Introduction

From stone age to modern times what humans have achieved is

the ability to find and make tools that made life easier.

From things as simple as toothbrush to space crafts are

nothing but tools made to achieve our objective with ease.

These tools and the technology more than often use solids.

What is it which makes different solids (natural or man made)

to serve different purpose through tools made with them?
 Introduction continued …
The properties of solids are due to the nature of particles forming
them and the nature and strength of their binding forces.

Thus it becomes important to know and understand the structure of

solids for making tools out of them for different purpose.

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, biocompliant solids for surgical implants,
lightweight and highly temperature and pressure resistant solids
for making space crafts, etc.
SOLID STATE

The Solid Behind the Scenes

 States of Matter
Matter exists in four states: Solid, Liquid, Gas and Plasma.
These are achieved in sequence with increasing temperature.
The stability of a state under given conditions of T and P
depend upon two factors:
Intermolecular interactions – they try to hold the particles
together.
Thermal energy – it tries to make particles free of all bondages.
Under room temperature condition for most of the elements it
is the intermolecular interactions which dominate over the
thermal energy factor and thus majority of them are found in
solid state. (DO NOT NOTE THIS)
 General Comparison of States of Matter
Properties Solid Liquid Gases
Motion of particle Vibration only Random motion Totally random
within confinement

Inter particle forces Very strong Intermediate Weak

Volume (Average Volume is fixed => Volume is fixed => Volume = Volume of
separation) Average Separation Average Separation container => no fixed
fixed fixed average separation
Shape Definite; due to Not definite; as Not definite; as location
fixed location of location of particles of particles is not fixed
particles is not fixed

Compressibility Incompressible Almost Highly compressible

incompressible

Heat Capacity Independent of Independent of Dependent on process

process process
 Types of Solids
• Crystalline Solids:
A solid is said to be crystalline if the constituents
arrange themselves in regular manner throughout
the three- dimensional network.

• Amorphous Solids:
A solid is termed as amorphous if the arrangement of
the building constituents is not consistent or regular
over long range. (short range order).
Note: Greek amorphos = no form
 Crystalline Vs Amorphous
Property Crystalline Solid Amorphous Solid
Geometry Regular with long range Irregular with short range
order order
Melting Point Sharp Melt over range of
temperature
Nature Anisotropic Isotropic
Rigidity Highly rigid; thus also called Less rigid; thus also called
true solid. super cooled liquids or pseudo
solids.
Cleavage Clean surface obtained Irregular surface obtained

Examples NaCl , KCl, sugar, quartz etc. Plastic, Glass, Rubber etc.

Crystalline solids have non uniformity in physical properties like refractive index,
electrical conductance, thermal expansion etc. when observed along
different directions so they are anisotropic whereas amorphous solids are isotropic
due to random arrangement of the constituent particles.
Some Figures and Images

Anisotropy Amorphous Glass

Some Figures and Images

Tetrahedron unit of glass Crystalline Vs Amorphous

 Types of Crystalline Solids
Ionic Solids Metallic Solids Covalent Molecular
Solids Solids
Constituent Cations and anions Positive kernels Atoms molecules
particles surrounded by sea of
free electrons
Binding force Electrostatic Metallic bond Covalent Intermolecular
attraction bond interactions
Hardness Hard and brittle Varying hardness, Very hard Soft and hard
malleable and ductile and brittle
Melting Point High Low to high High Low
Electrical Poor; can conduct Good Poor Poor
Conduction in molten state or
aq. Solution
Examples All ionic All metals Diamond, Ice, dry ice
compounds SiO2, (solid CO2),
Graphite Solid SO2 etc.
etc.
Crystallographic Coordinate System
Z

(0,0,c)

b a
(0,b,0)
Y

(a,0,0)

X
a, b,  are crystallographic angles/ axial angles/ interfacial angles
a, b and c are intercepts on X, Y and Z axis respectively and are known as
crystallographic distances/ axial distances.
a, b,  and a, b, and c are collectively called lattice parameters.
Seven Crystal Systems
Crystal System Lattice Parameters Bravais Lattices

Cubic (a = b = c, a = b =  = 90) P, F, I
Tetragonal (a = b  c, a = b =  = 90) P, I

Orthorhombic (a  b  c, a = b =  = 90) P, F, I, C

Rhombohedral (a = b = c, 90  a = b =  < 120 ) P

Hexagonal (a = b  c, a = b = 90,  = 120) P

Monoclinic (a  b  c, a =  = 90  b) P, C

Triclinic (a  b  c, a  b    90º) P

Primitive (P), Body Centered (I), End Centered (C), Face Centered (F)

Cubic and Triclinic system are most and least symmetric respectively
Cube and its properties
A cube has:
- 6 faces
- 8 corners
- 12 edges
- 12 face diagonals
- 4 body diagonals
If “a” is edge length of cube, then
Length of face diagonal = a2
Length of body diagonal = a3
Cube and its properties
Elements of Symmetry:
(1) Centre of Symmetry (COS)
Yes, 1.
(2) Plane of Symmetry (POS)
3+6=9
(3) Axis of Symmetry (AOS)
3 + 6 + 4 = 13
(C4) (C2) (C3)

There are total 23 elements of symmetry in a cube.

 Planes Of Symmetry (POS)

3 Body diagonal plane, 6

Axes Of Symmetry (AOS)

4 fold AOS, 3 axes 2 fold AOS, 6 axes 3 fold AOS, 4 axes

 Crystal Lattice
Crystal Lattice
Regular repeated arrangement of points in 3D space represents
crystal lattice.
Lattice Point
Each point in a lattice is called lattice point or lattice site.
In a solid each lattice point is occupied by atom, molecule, ions, or
group of them known as motif or basis. Example, two C atoms
make a basis in diamond.

