Solid State

SYNOPSIS

• Differences between crystalline solid and amorphous solid:
  
  

  Crystalline Solid	Amorphous Solid
  The internal arrangement of particles is well defined.	The internal arrangement of particles is not well defined.
  There is regularity in the external form when crystals are formed.	There is no regularity in the external form when amorphous solids are formed.
  These have a sharp melting point.	These melt over a range of temperatures.
  These have characteristic heat of fusion.	These do not have characteristic heat of fusion.
  Crystalline solids give a regular cut when cut with a sharp-edged knife.	Amorphous solids give an irregular cut.
  Crystalline solids are regarded as true solids.	Amorphous solids are super-cooled liquids or pseudo solids.
  These are generally incompressible.	These may be compressed to an extent.

• Classification of crystals into seven systems:
  
  

  Crystal system	Unit cell dimensions and angles	Bravais Examples	Lattices
  Cubic	a = b = c; α= β= γ= 90°	SC, BCC, FCC	NaCl
  Orthorhombic	a ≠b ≠c; α= β= γ= 90°	SC, BCC, end centred & FCC	SR (Rhombic sulphur)
  Tetragonal	a = b ≠c; α= β= γ= 90°	SC, BCC	Sn, ZnO2
  Monoclinic	a ≠b ≠c; α= γ= 90°≠β	SC, end centred	SM (Monoclinic sulphur)
  Rhombohedral	a = b = c; α= β= γ = 90°	SC	Quartz
  Triclinic	a ≠b ≠c; α≠β≠γ≠90°	SC	H3BO3
  Hexagonal	a = b ≠c; α= β= 90°;γ= 120°	SC	Graphite

• Analysis of cubical system:
  
  
  

  	Property	SC	BCC	FCC
  	Atomic radius (r) a = edge length
  	No. of atoms per unit cell (Z)	1	2	4
  	C. No.	6	8	12
  	Packing efficiency	52%	68%	74%
  	No. of voids (a) octahedral (Z) (b) tetrahedral (2Z)	- -	- -	4 8

  
  
  
• Neighbourhood of a particle:

1. Simple cubic (SC) structure:
   
   

   Type of neighbour	Distance	No. of neighbours
   nearest	a	6 (shared by 4 cubes)
   (next)1		12 (shared by 2 cubes)
   (next)2		8 (unshared)

2. Body-centred cubic (BCC) structure:
   
   

   Type of neighbour	Distance	No. of neighbours
   nearest		8
   (next)1	=a	6
   (next)2		12
   (next)3		24
   (next)4		8

3. Face-centred cubic (FCC) structure:
   
   

   Type of neighbour	Distance	No. of neighbours
   nearest
   (next)1	a
   (next)2		24
   (next)3		12
   (next)4		24

Packing of constituents in crystals:

• Ionic crystals:
  
  

  C. No.	Limiting radius ratio
  3	0.155 - 0.225 (triangular)
  4	0.225 - 0.414 (tetrahedral)
  6	0.414 - 0.732 (octahedral)
  8	0.732 - 0.999 (cubic)

• Crystal defects (Imperfections):
  
  
• Stoichiometric effect:

• Schottky defect: