Materials Science : Objectives · Materials are available in Solid, Liquid and Gaseous state, but,...

Class Notes of Materials Science # Unit – 1 # 1

Materials Science : The science which deals with natural and man made (synthetic) materials so as to know their properties, constitutional details and behaviour to make the best use for the products of engineering technologies, is known as materials science.

Materials are available in Solid, Liquid and Gaseous state, but, the study of materials in materials science is restricted to the solid materials and for those who are having application in engineering.

Objectives : ♦ To know the properties and behaviour of materials under various conditions during its use

♦ To know the best possible availability of materials depending upon the practical use for a product or system

♦ To know about the physics and chemistry of materials

♦ To know the best suited materials for operations, for fabrication, for life, for stability and economic use

Areas : The various areas of materials selection and uses are as :

♦ Machines : IC Engines, Lathe Machine, Robots etc

♦ Structures : Bridges, Transformer, Trusses

♦ Devices : Integrated Circuits, Control Switches

♦ Instruments : Thermocouples, Pressure Gauges

Present Era of Materials : Following are the some example where materials selection and use emphasis a lot and is a key requirement for the functioning of product. Some of the examples are as :

♦ Materials for Aerospace Uses like Aircrafts, Aero-plane, Rockets etc. (Light in Weight, High Strength)

♦ Materials Marine uses as Ships (least corrosion, High strength, Light weight)

♦ Materials for Tanks, Gun etc

♦ Materials for Metallurgical areas, Ceramics, Polymers, Semiconductors etc

♦ Materials for Manufacturing Technologies, Cutting Tools and High strength Products

Brijesh Singh, Mech. Engg. Department KKAANNPPUURR IINNSSTTIITTUUTTEE OOFF TTEECCHHNNOOLLOOGGYY, Kanpur – 208 007 (UP) INDIA


Classification of Materials : Materials are classified according to the followings :

a. Based on Materials

b. Materials based on the engineering disciplines

c. New or Latest Materials

a. Materials :

1. Metals :

i. Ferrous Metals

ii. Non-Ferrous Metals

2. Non-Metals :

i. Ceramics

ii. Organic Polymers

3. Materials due to combination :

i. Alloys

♦ Ferrous Alloys

♦ Non-ferrous Alloys

ii. Composites

♦ Whisker Reinforced Plastics

♦ Metal reinforced metal

♦ Metal ceramics

♦ Carbon reinforced rubber

♦ Ceramic Polymer

♦ Polymer Cement Concrete

b. Materials based on engineering discipline :

♦ Civil Engg Materials : RCC

♦ Electrical Engg Materials : Mica as an insulator

♦ Mechanical Engg Materials : Metals

♦ Electronics Engg Materials : Semi-conductors

♦ Nuclear Engg Materials : Uranium

♦ Marine Engg Materials



c. New or Latest Materials :

Those materials, which are capable of decision-making or provide one type of signal when some other type of signal is given, are known as smart or intelligent materials.

Example : Quartz ; When an emf is applied on it, it generated mechanical pulse or vibrations and when mechanical force or pulse is applied on it, it generates a signal of an emf. Thus, this can be used for decision making even in robot grippers.

The new or latest materials are as :

♦ Composites ♦ Ferrites ♦ Garnets

♦ Whiskers ♦ Ceramics ♦ Cermets

♦ Super-conductors ♦ Ruby Laser ♦ Super-Alloys etc.

Selection of Materials : Following are the salient features and properties owing to which selection of material for a product is dependent :

♦ Availability of Material

♦ Fabrication Ease

♦ Service Condition

♦ Operational Needs

♦ Process Control

♦ Economy

♦ Durability and Dependability

♦ Dimensional Stability

♦ Resistance to adverse condition like corrosion, Cavitations, Moisture, Radiation, Chemical, Wear and Tear and Flame etc.

♦ Elasticity and Plasticity, depending upon service requirement

♦ Strength values and Impact Strength

Levels of Material Structure : The structure of materials can be classified as :

♦ Crystalline : Metals

♦ Semi-crystalline : HDPE (High Density Poly ethylene)

♦ Non-crystalline : Plastics, Ceramics, Rubbers, LDPE (also known as amorphous)



Based on the observation made by human being or not, materials structures are broadly classified as :

♦ Macro Structure : observed by naked human eyes, 0.1 mm resolution

♦ Micro-Structure : Can be observed with the help of some instrument or external aids

Micro-structure : Order of 10-4 to 10-6 m : Crystal

i. Sub-structure : order of 10-6 to 10-8 m , Observation Level - Crystal

ii. Crystal Structure : order of 10-8 to 10-10 m , Ob. Level - Unit Cell

iii. Electron Structure : order of 10-6 to 10-8 m , Ob. Level – electron of outer shell

iv. Nuclear Structure : order of < 10-10 m , Ob. Level – Proton and Neutron

Smart Materials or Intelligent Materials : The materials, which can sense, process, stimulate and actuate a response, are known as smart materials. Their functioning is analogous to human brain, slow and fast muscles action or living organisms.

The intelligent materials comprises three basic components :

♦ Sensor : for signal input : Piezoelectric polymers, optical fibers

♦ Processors : for processing/analyzing :Micro-chips

♦ Actuators : for actual functioning / output : Shape memory alloys, Polypyrrole

These materials have ability to change their inherent properties with surrounding condition. They may change their dimensions with respect to environmental radiations, stress, temperature, pressure, voltage etc.

Example :

♦ Piezoelectric Ceramics : generates emf from mechanical pulse or vise-versa, Quartz

♦ Visco-elastic (VE) : Damping in space-crafts, earthquake prone structures

♦ Shape Memory Alloys (SMA) : Change in dim (plastic deformation) after transition temperature and used in Fire alarm



Crystallography : The study of geometry and structure of solids is known as crystallography. The solids are of :

♦ Crystalline Solids

♦ Non-crystalline or amorphous solids

The solids, which possess regular and periodically repeated arrangement of atoms, the solids are termed as crystalline solids. The solids in which there is no regular arrangement of atoms are known as amorphous solids.

Factors for formation of non-crystalline solids : Periodically repeated and regular arrangement of atoms get distorted owing to following reasons :

♦ Larger free energy

♦ Fast rate of cooling

♦ Absence of primary bonds in all directions

♦ Weak secondary bonding

♦ Open network of atomic packing

♦ Non-parallel, entangled chain configuration

♦ Formation 1D chain molecules or 2D sheet molecules

Mono-crystalline solids are those solids, which are having single crystal for its use or smallest part, while polycrystalline solids are those, which are having more than one crystal for its use or smallest part.

Space Lattice or Bravais Lattice : An infinite array of points in 3 Dimensional space in which each point has identical surroundings is known as space lattice or Bravais Lattice.

Unit Cell : The smallest cell or portion of points or atoms or molecules which when repeated infinitely, generates the space lattice. Mono-atomic unit cell contains one atom (one molecule that comprises one atom) at its each point. Diatomic unit cell contains two atoms (one molecule that comprises two atoms) at its each point. Poly-atomic or multi-atomic unit cell are those which contains more than two atoms (one molecule that comprises more than two atoms) at each point.



Crystal : When many unit cells are repeated in a definite order in 3 dimensional space, a crystal is generated. It is the smallest ordered portion of material, which may be in use.

Crystals may be mono-atomic (that contains one atom at each lattice point), diatomic (that contains two atom at each lattice point) and poly-atomic (that contains more than two atom at each lattice point). Diatomic and poly-atomic crystals are known as molecular crystals.

Basis : Replacing of points in space lattice by atoms or molecules is known as basis.

Space lattice + Basis (replacing all points by atoms or molecules) = Unit Cell

Bravais Crystal System and Space Lattices : To represent a unit cell in 3 dimensional space, three linear vectors are required along all three Cartesian coordinate axes ie x-axis, y-axis, and z-axis. These are a, b, c. along which these tree linear vector, three angular position with respect to these axes are also required. These areα, β, γ. Thus total required parameters are a, b, c (three linear vectors) and α, β, γ (three angles).