Note:
(1) The particles at lattice sites are considered as identical rigid spheres.
(2) An infinite lattice should look identical from any lattice site.
 Unit Cell
Primitive Unit Cell
It is defined as the smallest possible volume of space
lattice by which whole space lattice can be generated by
translational repetition of it in all possible directions
without causing any overlapping or gaps.

Unit Cell
Same characteristic as explained above but it need not be
smallest in volume.
Q. Correctly identify the Unit Cells and mark the primitive unit cells in the 2D lattice.
Crystal Lattice and Unit Cell
Types of Unit Cell
1. Primitive or Simple Unit Cell (P)
Particles only at the corners of the unit cell.

2. Non- primitive or Centered Unit Cells

a) Face Centered (F): Particles at corners and at each of the
face centers of unit cell.
b) End Centered (C): Particles at corners and at the ends of
two opposite faces of unit cell.
c) Body Centered (I): Particles at corners as well as at the
body center of the unit cell.
Types of Unit Cell

Body Centered
Bravais Lattices
Bravais Lattices
Some Important Definitions
Rank of a Unit Cell, Z
It is the number of particles (spheres) effectively present in one unit cell.

Co-ordination Number
The number of nearest neighbour of a particle in a crystal lattice is called its
Co-ordination number. It is also referred to as 1st nearest neighbour.

Note: 2nd nearest neighbour (or next nearest neighbour) and 3rd nearest
Neighbour are also important to observe.

Packing Fraction of Packing Factor ()

It is the fraction of volume occupied by the particles in a unit cell.
Some Important Definitions
Density of Solid, d or 
Density of a crystalline solid is same as density of its unit cell.

Z = Rank of the Unit Cell

M = Molar mass or Formula mass of the substance
Unit Cells of Cubic Crystal System
(1) Simple Cubic (SC)

Particles only at corners of the cubic unit cell.

Unit Cells of Cubic Crystal System
Important Points about SC Unit Cell

(1) Each particle touches its adjacent particles and does not touch the particles
diagonally placed (face diagonal or body diagonal)

(2) Effective no. of particles per UC or Rank, Z = 8 x 1/8 = 1

(3) If ‘a’ is edge length of SC unit cell and ‘r’ be the radius of particle then
a = 2r

(4) Packing fraction, ø = π/6 = 0.52 or 52%

(5) density, d = ?
Particles viewed in different planes
Neighbour Counting for SC
Unit Cells of Cubic Crystal System
(2) Body Centered Cubic (BCC)

Particles at corners and body center of the Unit Cell.

Important Points about BCC Unit Cell

(1) Particle at body center touches all the eight particles at corners of the cube.
The particles at corners do not touch each other.

(2) Effective no. of particles per UC or Rank, Z = 8 x 1/8 + 1 x 1 = 2

(3) If ‘a’ is edge length of SC unit cell and ‘r’ be the radius of particle then
3 a = 4r
(4) Packing fraction, ø = 0.68 or 68%

(5) density, d = ?
Particles viewed in different planes
Neighbour Counting for BCC
Unit Cells of Cubic Crystal System
(3) Face Centered Cubic (FCC)

Particles at corners and at each face center of the Unit Cell.

Important Points about FCC Unit Cell

(1) Particle at face center touches particles at the corners of face and adjacent
face centers. The particles at corners do not touch each other.

(2) Effective no. of particles per UC or Rank, Z = 8 x 1/8 + 6 x 1/2 = 4

(3) If ‘a’ is edge length of SC unit cell and ‘r’ be the radius of particle then
2 a = 4r
(4) Packing fraction, ø = 0.74 or 74%

(5) density, d = ?
Particles viewed in different planes
Neighbour Counting in FCC
RECAP

The number of particles effectively present in a unit cell is called its rank, Z.
 RECAP
Type of Unit Lattice points Lattice points at Lattice points Z = No. of
Cell at corners face centers at body center Lattice points
per unit cell

SC 8 0 0 8 x 1/8 = 1

BCC 8 0 1 8 x 1/8 + 1 = 2

8 x 1/8 + 6 x 1/2
FCC 8 6 0
=4
RECAP
1. Simple Cubic or Primitive:

Edge length of unit cell, a = 2r

Atomic Radius, r = a/2

RECAP
2. Body Center Cubic:

Edge length of unit cell, a = 4r/√3

Atomic Radius, r = (√3/4)a

RECAP
3. Face center cubic/ cubic close packed:

Edge length of unit cell, a = 4r/√2

Atomic Radius, r = (√2/4)a

 RECAP
Packing Fraction = Vol. of atoms in cube/ Total Vol. of Cube
S. No. Item Primitive BCC FCC

1. Atoms Occupy: 8 corners 8 corners, 1 8 corners, 6

center face centers
2. Number of atoms 8 x 1/8 = 1 8 x 1/8 + 1 = 2 8 x 1/8 + 6 x ½ =
contributed 4
3. Total Vol. of atoms of 1 x 4/3 π r3 2 x 4/3 π r3 4 x 4/3 π r3
radius r
4. Edge of Cube in terms of r a = 2r a = 4r/√3 a = 4r/√2

5. Vol. of cube, a3 (2r)3 (4r/√3)3 (4r/√2)3

6. Fraction of Vol. Occupied π/6 √3/8 π √2/6 π

7. Percentage Vol. Occupied 52% 68.02% 74.05%