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