Based one the symmetry of possible geometries of unit cell and 3 dimensional space, there for 14 types of Bravais Lattices or Space Lattices which are grouped under 7 crystal systems. These are as :

C T O R H M T

3 2 4 1 1 2 1 (except in Monoclinic – Simple and End Centered) Crystal Systems :

1. Simple : That contains atoms at all lattice points (corners)

2. Body Centered : That contains eight atoms at all corners (at all eight points) and one atom at the center of body (cutting point of both body diagonals)

3. Face Centered : That contains eight atoms at all corners (at all eight points) and one atom at the center of each face (cutting point of diagonal of each face, at all six faces)

4. End Centered : That contains eight atoms at all corners (at all eight points) and one atom at the center of opposite face (cutting point of face diagonal, at only three, alternate)

Other than these, there are two types other structures as HCP and DC.

Hexagonal Closed Pack (HCP) :

HCP is more denser than the hexagonal one as HCP unit cell shares 17 number of atoms. There are 12 atoms at all angular points of two faces of hexagonal (top and bottom). One atom is at the center of these top and bottom face. Three atoms are present at the center of alternate vertical planes. Effective number of atoms for HCP is 6 and coordination number is 12. Its APF is 0.74.



Diamond Cubic Structure (DC) :

Carbon exists in two hybrid covalent bonding forms as sp2 and sp3 . Diamond has sp3 hybrid covalent bond. Each of its atom has four bonds and are directional in nature. This primary bonding is extended to 3 Dimensional network. The bond angle is 109.50. It is the known hardest solid. Effective numbers of atoms in the unit cell of DC are 8 and has APF of 0.34.

DC structure shares 18 atoms in its unit cell. 8 atoms are present at all eight corners of a cube. One atoms is present at the center of each face. Two atoms are present at 1/4th distance from the base and two are present at 3/4th distance from base along the body diagonal, all of them are inside the unit cell.

Graphite Structure :

Graphite is the another form of carbon that has sp2 hybrid cov1lent bonding. It has hexagonal honey bee type of sheet structure. In a plane, unit cell comprises primary bonding along the sheet while atomic planes are bonded by secondary bonding like Ver dar Waals type (along its thickness). Bond angle is 1200. It has directional property and is used as solid lubricant. Graphite fibers are used to make fibrous composites and also used as moderator in nuclear reactors. Graphite is very useful to use at high temperature and pressure because of its low coefficient of friction. It can be converted into synthetic diamond at 16000C by the application of pressure of about 50,000 to 60,000 atmospheric.

Most symmetric crystal system : Cubic

Most un-symmetric crystal system : Triclinic

Details of crystal system :

S. No.

Name of Crystal System

Linear Vectors Angles Space Lattices Examples

1 Cubic a = b = c α = β = γ = 900 SC, BCC, FCC

2 Tetragonal a = b c α = β = γ = 900 ST, BCT

3 Orthorhombic a b c α = β = γ = 900 SO, BCO, FCO, ECO

4 Rhombohedral a = b = c α = β = γ 900 SR

5 Hexagonal a = b c α = β = 900, γ = 1200 SH

6 Monoclinic a b c α = β = 900, γ SM, ECM

= = =

=

7 Triclinic a b c α β γ 900 Simple Triclinic

= = =

= =

= = = =



Primitive Unit Cells : Primitive unit cells are those unit cells, which contains atoms or molecules at the corners of lattice only. Thus, all simple types of space lattices are primitive unit cells. The unit cells which contains atoms or molecules at all corner points and at center of body or face, are not primitive cells are known as non-primitive cells.

Coordination Number : It is the number of nearest and equidistant atoms in a unit cell. For this, it is assumed that atoms are of spherical shape and are in contact (or touch each other, whenever possible).

Coordination number for SC is 6, BCC is 8 and for FCC, it is 12. for dense liquids, it is nearly 10.

Voids : The space, which remains empty when atoms are in contact, is known as voids. There are two types of voids as Tetrahedral and Octahedral.

When three atoms in a plane is covered by a single atom on their top (in middle of these three atoms), then the formed void is termed as Tetrahedral void.

When 3 atoms are present in a plane and this atomic plane is covered by another plane of three atoms such that their centers are not matching, then the formed void is known as octahedral void. The space available in octahedral voids is more with respect to tetrahedral voids.

The max permissible size for an atom to fit in tetrahedral void without distortion is 0.0225 r where r is the radius of parent atom. The example is availability of alloying elements in alloys.

The max permissible size for an atom to fit in octahedral void without distortion is 0.414 r where r is the radius of parent atom. The example is Iron in which Carbon takes position in octahedral voids in its FCC form.

Relation between atomic radius and Lattice constant : For SC, FCC and BCC # Consult class

Effective Number of Atoms : It is different from total number of atoms in the unit cell. Total number of atoms are the number of total atoms which are available in unit cell or are the part of unit cell whether fully or partially.

Effective Number of atoms are those atoms which are dedicated to the unit cell or possessed by the unit cell. These are : For SC – 1, For BCC – 2, For FCC – 4.



Atomic Packing Fraction or Efficiency : It is the ratio of total volume of atoms (occupied by atoms) to the volume of the unit cell. It represents that how much volume of total unit cell is occupied by the atoms. It is also termed as Atomic Packing Efficiency (APF or APE).

APF = v / V

For such calculations, atom is assumed to be a sphere and is in touch or contact.

APF for SC, BCC and FCC : discussed in detail in Class

Density : The density of a material is defined as the ratio of mass of the unit cell to the volume of the unit cell.

Where : A . N ρ : Density of material ρ =

w e

Aw : Atomic Weight or Molecular Weight

Ne : Number of effective atoms in the unit cell

NA : Avogadro’s Number

a3 : Volume of unit cell (cubic)

NA. a3



Miller Indices : Miller is the name of scientist and indices is the plural of Index. It is the system to designate or to represent the crystal plane and direction.

Miller Indices are the smallest integer number that represents the plane and its direction in a unit cell or crystal. It comprises three numeric values as h, k, l (name of variables). The representation is as :

( h k l ) : to represent a plane

{ h k l } : to represent the family of the plane

[ h k l ] : to represent the direction

< h k l > : to represent family of directions

When h, k, l values are of single digit, they are not separated by commas, but, if, these are of two or more digits, then comma is used to separate the h, k, l values with in the brackets.

Procedure to find the Miller Indices of a Plane : ♦ Choose an origin and designate x, y and z axes in the unit cell.

♦ Find the intercepts on these three linear axes. Say these are c1, c2 and c3 along x axis, y-axis and z-axis respectively.

♦ Represent them in terms of axial units ie represent them with respect to linear dimensions of the unit cell (a, b, c) as:

C1 = p.a C2 = q.b C3 = r.c

Or p = c1 / a q = c2 / b r = c3 / c

Where p, q, r the intercepts on x, y, z axes respectively.

♦ Take the reciprocal of these intercepts as

h = 1 / p k = 1 / q l = 1 / r

♦ Represent them in order within the brackets as ( h k l ) and convert them into smallest integer part by taking common outside the bracket (or multiplying by LCM)

♦ Neglect the common factor, which is outside the bracket and represent these smallest integer values that are inside the bracket as ( h k l )

Important Points :

♦ For negative planes, bar is used as 1 or ( h k l ), in which h value is negative.

♦ Parallel planes intercepts at infinity. Thus, value of intercept will be infinity and reciprocal of infinity is zero. So, Miller Indices for parallel plane will be zero.



Family of Planes : It is represented by { h k l }. It comprises the members as (h k l) in all possible orders, both negative and positive. For example {hkl} will have planes as (hkl), (klh), (khl) and other three negative planes.

To draw a plane whose Miller Indices are Given : ♦ The given values are ( h k l ). These are the miller indices with respect to x, y, z axes

respectively.

♦ Take reciprocal of these Miller Indices and the value will be of Intercepts along x, y and z axes respectively. As :

p = 1 / h q = 1 / k r = 1 / l

♦ Convert them with respect to linear vectors or linear dimensions of unit cell i.e. with respect to a, b, c along x, y and z axes respectively.

♦ Choosing origin, mark the intercepts and join them to draw the plane.

Crystal Directions : Miller Indices are also used to represent the directions with in a unit cell or crystal. These are designated by [ h k l ]. The family of directions contains all possible orders or h k l values including negative and positive directions. The family of directions is represented by < h k l >.

For Parallel : Miller Indices = 0

For Negative directions : Use bar

Salient Points of Miller Indices : ♦ Miller Indices of parallel planes are same.

♦ For parallel planes, Miller Indices value will be zero as they intercepts at infinity and reciprocal of infinity is zero.

♦ The plane passing through origin will have non-zero miller indices.

♦ Any two planes will be perpendicular if : h1 . h2 + k1 . k2 + l1 . l2 = 0

♦ When Miller Indices contains more than single digits, they can be separated by commas or spaces.

♦ All members of a family of planes may not be parallel to each other.



Inter-planer Distance : The distance between a plane ( h k l ) and the other parallel plane passing through origin is called inter-planer spacing or inter-planer distance.

Mathematically : d{hkl} =

h2 + k2 + l2

a For Cubic Unit Cell

d{hkl} = (a2 / c2) h2 + k2 + l2

a For Tetrahedral Unit Cell

Linear Density (ρL): The ratio of number of effective atoms (NeL) per unit cell length on certain length (L) along any direction to the length of unit cell in that direction (ie L) in a unit cell or crystal is called Linear Density (ρL). Mathematically,

ρL = NeL / L

For example, in FCC, Plane [110] direction :

NeL = (1/2) + 1 + (1/2) = 2 and L = (a2 + a2)1/2

Thus, ρL = 2 / { (a) . 21/2 } = 21/2 / a ρL = 21/2 / a

Planer Density (ρP) : The ratio of atoms per unit area of crystal plane is called planer density. It express the packing of atoms on a plane. Mathematically,

ρL = Ne / A where : Ne is the number of effective number of atoms on a plane

: A is the area of that plane

Crystal Structure Determination Techniques :

♦ Bragg’s Law Refer old notes ♦ Powder Method

Calculation of Planer Density for various planes in SC, FCC and BCC Unit cells :

refer class discussion



Crystal Imperfections : The crystal which are having periodically repeated arrangement of atoms (regular) in the space lattice is known as ideal or perfect crystal.

But, due to some natural processes or owing to intentional mixing, the regular arrangement of atoms gets deviated from its ideal nature. Such crystals do not possess regular arrangement of atoms, which are periodically repeated in the space lattice, are known as real crystals or imperfect crystal.

Intentional : Doping to make materials for transistors, ICs in electronics applications, Alloy

Formation like mixing of Carbon in the matrix of Iron to form steels, cast irons etc.

Natural : presence of any foreign material (based on dimensions) during cooling,

solidification, manufacturing processes

Imperfections in Crystalline Solids :

The deviation of real crystal from its ideal one is termed at defect or imperfection. Imperfections can be classified according to the dimension occupied at atomic level by the impurity material or alloying material. These are :

♦ Point Imperfections : Zero Dimensional

♦ Line Imperfections : One Dimensional

♦ Surface Imperfections : Two Dimensional

♦ Volume Imperfections : Three Dimensional

Based on the dimension of defect, these may be :

♦ Nano Level Imperfections : order of 10-9 m

♦ Angstrom Level Imperfections : order of 10-10 m

♦ Micro Level Imperfections : order of 10-6 m

Point Imperfections : These are zero dimensional defects and imperfect or defected regions are like a point in the crystal. These defects are of one or two atomic diameters only. The various types of point imperfections are :

♦ Vacancy Defects

♦ Interstitial Defects

♦ Substitutional defects

♦ Frenkel’s Defect

♦ Schottky’s Defect



Missing atom Vacancy Imperfections :

Real Arrangement of Crystal

Ideal Arrangement of Crystal

In such defect, atom from its regular position

is missing and creates a vacant site. Atomic

bonding forces at this location are not continuous.

Vacant places are of one two atomic diameters

And does not obey any rule or regular arrangement.

Foreign atom


Interstitial Defect :


The small sized foreign atoms

(size difference < 15%) occupies a void space

in the parent crystal. Such defect is called

interstitial defect.

Substitutional Defect : Foreign atom


When foreign atom is of larger size ie


(size difference > 15%) is present in the

matrix of parent atom, it may acquire the

place of regular atom by replacing it.

Such defect is known as Substitutional defect.

Movement of cation


AnionsCations


Frenkel’s Defect :

The defect in which an ion displaces from

its regular position to interstitial location in

an ionic solid is called Frenkel’s Defect.

Cations are of smaller size with respect to

Anions , Thus cations may move from its

regular position to any interstitial location,

causing Frenkel’s defect. Overall electrical neutrality is being maintained. It occurs only in Ionic solids.



One pair of Anion & Cation is missing


Anions

Cations


Schottky’s Defect :

the defect, in which one pair of anion and

cation is absent from its regular arrangement

in an ionic crystal, is called Schottky’s Defect.

Overall electrical neutrality is being maintained

and such defect occurs in Ionic solids.

Effect of Point Imperfections :

♦ In case of vacancy, there is absence of bonding forces with neighbouring atoms.

♦ In case of Substitutional impurity, an elastic strain is being developed in surrounding regions due to size difference of foreign atom. If foreign atom is of larger size with respect to parent atom, then compressive shear stress and strains will be developed. If foreign atom is of smaller size with respect to parent atom, then tensile shear stress and strains will be developed.

♦ An interstitial atom creates strain around its surroundings.

♦ Presence of point imperfection causes lowering of total energy of crystal that affect the stability of crystal.

♦ Point imperfections are thermodynamically stable.

Causes of Point Imperfections or its Origin :

♦ Mechanical Deformations : Casting, Rolling, Forging etc

♦ Thermal Shocks : Quenching

♦ Thermal Fluctuations : Heating and Cooling during operations

♦ High Energy Particles Bombardment : displacement of atomic electrons with bombardment

particles of X-ray

To create a point imperfection, some work is required to be done. This work is known as Enthalpy or Potential Energy of Formation and is abbreviated as Hf.

The equilibrium concentration of vacancies in a crystal will be :

n = NA . e-Hf / RT where, n : No. of vacancies per mole of crystal NA : Avogadro No.

R : Gas Constant T : Absolute Temperature

At absolute zero temperature, number of vacancies formation will be zero.



Line Imperfections : These are known as Dislocations. There are two types of dislocations as :

♦ Edge Dislocation

♦ Screw Dislocation

Edge Dislocation :

The distortion caused because of any

incomplete atomic plane, in the regular

arrangement of atoms, is known as

Edge Dislocation

In perfect crystal, atoms are in equilibrium

Position. Just above the incomplete plane,

atoms are squeezed together and are in state of compression. The bond length is smaller than the equilibrium value. But. Below this edge, atoms are pulled apart and are in tensile state. The bond length is more than the normal value.

The potential energy increase for both condition, either increase in bond length or decrease in bond length. Thus, there is extra stain energy owing to incomplete plane.

The direction and magnitude is represented by Burger’s Vector.

To know the direction and magnitude of Burger’s

Vector, take a closed path by mving in +Y direction

from any atom to some atoms (say b) , then

move in +X direction by some no. of atoms (say a).


Distorted Region because of incomplete atomic plane


E S Then move in –Y direction by respective same

no. of atoms as b and then in –X direction by

respective same no. of atoms ie a. if path Burger’s Vectorbecomes complete and comes at starting point, then there is no incomplete plane. If, end point is apart from starting point, then there is incomplete plane.

Magnitude of Burger’s Vector will be equal to the magnitude of atomic distance, which is required to come from end point to starting point. Also, the same will be the direction of vector as of closing vector.

Here, a = b = 4 atomic distances, Berger Vector is Perpendicular to edge dislocation.

+ Edge Dislocation : Negative Edge Dislocation



Screw Dislocation :

Screw dislocation is formed when a part of crystal displaces angularly over the remaining part. Thus, the plane of atoms converted into helical surfaces or a screw.

Angular Displacement

Symbolically they are represented by

Burger’s Vector is parallel to screw dislocation

or

+ ve (CW) and -ve (CCW)

Mixed Dislocation :

When a crystal has edge dislocation as well as screw dislocation, then the imperfection is said to be mixed dislocation. In such case an extra or incomplete plane of atoms accompanies with angular shift of a part of real crystal. These are generally emerged with curved boundaries.

Characteristics of Dislocations :

♦ A crystal incorporates large number of dislocations and thus there exist numerous Burger’s Vectors. They meet at a point and this point is called nodal point. Sum of all Burger’s vector inside a crystal remain zero.

♦ Dislocations vanishes at nodal points only (not ends abruptly)

♦ Owing to dislocations, strain energy is developed inside the crystal and is the part of crystal instability.

♦ Dislocations have inherent tendency to keep smallest possible Burger’s Vector.

♦ Edge dislocations travel much faster ( about 50 times) than screw dislocation.

♦ Two edge dislocations of opposite nature (sigh) of equal Burger’s vector and on the same slip plane cancel-out.



Other terms related to Dislocations :

Glide Motion of Dislocation :

A edge dislocation can move along slip plane from its intermediate position to the surface under the influence of externally applied shear stress. Such movement is called Glide Motion and the plave of motion is called Glide Plane. A screw dislocation can not have glide motion.

τ

Incomplete Plane

τ

Incomplete Plane

τ

Incomplete Plane

τ

Incomplete Plane

τ

Incomplete Plane

Edge Dislocation Edge Dislocation Edge Dislocation Edge Dislocation Edge Dislocation : Disappears

Dislocation Climb :

The plane perpendicular to glide plane is called climb plane. When edge dislocation moves above or down to the slip plane in perpendiculat (+Y or –Y Direction), then the motion of edge dislocation is called Climb Motion. The Climb motion in +Y direction is called “Climb Up” and in “–Y” direction, the climb motion is called “Climb –Down”. Dislocation Climb is a diffusion-controlled process. Screw Dislocation can not Climb up or climb down. It creates vacancy in crystals. Climb motion is slower process than the glide motion.

Cross Slip :

Under the influence of Shear Stress, Screw dislocation can chage its slip plane while in motion owing to any obstruction. Such motion is known as Cross-Slip. An edge or mixed dislocation can not have cross-slip motion. The cross slip in FCC crystals are close packed {111}.

Jogs in Dislocation :

A dislocation of Burger’s Vector “b” lying in a plane other than the slip plane or glide plane is called Jogs. The Burger Vector should be equal to the Burger Vector of a dislocation lying in a slip plane. Thus, dislocation can jump from one plane to another and Jogs are treated as Shorter Dislocation. (Here slip plane get changed along with motion of edge dislocation, means both, together jumps from one location to another location of crystal)



Salient Features of Dislocations :

♦ Dislocations are not thermodynamically stable.

♦ Presence of dislocations, lowers the energy of the crystal.

♦ Vacancy diffusion helps in dislocation climb.

♦ Interstitial atoms may fir into larger spaced regions of edge dislocation. (C in BCC crystal of Iron).

Sources of Dislocations :

♦ Mishandling during grain growth (crystals are formed by the process of crystallization)

♦ Mechanical Deformation

Affects of Dislocation :

♦ Lowers the mechanical strength.

♦ Uneconomical machine structures more material is required for same strength)

♦ Reduces electrical conduction

♦ Adversely affect surface-sensitive properties

Remedies :

♦ Controlled process of Solidification (Nucleus formation during solidification, Grain Growth and Recovery) and Re-crystallization etc)

♦ Use of thermal energies

♦ Prevention of undesirable mechanical deformations

Surface Imperfections : These are observed on the surface of crystals and are two dimensional in nature. Due to finite size of crystal, bonds are broken on the surface as no neighbouring atoms are present for bonding. During solidification, solidifications starts from more than one locations and all such crystals may have different atomic arrangement. Interaction of such crystals may provide imperfection on mating areas or surface. Various types of surface imperfections are as :

♦ Grain Boundaries

♦ Twining or Twin Boundaries

♦ Low angle Tilt Boundaries

♦ High Angle Boundaries

♦ Twist Boundaries

♦ Stacking Fault



Grain Boundaries :

During the solidifications and re-crystallization process,

initially there is formation of tiny particles as nucleus

and then solidification grows from these points which

is known as gain growth. In poly-crystalline materials,

atoms solidification starts from more than one point and

neighbouring atoms acquire the structure of this crystals

and in total there are more than one nucleus. Their

orientation is somewhat different from each other.

The boundary atoms acquired compromising position.

Finally, there is boundary formation at the surface crystals.

Such boundary is termed as Grain Boundary.

The angle between the boundaries is termed as Grain Boundary Angle.

θ is the angle of Grain Boundary

A

D C

B

Crystal Boundaries : Grain Boundaries

Twin Boundaries or Twining :

Twin boundaries occur in pair. The arrangement

of atoms is such that atomic arrangement on

one side of boundary is mirror image of second

side atomic arrangement. Such defect is known

as Twin Boundary or Twining or Twin. The zone

ABCD is known as Twinned Zone. Twins can be

visualized by optical microscope. Annealing twins are those, which are formed by annealing process. Deformation Twins are those twins, which are formed by the process of mechanical deformation.

Low Angle Tilt Boundaries :

Poly-crystalline materials possess the angular orientation at their boundaries. If this angle of orientation or of grain boundaries is less than 100, then the formed grain boundaries are termed as low angle Tilt boundaries.

High Angle Tilt Boundaries :

Poly-crystalline materials possess the angular orientation at their boundaries. If this angle of orientation or of grain boundaries is more than 100, then the formed grain boundaries are termed as low angle Tilt boundaries.



Stacking Fault :

Say, there are three layers of atomic planes in regular order to form a crystal. The sequence is as ABC ABC ABC ABC ….

Due to any reason, if any intermediate atomic plane is missing from its regular sequence, and is as :

ABC AC ABC….. Here, B atomic plane is missing in its regular arrangement.

Thus, the formed defect is known as Stacking Fault.

Volume Imperfections : These are three dimensional defects. They may be formed by any of the following reasons :

♦ Foreign Particle inclusions

♦ Regions of Non-crystalline

♦ Pores or Holes

♦ Dissimilar Natured Regions

The dimensions of such defects are the order of tens of A0. the above said imperfections are randomly located inside the material from one or more than locations.

Whisker : Whiskers are obtained by elongating single crystal into fibrous form. With this process, imperfections like grain boundaries are fully eliminated and other are reduced. The diameter of whiskers varies between 2 to 20 microns. Greater strength is usually observed in whickers of smallest diameters. Strength nearly 2.7 GPa and 13.2 GPA have been achieved in Copper and Iron whiskers respectively.

For Mild Steel, Strength in Bulk form is about 0.48 GPA and with whisker , it is about 12.8 Gpa. Young’s Modulus of bulk form of Mild Steel is about 200 GPa and with whisker, young’s modulus of Mild Steel is about 1000 G Pa. Elastic deformation of MS in bulk form are about 0.2% and with whisker, these are about 5%.

Whiskers are available in metallic as well as in non-metallic, in organics and inorganic materials. In 1970, first synthetic whiskers were produced. The natural whiskers are Spider’s web, Bamboo Flakes, Human Bone Flakes, some kind of grass etc.

These are necessary to obtain the theoretical strength as Ultimate strength = Modulus of Elasticity or Young’s Modulus.


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Materials Science : Objectives · Materials are available in Solid, Liquid and Gaseous state, but,...

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