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BASICS OF MATERIAL SCIENCE
UNIT I
Atomic structure and Electronic Configuration: Introduction – Atomic Structure – Electron –
Properties of Cathode Rays – Nucleus – Atomic Number - Atomic Weight – Isotope – Isobar
– Avogadro Number – Atomic Model - Vector Model – Quantum Numbers – Pauli Exclusion
principle.
Section – A
1. Define atom
The atom is considered to be made up of a heavy nucleus, consisting of protons and
neutrons, surrounded by highly structured configurations of electrons, revolving around the
nucleus in shells or orbits at a relatively greater distance from nucleus.
2. What is a proton?
Subatomic particles present in the nucleus with positive charge is called Proton
3. Define Neutrons
A particle with no charge (neither positive nor negative) that is present in the nucleus
is called Neutron
A particle that appears in the nucleus of all atoms except hydrogen
Section – B
1. Give an account on the mass, charge and important properties of few elementary
particles
2. Explain Isobar and Avogadro number
Isobar
Atoms with the same mass but belonging to different chemical elements are called
isobars. Obviously, isobars possess different number of protons and electrons in their atoms.
Total number of protons and neutrons in each of their nuclei is also same. The example of
first pair of isobars is argon and calcium. Argon (atomic number 18) has 18p, 18e and 22 n in
its atom. Calcium (atomic number 20) has 20p, 20e, and 20 n in its atom.
Avogadro number
The number of atoms per gm-mole of a substance is called as Avogadro’s number and
denoted by N. Its value is 6.023 X 1023 mol. It is a universal constant.
Section – C
1. What is an atom? Describe briefly the important constituents of an atom.
The atom is considered to be made up of a heavy nucleus, consisting of protons and
neutrons, surrounded by highly structured configurations of electrons, revolving around the
nucleus in shells or orbits at a relatively greater distance from nucleus.
Electrons
M. Faraday in 1983, in his experiments on the laws of electrolysis, provided the first
experimental evidence that electrical charge was not infinitely divisible, but existed in
discrete units. In 1897, J.J. Thomson, while studying the passage of electricity through gases
at low pressure, observed that the rays of light appear to travel in straight lines from the
surface of the cathode and move away from it in the discharge tube. These rays are called
cathode rays since they start from the cathode of the discharge tube. W. Crookes studied the
properties of these cathode rays and showed that the rays, (i) travel in straight line and cast
shadows (ii) carried negative charge and sufficient momentum (iii) possess high kinetic
energy and can induce some chemical reactions, excite fluorescence on certain substances.
Protons
The nucleus of hydrogen atom is called the proton. A proton has a unit positive charge of
same magnitude as that of electron (= 1.602 X 10–19 C). The mass of a proton is 1.672 X10–27
kg. The proton and the neutron are considered to be two different charge states of the same
particle which is called a nucleon. The number of protons in a nucleus is called the charge Z
of the given nucleus, or the charge number.
Neutrons
These are electrically neutral particles and 1.008 times heavier than protons. The mass of
each neutron is
1.675 X 10–27 kg. Each neutron is composed of one proton and one electron, i.e.
Neutron = Proton + Electron
The number of neutrons in a nucleus is denoted by N. For all nuclei N ≥ Z (with the
exception of 1H1, 2He3 and other neutron deficient nuclei). The total number of nucleons in a
nucleus A = N + Z is called the mass number of the nucleus. In addition to the above
mentioned three particles, there are other particles, e.g. positrons or positive electrons,
neutrino and antineutrino, mesons, deutrons, alpha particle etc. Particles having mass
intermediate between the electron and the proton are called mesons. Mesons are of two types:
π (pie) and μ (mu) mesons, the former being somewhat heavier than the latter. Both the types
of mesons may be either positively or negatively charged. There are also particles of small
mass and zero charge called neutrinos (ν) and antineutrinos (ν). The existence of these
particles has been postulated to account for energy changes during the radioactive emission
of electrons and positrons respectively. Neutrino is supposedly associated with and shares the
energy of electron, whereas antineutrino occupies the same position with respect to the
positron. Table below gives the mass, charge and important properties of few elementary
particles.
Properties of few elementary particles
2. Explain atomic mass and mass number. What is an isotope?
Atomic mass and mass number
The atomic weight of an element is the average relative weight of its atom as
compared to the weight of one atom of oxygen which is taken to be 16, i.e. it is the ratio
between the weight of one atom of the element and 1/16 th of the weight of an atom of
oxygen. We should not confused this with the mass number. The mass number is equal to the
sum of the number of protons and neutrons. The mass number is usually denoted by A.
A = Number of protons + Number of neutrons
For example chlorine atom has 17 protons and 18 neutrons in its nucleus. Obviously, mass
number of chlorine is 35. We can see that the mass number of an element is always a whole
number and its value is
very close to the atomic weight. The mass of the nucleus is directly proportional to the mass
number. We can see that most elements have fractional atomic weights due to the existence
of different isotopes of the same element.
The mass of an atom is usually expressed in terms of atomic mass unit (amu).
1 amu = 1.6603 _ 10–24 g
Hydrogen has one mass unit and carbon 12 amu respectively.
Once the atomic number (Z) and mass number (A) of an element are known, one can
easily determine the number of neutron in its nucleus (see Table)
Isotopes
All atoms having different atomic weights but belonging to the same element are termed as
isotopes, i.e. atomic number of isotopes of an element remains the same. Obviously, isotopes
contain same number of protons and electrons. Thus the isotopes are atoms of different
weight belonging to the same element and having the same atomic number. The difference in
the masses of the isotopes of the same element is due to the different number of neutrons
contained in the nuclei. For example, hydrogen exists in three isotopic forms. Atomic number
of hydrogen is 1. Three isotopes of hydrogen are:
(i) Ordinary hydrogen (1H1) with atomic mass equal to 1.
