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CHEMISTRY
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The correlation between structure and properties helps in
discovering new solid materials with desired properties
like ……
high temperature
superconductors,
magnetic materials,
biodegradable polymers for packaging,
bio-compliant solids for surgical implants, etc.
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1 . 1 General Characteristics of Solid State
(i) They have definite mass, volume and shape.
(ii) Intermolecular distances are short.
(iii) Intermolecular forces are strong.
(iv) Their constituent particles (atoms, molecules or ions)
have fixed positions and can only oscillate about their
mean positions.
(v) They are incompressible and rigid.
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1.2 Amorphous and Crystalline Solids
S
o
l
i
d
s
Crystalline
Amorphous
(Greek amorphous = no form)
-long range order
-short range order
eg : Sodium chloride and quartz
are typical examples
eg : Glass, rubber and plastics
are typical examples
-sharp MP
-range of MP
The structure of amorphous solids is
similar to that of liquids.
On heating Amorphous
crystalline at some temperature.
Eg : Some glass objects from ancient civilizations are found to become milky
in appearance because of some crystallization.
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Amorphous solids are also called as pseudo solids or super cooled liquids.
b.coz they have tendency to flow like liquids.
Window panes are thicker at bottom !
Crystalline solids are Anisotropic
i.e. some of their physical properties like
electrical resistance or
refractive index
show different values when measured along
different directions in the same crystals.
( b’coz of different arrangement of particles
in different directions)
Amorphous solids are Isotropic
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Suming up
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1.3 Classification of Crystalline Solids
On the basis of nature of intermolecular forces
operating between them, solids are classified into
4 categories …..
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1.3 Classification of Crystalline Solids
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Metallic bond
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1.4 Crystal Lattices and Unit Cells
characteristic
Crystal lattice : A regular three dimensional arrangement
of points in space is called a crystal
lattice.
There are only 14 possible three dimensional lattices. These are called Bravais
Lattices
Characteristics of a crystal lattice:
(a) Each point in a lattice is called lattice point or lattice site.
(b) Each point in a crystal lattice represents one constituent particle which may be
an atom, a molecule (group of atoms) or an ion.
(c) Lattice points are joined by straight lines to bring out the geometry of the lattice.
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Unit cell : is the smallest portion of a crystal
lattice which, when repeated in different
directions, generates the entire lattice.
Characteristics of a unit cell :
(i) a, b and c - sides - may or may not be
mutually perpendicular.
perpendicular.
(ii) a, ß &
- angles
Thus, a unit cell is characterized by six
parameters, a, b, c, a, ß and .
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1.4.1 Primitive and Centered Unit Cells
Unit cells
Primitive Unit Cell
Centred Unit Cells
particles are present only on the
corner positions.
one or more constituent particles at
positions other than corners in addition to
those at corners, it is called
a centered unit cell.
(i) Body-Centred Unit Cells (bcc)
(ii) Face-Centred Unit Cells (fcc)
(iii) End-Centred Unit Cells
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1.5 Number of Atoms in a Unit Cell
17
Shows
contribution of
each sphere
1.5.1 Primitive
Cubic Unit Cell
Only centre of
sphere and not
actual size
Actu
al
size
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Corners 8 x 1/8 = 1 atom
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1.5.2 Body- Centered
Cubic Unit Cell
8 corners × 1/8
1 at body centre
= 1 atom
+
= 1 atom
Total per unit cell = 2 atoms
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1.5.3 Face- Centred
Cubic Unit Cell
8 corners x 1/8
= 1 atom
6 at faces x 1/2 = 3 atoms
Total per unit cell
cell == 44 atoms
atoms
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1.6 Close Packed Structures
Coordination number : is the number of nearest neighbors of a
particle.
(a) Close Packing in
1D
C.N. = 2
(b) Close Packing in
2D
C.N. = 4
C.N. = 6
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(c) Close Packing in 3D
(i) Square close-packed in
3D
AAAAAA…
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(ii) hexagonal close packing in 3D
(a) Placing second layer (B) over the first layer (a)
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Voids are formed…
For N spheres in closed packed spheres there are
N octahedral voids &
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tetrahedral voids
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(b) Placing third layer over the second layer
Covering Tetrahedral Voids:
ABABAB…. (hcp)
Covering Octahedral Voids:
ABCABCABC….(ccp or fcc)
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Covering octahedral voids
ABCABC…
ccp
Covering tetrahedral voids
ABAB…
hcp
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1.6.1 Formula of a Compound
and Number of Voids Filled
Tetrahedral voids in ccp / fcc
Total no. of tetrahedral voids = 1 x 8 =
8
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Octahedral voids in ccp / fcc
at edge centre :
at body centre :
¼ x 12 = 3
1x1=1
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Summing up ….
