2 2
a
a = edge length
(ii) No. of atoms per
unit cell (Z) 1 2 4
(iii) C.No. 6 8 12
(iv) Packing efficiency 52% 68% 74%
(v) No. voids
(a) octahedral (Z) __ __ 4
(b) Tetrahderal (2Z) __ __ 8
? NEIGHBOUR HOOD OF A PARTICLE :
(I) Simple Cubic (SC) Structure :
Type of neighbour Distance no.of neighbours
nearest     a 6 (shared by 4 cubes)
(next)
1
  
2 a
12 (shared by 2 cubes)
(next)
2
  
3 a
8  (unshared)
  
(II) Body Centered Cubic (BCC) Structure :
Type of neighbour Distance no.of neighbours
nearest 2r = 
2
3
a 8
(next)
1
= a 6
(next)
2
= 
2 a
12
(III) Face Centered Cubic (FCC) Structure :
Type of neighbour Distance no. of neighbours
nearest
2
a
     12 = 
?
?
?
?
?
? ?
2
8 3
(next)
1
 a     6 = 
?
?
?
?
?
? ?
4
8 3
(next)
2
2
3
a
24
? DENSITY OF LATTICE MATTER (d) = 
A
N
Z
 
?
?
?
?
?
?
?
?
3
a
M
where N
A
 = Avogadro?s No. M = atomic mass or molecular mass.
? IONIC CRYSTALS
C.No. Limiting radius ratio 
?
?
?
?
?
?
?
?
?
?
r
r
  3 0.155 ? 0.225 (Triangular)
  4 0.225 ? 0.414 (Tetrahedral)
  6 0.414 ? 0.732 (Octahedral)
  8 0.732 ? 0.999 (Cubic).
? EXAMPLES OF A IONIC CRYSTAL
(a) Rock Salt (NaCl) Coordination number (6 : 6)
(b) CsCl  C.No. (8 : 8)
Edge length of unit cell :-
a
sc
 = 
) r r (
3
2
?
?
?
(c) Zinc Blende (ZnS) C.No. (4 : 4)       a
fcc
 = 
3
4
 
) r r ( 2 2
s Zn
? ? ?
(d) Fluorite structure (CaF
2
) C.No. (8 : 4)     a
fcc
 = 
) r r ( 
3
4
? 2
F Ca
? ?
Crystal Defects (Imperfections)