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Module 1 Structure of Materials
Subject: Material Science and Engineering Subject Code: BME303
Syllabus
Structure of Materials Introduction: Classification of materials, crystalline and non-
crystalline solids, atomic bonding: Ionic Bonding and Metallic bonding.
Crystal Structure: Crystal Lattice, Unit Cell, Planes and directions in a lattice, Planar Atomic
Density, Coordination number, atomic Packing Factor of all the Cubic structures and Hexa
Close Packed structure. Classification and Coordination of voids, Bragg’s Law.
Imperfections in Solids: Types of imperfections, Point defects: vacancies, interstitials, line
defects, 2-D and 3D-defects, Concept of free volume in amorphous solids. Slip, Twinning.
Disclaimer: The study material is not for circulation. The contents here are from the text book
authored by William Callister, a popular author on the subject of material science. The contents
are purely for educational purpose and no commercial benefits shall be accrued from this by
anyone. The publisher does not take any responsibility for any legal action or otherwise. The
contents may be from other sources as well.
Introduction:
When we say ‘materials’ we think of nearly all materials known to science and in all states
of matter like solid, liquid & gaseous.
But material science concern itself basically with the nature & behaviour of only solid
materials.
‘Solid engineering materials’ are those which helps engineers to build machines, structures,
automobiles, and air craft.
Classifications of engineering materials:
(i) Metals & alloys: Ex: cast iron, steels, aluminium, copper, silver, gold, brass &
bronge
(ii) Ceramics & glasses : Ex: MgO, ZnO, SiC, concrete & cement
(iii) Polymers: plastics, polyethylene, PVC, nylon, cotton & rubber
(iv) Composites: metal-matrix composites
Each of above group of materials has their own set of properties. Some of the most
engineering materials as follow:
✓ Mechanical: strength, hardness, ductility, malleability, toughness, resilience &
fatigue
✓ Physical: shape, size, density, porosity & colour
✓ Chemical: acidity, alkalinity, composition, corrosion resistance, atomic number &
molecular weight
✓ Electrical: conductivity, resistivity, dielectric constant, dielectric strength & power
factor
✓ Thermal: Specific heat, refractoriness & conductivity
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✓ Aesthetic: feel, texture, appearance, lustre
The above properties of the materials which guide us in the selection of the materials for
specific operations. Ex: (i) an aircraft structure has to be built with materials having low
density but high strength, (ii) a steel melting furnace has to be lined with refractory
materials to with stand high temperature, (III) buildings & structures have to be built with
materials having high compressive strength to with stand heavy loads.
Crystalline and non-crystalline solids:
1. Crystalline solids,
2. Non- Crystalline solids
Non- Crystalline solids/
Crystalline solids amorphous solids
1. The basic structural unit is a The basic structural unit is a molecule &
crystal [a slid whose constituent chains of these molecule come together to
molecules or atoms are arranged in form an amorphous solids
a systematic geometric pattern.
2. Each crystal [also called as a The chains of molecules are random
grain] is made up of a number of within the solid & occur in no particular
respective blocks called unit cells[ relation to each other. They are irregular
the smallest group of atoms & lack symmetry
possessing the symmetry of the
crystal] which are arranged neatly
in relation to each other
3. Compare crystalline solid with a In this, crowd where people are random &
military parade where all soldiers not arranged in order with respect to each
are arranged in order with respect other.
to each other.
4. A crystalline solid therefore is In this it is made up of millions of
made up of millions of unit cells molecules disorderly arranged
orderly arranged. Each unit cell is
itself made up of atoms & the
number of atoms depends on the
type of unit cell.
5. Metals, alloys, some salts like Glass, polymers, rubber & plastics
NaCl, KCl, many oxides &
ceramics, non metals like
diamond, Gem stones
6. Density of crystalline solids is Generally low because molecules cannot
generally high. They have higher be compacted. They have lower melting
melting point & strength point & strength
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7. Structures are stable & materials Structures are unstable & materials are
are stronger less stronger
Aggregates: some materials are obtained both in crystal as well as amorphous. Ex: silicate can
occur as crystalline solid [quartz] or a Non- Crystalline solids/ amorphous solids [silicate
glass]. Aggregates type of materials which have short range order but no long-range order. Ex:
concrete, rocks & minerals.
