This document provides an introduction to solid state physics and crystallography. It defines key terms like crystalline, non-crystalline, lattice, basis, unit cell and discusses common crystal structures including simple cubic, body centered cubic, and face centered cubic. It also covers topics like Miller indices, atomic packing fraction, coordination number, and examples of crystal structures in sodium chloride and cesium chloride.

1. Introduction to Solid State Physics
Unit cell
SC
FCC
Prof. Dr. Md. Mohi Uddin
PhD (Tohoku University, Japan)
JSPS Doctoral fellow, Tohoku University, Japan
G-COE Scholar, Tokyo Institute of Technology, Japan

2. Dr. M M Uddin 2
The science of crystallography is concerned with the enumeration
and classification of all possible types of crystal structures and
determination of the actual structure of the crystalline solids.
Crystalline: Elements and their chemical compounds are found
to occur in three states, i.e., solids, liquids and gases. If the
atoms or molecules in a solid are arranged in some regular
fashion, it is known as crystalline materials.

3. Dr. M M Uddin 3
Non-crystalline or amorphous: When the atoms or molecules
in a solid are arranged in an irregular fashion, it is known as non-
crystalline or amorphous.
In single crystals the same periodicity extends throughout the
material.

4. Dr. M M Uddin 4
Whereas in polycrystalline crystals the same periodicity does not
extend throughout the crystal but is interrupted at grain boundaries.

5. Lattice: A lattice is a hypothetical regular and periodic arrangement
of points in space. It is used to describe the structure of a crystal.
Basis: A basis is a collection of atoms in particular fixed
arrangement in space. We could have a basis of a single atom as
well as a basis of a complicated but fixed arrangement of hundreds
of atoms. Below we see a basis of two atoms inclined at a fixed
angle in a plane.

6. Let us now attach the above basis to each lattice point (in black) as
follows.
Next remove the lattice points in black (remember that the lattice
is an abstract entity). Lets see what we have got?

7. We have got the actual two-dimensional crystal in real space. So
we may write:
lattice + basis = crystal
We have seen that the atomic order in crystalline solids indicates
that the smallest groups of atoms form a repetitive pattern. Thus
in describing crystal structures, it is often convenient to
subdivide the structure into repetitive small repeat entities called
unit cell, i.e. in every crystal some fundamental grouping of
particles is repeated.
Unit cell:

8. 8
Fig.: Optimized unit cell of the M2InC (M= Zr, Hf, and Ta) compound.

9. 9
Lattice types in 2 dimensional system
3D- Bulk materials
2D-Quantum well
1D- Quantum wire
0D- Quantum dot

10. 10
Optimized InSb QWFET layer structure
Semi-insulator GaAs
Substrate
3 μm Al 0.15In0.85Sb with
Al 0.2In0.8NSb interlayer
45 nm Al 0.15In0.85Sb
Al2O3 ( 10 nm)
In
Gate
InSb (20 nm)
Ec
Ev

11. Dr. M M Uddin 11
Bravais space lattice in three dimensions
C = body-centered
P = primitives
B =base-centered F = face-centered

12. 12
P, C, B, F
Hexagonal P a= b  c  =  =90,
=120
SiO2, Zn

13. Dr. M M Uddin 13
As stated in the previous slide, each corner atom in a cubic cell is
shared by a total number of eight unit cells so that each corner
atom contributes only 1/8 of its effective part to a unit cell. Since
there are in all 8 corner atoms there total contribution is equal
to . Thus the number of atoms per unit simple cubic cell is
one.
Simple cubic (sc) cell
1
8
8
1



14. The contribution of body centered is full, i.e., one. This is in
addition to eight corner atoms. So number of atoms per unit face
centered cubic cell.
1+ = 2
8
8
1

14
Body centered cubic (bcc) cell

15. 8
8
1

Dr. M M Uddin 15
Face centered cubic (fcc) cell
Each face centered atom is shared by two unit cells. There are six
faces of a cube and there are eight corner atoms. So Number of
atoms per unit face centered cubic cell
6/2 + = 4

16. Dr. M M Uddin 16
Example1: A compound formed by elements A and B has a cubic
structure in which A atoms are at the corners of the cube and B
atoms are at face centres. Derive the formula of the compound.
Solution:
As ‘A’ atom are present at the 8 corners of the cube therefore no of
atoms of A in the unit cell = 1/8 × 8 = 1
As B atoms present at the face centres of the cube, therefore no of
atoms of B in the unit cell = 1/2 × 6 = 3
Hence the formula of compound is AB3.

17. Atomic radius is denoted by r and expressed in terms of cube edge
element a. Atomic radius can be calculated by assuming that
atoms are spheres in contact in crystal.
In the case of a simple cube, if r if the atomic radius and lattice
parameter is a then a = 2r or r = a/2. And area
Dr. M M Uddin 17
Atomic Radius
2
2
4r
a 

18. In case of a body centered cube, the atoms touch each other along
the diagonal of the cube as shown below.
Obviously, the diagonal in this case is 4r. Also,
2
2
2
2
2
2
2a
a
a
BC
AB
AC 




2
2
2
2
2
2
3
2 a
a
a
CD
AC
AD 




2
3
2
3
4 a
r
and
r
a 

4
3
a
r 
Dr. M M Uddin 18
3
16 2
2 r
a 

19. In case of a face centered cube the atoms are in contact along the
diagonal of the faces as shown below. The diagonal has a length of
4r.
2
2
2
BC
AB
AC 

  2
2
2
2
2
4 a
a
a
r 


2
2
4
2 a
a
r 

2
2
8r
a 
Dr. M M Uddin 19

20. Dr. M M Uddin 20
Coordination number
Simple cubic
An atom in a simple cubic lattice structure contacts six other atoms, so it
has a coordination number of six (6).

21. Dr. M M Uddin 21
Body centered cubic (BCC)
Each lattice points has 8 nearest neighbours (in the centers of the neighboured
cubes) and 6 next-nearest neighbours (located at the neighboured vertices of the
lattice). So, the coordination number of BCC is 8.

22. Dr. M M Uddin 22
Face centered cubic (FCC)
Each atom has 12 nearest neighbours (the neighboured face atoms) and 6
next-nearest neighbours (located along the vertices of the lattice). So,
coordination number of FCC/HCP is 12.

23. In a simple cubic (sc) structure the number of atoms per unit cell is
one. The atomic radius is given by half the primitive, i. e., a/2.
So the volume occupied by the atom in the unit cell
3
3
2
3
4
3
4








a
r 

23
Atomic packing fraction
The packing fraction is the maximum proportion of the available
volume that can be filled hard spheres.
Or,
The fraction of volume occupied by spherical atoms as compared to
the total available volume of the structure.

24. Dr. M M Uddin 24
Volume of the unit cell = ; so the packing fraction
3
a
Thus the atoms are loosely packed. Polonium at a certain
temperature exhibits such structure.
%
52
6
2
3
4
3
3











a
a
f
f =
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑒𝑠
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑢𝑏𝑖𝑐

25. In a body centered cubic lattice there are two atoms per unit cell.
The atomic radius
So volume occupied by the atoms in the unit cell
Volume of the unit cell =
So, facking fraction
Common substances with bcc lattice are barium, chromium,
sodium, iron and cesium chloride.
3
4
,
4
3 r
a
a
r 

3
3
3
2
3
3
8
3
4
3
3
4
2
3
4
2 a
a
r 

 




%
68
8
3
8
3
3
3





a
a
f
3
a
Dr. M M Uddin 25
Body Centered Cube (bcc)

26. In a face centered cubic lattice there are four atoms per unit cell.
The atomic radius
So the volume occupied by the atoms in the unit cell
Volume of the unit cell
So packing fraction
2
2
a
r 
3
3
3
3
2
3
2
2
2
3
16
3
4
4 a
a
r


 



3
a
%
74
2
3
2
3
3
3





a
a
f
Dr. M M Uddin 26
Common examples of this type of structure is Ni, Cu, Au, Al, Ag,
Li, K, etc.
Face Centered Cube (fcc)

27. Dr. M M Uddin 27
Calculation of lattice constant
Let us consider the case of a cubic lattice of lattice constant a. If 
be the density of the crystal then,
Volume of the unit cell=a3
 Mass of each unit cell=a3
Let there be n molecules (lattice point) per unit cell, M be the
molecular weight and N be the Avogadro’s number. Then,
------------ (1)
------------ (2)

28. Dr. M M Uddin 28
From equation (1) and (2), we have
------------ (3)
The value of lattice constant a can be calculated using equation (3).

29. Hexagonal Closed Packed (hcp)
In hexagonal closed packed (hcp) structure unit cell contains one atom at each
corner of the hexagonal prism, one atom at each at the center of the hexagonal
faces and three more atoms within the body of the cell. This type of structure is
denser than the simple hexagonal structure. Total number of atoms inside is 6.
Each corner atoms is shared by 6 other unit
lattices or each corner has 1/6 atom.
Number of atoms in upper hexagonal plane
Number of atoms in lower hexagonal plane
We note that each central atom is shared by
two unit cells which means upper and
lower planes contain atom each.
1
6
6
1



1
6
6
1



2
1
2

Dr. M M Uddin
29

30. 30
Three interstitial atoms with BCC structure, so contains 3 atoms
So, Total number of atoms in hcp crystal = 1+ 1 + 1 + 3 = 6
R
R
sin60=3/2 Volume=area  height

31. 31

32. Dr. M M Uddin 32

33. Dr. M M Uddin 33
Problem: Rhenium has an HCP crystal structure, an atomic radius
of 0.137 nm, and a c/a ratio of 1.615. Compute the volume of the
unit cell for Re.

34. Dr. M M Uddin 34
Problem-1: Iron has a BCC crystal structure. If the density of 7.86
g/cm3, what is the radius of the Iron atom?
Answer:
=7.86 g/cc, n=2, Atomic weight M= 55.85
We know,
3
4r
a 
and

35. Dr. M M Uddin 35
Answer: We know,
Problem-2: NaCl crystals have FCC structure. The density of
sodium chloride is 2.18 g/cm3. Calculate the distance between two
adjacent atoms. Atomic weight of sodium=23 and that of
chloride=35.5.

36. Miller Indices
Miller index of a crystal face or plane is
given by three smallest figures which are
inversely proportional to the numerical
parameters of the face.
In order to make the designation the following procedure has been
adopted.
1. Determine the intercepts of the plane along a, b, c in terms of lattice
constants.
2. Invert the intercepts, that is, write the numbers as their reciprocals.
3. If fraction results, multiply them by lowest common denominator.
Dr. M M Uddin 36
William Hallowes Miller
(1801 -1880)
British Mineralogist and
Crystallographer

37. 37
The resulting integers are called Miller indices of a plane and conventionally
closed in parentheses (h k l).
The meaning of these indices is that a set of parallel planes (h k l) cuts the a-
axis into h parts, the b-axis into k parts and the c-axis into l parts.

38. Dr. M M Uddin 38

39. Dr. M M Uddin 39
(632)

40. Dr. M M Uddin 40
(100) plane (110) plane (111) plane
Draw the planes

41. Dr. M M Uddin 41

42. Dr. M M Uddin 42

43. Dr. M M Uddin 43

44. Dr. M M Uddin 44

45. NaCl structure
The Bravais lattice of NaCl crystal is a face-centered cube as
shown in Figure below. NaCl is an ionic crystal, it consists of
two fcc sub-lattice, one of Cl- ions having origin at (000) and the
other of Na+ ion having origin at one half separated by one-half
the body diagonal of a unit cube.
Dr. M M Uddin 45

46. (a) Rectangular x, y, and z axes for locating atom positions in cubic units. (b)
atoms positions in a bcc unit cell.
2
1
2
1
0
2
1
0
2
1
0
2
1
2
1
000
Na 00
2
1
0
2
1
0
2
1
00
2
1
2
1
2
1
Cl
There are four units of NaCl in each unit cube with atoms in positions
Dr. M M Uddin 46

47. CsCl structure
The Bravais lattice of CsCl is a simple cube. It is an ionic
compound. It is considered as the interpenetration of two
simple cubic lattices of cesium and chlorine ions having half
the body diagonal of a unit cell.
The Bravais lattice of CsCl is a simple cube. It is
an ionic compound. It is considered as the
interpenetration of two simple cubic lattices of
cesium and chlorine ions having half the body
diagonal of a unit cell. Chloride ions occupy the
corners of a cube, with a cesium ion in the center
or vice versa.
If Cl ion present at the origin (000), then Cs
ion is present at the center point 





2
1
2
1
2
1
of the cube.
Dr. M M Uddin 47

48. Bragg’s Law
The Bragg
’s Law is one of most important laws used for
interpreting X-ray diffraction data. In 1913, W. H Bragg and his
son W. L Bragg discovered this law.
Dr. M M Uddin 48
H. L. Bragg
(1862-1942)
W. L. Bragg
(1890-1971)

49. A beam containing X-rays of wavelength  is incident upon a crystal at an angle 
with a family of Bragg planes whose spacing d. The beam goes past from A in the
first plane and atom C in the next, and each of them scatters part of the beam in
random directions. Constructive interference takes place only between those
scattered rays that are parallel and whose paths differ by exactly , 2, 3 and so
on. That is the path difference must be n, where n is an integer.

Path difference,
BE + EF - AC =BE – AC + EF
=DE+ EF
 
2
2
2
l
k
h
a
d



10-8 cm
6000/cm

50. Dr. M M Uddin 50

51. sin
EF d 

2 sin
DE EF d 
 
2 sin
n d
 

Constructive Interference:
sin
DE d 

where, =wavelength of X-ray
d= spacing of two planes
 =scattering angle
n= an integer representing the order of the diffraction peak.
------- (1)
Equation (1) is called Bragg’s law.

52. X-Ray Diffraction (XRD)
How it works?
Philips X-pert Pro X-ray
diffractometer
(Atomic Energy Centre,
Dhaka, AECD)
 X-ray diffraction (XRD) is a versatile non-
destructive technique for structure analysis and
phase identification of a wide range of
materials including metals, composites,
polymers, biological materials, electronic and
optoelectronic materials.
 Short wavelength X-rays (hard X-rays) in the
range of a few angstroms to 0.1 angstrom (1
keV-120 keV) are used in the diffraction
applications. Because the wavelength of X-rays
is comparable to the size of atoms, they are
ideally suited for probing the structural
arrangement of atoms and molecules in a wide
range of materials.

53. R. Zahir, F.-U.-Z Chowdhury, M.M. Uddin and M.A. Hakim “J.
Magn. Magn. Mater. 410, 55–62 (2016)
Rumana Zahir
University of Central Florida
Florida, USA

54. 20 30 40 50 60 70
x=0.12
x=0.10
x=0.08
x=0.06
x=0.04
x=0.02
Intensity
(a.u.)
2 (degree)
(111)
(220)
(311)
(222)
(400)
(422)
(511) (440)
x=0.00
The XRD patters of the stoichiometric compositions of Co0.5Zn0.5YxFe(2-
x)O4 where (x=0.0, 0.02, 0.04,0.06, 0.10) at Ts=1050C
Mithila Das
University of Coimbra
Coimbra, Portugal
M. Das, M.N.I. Khan, M.A. Matin and M.M. Uddin, Journal of Superconductivity
and Novel Magnetism (2019) (Springer)

55. Characteristic features of Bragg's law
Bragg's law is a consequence of the periodicity of the space lattice.
The law does not refer to the arrangement or basis of atoms associated
with its lattice points.
Bragg reflection can occur only for wavelength   2d. This is the
reason why visible wavelength cannot be used in diffraction.
For the same order and spacing the angle  decreases as the
wavelength decreases.
Dr. M M Uddin 55

56. Dr. M M Uddin 56

57. Dr. M M Uddin 57

58. Relation between interplanar spacing d and lattice constant a
Suppose that the plane shown
in figure belongs to a family of
planes whose Miller indices
are (hkl). The perpendicular
ON from origin to the plane
represents the interplanar d of
this family of planes. Let the
direction cosines of ON be
cos, cos, and cos. The
intercepts of the plane of the
three axes are:
Dr. M M Uddin 58
M
B
y
z
a
A
x
C
a
a
a
O
N




59. cos𝛼 =
𝑑ℎ𝑘𝑙
𝑎
ℎ
=
ℎ 𝑑ℎ𝑘𝑙
𝑎
First direction cosine of ON is
𝒅𝒉𝒌𝒍 of crystal with orthogonal axes α = 𝛽 = 𝛾 == 90°
(Cubic, tetragonal, orthorhombic)
a=b=c, a=b≠c a ≠ b≠c
y
z
A
x
C
O
N



B
𝒅𝒉𝒌𝒍 = interplanar spacing between successive hkl planes
passing through the corners of the unit cell
= distance between the origin and the nearest (hkl) plane
ON ⊥ 𝐀𝐁𝐂 (𝒉𝒌𝒍)

60. 60
Second direction cosine of ON is
y
z
A
x
C
O
N



B
cos𝛽 =
𝑑ℎ𝑘𝑙
𝑏
𝑘
=
𝑘 𝑑ℎ𝑘𝑙
𝑏
O
N
B
y
dhkl
𝑏
𝑘

dhkl
𝜸
𝑐
𝑙
Third direction cosine of ON is
cos𝛾 =
𝑑ℎ𝑘𝑙
𝑐
𝑙
=
𝑙 𝑑ℎ𝑘𝑙
𝑐

61. 1
cos
cos
cos 2
2
2


 


1
2
2
2





















c
ld
b
kd
a
hd hkl
hkl
hkl
  1
2
2
2
2
2


 l
k
h
a
dhkl
 
2
2
2
2
2
l
k
h
a
dhkl



 
2
2
2
l
k
h
a
dhkl



61
This is the relation between interplaner spacing & Miller indices
For cubic crystal system
a=b=c

62. Dr. M M Uddin 62
Tetragonal a=b≠c
Orthorhombic a ≠ b≠c)

63. Dr. M M Uddin 63
Answer:
We know,
 
2
2
2
l
k
h
a
d



  3
1
1
1
111
a
a
d 



2 sin
n d
 

and

64. Problem-5: X-rays of  = 0.3 Å are incident on a crystal with lattice
spacing 0.5 Å. Find the angles at which the second and third Bragg's
diffraction maxima are observed.

 sin
2d
n 
 
n
n
d
n
3
.
0
sin
10
5
2
10
3
sin
2
sin 11
11
1
1




















 


 

    0
1
9
.
36
6
.
0
sin
2
3
.
0
sin 


 

    0
1
64
9
.
0
sin
3
3
.
0
sin 


 

Bragg's equation for X-ray of wavelength  is given by
Here, we have  = 0.3 Å = 3.0  10-11 m, d = 0.5 Å = 5.0  10-11 m.
Hence,
For, n = 2,
For, n = 3,
64

65. Defect in crystals
 The defect may scatter conduction electrons in a metal,
increasing its electrical resistance by several percent in many
pure metals and much more in alloys.
 Some defects decrease the strength of the crystals.
 Pure salts having impurities and imperfection are often colored.
A defect in solid is any deviation from periodicity in the solid or, a
discontinuity in a crystal lattice. The defects influence the
properties of the solid in the following different ways:
Dr. M M Uddin 65

66. 66
Classification of defect
Point defects (Zero dimensional defects)
• Vacancy
• Interstitial atom
• Frankel defects
• Substitutional impurity atom
• Schottky defects
Line defects (One dimensional defects)
• Edge dislocation
• Screw dislocation
Plane defects (Two dimensional defects)
• Lineage boundary
• Grain boundary
• Stacking fault
Electronic imperfections
Excitation states of crystals
Transient imperfection

67. x = 0.00 x = 0.02
x = 0.04 x = 0.06
FESEM Images of Co0.5Zn0.5YxF2-xO4
67

68. x=0.08
68
0.00 0.02 0.04 0.06 0.08
550
600
650
700
750
800
Grain
size,
D
m

n
m)
Y content, x (wt%)
50 100 150 200 250
0
1
2
3
Resistivity,
/m10
6
)
Temperature,T(C)
x=0.00
x=0.02
x=0.04
x=0.06
x=0.08
-10 -5 0 5 10
-60
-40
-20
0
20
40
60
M
(emu/gm)
Applied field (kOe)
x=0.00
x=0.02
x=0.04
x=0.06
x=0.08