(ii) Deuterium (1D2) with atomic mass equal to 2.
(iii) Tritium (1T3) with atomic mass equal to 3.
Similarly, chlorine has two isotopes, 17Cl35 and 17Cl37. These isotopes are available in the
ratio of 3:1. Their average atomic weight is 37X3+35X1/ 4 = 35.48
3. Describe atomic model
During the latter part of the nineteenth century it was realized that many phenomena
involving electrons in solids could not be explained in terms of classical mechanics. What
followed was the establishment of a set of principles and laws that govern systems of atomic
and subatomic entities that came to be known as quantum mechanics. An understanding of
the behavior of electrons in atoms and crystalline solids necessarily involves the discussion of
quantum-mechanical concepts. However, a detailed exploration of these principles is beyond
the scope of this book, and only a very superficial and simplified treatment is given.
One early outgrowth of quantum mechanics was the simplified Bohr atomic model,
in which electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and
the position of any particular electron is more or less well defined in terms of its orbital. This
model of the atom is represented in Figure.
Another important quantum-mechanical principle stipulates that the energies of
electrons are quantized; that is, electrons are permitted to have only specific values of energy.
An electron may change energy, but in doing so it must make a quantum jump either to an
allowed higher energy (with absorption of energy) or to a lower energy (with emission of
energy). Often, it is convenient to think of these allowed electron energies as being associated
with energy levels or states.
Schematic representation of the Bohr atom
These states do not vary continuously with energy; that is, adjacent states are
separated by finite energies. For example, allowed states for the Bohr hydrogen atom are
represented in Figure. These energies are taken to be negative, whereas the zero reference is
the unbound or free electron. Of course, the single electron associated with the hydrogen
atom will fill only one of these states.
Thus, the Bohr model represents an early attempt to describe electrons in atoms, in
terms of both position (electron orbitals) and energy (quantized energy levels).
This Bohr model was eventually found to have some significant limitations because of
its inability to explain several phenomena involving electrons. A resolution was reached with
a wave-mechanical model, in which the electron is considered to exhibit both wavelike and
particle-like characteristics. With this model, an electron is no longer treated as a particle
moving in a discrete orbital; but rather, position is considered to be the probability of an
electron’s being at various locations around the nucleus. In other words, position is described
by a probability distribution or electron cloud. Figure compares Bohr and wave-mechanical
models for the hydrogen atom. Both these models are used throughout the course of this
book; the choice depends on which model allows the more simple explanation.
4. Discuss about quantum numbers
Using wave mechanics, every electron in an atom is characterized by four parameters
called quantum numbers. The size, shape, and spatial orientation of an electron’s
probability density are specified by three of these quantum numbers. Furthermore, Bohr
energy levels separate into electron subshells, and quantum numbers dictate the number of
states within each subshell. Shells are specified by a principal quantum number n, which may
take on integral values beginning with unity; sometimes these shells are designated by the
letters K, L, M, N, O, and so on, which correspond, respectively, to n = 1, 2, 3, 4, 5, . . . , as
indicated in Table. It should also be noted that this quantum number, and it only, is also
associated with the Bohr model. This quantum number is related to the distance of an electron
from the nucleus, or its position.
The second quantum number, l, signifies the subshell, which is denoted by a
lowercase letter—an s, p, d, or f ; it is related to the shape of the electron subshell. In
addition, the number of these subshells is restricted by the magnitude of n. Allowable
subshells for the several n values are also presented in Table. The number of energy states for
each subshell is determined by the third quantum number, ml . For an s subshell, there is a
single energy state, whereas for p, d, and f subshells, three, five, and seven states exist,
respectively (Table 2.1). In the absence of an external magnetic field, the states within each
subshell are identical. However, when a magnetic field is applied these subshell states split,
each state assuming a slightly different energy.
Associated with each electron is a spin moment, which must be oriented either up or
down. Related to this spin moment is the fourth quantum number, ms , for which two values
are possible (+1/2 and – 1/2), one for each of the spin orientations. Thus, the Bohr model was
further refined by wave mechanics, in which the introduction of three new quantum numbers
gives rise to electron subshells within each shell. A comparison of these two models on this
basis is illustrated, for the hydrogen atom, in Figures.
A complete energy level diagram for the various shells and subshells using the wavemechanical model is shown in Figure. Several features of the diagram are worth noting. First,
the smaller the principal quantum number, the lower the energy level; for example, the
energy of a 1s state is less than that of a 2s state, which in turn is lower than the 3s. Second,
within each shell, the energy of a subshell level increases with the value of the l quantum
number. For example, the energy of a 3d state is greater than a 3p, which is larger than 3s.
Finally, there may be overlap in energy of a state in one shell with states in an adjacent shell,
which is especially true of d and f states; for example, the energy of a 3d state is greater than
that for a 4s.
(a)The first three electron energy states for the Bohr hydrogen atom. (b) Electron energy states for the first three
shells of the wavemechanical hydrogen atom.
Comparison of the (a) Bohr and (b) wavemechanical atom models in terms of electron distribution.
5. State the Pauli exclusion principle.
Pauli exclusion principle stipulates that each electron state can hold no more than two
electrons, which must have opposite spins. Thus, s, p, d, and f subshells may each
accommodate, respectively, a total of 2, 6, 10, and 14 electrons.
Of course, not all possible states in an atom are filled with electrons. For most atoms,
the electrons fill up the lowest possible energy states in the electron shells and subshells, two
electrons (having opposite spins) per state. The energy structure for a sodium atom is
represented schematically in Figure. When all the electrons occupy the lowest possible
energies in accord with the foregoing restrictions, an atom is said to be in its ground state.
However, electron transitions to higher energy states are possible. The electron
configuration or structure of an atom represents the manner in which these states are
occupied. In the conventional notation the number of electrons in each subshell is indicated
by a superscript after the shell–subshell designation. For example, the electron configurations
for hydrogen, helium, and sodium are, respectively, 1s1, 1s2, and 1s22s22p63s1. Electron
configurations for some of the more common elements are listed in Table.
Schematic representation of the filled energy states for a sodium atom.
At this point, comments regarding these electron configurations are necessary. First,
the valence electrons are those that occupy the outermost filled shell. These electrons are
extremely important; as will be seen, they participate in the bonding between atoms to form
atomic and molecular aggregates. Furthermore, many of the physical and chemical properties
of solids are based on these valence electrons.
In addition, some atoms have what are termed ‘‘stable electron configurations’’; that
is, the states within the outermost or valence electron shell are completely filled. Normally
this corresponds to the occupation of just the s and p states for the outermost shell by a total
of eight electrons, as in neon, argon, and krypton; one exception is helium, which contains
only two 1s electrons. These elements (Ne, Ar, Kr, and He) are the inert, or noble, gases,
which are virtually unreactive chemically. Some atoms of the elements that have unfilled
valence shells assume stable electron configurations by gaining or losing electrons to form
charged ions, or by sharing electrons with other atoms. This is the basis for some chemical
reactions, and also for atomic bonding in solids.
Under special circumstances, the s and p orbitals combine to form hybrid spn orbitals,
where n indicates the number of p orbitals involved, which may have a value of 1, 2, or 3.
The 3A, 4A, and 5A group elements of the periodic table are those which most often form
these hybrids. The driving force for the formation of hybrid orbitals is a lower energy state
for the valence electrons. For carbon the sp3 hybrid is of primary importance in organic and
polymer chemistries.
A Listing of the Expected Electron Configurations for Some of the Common Elements
UNIT II
Crystal Structure : Introduction – Crystal Structure – Space Lattice – Unit Cell – Crystal
Systems – Atomic Packing – Coordination Number – Crystal Symmetry – Atomic Radius –
Atomic Packing factor.
Section – A
1. What is Bravais lattice?
If all the atoms at the lattice points are identical, the lattice is said to be Bravais
lattice.
2. Define Unit Cell
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 cells, i.e. in every crystal some
fundamental grouping of particles is repeated.
3. Define Bravias lattice
The totality of lattice points forms a crystal lattice or space lattice. If all the atoms,
molecules or ions at the lattice points are identical, the lattice is called a Bravias lattice.
Section – B
1. Describe APF and Coordination Number
Not all metals have unit cells with cubic symmetry; the final common metallic crystal
structure to be discussed has a unit cell that is hexagonal. Figure shows a reduced-sphere unit
cell for this structure, which is termed hexagonal close-packed (HCP); an assemblage of
several HCP unit cells is presented in Figure. The top and bottom faces of the unit cell consist
of six atoms that form regular hexagons and surround a single atom in the center. Another
plane that provides three additional atoms to the unit cell is situated between the top and
bottom planes. The atoms in this midplane have as nearest neighbors atoms in both of the
adjacent two planes. The equivalent of six atoms is contained in each unit cell; one-sixth of
each of the 12 top and bottom face corner atoms, one-half of each of the 2 center face atoms,
and all the 3 midplane interior atoms. If a and c represent, respectively,
For the hexagonal close-packed crystal structure, (a) a reduced-sphere unit cell (a and c represent the short and
long edge lengths, respectively), and (b) an aggregate of many atoms. (Figure (b)
the short and long unit cell dimensions of Figure, the c/a ratio should be 1.633; however, for
some HCP metals this ratio deviates from the ideal value.
The coordination number and the atomic packing factor for the HCP crystal structure
are the same as for FCC: 12 and 0.74, respectively.
2. What is unit cell? Add a note on it.
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 cells, i.e. in every crystal some
fundamental grouping of particles is repeated. Obviously, a unit cell is the smallest
component of the space lattice. The unit cell is the basic structural unit or building block of
the crystal structure by virtue of its geometry and atomic positions within. We must
remember that space lattices of various substances differ in the size and shape of their unit
cells. Figure shows a unit cell of a three-dimensional crystal lattice. The distance from one
atom to another atom measured along one of the axis is called the space constant. The unit
cell is formed by primitives or intercepts a, b and c along X, Y and Z axes respectively.
A unit cell can be completely described by the three vectors a, b, and c (OP, OQ and
OR) when the length of the vectors and the angles between them (α, β, γ) are specified. The
three angles α, β and γ are called interfacial angles. Taking any lattice point as the origin, all
other points on the lattice, can be obtained by a repeated of the lattice vectors a, b and c.
These lattice vectors and interfacial angles constitute the lattice parameter of a unit cell.
Obviously, if the values of these intercepts and interfacial angles are known, one can easily
determine the form and actual size of the unit cell.
Section – C
1. Explain the concepts of lattice, basis and crystal structure. How are they related?
Crystals are solids which have a regular periodic arrangement in their component
parties, bounded by flat faces, orderly arranged in reference to one another, which converge
at the edges and vertices. A crystal is symmetrical about its certain elements like points, lines
or planes and if it rotated about these elements, it is not possible to distinguish its new
position from the original position. This symmetry is an important characteristic based on
internal structure of crystal. Symmetry helps one to classify crystals and describing their
behavior. At temperatures below that of crystallization, the crystalline state is stable for all
solids.
Space Lattice
The atomic arrangement in crystal is called the crystal structure. In perfect crystal,
there is a regular arrangement of atoms. In a model of a crystal, ions, atoms or molecules that
constitute its tructure can be imagined to be spheres which touch one another and are
arranged regularly in different directions. In a simple model of crystal structure, spheres are
replaced by points representing the centres of ions, atoms or molecules. The periodicity in the
arrangement of ions, atoms or molecules generally varies in different directions. It is very
convenient to imagine points in space about which these atoms, ions or molecules are located.
Such points in space are called lattice points. The totality of lattice points forms a crystal
lattice or space lattice. If all the atoms, molecules or ions at the lattice points are identical,
the lattice is called a Bravias lattice. The space lattice of a crystal is described by means of a
three-dimensional co-ordinate system in which the coordinate axis coincide with any three
edges of the crystal that intersect at one point and do not lie in a single plane. Obviously, the
three-dimensional space-lattice may be defined as a finite array of points in three dimensions
in which every point has identical environment as any other point in the array. The space
lattice is very useful as a reference in correlating the symmetry of actual crystals. A space
lattice provides the framework with reference to which a crystal structure can be described. It
is essential to distinguish a lattice from a crystal structure; a crystal structure is formed by
associating with every lattice point an assembly of atoms identical in composition,
arrangement, and orientation. The space-lattice concept was introduced by R.J. Hauy as an
explanation for the special geometric properties of crystal polyhedrons. It was postulated that
an elementary unit, having all the properties of the crystal, should exist, or conversely that a
crystal was built up by the juxaposition of such elementary units. If the mathematical points
forming the vertices of a parallelopiped OABC (defined by three vectors OA, OB and OC)
are considered (Fig. 3.3), a space lattice is obtained by translations parallel to and equal to
OA, OB and OC. The parallelopiped is called the unit cell.
In metals, we frequently encountered with the complex lattices-comprise of several
primitive translation lattices displaced in relation to each other. Most of metallic crystals have
highly symmetrical structures with closed packed atoms. The most common types of space
lattices are: Body centred cubic (BCC) lattices, Face centred cubic (FCC) lattices and
Hexagonal closed packed (HCP) lattices.
Unit Cell
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 cells, i.e. in every crystal some
fundamental grouping of particles is repeated. Obviously, a unit cell is the smallest
component of the space lattice. The unit cell is the basic structural unit or building block of
the crystal structure by virtue of its geometry and atomic positions within. We must
remember that space lattices of various substances differ in the size and shape of their unit
cells. Figure shows a unit cell of a three-dimensional crystal lattice. The distance from one
atom to another atom measured along one of the axis is called the space constant. The unit
cell is formed by primitives or intercepts a, b and c along X, Y and Z axes respectively.
A unit cell can be completely described by the three vectors a, b, and c (OP, OQ and
OR) when the length of the vectors and the angles between them (α, β, γ) are specified. The
three angles α, β and γ are called interfacial angles. Taking any lattice point as the origin, all
other points on the lattice, can be obtained by a repeated of the lattice vectors a, b and c.
These lattice vectors and interfacial angles constitute the lattice parameter of a unit cell.
Obviously, if the values of these intercepts and interfacial angles are known, one can easily
determine the form and actual size of the unit cell.
2. What is Bravais lattice? What is the maximum number of Bravais lattices possible?
How will you account for the existence of thousands of structures from these lattices?
If all the atoms at the lattice points are identical, the lattice is said to be Bravais
lattice. There are four systems and five possible Bravais lattices in two dimensions (Fig.).
The four crystal systems of two dimensional space are oblique, rectangular, square and
hexagonal. The rectangular crystal system has two Bravais lattices, namely, rectangular
primitive and rectangular centered. In all, there are five Bravais lattices which are listed in
Table along with the corresponding point groups.
Based on pure symmetry considerations, there are only fourteen independent ways of
arranging points in three-dimensional space, such that each arrangement is in accordance or
in confirmation with the definition of a space lattice. These 14 space lattices with 32 point
groups and 230 space groups are called Bravais lattices (Fig.). If considered as solids, the
combination of symmetry elements they exhibit can be determined. Each space lattice can be
defined by reference to a unit cell which, when repeated in space an infinite number of times,
will generate the entire space lattice. To describe basic crystal structures, the 14 types of unit
cells are grouped in seven different classes of crystal lattices, i.e. to describe basic crystal
structures, seven different co-ordinate systems of reference axes are required (Fig.).
Every type of unit cell is characterized by the number of lattice points (not the atoms)
in it. For example, the number of lattice points per unit cell for simple cubic (SC), body
centered cubic (BCC) and face centered cubic (FCC) lattices are 1, 2 and 4, respectively. We
must note that our knowledge about unit cell may not be complete without having a
quantitative estimate of its volume. This can be calculated with the help of the relation
UNIT III
Bonds in Solids : Introduction – Types of bond – Mechanism of Bond Formation – Ionic
Bond – Covalent Bond – Metallic Bond – Comparison of bonds – Secondary Bonds – Mixed
Bonds – Chemical Bonding and Properties of Solid Materials.
Section – A
1. Ionic bond
An ionic bond is a type of chemical bond formed through an electrostatic attraction
between two oppositely charged ions. Ionic bonds are formed between a cation, which is
usually a metal, and an anion, which is usually a nonmetal.
2. What is covalent bond?
A covalent bond is a form of chemical bonding that is characterized by the sharing of
pairs of electrons between atoms. The stable balance of attractive and repulsive forces
between atoms when they share electrons is known as covalent bonding
3. Define metallic bond
Metallic bonding is the electrostatic attractive forces between the delocalized
electrons, called conduction electrons, gathered in an "electron sea", and the positively
charged metal ions.
Section – B
1. Discuss about preliminary information on bonds in solids
In nature one comes across several types of solids. Many solids are aggregates of
atoms. The arrangement of atoms in any solid material is determined by the character,
strength and directionality of the chemical binding forces, cohesive forces or chemical bonds.
We call these binding forces as atomic interaction forces. The atoms, molecules or ions in a
solid state are more closely packed than in the gaseous and liquid states and are held together
by strong mutual forces of attraction and repulsion. One can describe the atomic arrangement
in elements and compounds on the basis of this. The type of bond that appears between atoms
in crystal is determined by the electronic structure of interacting atoms. Atoms in a crystal
approach one another to certain distances at which the crystal is in the state of the highest
thermodynamic stability. These distances depend on the interaction forces that appear in
crystals. The attractive forces between atoms are basically electrostatic in origin. Its
magnitude is proportional to some power of the interatomic distance r. The different types of
bonding depends on the electronic structure of the atoms concerned and hence directly related
to the periodic table. The type of bonding within a material plays a major role in determining
the electrical, chemical and physical properties of the material. The repulsive forces which
come into existence when the distance between the atoms is decreased to such an extent that
they are very close to one another and increase more intensively than attractive forces do. The
repulsion between positively charged nuclei also contributes to the repulsive forces. The
magnitude of the total repulsive force is also proportional to some power of r. A state of
equilibrium is reached when these attractive and repulsive forces balance and this happens
when two atoms or molecules are at an equilibrium distance r0.
2. Explain the properties of solid material
3. Compare between bonds
Section – C
1. What are the types of bonds? Add a note on it
Seitz in 1940 classified solids into five types according to the bonding of atoms, which has
become a generally adapted classification
The atoms of different types come closer and join together during chemical reaction and
usually these bonds are referred to as chemical bonds. There are basically two groups which
classify common bonds on the basis of strength, directionality of bonding forces, cohesive
forces (chemical bonds) and the character of any solid material: These are
(i) Primary Bonds: These are inter-atomic bonds in which electrostatic force holds the atoms
together. Relatively large atomic forces develop in these bonds, making them more stable and
imparting high strength. They have bond strength varying from 1-1.5 eV. these bonds are also
known as attractive bonds. The inter-atomic distance is usually 1-2r. Following three types of
primary bonds are found in different materials
(i) Ionic or electrostatic bonds
(ii) Covalent, atomic or homopolar bonds
(iii) Metallic bonds
(ii) Secondary Bonds: A secondary bond is an intermolecular bond and weaker and less
stable than primary bond. In this type of bonds, the forces hold the molecules together. These
secondary bonds result from intermolecular or dipole attractions. Asymmetrical electron
distribution in molecules and atoms creates dipoles. Due to dipoles the molecules are
attracted towards other molecules having opposite dipoles. Similar asymmetric electron
distribution in atoms causes dipole to exist in them. We must note that the atomic dipolar
bonds are weaker than molecular dipole bonds and moreover atomic dipolar bonds keep on
fluctuating as electron distribution in atomic outer shells keeps changing. Common examples
of secondary bonds are Vander Waals bonds and hydrogen bonds.
UNIT IV
Semiconducting materials: Introduction - Types of Semiconductors on the basis of Fermi
level and Fermi Energy – Transistor – Piezoelectricity and Ferroelectricity.
Section – A
1. Define semiconductors
Semiconductors
are
defined
by their
unique
electric
conductive behavior. Metals are good conductors because at their Fermi level, there is a large
density of energetically available states that each electron can occupy. Electrons can move
quite freely between energy levels without a high energy cost. Metal conductivity decreases
with temperature increase because thermal vibrations of crystal lattice disrupt the free motion
of electrons. Insulators, by contrast, are very poor conductors of electricity because there is a
large difference in energies (called a band gap) between electron-occupied energy levels and
empty energy levels that allow for electron motion.
2. What is Fermi energy?
The Fermi energy is a concept in quantum mechanics usually
referring to the energy of the highest occupied quantum state in a system of fermions at
absolute zero temperature.
3. Define Ferroelectricity
Ferroelectricity is a property of certain materials which possess a spontaneous
electric polarization that can be reversed by the application of an external electric field. The
term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic
moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in
Rochelle salt by Valasek. Thus, the prefix ferro, meaning iron, was used to describe the
property despite the fact that most ferroelectric materials do not contain iron.
Section – B
1. Explain briefly about Fermi level semiconductors
The Fermi level plays an important role in describing the behavior of doped
semiconductors. A substance’s Fermi level is defined as the highest occupied energy level
found in that substance at absolute zero temperature (0 kelvins or -273 °C). At higher
temperatures, energy from heat is available to promote electrons into slightly higher energy
levels. However, picturing density of states to be filled to the Fermi level helps scientists
understand different behaviors between insulators, metals, and intrinsic and extrinsic
semiconductors. As seen in figure one, the Fermi level of n-type semiconductors is elevated
from that of the corresponding un-doped intrinsic semiconductor. This makes the conduction
band much more thermally accessible at temperatures above absolute zero.
2. What are the applications of ferroelectricity
The nonlinear nature of ferroelectric materials can be used to make capacitors with
tunable capacitance. Typically, a ferroelectric capacitor simply consists of a pair of electrodes
sandwiching a layer of ferroelectric material. The permittivity of ferroelectrics is not only
tunable but commonly also very high in absolute value, especially when close to the phase
transition temperature. Because of this, ferroelectric capacitors are small in physical size
compared to dielectric (non-tunable) capacitors of similar capacitance.
The spontaneous polarization of ferroelectric materials implies a hysteresis effect
which can be used as a memory function, and ferroelectric capacitors are indeed used to make
ferroelectric RAM for computers and RFID cards. In these applications thin films of
ferroelectric materials are typically used, as this allows the field required to switch the
polarization to be achieved with a moderate voltage. However, when using thin films a great
deal of attention needs to be paid to the interfaces, electrodes and sample quality for devices
to work reliably.
Ferroelectric materials are required by symmetry considerations to be also
piezoelectric and pyroelectric. The combined properties of memory, piezoelectricity, and
pyroelectricity make ferroelectric capacitors very useful, e.g. for sensor applications.
Ferroelectric capacitors are used in medical ultrasound machines (the capacitors generate and
then listen for the ultrasound ping used to image the internal organs of a body), high quality
infrared cameras (the infrared image is projected onto a two dimensional array of
ferroelectric capacitors capable of detecting temperature differences as small as millionths of
a degree Celsius), fire sensors, sonar, vibration sensors, and even fuel injectors on diesel
engines.
Another idea of recent interest is the ferroelectric tunnel junction (FTJ) in which a
contact made up by nanometer-thick ferroelectric film placed between metal electrodes. The
thickness of the ferroelectric layer is small enough to allow tunneling of electrons. The
piezoelectric and interface effects as well as the depolarization field may lead to a giant
electroresistance (GER) switching effect.
3. Write about Piezoelectricity
Piezoelectricity is the charge which accumulates in certain solid materials (notably
crystals, certain ceramics, and biological matter such as bone, DNA and various proteins) in
response to applied mechanical stress. The word piezoelectricity means electricity resulting
from pressure. It is derived from the Greek piezo or piezein, which means to squeeze or press,
and electric or electron, which stands for amber, an ancient source of electric charge.
Piezoelectricity is the direct result of the piezoelectric effect.
The piezoelectric effect is understood as the linear electromechanical interaction
between the mechanical and the electrical state in crystalline materials with no inversion
symmetry. The piezoelectric effect is a reversible process in that materials exhibiting the
direct piezoelectric effect (the internal generation of electrical charge resulting from an
applied mechanical force) also exhibit the reverse piezoelectric effect (the internal generation
of a mechanical strain resulting from an applied electrical field). For example, lead zirconate
titanate crystals will generate measurable piezoelectricity when their static structure is
deformed by about 0.1% of the original dimension. Conversely, those same crystals will
change about 0.1% of their static dimension when an external electric field is applied to the
material.
Piezoelectricity is found in useful applications such as the production and detection of
sound, generation of high voltages, electronic frequency generation, microbalances, and
ultrafine focusing of optical assemblies. It is also the basis of a number of scientific
instrumental techniques with atomic resolution, the scanning probe microscopies such as
STM, AFM, MTA, SNOM, etc., and everyday uses such as acting as the ignition source for
cigarette lighters and push-start propane barbecues.
Section – C
1. Discuss in detail about the Fermi energy
The Fermi energy is the maximum energy occupied by an electron at 0K. By the Pauli
exclusion principle, we know that the electrons will fill all available energy levels, and the
top of that "Fermi sea" of electrons is called the Fermi energy or Fermi level. The conduction
electron population for a metal is calculated by multiplying the density of conduction electron
states r(E) times the Fermi function f(E). The number of conduction electrons per unit
volume per unit energy is
The total population of conduction electrons per unit volume can be obtained by integrating
this expression
At 0K the top of the electron energy distribution is defined as EF so the integral becomes
This expresses the conduction electron density n in terms of the Fermi energy E F. We can
also turn this around and express the Fermi energy in terms of the free electron density.
2. Describe the types of semiconductors
Fermi level" is the term used to describe the top of the collection of electron energy
levels at absolute zero temperature. This concept comes from Fermi-Dirac statistics.
Electrons are fermions and by the Pauli exclusion principle cannot exist in identical energy
states. So at absolute zero they pack into the lowest available energy states and build up a
"Fermi sea" of electron energy states. The Fermi level is the surface of that sea at absolute
zero where no electrons will have enough energy to rise above the surface. The concept of the
Fermi energy is a crucially important concept for the understanding of the electrical and
thermal properties of solids. Both ordinary electrical and thermal processes involve energies
of a small fraction of an electron volt.
At higher temperatures a certain fraction, characterized by the Fermi function, will
exist above the Fermi level. The Fermi level plays an important role in the band theory of
solids. In doped semiconductors, p-type and n-type, the Fermi level is shifted by the
impurities, illustrated by their band gaps.
A P-type semiconductor (P for Positive) is obtained by carrying out a process of
doping: that is, adding a certain type of atoms to the semiconductor in order to increase the
number of free charge carriers (in this case positive holes).
When the doping material is added, it takes away (accepts) weakly bound outer
electrons from the semiconductor atoms. This type of doping agent is also known as an
acceptor material and the vacancy left behind by the electron is known as a hole.
The purpose of P-type doping is to create an abundance of holes. In the case of
silicon, a trivalent atom (typically from Group 13 of the periodic table, such as boron or
aluminium) is substituted into the crystal lattice. The result is that one electron is missing
from one of the four covalent bonds normal for the silicon lattice. Thus the dopant atom can
accept an electron from a neighboring atom's covalent bond to complete the fourth bond. This
is why such dopants are called acceptors. The dopant atom accepts an electron, causing the
loss of half of one bond from the neighboring atom and resulting in the formation of a "hole".
Each hole is associated with a nearby negatively charged dopant ion, and the semiconductor
remains electrically neutral as a whole. However, once each hole has wandered away into the
lattice, one proton in the atom at the hole's location will be "exposed" and no longer cancelled
by an electron when you have 3 electrons and 1 hole surrounding a particular nucleus with 4
protons. For this reason a hole behaves as a quantity of positive charge. When a sufficiently
large number of acceptor atoms are added, the holes greatly outnumber the thermally excited
electrons. Thus, the holes are the majority carriers, while electrons are the minority carriers
in P-type materials. Blue diamonds (Type IIb), which contain boron (B) impurities, are an
example of a naturally occurring P-type semiconductor.
Therefore, to a first approximation, sufficiently doped P-type semiconductors can be
thought of as only conducting holes.