Atomic bonding
In a substance atom of interact with each by forming bonds to create molecules and
macroscopic materials. There are three basic ways that the outer electrons of atoms can form
bonds:
Ionic bond -Electrons can be transferred from one atom to another
Covalent bond Electrons can be shared between neighbouring atoms
metallic bond-Electrons can be shared with all atoms in a material
Secondary Bonding
Ionic bond: Ionic bonding forms between two oppositely-charged ions which are produced by
the transfer of electrons from one atom to another. Electropositive elements such as the alkali
metals have small ionization potentials. Electronegative elements such as halogens have large
electron affinities. Hence ionic bonds form most readily between electropositive and
electronegative elements.
Ex: Consider as an example an atom of sodium, which has one electron in its outermost orbit,
coming near an atom of chlorine, which has seven. Because it takes eight electrons to fill the
outermost shell of these atoms, the chlorine atom can be thought of as missing one electron.
The sodium atom donates its single valence electron to fill the hole in the chlorine shell,
forming a sodium chloride system at a lower total energy level.
The ionic bond is nondirectional because the electron transfer results in the inert gas
configuration around both the nuclei and has spherical symmetry of the electron probability
cloud. Therefore, the bonding force between the ions is the same in all directions.
Metallic bond: In metallic bonding the sharing of electrons between neighbouring atoms
now becomes delocalised as there are not enough electrons to produce the inert
gas configuration around each atom. The metallic sharing changes with time and
the bonding electrons resonate between different atoms. The metallic state can
be visualized as an array of positive ions, with a common pool of electrons to
which all the metal atoms have contributed their outer electrons. This common
pool is called the free electron cloud or the free electron gas. These electrons
have freedom to move anywhere within the crystal and act like an all-pervasive,
mobile glue holding the ion cores together. The electron freedom in metallic bonding makes
the metallic bonds nondirectional.
Ex: Cu, Ag etc.
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Crystal Structure
Refers to the manner in which atoms, ions, or molecules are spatially arranged
Space lattice is defined as an infinite array of points in three dimensions in which every point
has surroundings identical to that of every other point in the array
Unit cell: it is the smallest repeatable unit of a crystalline solid. In other words every unit cell
is a crystalline solid consists of a group of atoms arranged in a definite order.
Crystal Lattice: crystal lattice is the symmetrical three-dimensional structural arrangements
of atoms, ions or molecules (constituent particle) inside a crystalline solid as points.
Planes and directions in a lattice:
Crystal directions are obtained using the system devised by Miller. Consider the figure below
the vector r, passing through the origin o to a lattice point, can be expressed in terms of the
fundamental translation vectors a, b and c, which form the crystal axes, as r = rla + r2b + r3c.
where r1, r2 and r3 are integers. The c-axis is not shown in the figure as r is assumed to lie on
the ab plane. The components of r along the three axes are: r1 = 2, r2 = 3 and r3 = 0. Then the
crystal direction denoted by r is written as [230] in the Miller notation, with square brackets
enclosing the indices.
Figure: The Miller indices of the crystal direction denoted by vector r are [230]
If there is a negative component along a crystal axis such as –2, it is written as 2 and read as
bar 2. A family of directions is obtained by all possible combinations of the indices, both
positive and negative. The family [230], [203], [203], [302], [320], etc., is represented by
<230>, where the angular brackets < > denote the entire family.
The crystal directions [230], [460] and [1 1½ 0] all have the same direction, but different
magnitudes. Since Miller indices for directions are usually specified as the smallest possible
integers, the differences in magnitude for the above three directions are indicated using the
following convention: [230], 2[230] and 1/2[230]
The Miller indices of a crystal plane are determined as follows. Referring to the plane shown:
Module 1 Structure of Materials
Subject: Material Science and Engineering Subject Code: BME303
Syllabus
Structure of Materials Introduction: Classification of materials, crystalline and non-
crystalline solids, atomic bonding: Ionic Bonding and Metallic bonding.