Formula of fcc/ccp
If in fcc or ccp, atoms
A occupy all octahedral voids and B occupy the
Lattice points
points ,, the
the unit
unit cell
cell contains
contains
4
A and 4 A i.e. the formula of the crystal is AB
If in fcc or ccp
A occupy all tetrahedral voids and B occupy the
Lattice points , the unit cell contains
8
A and 4 B i.e. the formula of the crystal is A 2B
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Example 1.1 A compound is formed by two elements X and Y. Atoms of the
element Y (as anions) make ccp and those of the element X (as
cations) occupy all the octahedral voids. What is the formula of the
compound?
Ans : XY
Example 1.2 Atoms of element B form hcp lattice and those of the element A occupy
2/3rd of tetrahedral voids. What is the formula of the compound formed
by the elements A and B?
Ans : A4B3
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1.7 Packing Efficiency
What is packing efficiency?
Packing efficiency is the percentage of total space filled by the particles.
So, If
total vol. of the unit cell
100%
Vol. occupied by the spheres in the unit cell
? (packing efficiency)
Packing efficiency = vol. occupied by the spheres in the unit cell
total vol. of the unit cell
x 100 %
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1.7 Packing Efficiency
1.7.1 Packing Efficiency in hcp
and
ccp
Structures
74%
Packing efficiency = vol. occupied by 4 spheres in the unit cell x 100 %
total vol. of the unit cell
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1.7.2 Efficiency of Packing in
bcc
68%
Structures
Packing efficiency = vol. occupied by 2 spheres in the unit cell x 100 %
total vol. of the unit cell
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1.7.3 Packing Efficiency in Simple
simple cubic
52.4 %
Packing efficiency = vol. occupied by 1 sphere in the unit cell x 100 %
total vol. of the unit cell
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1.8 Calculations Involving Unit Cell Dimensions
Density of the unit cell, d = mass of the unit cell
volume of the unit cell (v)
= z.m
a3
d= z. M
a3 NA
, z = no. of atoms in unit cell
a = edge length of unit cell
m = mass of an atom in unit cell
( b’coz, m = M / NA )
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Example 1.3
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An element has a body-centred cubic (bcc) structure with a cell edge
of 288 pm. The density of the element is 7.2 g/cm3. How many atoms
are present in 208 g of the element?
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1.9 Imperfections in Solids
• Crystals though have long range order ---- are not perfect
• Solids consists aggregate of large no. of small crystals.
• crystals have defects ---when crystallization takes place at moderate or fast rate
• even at extremely slow rate ---- crystals are not free from defects (imperfections)
Crystal defects : are basically irregularities in the arrangement of constituent
particles.
Line defects : are the irregularities
or deviation from ideal arrangement
in entire row
Point defects : are the irregularities
or deviation from ideal arrangement
around a point or an atom
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Crystal defects
Line defects
Point defects
Stoichiometric
defects
These are the point defects
that do not disturb the
stoichiometry of the solid.
They are also called intrinsic
or thermodynamic defects.
Impurity defects
Metal excess defects
Non-Stiochiometic
defects
Metal deficient defects
Due to anionic
vacancies
1. Vacancy defects
2. Interstitial defects
Due to extra cations
in the interstital
3. Frenkel defects
4. Schottky defects
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1. Vacancy defects
When some of the lattice sites are vacant, the crystal is said to
have vacancy defect (Fig. 1.23).
- density of the substance decreases.
-This defect can also develop when a substance is heated.
- Shown by non-ionic solids
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2. Interstitial defects
When some constituent particles (atoms or molecules) occupy
an interstitial site, the crystal is said to have interstitial defect.
-density of the substance increases
- shown by non-ionic solids
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Note : Ionic solids must always maintain electrical neutrality. Rather than simple
vacancy or interstitial defects, they show these defects as Frenkel and
Schottky defects.
3. Frenkel defects When the smaller ion (usually cation) is dislocated from its normal
site to an interstitial site it is called Frenkel defect.
- It creates a vacancy defect at its original site and an interstitial
defect at its new location.
- Frenkel defect is also called dislocation defect.
- density of the solid does not change.
- shown by ionic substance in which there is a large difference in
the size of ions,
- for example, ZnS, AgCl, AgBr and AgI due to
Vacancy
Interstitial
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4. Schottky defects
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In this defect equal number of cations and anions are missing from
their positions.
- basically a vacancy defect.
- Electrical neutrality is maintained.
- density of crystal decreases
- Eg : in NaCl there are approximately 106 Schottky pairs per cm3
at room temperature. In 1 cm3 there are about 1022 ions. Thus,
there is one Schottky defect per 1016 ions.
- shown by ionic substances in which the cation and anion are of
almost similar sizes.
- Eg : NaCl, KCl, CsCl and AgBr.
- Note : AgBr shows both, Frenkel as well as Schottky defects.
Vacancy
Vacancy
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Impurity defects
When some foreign impurities replace the ions of the
crystal, the crystal is said to have Impurity defect.
- e.g : SrCl2 in NaCl. Each Sr+2 replaces two Na+ ions to maintain
the stoichiometry.
One site is occupied while other remains vacant (cationic vacancy).
hence equal no. of cationic vacancies are generated in this case.
- e.g : CdCl2 + AgCl solid solution
Foreign ion
Vacancy
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Metal excess defects
Due to anionic
vacancies
e.g : NaCl & KCl
When,
NaCl(crystal) ----- Na(vapours)
- NaCl
- LiCl
- KCl
F-Centers
yellow
pink
violet ( or liliac)
F-centre
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Metal excess defects
Due to extra cations
in the interstital
ZnO
White
---
Zn+2 + ½ O2 + 2eyellow
- O is lost as O2 reversibly.
- excess of Zn+2 occupies the interstitial nearby.
- thus, Zn1+xO
Metal deficient defects
Many solids – difficult to prepare in stoichiometric composition
- More anions than metals
- Fe0.93O to Fe0.96O
- some Fe+2
Fe+3 + e- to maintain the electrical neutrality of the crystal
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1.10 Electrical properties
Solids 10-20 - 107 ohm-1m-1
Conductors
104
-
107
ohm-1m-1
Semi-conductors
10-6 -104 ohm-1m-1
Insulators
10-20 -10-10 ohm-1m-1
good
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Band : the atomic orbitals of metal atoms form molecular orbitals which are
so close in energy to each other as to form a band.
Conduction
band
Valence
band
Conduction band : lowest unoccupied band
Valence band : highest occupied
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Conductors
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Insulators
Semi-conductors
Conductivity decreases Conductivity increases with rise in temperature
with rise in temperature Eg : Si & Ge
- Also called
Intrinsic semi conductors
-
Cond. can
can be
be increased
increased
by adding suitable
Impurities ( Doping)
Electronic defects
Electron deficient impurities
Electron rich impurities
Si (gr.14) doped with P or As (gr.15)
Si (gr.14) doped with B Al or Ga (gr.13)
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Applications of n-type and p-type semi conductors :
• diode
p-type and n-type semiconductors & is used as a rectifier
• transistors
npn & pnp
amplify radio or audio signals.
• photo-diode
solar cells
• Combination of different group atoms to give average of 4e-s
gr. 12 + gr. 16
e.g: ZnS, CdS, CdSe and HgTe
gr. 13 + gr. 15
e.g: InSb, AlPb and GaAs
have very fast
response
• In these compounds, the bonds are not perfectly covalent and the ionic
character depends on the electronegativities of the two elements.
• interesting !
transition metal oxides (TiO, CrO2 and ReO3) behave like metals!!
ReO3 is like metallic copper in its conductivity and appearance.
VO, VO2, VO3 and TiO3 show metallic or insulating properties
depending on temperature.
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1.11 Magnetic properties
Every substance
magnetic properties
due to e-s
behave like
tiny magnets
Magnetic moment
Spin motion
Orbital motion
• Electron being a charged particle and undergoing these motions can be considered
as a small loop of current which possesses a magnetic moment.
• Each electron has a permanent spin and an magnetic moment
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Bohr magneton,
2
µB = 9.27 × 10–24A m
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1. Paramagnetism :
due to presence of unpaired electrons
weakly attracted by the magnetic field
magnetized in a magnetic field in the same direction
lose magnetism in the absence of mag. field
e.g : O2, Cu2+, Fe3+, Cr3+
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Diamagnetism:
• weakly repelled by a magnetic field.
• eg: H2O, NaCl and C6H6
• They are weakly magnetised in a magnetic field in opposite direction.
• shown by those substances in which all the electrons are paired and
there are no unpaired electrons.
• Pairing of electrons cancels their magnetic moments and they lose their
magnetic character.
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Ferromagnetism:
• A few substances like iron, cobalt, nickel, gadolinium and CrO2 are attracted
very strongly by a magnetic field. Such substances are called ferromagnetic
substances.
• can be permanently magnetised.
• In solid state, the metal ions of ferromagnetic substances are grouped
together into small regions called domains. Thus, each domain acts as a tiny
magnet.
• In an unmagnetised piece of a ferromagnetic substance the domains are
randomly oriented and their magnetic moments get cancelled. When the
substance is placed in a magnetic field all the domains get oriented in the
direction of the magnetic field and a strong magnetic effect is produced. This
ordering of domains persist even when the magnetic field is removed and
the ferromagnetic substance becomes a permanent magnet.
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Antiferromagnetism:
• Substances like MnO showing antiferromagnetism have domain structure similar to
ferromagnetic substance, but their domains are oppositely oriented and cancel out each
other's magnetic moment
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Ferrimagnetism:
• the magnetic moments of the domains in the substance are aligned in parallel and antiparallel directions in unequal numbers.
• weakly attracted by magnetic field as compared to ferromagnetic substances.
• Examples: Fe3O4 (magnetite) and ferrites like MgFe2O4 and ZnFe2O4 are examples of
such substances.
• These substances also lose ferrimagnetism on heating and become paramagnetic.
End of chapter
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