Neither pure silicon (Si) nor germanium (Ge) are great conductors. They form a
crystal lattice by having each atom share all of its 4 valence electrons with neighbouring
atoms. The total of eight electrons cannot easily be jiggled out of place by an incoming
current.
If, however, the crystalline array is “doped”(mixed with an impurity) with arsenic
which has five valence electrons, the behavior of the lattice will change. Four bonds will be
still be made but there will be a leftover electron that can wander through the crystal. This is
called an n-type semiconductor.
Boron can also be used to dope a pure crystal of silicon. But since boron only offers 3 of the
four electrons that a silicon atom needs, each silicon center is left with a hole. Semiconductors
made in this manner are called p-type.
In a p-type material if an atom from a neighbouring atom fills the hole, it will leave a
hole adjacent to it. This process will continue in a domino effect and the hole will be moving
in the direction opposite to electron-flow. In reality the atoms are remaining fixed in the
lattice, but there is an illusion that the holes are physically moving.
3. What are the applications of Piezoelectricity
High voltage and power sources
Direct piezoelectricity of some substances like quartz, as mentioned above, can generate
potential differences of thousands of volts.

The best-known application is the electric cigarette lighter: pressing the button causes
a spring-loaded hammer to hit a piezoelectric crystal, producing a sufficiently high
voltage electric current that flows across a small spark gap, thus heating and igniting
the gas. The portable sparkers used to light gas grills or stoves work the same way,
and many types of gas burners now have built-in piezo-based ignition systems.

A similar idea is being researched by DARPA in the United States in a project called
Energy Harvesting, which includes an attempt to power battlefield equipment by
piezoelectric generators embedded in soldiers' boots. However, these energy
harvesting sources by association have an impact on the body. DARPA's effort to
harness 1-2 watts from continuous shoe impact while walking were abandoned due to
the impracticality and the discomfort from the additional energy expended by a person
wearing the shoes. Other energy harvesting ideas include harvesting the energy from
human movements in train stations or other public places and converting a dance floor
to generate electricity. Vibrations from industrial machinery can also be harvested by
piezoeletric materials to charge batteries for backup supplies or to power low power
microprocessors and wireless radios. A piezoelectric transformer is a type of AC
voltage multiplier. Unlike a conventional transformer, which uses magnetic coupling
between input and output, the piezoelectric transformer uses acoustic coupling. An
input voltage is applied across a short length of a bar of piezoceramic material such as
PZT, creating an alternating stress in the bar by the inverse piezoelectric effect and
causing the whole bar to vibrate. The vibration frequency is chosen to be the resonant
frequency of the block, typically in the 100 kilohertz to 1 megahertz range. A higher
output voltage is then generated across another section of the bar by the piezoelectric
effect. Step-up ratios of more than 1000:1 have been demonstrated. An extra feature
of this transformer is that, by operating it above its resonant frequency, it can be made
to appear as an inductive load, which is useful in circuits that require a controlled soft
start. These devices can be used in DC-AC inverters to drive cold cathode fluorescent
lamps. Piezo transformers are some of the most compact high voltage sources.
Sensors

Piezoelectric elements are also used in the detection and generation of sonar waves.

Power monitoring in high power applications (e.g. medical treatment, sonochemistry
and industrial processing).

Piezoelectric microbalances are used as very sensitive chemical and biological
sensors.

Piezos are sometimes used in strain gauges.

Piezoelectric transducers are used in electronic drum pads to detect the impact of the
drummer's sticks.

Automotive engine management systems use piezoelectric transducers to detect
detonation by sampling the vibrations of the engine block and also to detect the
precise moment of fuel injection (needle lift sensors).

Ultrasonic piezo sensors are used in the detection of acoustic emissions in acoustic
emission testing.

Crystal earpieces are sometimes used in old or low power radios
UNIT V
Organic Materials : Introduction – Polymers – Mechanism of Polymerization – Additions in
Polymers – Polymer Structure – Plastics – Elastomers and Rubbers – Fibers and Filaments –
Composite Materials – Single Crystals – Accommodated Structures – protective Coatings
Section – A
1. What is a polymer?
Polymer is a large molecule (macromolecule) composed of repeating structural units.
These subunits are typically connected by covalent chemical bonds.
2. What are meant by the terms saturated and unsaturated in relation to polymers?
Organic molecules that have double and triple bonds are termed unsaturated, i.e., in
these compounds, each carbon atom is not bonded to the maximum (four other atoms; as
such, it is possible for another atom or group of atoms to become attached to the orginal
molecule. On the otherhand, for a saturated hydrocarbon, all bonds are single ones; (and
saturated), i.e., no new atoms may be joined without the removal of others that are already
bonded.
3. Elastomers
Materials have properties similar to polymers. These materials may be repeated
stretched or elongated and will return to their original condition upon release of the force
producing the elongation. They, exhibit elastic behaviour, as compared to polymers, which
exhibit greater plastic properties. Included in this category are rubber and rubber like
materials. A distinction is made between rubber and elastomers. Rubber must withstand a
200% elongation and rapidly return to its original dimensions. This property of a material to
recover from elastic deformation is termed as resilience.
Section – B
1. Write the Mechanism of Polymerization
(i) Elastic Deformation Mechanism: The elastic deformation depends upon the
amount of bond-straightening) and bond lengthening. The mechanism of elastic deformation
in semicrystalline polymers in response to tensile stresses is the elongation of the chain
molecules from their stable conformations, in the direction of the applied stress, by the
bending and stretching of the strong chain covalent bonds. There may also be some slight
displacement of adjacent molecules, which is resisted by relatively weak secondary or
Vander Waals bonds. Semicrystalline materials may be considered as composite materials
since they are composed of both crystalline and amorphous regions. Obviously, one may take
elastic modulus as some combination of the moduli of crystalline and amorphous phases.