Crystal Structure: Crystal Lattice, Unit Cell, Planes and directions in a lattice, Planar Atomic
Density, Coordination number, atomic Packing Factor of all the Cubic structures and Hexa
Close Packed structure. Classification and Coordination of voids, Bragg’s Law.
Imperfections in Solids: Types of imperfections, Point defects: vacancies, interstitials, line
defects, 2-D and 3D-defects, Concept of free volume in amorphous solids. Slip, Twinning.
Disclaimer: The study material is not for circulation. The contents here are from the text book
authored by William Callister, a popular author on the subject of material science. The contents
are purely for educational purpose and no commercial benefits shall be accrued from this by
anyone. The publisher does not take any responsibility for any legal action or otherwise. The
contents may be from other sources as well.
Introduction:
When we say ‘materials’ we think of nearly all materials known to science and in all states
of matter like solid, liquid & gaseous.
But material science concern itself basically with the nature & behaviour of only solid
materials.
‘Solid engineering materials’ are those which helps engineers to build machines, structures,
automobiles, and air craft.
Classifications of engineering materials:
(i) Metals & alloys: Ex: cast iron, steels, aluminium, copper, silver, gold, brass &
bronge
(ii) Ceramics & glasses : Ex: MgO, ZnO, SiC, concrete & cement
(iii) Polymers: plastics, polyethylene, PVC, nylon, cotton & rubber
(iv) Composites: metal-matrix composites
Each of above group of materials has their own set of properties. Some of the most
engineering materials as follow:
✓ Mechanical: strength, hardness, ductility, malleability, toughness, resilience &
fatigue
✓ Physical: shape, size, density, porosity & colour
✓ Chemical: acidity, alkalinity, composition, corrosion resistance, atomic number &
molecular weight
✓ Electrical: conductivity, resistivity, dielectric constant, dielectric strength & power
factor
✓ Thermal: Specific heat, refractoriness & conductivity
, Downloaded From easenotes.com
✓ Aesthetic: feel, texture, appearance, lustre
The above properties of the materials which guide us in the selection of the materials for
specific operations. Ex: (i) an aircraft structure has to be built with materials having low
density but high strength, (ii) a steel melting furnace has to be lined with refractory
materials to with stand high temperature, (III) buildings & structures have to be built with
materials having high compressive strength to with stand heavy loads.
Crystalline and non-crystalline solids:
1. Crystalline solids,
2. Non- Crystalline solids
Non- Crystalline solids/
Crystalline solids amorphous solids
1. The basic structural unit is a The basic structural unit is a molecule &
crystal [a slid whose constituent chains of these molecule come together to
molecules or atoms are arranged in form an amorphous solids
a systematic geometric pattern.
2. Each crystal [also called as a The chains of molecules are random
grain] is made up of a number of within the solid & occur in no particular
respective blocks called unit cells[ relation to each other. They are irregular
the smallest group of atoms & lack symmetry
possessing the symmetry of the
crystal] which are arranged neatly
in relation to each other
3. Compare crystalline solid with a In this, crowd where people are random &
military parade where all soldiers not arranged in order with respect to each
are arranged in order with respect other.
to each other.
4. A crystalline solid therefore is In this it is made up of millions of
made up of millions of unit cells molecules disorderly arranged
orderly arranged. Each unit cell is
itself made up of atoms & the
number of atoms depends on the
type of unit cell.
5. Metals, alloys, some salts like Glass, polymers, rubber & plastics
NaCl, KCl, many oxides &
ceramics, non metals like
diamond, Gem stones
6. Density of crystalline solids is Generally low because molecules cannot
generally high. They have higher be compacted. They have lower melting
melting point & strength point & strength
, Downloaded From easenotes.com
7. Structures are stable & materials Structures are unstable & materials are
are stronger less stronger
Aggregates: some materials are obtained both in crystal as well as amorphous. Ex: silicate can
occur as crystalline solid [quartz] or a Non- Crystalline solids/ amorphous solids [silicate
glass]. Aggregates type of materials which have short range order but no long-range order. Ex:
concrete, rocks & minerals.