69. Energy Dispersive Spectroscopy Spectra of Co0.5Zn0.5YxF2-xO4
x= 0.00 x = 0.02
 Peak obtain for Co, Zn, Y, Fe, O indicate purity of CZYFO.
69

70. Dr. M M Uddin 70

71. If the deviation from regularities is confined to a very small region
of only about a few lattice constants, it is called a point defect. We
have the following types of point defects:
The simplest point defect is a vacancy.
This refers to an empty (unoccupied)
site of a crystal lattice, i.e. a missing
atom or vacant atomic site such
defects may arise either from
imperfect packing during original
crystallization or from thermal energy
due to vibration is increased, there is
always an increased probability that
individual atom will jump out of their
positions of lowest energy. Dr. M M Uddin 71
Point defect
(a) Vacancy:

72. In this case there is a presence of an extra atom somewhere in the
interstice of the lattice but not on regular lattice sites.
Dr. M M Uddin 72
(b) Interstitial atom (Huckle defect):

73. When an atom or ion leaves its normal site and is found to occupy
another position in the interstice is known as Frenkel defect.
This type of defects is more common in ionic crystals, because the
positive ions, being smaller in size, get lodge easily in the
interstitial positions.
Dr. M M Uddin 73
(c) Frenkel defect:

74. The presence of a foreign atom in the lattice. It may be present at
any interstitial position, or at any substitutional position, i.e., in
place of any regular lattice site. In this type of defect, the atom
which replaces the parent atom may be of same size or slightly
smaller or greater than that of the parent atom.
Dr. M M Uddin 74
(d) Substitutional impurity atom:

75. These imperfections are similar to vacancies. This defect is caused,
whenever a pair of positive and negative ions is missing from a
crystal. This type of imperfection maintains charge neutrality. In
this type, anions and cations are taken away from their correct
position and are placed them on surface in equal numbers.
Dr. M M Uddin 75
(e) Schottky defect:

76. Dr. M M Uddin 76

77. Dislocations are another type of defect in crystals. Dislocations
are areas were the atoms are out of position in the crystal
structure. Dislocations move under applied stresses, and thus
cause plastic deformation in solids.
Dr. M M Uddin 77
The edge dislocation, shown above can be easily visualized as an
extra half plane of atoms in a lattice. The dislocation is called a
line defect because the locus of defective points produced in the
lattice by the dislocation lie along a line. This line runs along the
top of the extra half-plane. The inter-atomic bonds are significantly
distorted only in the immediate vicinity of the dislocation line. In a
sketch/drawing an edge dislocation is represented as a T or
inverted T.
Edge dislocation
Line Defect

78. Dr. M M Uddin 78

79. The screw dislocation is slightly more difficult to visualize. The
motion of a screw dislocation is also a result of shear stress, but the
defect line movement is perpendicular to direction of the stress and
the atom displacement, rather than parallel. The screw dislocation is
parallel to the direction in which the crystal is being displaced
(Burgers vector is parallel to the dislocation line).
Dr. M M Uddin 79
Screw dislocation

80. Dr. M M Uddin 80
Plane Defect
A Grain Boundary is a
general planar defect that
separates regions of different
crystalline orientation (i.e.
grains) within a
polycrystalline solid. The
atoms in the grain boundary
will not be in perfect
crystalline arrangement.
Grain boundaries are usually
the result of uneven growth
when the solid is crystallising.
Grain sizes vary from 1 nm to
1 mm.
(a) Grain Boundary

81. Dr. M M Uddin 81
Staking faults are defects in the ‘stacking’
of atomic layers most commonly a fault in
the stacking sequence of the layers, a
missing layer or an added layer, either of
the same type or of a different type with
respect to the bulk layers. Unsurprisingly,
stacking faults are common in layered
structures, but are also encountered in
isotropic structures: in fact, perhaps the best
known type of stacking fault occurs in FCC
metals, and is a fault of
the ...ABCABCABC... stacking sequence
of the (111) layers, as, for example,
in ...ABCABABCABC... Stacking faults.
(b) Staking faults

82. Dr. M M Uddin 82
It is a boundary between two adjacent perfect regions in the
same crystal which are slightly tilted with respect to each other.
(c) Lineage boundary
Ideal crystal Crystal with
lineage boundary

83. Dr. M M Uddin 83
Electronic imperfection
Errors in charge distribution or energy in solids are called
electronic defects. These are defects on a sub-atomic scale which
are responsible for important electrical and magnetic properties.