(ii) Plastic Deformation Mechanism: Plastic deformation occurs due to slip between
adjacent molecules of polymer material. Since the molecules are bonded by weak attractive
forces and hence the slip occurs very easily. Plastic deformation is more prominent where
alignment of molecules is linear. Plastic deformation occurs due to the slippage at the weaker
points between the molecules and not due to the breaking of intermolecular bonds. The linear
polymers with crosslinking show high degree of plastic deformation, whereas network
polymers do not show high deformation and they are thus brittle. The mechanism of plastic
deformation can be best described by the interactions between lamellar and intervening
amorphous regions in response to an applied tensile load. This process occurs in several
stages.
2. Describe about addition in polymers
An addition polymer is a polymer which is formed by an addition reaction, where
many monomers bond together via rearrangement of bonds without the loss of any atom or
molecule. This is in contrast to a condensation polymer which is formed by a condensation
reaction where a molecule, usually water, is lost during the formation.
With exception of combustion, the backbone of addition polymers are generally
chemically inert. This is due to the very strong C-C and C-H bonds and lack of polarisation
within many addition polymers. For this reason they are non-biodegradable and hard to
recycle. This is, again, in contrast to condensation polymers which are bio-degradable and
can be recycled.
Many exceptions to this rule are products of ring-opening polymerization, which
tends to produce condensation-like polymers even though it is an additive process. For
example, poly[ethylene oxide] is chemically identical to polyethylene glycol except that it is
formed by opening ethylene oxide rings rather than eliminating water from ethylene glycol.
Nylon 6 was developed to thwart the patent on nylon 6, 6, and while it does have a slightly
different structure, its mechanical properties are remarkably similar to its condensation
counterpart.
One universal distinction between polymerization types is development of molecular
weight by the different modes of propagation. Addition polymers form high molecular weight
chains rapidly, with much monomer remaining. Since addition polymerization has rapidly
growing chains and free monomer as its reactants, and condensation polymerization occurs in
step-wise fashion between monomers, dimers, and other smaller growing chains, the effect of
a polymer molecule's current size on a continuing reaction is profoundly different in these
two cases. This has important effects on the distribution of molecular weights, or
polydispersity, in the finished polymer.
3. Discuss about plastic in polymer
These polymers often exhibit plastic, ductile properties. They can be formed at
elevated temperatures, cooled and remelted and reformed into different shapes without
changing the properties of polymer. However, the heat used to melt and remelt the
thermoplastic must be carefully controlled or material will decompose. Most linear polymers
and those having some branched structures with flexible chains are thermoplastic. These
materials are normally fabricated by the simultaneous application of heat and pressure. The
properties of these materials are determined by the bonding method between polymer chains;
in thermoplastic materials these bonds are weak, secondary bonds, as in Vander Waals forces.
Through the application of heat and pressure, these bonds can be weakened, and the materials
can be reshaped. Once the heat and pressure are removed, thermoplastic materials reharden in
the new shape. Common thermoplastic polymers include acrylic, nylon (polyamide),
cellulose, polystyrene, polyethylene, fluorocarbons, and vinyl. These are used for plastic
walls and floor tiles, flouroscent light, plastic lenses, etc.
Section – C
1. Give the characteristic features of some plastic materials
2. Give some important characteristic and application of elastomers
3. Write about fibers and filaments
Fibers consist of long molecular chains and all the chains are aligned in the direction
of length of the fibre. The directional properties are improved by alignment, i.e. the strength
of fibres are greatly enhanced in the direction parallel to the fibre length. These provide
strength to the molecular units. The fibre polymers are quite capable of being drawn into long
filaments having at least a 100 : 1 length to diameter ratio. Some polymers used as fibres,
such as nylon and cellulose acetate, serve equally well as plastics. Most commercial fibre
polymers are utilized in the textile industry, being woven or knit into cloth or fabric. In
addition, the aramid fibres are widely employed in composite materials. A fibre polymer, to
be used as a textile material must have some restrictive physical and chemical properties.
Fibres, while is use may be subjected to a variety of mechanical deformations, e.g. stretching,
twisting, shearing and abrasion. Obviously, they must have a high tensile strength over a
relatively wide temperature range and a high modulus of elasticity and also abrasion
resistances. We may note that these properties are governed by the chemistry of polymer
chains and also by fibre drawing process. Fibres materials should have relatively high
molecular weight. The structure and configuration of the chains should allow the production
of a highly crystalline polymer as the tensile strength increases with degree of crystallinity.
This translates into a requirement for linear and unbranched chains that are symmetrical and
have regularly repeating mer units. Synthetic fibres are produced by the following methods:
(i) Melt spinning (ii) Dry spinning and wet spinning. To improve fibres properties, i.e., to
increase/decrease resistance, water or fire proofs, etc., chemical treatment is done. The choice
of method mainly depends upon the properties of polymers, i.e., heat stability, melting point
and solubility in suitable solvents. The thermal properties of fibre polymers are important
from the point of view of washing and maintainin clothes. These properties include melting
and glass transition temperatures. Also, fibre polymers must show chemical stability to a
rather extensive variety of enviornments, including acids, bases, dry cleaning solvents,
bleaches, and sunlight. Moreover, they must be relatively non flammable and amenable to
drying.
Metallic and ceramic fibres have also similar qualities as that of polymeric fibres.
However, metallic and ceramic fibres have very high strength and therefore they have many
industrial applications. There are also natural fibres, e.g. cotton, silk, wool, cellulose, etc.
Cellulose fibres are flexible and are strong in tension. Cotton is produced naturally as a plant
fibre. However, the synthetic fibres are cheap, durable and have more dimensional stability
and that is why they have almost replaced the natural fibres.