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Solid State

Classification of solids:
Crystalline and Amorphous solids:
S.No.
Crystalline Solids
Amorphous solids
1
Regular internal arrangement  of particles

irregular internal arrangement  of particles

2
Sharp melting point

Melt over a rage of temperature

3
Regarded as true solids

Regarded as super cooled liquids or pseudo solids

4
Undergo regular cut  
Undergo irregular cut.

5
Anisotropic in nature

Isotropic in nature

Based on binding forces:
Crystal Classification 
Unit Particles 
Binding Forces 
Properties 
Examples 
Atomic
Atoms
London dispersion forces
Soft, very low melting, poor thermal and electrical conductors
Noble gases
Molecular
Polar or
non – polar molecules
Vander Waal’s forces (London dispersion, dipole – dipole forces hydrogen bonds)
Fairly soft, low to moderately high melting points, poor thermal and electrical conductors
Dry ice (solid, methane
Ionic
Positive and negative ions
Ionic bonds
Hard and brittle, high melting points, high heats of fusion, poor thermal and electrical conductors
NaCl, ZnS
Covalent
Atoms that are connected in covalent bond network
Covalent bonds
Very hard, very high melting points, poor thermal and electrical conductors
Diamond, quartz, silicon
Metallic Solids
Cations in electron cloud
Metallic bonds
Soft to very hard, low to very high melting points, excellent thermal and electrical conductors, malleable and ductile
All metallic elements, for example, Cu, Fe, Zn
Bragg Equation:                                          
nλ = 2dsinθ,
Where
·         d= distance between the planes
·         n = order of refraction
·         θ= angel of refraction
·         λ = wavelength
Crystal Systems:
·         Total number of crystal systems: 7 
·         Total number of Bravais Lattices: 14
Crystal Systems
Bravais Lattices 
Intercepts 
Crystal angle 
Example
Cubic 
Primitive, Face Centered, Body Centered 
a = b = c
a = b = g = 90o 
Pb,Hg,Ag,Au Diamond, NaCl, ZnS 
Orthorhombic
Primitive, Face Centered, Body Centered, End Centered
a ≠ b ≠ c
a = b = g = 90o
KNO2, K2SO4
Tetragonal
Primitive, Body Centered
a = b ≠ c
a = b = g = 90o
TiO2,SnO2
Monoclinic
Primitive, End Centered
a ≠ b ≠ c
a = g = 90o, b≠ 90o
CaSO4,2H2O
Triclinic
Primitive
a ≠ b ≠ c
a≠b≠g≠900
K2Cr2O7, CaSO45H2O
Hexagonal
Primitive
a = b ≠ c
a = b = 900, g = 120o
Mg, SiO2, Zn, Cd
Rhombohedra
Primitive
a = b = c
a = g = 90o, b≠ 90o
As, Sb, Bi, CaCO3 
Number of atoms in unit cells.
Primitive cubic unit cell:
·         Number of atoms at corners = 8×1/8 =1
·         Number of atoms in faces = 0
·         Number of atoms at body-centre: =0
·         Total number of atoms = 1
 Body-centred cubic unit cell:
·         Number of atoms at corners = 8×1/8 =1
·         Number of atoms in faces = 0
·         Number of atoms at body-centre: =1
·         Total number of atoms = 2
Face-centred cubic or cubic-close packed unit cell: 
·         Number of atoms at corners = 8×1/8 =1
·         Number of atoms in faces = 6×1/2 = 3
·         Number of atoms at body-centre: = 0
·         Total number of atoms = 4
Packing Efficiency
Packing Efficiency = (Volume occupied by all the atoms present in unit cell / Total volume of unit cell)×100
Close structure
Number of atoms per unit cell ‘z’.
Relation between edge length ‘a’ and radius of atom ‘r
Packing Efficiency
hcp and ccp or fcc
4
r = a/(2√2)
74%
bcc
2
r = (√3/4)a
68%
Simple cubic lattice
1
r = a/2
52.4%
Density of crystal lattice:
r = (Number of atoms per unit cell × Mass number)/(Volume of unit cell × NA)

Octahedral and Tetrahedral Voids:                             
Number of octahedral voids = Number of effective atoms present in unit cell
Number of tetrahedral voids = 2×Number of effective atoms present in unit cell
So, Number of tetrahedral voids = 2× Number of octahedral voids.
Coordination numbers and radius ratio:
Coordination numbers
Geometry
Radius ratio (x)
Example
2
Linear
x < 0.155
BeF2
3

Planar Triangle
0.155 ≤ x < 0.225
AlCl3
4

Tetrahedron
0.225 ≤ x < 0.414
ZnS
4

Square planar
0.414 ≤ x < 0.732
PtCl42-
6

Octahedron
0.414 ≤ x < 0.732
NaCl
8
Body centered cubic
0.732 ≤ x < 0.999
CsCl
Classification of Ionic Structures: 
Structures
Descriptions
Examples
Rock Salt Structure
Anion(Cl-) forms fcc units and cation(Na+) occupy octahedral voids. Z=4 Coordination number =6
NaCl, KCl, LiCl, RbCl
Zinc Blende Structure
Anion (S2-) forms fcc units and cation (Zn2+) occupy alternate tetrahedral voids Z=4 Coordination number =4
ZnS , BeO
Fluorite Structures
Cation (Ca2+) forms fcc units and anions (F-) occupy tetrahedral voids Z= 4 Coordination number of anion = 4 Coordination number of cation = 8
CaF2, UO2, and ThO2
Anti- Fluorite Structures

Oxide ions are face centered and metal ions occupy  all the tetrahedral voids.
Na2O, K2O and Rb2O.
Cesium Halide Structure
Halide  ions are primitive cubic while the metal ion occupies the center of the unit cell.
Z=2
Coordination number of = 8
All Halides of Cesium.
Pervoskite Structure
 One of the cation is bivalent and the other is tetravalent. The bivalent ions are present in primitive cubic lattice with oxide ions on the centers of all the six square faces. The tetravalent cation is in the center of the unit cell occupying octahedral void.
CaTiO3, BaTiO3
Spinel and Inverse Spinel Structure
Spinel :M2+M23+O4, where M2+ is present in one-eighth of tetrahedral voids in a FCC lattice of oxide ions and M3+ ions are present in half of the octahedral voids. M2+ is usually Mg, Fe, Co, Ni, Zn and Mn;  M3+ is generally Al, Fe, Mn, Cr and Rh.
MgAl2O4 , ZnAl2O4, Fe3O4,FeCr2O4etc.
Defects in crystal:
Stoichiometric Defects
1. Schottky Defects
·          Some of the lattice points in a crystal are unoccupied.
·         Appears in ionic compounds in which anions and cations are of nearly same size.
·         Decreases the density of lattice
·         Examples: NaCl and KCl
2.  Frenkel Defects
·      Ion dislocate from its position and occupies an interstitial position between the lattice points
·         Appears in crystals in which the negative ions are much larger than the positive ion.
·         Does not affect density of the crystal.
·         Examples: AgBr, ZnS
Non-Stoichiometric Defects
1. Metal Excess defect: 
Metal excess defect occurs due to
·         anionic vacancies or
·         presence of extra cation.
·         F-Centres: hole produced due to absence of anion which is occupied by an electron.
2. Metal deficiency defect: 
Metal deficiency defect occurs
·         due to variable valency of metals
·         when one of the positive ions is missing from its lattice site and the extra negative charge is balanced by some nearby metal ion acquiring two charges instead of one


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Classification of solids: Crystalline and Amorphous solids: S.No. Crystalline Solids Amorphous solids ...