84. Dr. M M Uddin 84
Excitation states of crystals
Excitation states are quantized things. These are imperfections as
these cause deviations from perfect crystal summary. Some
examples are;
i) Phonons and Magnons which are quantized lattice vibration
and spin waves respectively.
ii) Conduction electrons and holes which are excited thermally
from filled bands or impurity levels.
iii) Excitons which are quantized electron-hole pairs.
iv) Quantized plasma waves.

85. Dr. M M Uddin 85
Transient imperfection
These imperfections are introduce into the crystal from external
sources. e.g.,
i) Photons which are ordinary quantized e.m. waves.
ii) High energy charged particles like, electrons, protons, mesons
and ions.
iii) High energy uncharged particles such as neutrons and neutral
atoms. These imperfections are used in experimental work.

86. Dr. M M Uddin 86
Point defect at a glance

87. Types of Bonding in Solids
 Ionic Bonding
 Covalent Bonding
 Metallic Bonding
 Hydrogen Bonding
 Van Der Wall’s Bonding

88. An ionic bonding is the Attractive Force existing between positive ion
and a negative ion when they are brought into close proximity or
surrounding.
They are formed when atoms of different elements lose or gain their
electrons in order to achieve stabilized outermost electronic configuration.
Ionic Bond
Ionic Bonding in NaCl

89.  Ionic solids are rigid, unidirectional and crystalline in nature.
 They have high melting and boiling points.
 Ionic solids are good insulators of electricity in their solid state and
good conductor of electricity in their molten state.
 Ionic solids are soluble in water and slightly soluble in organic
solvents.
Properties of Ionic bonds

90. A covalent bond is formed, when two or more electrons of an atom, in its
outermost energy level, are shared by other atoms. e.g.-Chlorine molecule.
In this bonding a stable arrangement is achieved by sharing of electrons
rather than transfer of electrons.
Sometimes a covalent bond is also formed when two atoms of different
non-metals share one or more pair of electrons in their outermost energy
level.
e.g.- Water molecule
Covalent Bonds
Bonding between two atoms of same element Bonding between two different non-metals

91. Properties of Covalent bonds
 Covalent compounds are bad conductors of electricity.
 Covalent compounds are having low melting and boiling points.
 Insoluble- in water
 Soluble- in organic solvents like Benzene

92. It has been observed that in a metal atoms, the electrons in their
outermost energy levels are loosely held by their nucleii.
Thus a metal may be considered as a cluster of positive ions surrounded
by a large number of free electrons, forming electron cloud.
e.g.- all metals
Metallic Bonds

93. Properties of Metallic bonds
 High thermal and electrical conductivity
 Low melting and boiling point temperature
Metallic solids are malleable and ductile

94. Hydrogen Bonds
Covalently bonded atoms often produce an Electric dipole
configuration with hydrogen atom as the positive end of the
dipole. If bonds arise as a result of electrostatic attraction between
atoms, it is known as hydrogen bonding.

95. The hydrogen bonds are directional
 Relatively strong bonding
 These solids have low melting point
 No valence electrons hence good insulators
 Soluble in both polar and non-polar solvents
 They are transparent to light
e.g. – water molecule, ammonic molecules
Properties of Hydrogen Bonds

96. Weak and temporary bonds between molecules of the same
substance are known as Van der Walls bonding.
Types of Van der walls forces
1) dipole-dipole
2) dipole-induced dipole
3) dispersion
Van der walls bonding

97. The main contribution to the binding energy of ionic crystal is
electrostatic and is called the Madelung energy.
Calculation of Medelung constant for NaCl structure
If we take the reference ion as a negative charge, the plus sign will apply
to positive ions and the minus sign to negative ions.