Atomic bonding
In a substance atom of interact with each by forming bonds to create molecules and
macroscopic materials. There are three basic ways that the outer electrons of atoms can form
bonds:
Ionic bond -Electrons can be transferred from one atom to another
Covalent bond Electrons can be shared between neighbouring atoms
metallic bond-Electrons can be shared with all atoms in a material
Secondary Bonding
Ionic bond: Ionic bonding forms between two oppositely-charged ions which are produced by
the transfer of electrons from one atom to another. Electropositive elements such as the alkali
metals have small ionization potentials. Electronegative elements such as halogens have large
electron affinities. Hence ionic bonds form most readily between electropositive and
electronegative elements.
Ex: Consider as an example an atom of sodium, which has one electron in its outermost orbit,
coming near an atom of chlorine, which has seven. Because it takes eight electrons to fill the
outermost shell of these atoms, the chlorine atom can be thought of as missing one electron.
The sodium atom donates its single valence electron to fill the hole in the chlorine shell,
forming a sodium chloride system at a lower total energy level.
The ionic bond is nondirectional because the electron transfer results in the inert gas
configuration around both the nuclei and has spherical symmetry of the electron probability
cloud. Therefore, the bonding force between the ions is the same in all directions.
Metallic bond: In metallic bonding the sharing of electrons between neighbouring atoms
now becomes delocalised as there are not enough electrons to produce the inert
gas configuration around each atom. The metallic sharing changes with time and
the bonding electrons resonate between different atoms. The metallic state can
be visualized as an array of positive ions, with a common pool of electrons to
which all the metal atoms have contributed their outer electrons. This common
pool is called the free electron cloud or the free electron gas. These electrons
have freedom to move anywhere within the crystal and act like an all-pervasive,
mobile glue holding the ion cores together. The electron freedom in metallic bonding makes
the metallic bonds nondirectional.
Ex: Cu, Ag etc.
, Downloaded From easenotes.com
Crystal Structure
Refers to the manner in which atoms, ions, or molecules are spatially arranged
Space lattice is defined as an infinite array of points in three dimensions in which every point
has surroundings identical to that of every other point in the array
Unit cell: it is the smallest repeatable unit of a crystalline solid. In other words every unit cell
is a crystalline solid consists of a group of atoms arranged in a definite order.
Crystal Lattice: crystal lattice is the symmetrical three-dimensional structural arrangements
of atoms, ions or molecules (constituent particle) inside a crystalline solid as points.
Planes and directions in a lattice:
Crystal directions are obtained using the system devised by Miller. Consider the figure below
the vector r, passing through the origin o to a lattice point, can be expressed in terms of the
fundamental translation vectors a, b and c, which form the crystal axes, as r = rla + r2b + r3c.
where r1, r2 and r3 are integers. The c-axis is not shown in the figure as r is assumed to lie on
the ab plane. The components of r along the three axes are: r1 = 2, r2 = 3 and r3 = 0. Then the
crystal direction denoted by r is written as [230] in the Miller notation, with square brackets
enclosing the indices.
Figure: The Miller indices of the crystal direction denoted by vector r are [230]
If there is a negative component along a crystal axis such as –2, it is written as 2 and read as
bar 2. A family of directions is obtained by all possible combinations of the indices, both
positive and negative. The family [230], [203], [203], [302], [320], etc., is represented by
<230>, where the angular brackets < > denote the entire family.
The crystal directions [230], [460] and [1 1½ 0] all have the same direction, but different
magnitudes. Since Miller indices for directions are usually specified as the smallest possible
integers, the differences in magnitude for the above three directions are indicated using the
following convention: [230], 2[230] and 1/2[230]
The Miller indices of a crystal plane are determined as follows. Referring to the plane shown:
