---
title: "Introduction to Material Science Engineering"
tags : "SEM3, MME"
---
# IMSE – MML 211

Interdisciplinary Subject
To familiarize with the concept of material

## Introduction

Tetrahedron of Structure and Property
Compostion - Chemical make-up of material
Structure - Description of arrangement of atoms at different levels of detail
Sythesis - How materials are made from naturally occuring or man-made chemicals
Processing - How materials are shaped into useful components to case change in properties

Performance of the material is the function of quality of the material which is a function of the structure of the material.
Bend wire repeatedly – wire becomes hard and brittle and resistivity increases
Acra physica Polonica A – Resistivity deformation

#### Ceramic Superconductor
- YBCO – Yttrium Barium Copper Oxide
- Ceramics usually do not conduct electricity
- YBCO under 150K is a superconductor

Tailoring the chemical structure to get a desired property
Thin Films
Performance is dependent on – Microstructure, Composition, and
Synthesis and processing

### Classification of material
- Metal and alloy (ex: Cu, cast iron, steels)
- Ceramic, glass and glass-ceramic (ex: Al~2~O~3~, SiO~2~-Na~2~O-CaO, Barium Titanate Silica )
- Polymer (ex: Polythene,epoxy)
- Semiconductor (ex: Si, GsAs)
- Composite material (ex: WC-Co, Graphite-epoxy)

>#### Tutorial 1 – 3rd Aug, 2021 – BT20MME069_Om_T1
>>Q. Produce transparent glass for hyper speed car. Design the material that would minimize damage or at least protect the glass breaking into pieces.
Tempered Glass – Giving heat treatment to panel to strengthen a glass. Glass should remain intact, it should hold the break
>
>>Q. What properties should the head of a blacksmith hammer possess? How would you manufacture such hammer head?
Should not be deformed easily, it should be dense, withstand high temp. Point of contact of hammerhead and handle should not transfer vibrations
>
>>Q. Electrical contact and electrical switching
No change in property
>
>>Q. Coiled springs ought to be very strong and stiff. Ceramics are strong and stiff. Would you use ceramic for spring? Then what material?
Deformation, memory
>
>>Q. The hull of the space ship is made out of Aluminium, ceramic tiles on them
Aluminium - less dense, ceramic -

#### Metal and Alloys

Alloy - metal that contains additions of one or more metals or non-metals

Metals
- Good Conductivity and thermal conductivity
- High strength
- High stiffness, ductility or formability, and shock resistance

Copper :arrow_right: Conductor wire :arrow_right: High electrical conductivity, formability

Gray cast iron :arrow_right: Automobile engine block :arrow_right: good castability, vibration damping, machinable

Alloy Steels :arrow_right: Automobile chasis :arrow_right: Strength, heat treatable

#### Ceramics and glasses

Ceramics - Inorganic crystalline materials
- Porous - Do not conduct heat well
- Must be heated to very high temperature before melting
- Strong and hard, but also very brittle

Glass - Mostly often an amorphous material derived molten liquid
- Thermally tempered to make them stronger
<br>
- Very closely related each other - differ in heat treatment
- SiO2-Na2O-CaO :arrow_right: window glass :arrow_right: transparent, thermal insulating
- Al2O3, MgO, SiO2 :arrow_right: refractories (internallining in furnaces ) :arrow_right: thermal insulating, withstand high temperature, inert to molten metal
- Barium Titanate Silica :arrow_right: capacitor, optical fibre :arrow_right: ability to store charge, low optical losses
- Eutactic point whose melting point of tactic point is lower than the melting point of the components

#### Polymers

Polymers - Organic materials
High level of purity is required

- Polyethylene -> food packaging -> thin and flexible
- Epoxy -> encapsulation of integrated circuits-> electrically insulating, moisture resistant
- Phenolics -> Adhesives -> strong, moisture resistant
- Thermoplastic: ductility and formability
- Thermosetting: Strong but brittle

##### Semiconductor

- Silicon -> Transistor -> unique electrical behavior
- Gallium Arsenide -> optoelectronic system -> Laser, electrical signal to light
- Electrical conductivity is between ceramic insulators and metallic conductors
- Product form: Single crystal, thin films

##### Composites

- Graphite – epoxy -> Aircraft component -> light weight, high strength (High strength to weight ratio)
- Tungsten carbide- cobalt -> tools for machining -> high hot hardness, good shock resistance
- Titanium-clad steel -> Reactor vessels -> high strength, corrosion resistance

#### For Load bearing application

- Metallic Materials are entensively used for load bearing
- Mechanical property is very important
- Stress - F/A
- Strain

### Classification on the basis of appilcation

- Aerospace Material - Al alloys, Titanium alloy
- Biomedical Material - Titanium alloys, plastics, non-magnetic stainless steels, MRI: Nb-Sn based superconductors, Hydroxyapatite (bone material)- Ca~10~ (PO~4~)~6~ (OH)~2~
- Electronic Materials
- Energy
- Magnetic Materials
- Optical Materials
- Smart Materials
- Structural Materials

### Classification based on Structure

- Crystalline - Periodic arrangement of atoms
- Amorphous - No long range order of atoms - no crystal
- Single Crystal - Material as one crystal
- Polycrystal - many crystal in material

#### Microstructure of Polycrystalline

Etching - selective dissolving of material
Grain - Grain boundary - Liquid to Solid - the interface is formed and there is a solidification front - from the wall to center

#### Microstructure of single crystal turbine blade

CMSX - 6 - Ni based superalloy
Withstand high temperature, High stresses, and often highly oxidizing atmospheres

#### Amorphous (a-) vs

Amorphous - Liquid structures in solid form

### Structure-property relationship and surroundings

- Exposure to high or low temperature
- Cyclic stresses
- Sudden impact
- Corrosion and oxidation

Suitable design crie

#### Temperature

- Static Strength - Tensile Strength
- Materials fail at high temperature
- Solution - development of exotic materials -> HT

#### Fatigue

- Dynamic Strength
- Load and Unload

#### Strain Rate

- Linear pressure -
- "small rate of strain" or "high rate of strain"
- Higher the strain rate, material is prone to fail

#### Corrosion

- Reaction of oxygen or other gases at elevated temperature
- Attacked by corrosive liquids
- Making alloys
- Oxides will be formed - brittle
- Copper - Malachite green
- Sometimes Temperature, Fatigue, and Corrosion are interrelated
- Stress Corrosion Cracking
- Pipelines - Rolling
- Simultaneous action of tensile stress, potent environment

### From Structure to properties

- Atomic and microscopic scale - is important

#### Structure at different level

- Strength - bonding - Electronic Configuration

### Processing Technology

- Traditional Casting
- Contemporary microcircuit fabrication
- Metal Deforms - Ceramic Doesn't

### Sequence of choices in selecion material

- Gas tanks - Strength, Ductility, Cost
- Aluminium - Energy Material
- Materials available

>#### Tutorial 2 - 10th August
>
>>Q. Search the history and application of following materials
>> - Stainless Steel
>> - Ferrofluid
>> - $\beta$ - Titanium
>> - Diamond coated cutting tools
>> Present the result as a short report of about 200 words
>
>>Q. What type of instruments are used to study microstructure. Write steps to prepare metallic sample to study microstructure
>>A. Microscopes, Electron Microscopes
>> Cutting the sample, grinding, mounting, polishing
>
>>Q. What type of advanced instruments are used to determine atomic structure. Write working principle of any one instrument?
>
>>Q. What are single crystals and their applications? Write procedure by which single crystals are manufactured in industry.

## Atomic Structure

Structure of Materials at Five Different levels
1. Atomic Structure
2. Short- and Long-range atomic arrangements
3. Nanostructure
4. Microstructure
5. Macrostructure

### Classification based on atomic bonding

- Primary Bonding - Transfer or sharing of electrons
- Scondary Bonding - No Tansfer - electrons - relatively weak

>#### Tutorial 3 - 17th August
>
>>Q. The gold O-ring is used to form a gastight seal in high vacuum chamber. Consider the ring is formed from a 100 mm length of 2mm diameter wire. Calculate the number of gold atoms in the O-ring
>>A. $\frac {V\rho}{\text{Atomic Mass}}N_a$
>
>>Q. Household Aluminium foil is nearly pure aluminium. A box - 300mm wide by 22m long thickness 12.5 $\mu m$. Calc Number of atoms of Al in roll.
>>A. Similar - Reflective Property
>
>>Q. Nickel Area - 0.129032 m^2^ with a 0.00508cm thick layer. Number of atoms?
>>A. Similar
>
>>Q. Steel is coated with thin layer of ceramic to protect against corrosion. What do you expect to happen to the coating when the temperature of the steel is increased significantly? Explain.
>>A.

- Metallic Bond
- Electropositive atoms that donate their valence electrons to form a "sea" of electrons surrounding the atoms
- Positively charged ion cores held together by mutual attraction to the electrons, thus producinga strong metallic bond

- Covalent Bond
- Characterized by bonds - sharing of valance eletrons
- Bonds have fixed directional relationship - Bonds have a specific angle
- Very strong and hard
- High Temperature resistance - difficult process
- Limited ductility - directional bonding
- Low Electrical Conductivity - locked electrons (except Silicon)

- Ionic Bond
- When more than one atype of atom is present in a material, one atom may donate its valance electron to a diffrerent atom
- Mechanically Strong - strength of bond
- Electrical conductivity - limited - ions move

- Vander Waals Bond
- When a neutral atom is exposed to an internal or external electric field, the atom may become polarized (i.e., the centers of positive and negative charges separate)
- Secondary bonding
- Majorly observed in polarized molecule
- Boiling Point and Surface Tension
- Types
- London Forces - Induced dipoles
- Debye Interaction - Induced dipole and molecule with permanenet dipole
- Keesom Interaction - 2 permanently polarized molecules

- Mixed Bonds
- Combination of metallic and covalent bond
- Combination of metallic and ionic
- Large difference in electro negativity
- Combination of covalent and ionic
- combination of metallic and non metallic elements
- Fraction covalent = $\text {exp}(-0.25\Delta E^2)$
- Silica - SiO~2~ - Fraction covalent = 0.485

### Binding Energy and Interatomic spacing


- Equilibrium distance between atoms is caused by a balance between repulsive and attractive forces
- Equilibrium separation occurs when the total interatomic energy (IAE) of the pair of atoms is at a minimum
- Binding energy - The energy required to create or break the bond
- Modulus of Elasticity of a material is related to the slope of the force-distance curve
- Single crystal turbine blades

Microstructure and Atomic Structure dependent properties
Young's modulus - Atomic Structure dependent property
Yeild Strength - Microstructure dependent
Two Aluminium samples - same composition, different grain size - Young's modulus is same but yield strength is different

Thermal expansion coefficient - Linked to binding energy or interatomic force-distance curves

### Atomic and Ionic arrangement

Arrangement of atoms :arrow_right: Microstucture :arrow_right: Properties of materials

- No order - Atom randomly fill the space
- Short range Order - Limited to atomic nearest neighbour
- Dont have the drive to reach long range order
- Long range Order- Atomic arrangements to 100nm
- Liquid crystal
- Behave as amorphous materials in one state
- With external stimulus, polymer molecule undergo alignment

Polycrystalline Material
- Manysmall crystal with varying orientation in space
- Small crystals are known as grain
- The border between tiny crystals is known as grain boundaries
- Atom mobility stops - High strength

Liquid Crystal
- Polymeric Material
- Amorphous material (liquid like)
- on influence of electric field and temperature change polymer molecule undergo alignment and form small regions call "liquid crystal"

Amorphous Material
- Exhibit SRO
- Non-Crystalline
- Kinetics of process does not allow formation of periodic arrangements of atoms

#### a:Si-H

- H indicates material contains Hydrogen
- a:Si - silicon tetrahedral are not connected
- Some bonds are incomplete known as dangling

### Lattice

- Collection of points
- Surrounding of each lattice is identical
- Describes arrangement of atoms and ions
- Motif(basis) - group of atoms/ions, arranged in particular way in association with lattice point
- Crystal Structure = Lattice + Motif(basis)
Bravais Lattice
- Unit Cell
- Subdivision of lattice, retains characteristics of entier lattice
- Perioditcity

### Crystallography

#### Points in unit cell
- Used to locate atom position
- Right hand coordination system

#### Directions in the Unit cell
- Subtract Tail from head
- Reduce results to lowest integer
- Negative number with bar

#### Significance of Crystallographic directions
- Indicate particular orientation of Single Cystral, Polycrystalline material
- Easy to magnetize iron in [100] in comparision to [111] or [110]
- Metals Deform easily in closed packed planes
- Repeat Distance - The distance between lattice points along the direction (atoms must touch each other)
- Linear Density

#### Planes in Unit Cell
- Deformation happens in most tightly direction
- Influences surface energy
- Process
- Identify intercepted points(move origin)
- Take reciprocals
- Clear Fractions
- Express in parentheses

#### Miller-Bravais indices for Hexagonal unit cells

- Indices in form of (hkil) where (h + k = -i)
- Hexagonal structures can be divided into 3 equal parts
- We can use 3 axis coordinate system instead of 4 axis - inter-conversion is possible

$h \;= \frac 13 (2h'-k')$
$k \;= \frac 13 (2k'-h')$
$i \;= -\frac 13 (h'+k')$
$l \;= l'$

#### Closed packed planes and directions

- Closed packed direction - atoms are in continous contact


>#### Tutorial 5 - 26th August
>>Q1. One mole of solid MgO occupies a cube 22.37mm on a side. Calculate the density of MgO (in g/cc)
>>A. Used in high end vehicles - alloys
>>When combined with other oxides we can create flux - D = $\frac {40.3044}{(2.237)^3} = 3.60043 g/cc$
>
>>Q2. Calculate the dimensions of a cube con
>
>>Q3. Calculate the fraction of bonding of Aluminium Phosphide (AlP) that is ionic
>
>>Q4. Determine the density of BCC iron - lattice parameter of 0.2866nm. A typical paper clip weighs 0.59g and consists of BCC iron. (a)Calculate number of unit cells and (b)number of iron atoms in a paper clip
>>A.
>
>>Q5. Determine the planar density and packing fraction for FCC nickle in (100), (110) and (111) planes. Which if any of these planes is close packed?
>>A.

#### Isotropic and Anisotropic behavior

- Due to differences in atomic arrangements in the planes and directions within crystal
- Anisotropy - properties differ on the crstallographic direction
- Isotropy - Properties are identical

#### Interplanar spacing

- Distance between two adjacent parallel planes of atoms with same miller indices

$d_{hkl} = \frac a{\sqrt{h^2+k^2+l^2}}$

#### Interstitial sites

- Small holes between the crystal atoms into which smaller atoms may be placed
- Coordination number equal to the number of atoms the interstitial atom touches
<br>
- For simple cubic, CN = 8, Octahedral site
- For BCC, CN = 4, Tetrahedral site
- For FCC, CN = 6, Octahedral site
- For FCC, CN = 4, Tetrahedral site
- For FCC, CN = 6, Octahedral site

#### Rattle

Atoms/ions whose radii are smaller than the radius of the hole are not allowed to fit the interstitial site

#### Radius Ratio


#### Crystal Structure of ionic material

- Crystal structure assures electrical neutrality
- Closed packed structure of ions
- Ions fit into appropriate interstetial site
CsCl structure, NaCl structure, Perovskite Structure, Conrundum structure

CsCl Structure
Simple Cubic
Radius Ratio = $r_{Cs^+ / r_(Cl^-)} = 0.92$
CN = 8


NaCl Structure
Radius Ratio = 0.536
CN = 6
Ex - MgO, CaO, FeO

ZnS Structure
Radius Ratio - 0.402
CN = 4
Ex - GaAs, III-V semiconductor

Fluorite
Radius Ratio - 0.929
Ex - ZrO~2~, CeO~2~

Perovskite structure, BaTiO~3~
Corner site by Ba^2+^
Octahedral Site by Ti~4+~
Face center by O^2-^

#### Crystal structure of Covalent Material

- Diamond Cubic structure
- Tetrahedron coordination
- Ex - Si, Ge, Ge, $\alpha$-Sn, Carbon (in diamond form)

### Crystal Structure determination

- X-ray diffraction and electron diffraction
- Wavelength of magnitude of atomic spacing strikes the material, scattering takes place for x-ray beam
- Presence of certain Crystallographic planes
- Bragg's law is satisfied
- $\theta$ is recorded
- $\lambda$ is known
- "d" can be determined
- Electron diffracion
- By Transmission electron microscophy
- Electron are diffraction from electron transparent material
- Diffracted electron used for the determination of crystal structure
- Electron energy (100 KeV to 400 KeV)
$\lambda = \sqrt {\frac {1.5}V}$nm

## Crystalline Imperfections

- Solidification
- Forming, Forging

Imperfections like
- Point Defects
- Line Defects
- Surface Defects

Defects can be useful if added intentionally but they are bad if added process - Silicon Doping

Defects create deviation from perfect atomic or ionic arrangement

Grain Boundary is a defect

Iron - soft but steel - high strength

### Points Defects

- Involve one atom or ion
- Point defects are different from extended defects like dislocations, grain boundaries

#### Vacancy

- Atom/ion missing from its normal site in crystal structure
- Vacancy creates randomness (entropy), increases thermodynamic stability
- Vacancy is introduced during solidification
- Vacany determines diffusion of atoms/ions in solid state

$\qquad n_v = n \text{ exp}(\frac{-Q_v}{RT})$

n~v~ - number of vacancies (cm^-3^)
n - number of atoms per unit volume (atoms cm^-3^)
Q~v~ - Energy required to produce one mole of vacancies (cal mol^-1^ or J mol^-1^)
R - Gas constant, 1.987 cal mol^-1^ K^-1^ or 8.31 J mol ^-1^ K^-1^
T - Temperature (Kelvin)

#### Interstitial Defects

- Extra atom/ion is inserted into the crystal structure
- Smaller than atoms/ions located at lattice point - but larger than interstitial sites (results in distortion in surrounding region)
- Once introduced, the number of atoms/ions remain constant, even if temperature is changed - unlike

#### Substitution defects

- Occupy normal lattice site
- Larger or smaller than normal atoms/ions
- Disturb the surrounding crystal
- Defect is independent of temperature

#### Frenkel Defect

- Vacany-interstitial pair formed
- Ions jumps from normal lattice to interstitial site
- Can also occur in metallic and covalently bonded materials

#### Schottky Defect

- unique to ionic materials (ceramin)
- Type of vacany defect
- Stocichiometric number of anions and cations missing to preserve electrical neutrality in a crystal

>#### Tutorial 5 - 7th September
>>Q1. Calculate the Ionic packing factor for MgO, which has NaCl structure. Also calculate density of MgO
>>A. IPF
>
>>Q2. Calculate atomic packing factor for diamond cubic structure
>>A.
>
>>Q3. Calculate the linear density of atoms in a) BCC tungsten b) FCC aluminium
>>A. Repeat distance
>
>>Q4. Calculate linear density of ions in the [111] direction of MgO
>>A.
>
>>Q5. Determine the Miller indices for the directions in the cubic unit cell shown below.
>>A.
>
>>Q6. Calculate planar density of ions in the (111) plane of MgO.
>>A.

#### Charge Neutrality

- Charge balance must be maintained
- Mass balance must be maintained
- Number of crystallographic sites must be conserved

### Dislocation

- Line Imperfection
- Introduced during solidification or material deformation
- Usefule to explain strength in metallic materials

Types
- Screw dislocation
- Edge dislocation
- Mixed dislocation

#### Screw Dislocations

- Cutting partway and skewing crystal one atom spacing
- Revolution around the axis give rise to spacing
- The vector required to complete loop is burger vector 'b' and is // to screw dislocation

#### Edge Dislocation

Slicing a perfect crystal, spreading a crystal apart, partly filling the cut with extra plane of atoms
Clockwise loop, one atom spacing form starting point
Burger vector perpendicular to dislocation (point of difference)

#### Mixed Dislocation

Both Edge and Screw Dislocation
Screw dislocation at the front face of the crystal gradually changes to an edge dislocation

#### Dislocation Line and slip plane

Burger vector is able to explain how material deforms
Speed of dislocatopms movement in material is close or greater than speed of sound

Shear stress iin presence of dislocation

- Atoms are displaced along slip direction and crystal is deformed

#### Slip

- Process by which dislocation moves and causes material to deform
- Direction of dislocation move is slip direction
- The plane in which slip moves is called slip plane
- Slip direction + slip plane = slip system
- Disocation move in a direction perpendicular to burger vector in screw dislocation
- Crystal deform parallel to burger vector in case of screw dislocation
- Since burger vector is parallel to dislocations

#### Peierls-Nabarro Stress

- During slip, dislocation move from one set of surrounding to another set of identical surrounding
- Stress required to move from one equilibrium location to another is called Peierls-Nabarro Stress
$\qquad \tau = c \text{ exp}(-kd/b)$
$\tau$ - Shear stress required to move dislocation

> Tutorial 6 - 14th September
>>Q1. The Fraction of vacant sites in a crystal is typically small. For example, the fraction of Aluminium sites vacant at $400^\circ C$ is $2.29 \times 10^{-5}$. Calculate thedensity of these site (in units of m^-3^)
>>A. Atomic Density = $\rho$ /Atomic mass
>>Vacancy density = Atomic Density $\times$ Vacancy ratio
>
>>Q2. Calculate the magnitude of the Burgers Vector for (a) $\alpha$
>>A.
>
>>Q3. Would you expect UO~2~ to have the sodium chloride, zinc blede or fluorit structure? (a)Lattice Parameter (b)
>>A.
>
>>Q4. Determine the planar density and packing for any BCC metal in (100), (110), and (111) planes. Which, if any, of these planes is clased packed.
>>A.
>
>>Q5. Calculate the radius of the largest intersitial void in the FCC $\gamma$ iron lattice. The atomic radius of the iron atom is 0.129nm in the FCC lattice.
>>A. Radius Ratio

### Significance of dislocations

- Provide mechanism for plastic deformation
- Provides ductility in metal
- CPP is required to deform material
- Soft Metal - Dislocation Density - 10^6^ cm/cm^3^
- Deformed metal is 10^12^ cm/cm^3^
- If more disclocation - causes scattering of electrons - hence increases resistance

### Schmid's Law


$τ = σ \cdot cos (φ) cos (\lambda)$

- Critical resolved shear stress
- Shear stress required to break enough metallic bonds in order for slip to occure
- Causes metal to plastically deform
$\qquadτ_r = τ_{crss}$
<br>
- Schmid's law is applicable to single crystal
- Cannot apply Schmid's law to predict mechanical behaviour of polycrystalline materials

#### Critical Resolved Shear Stress

- If τ~crss~ is high - metal has high strength
- BCC metals tend to have high strength and lower ductility in comparison to FCC
- FCC has CPP - (111)
- BCC don't have such CPP

CRSS in HCP
- c/a > 1.633 in case of Zn
- c/a < 1.633 in case of Ti
- CPP is the Basal Plane
- d~c/a,Zn~ > d~c/a,Ti~
- τ~Ti~ > τ~Zn~
- Planar density is not high in HCP as observed in FCC metal

HCP crystal fail in brittle manner
- One set of parallel closed placked planes (0001)
- Three closed packed direction $\langle 1 0 0 \rangle$
- Total slip Systems = 3
- φ and $\lambda$ close to 45° is rare
- Slip cannot occure if the slip system is oriented either φ or $\lambda$ equal to $90 ^\circ$

Cross-Slip - It is the process by which a dislocation moving in a slip plane that encounters an obstacle which blocks further movement can continue to move by shifting the dislocation to a second intersecting slip system if it is properly oriented

### Surface Defects

Boundaries or planes that separate material region having same crystal structure but different orientation

Grain - Portion of the material within which the arrangement of the atoms is nearly identical, however the orientation if the atom arrangment or crystal structure is differnt for each adjoining grain.

Grain Boundaries - The surface that separates the individual grain, is narrow zone in which atoms are properly spaced

#### Grain Size

- By reducing grain size, we increase number of grains and increase the grain boundary area
- Dislocation is being stopped at grain boundary
- The strength of material increases with decrease in the average diameter of the grain

Hall-Petch Equation
$\qquad \sigma_y = \sigma_0 + Kd^{-\frac 12}$

$\sigma_y$ - Yield Strength
$\sigma_y$, K - Constant for metal
d - Average diameter of grain

ASTM Grain Size number - The number of grains per square inch is determined from a micrograph of a metal taken at magnification x100

$\qquad N = 2^{n-1}$

N - Number of grains per square inch
n - ASTM GSN

#### Small Angle Grain Boundary
- Array of dislocation produces a small misorientation between adjoining crystals
- Small angle grain boundary is not effective in blocking slip - The energy of surface with samll angle grain boundary is less than regular grain boundary
- Small angle boundaries formed by edge dislocations are called tilt boundaries

#### Stacking fault
- Error in stacking sequence of CPP
- Occur in FCC metals
- Perfect crystal stacking is ABCABCABC
- Stacking Fault - ABC**ABAB**ABC

#### Twin Boundaries
- Is a plane across which there is mirror image orientation of the crystal structure

Energies of Surface Imperfections


Importance of Defects
- Any imperfections raises the internal energy at location of imperfection due to atomic level compression and tension
- Defects in materials serve as stop sign for dislocation
- Strength can be controlled by number and type of imperfections

Common strengthening mechanisms

## Diffusion

Materials used in load beraing applications are rarely pure - because they are soft

Refers to net flux of species (ions, atoms, electrons, holes, molecules)
Depends on temperature and initial concentation gradient

Applications
- Carburization for Surface Hardening of Steels
- Carbon is diffused into steel components such as gears - increase hardness
- Control of Phase transformation needed for the heat treatment of metals and alloys
- Dopant Diffusion for Semiconductor Devices
- Conductive Ceramics
- Creation of Plastic Beverage Bottles

Drift - The movement of particles, atoms, ions, electrons, holes etc. under driving force (other than concentration gradient) is called drift.

### Arrhenius Equation

$\text{Rate } = C_0 \text{ exp}\left(\displaystyle\frac{-Q}{RT}\right)$

### Mechanisms for Diffusion

- Self Diffusion
- In materials containing vacancies, atoms move or "jump" from one lattice position to another
- Interdiffusion
- Diffusion of different atoms in different directions
- Vacancy Diffusion
- As diffusion continues, we have counterflow of atoms and vacancies
- Interstitial Diffusion
- When a small interstitial atom or ion is present in the crystal structure, the atom or ion moves from one interstitial site to another
- There are more interstitial sites than vacancies - It occurs easily as compared to Vacancy Diffusion

### Rate of Diffusion

Diffusion is dependent on temperature

Fick's First law
$J = -D \displaystyle\frac{dc}{dx}$

J - Flux
D - Diffusivity $\left(\frac{\text{cm}^2}{s}\right)$
$\displaystyle\frac{dc}{dx}$ - Concentration Gradient $\left(\frac{\text{atoms}}{\text{cm}^3\cdot\text{cm}}\right)$

Diffusivity - Temperature Dependence
$D = D_0 \text{ exp}\left(\frac{-Q}{RT}\right)$

High Activation energy is related to high strength of atomic bonds
- Rate of diffusion is low
- Anion can only enter other anion sites
- Small cation tend to diffuse faster

### Types of diffusion

- Volume Diffusion
- Atoms move from one reguar or interstitial site to another
- AE is large
- Diffusion is low
- Grain Boundary Diffusion
- Atom packing is poor
- AE is small
- Diffusion is Higher than volume diffusion
- Surface Diffusion
- Less Constraint
- Diffusion of atoms is higher than volume and grain boundary diffusion

$Q_{VD} > Q_{GB} > Q_{\text{Surface}}$


>Tutorial - 7 - 5-10-21
>>Q1. Atoms are found to move from one latice position to another at the rate of 5 x 10^5^ jumps/sec at 400$^\circ C$
>>A. Arrhenius Equation
>
>>Q2. The diffusion coefficient for Cr^+3^ in Cr~2~O~3~ is 6 x 10^-15^

### Factors affecting Diffusion

- Temperature
- Diffusion Coefficient
- Time - Long time may be required
- Prevention of diffusion is applied to develop non equilibrium structures

If diffusion is prevented atoms will not move and crystal will not form - structure will be amorphous

Steel quenched rapidly from high temperatures to prevent diffusion from non equilibrium structures and provide the basis for sophisticated heat treatments

- Bonding and crystal structure

Interstitial diffusion - occurs much faster than vacancy or substitutional diffusion - low-activation energy

Activation energies are usually
lower for atoms diffusing through open crystal structures than for close-packed crystal
structures.

### Permeability

- Permeability are important in polymers
- Polymers are polar molecules
- Gas and vapour permeate in polymer due to their small molecular dimension
- More compact the structure of polymers, the lesser the permeability

### Fick's Second Law

Describes the Dynamic(non-steady state of diffusion of atoms)

$\displaystyle \frac {\partial c}{\partial t} = \frac{\partial}{\partial x}\left(D\frac{\partial c}{\partial x}\right)$

c(x,t) = A + B erf$(\frac x{2\sqrt{Dt}})$

$\displaystyle\frac{c_s-c_x}{c_s-c_0} = \text{erf}\left(\frac x{2\sqrt{Dt}}\right)$

c~s~ - Concentration of diffusing atoms on surface of material
c~0~ - Initial uniform concentration of diffused atoms in material
c~x~ - Concentration of diffusing atoms at location "x" below the surface after time "t"

$erf(x) = \displaystyle\frac{2}{\sqrt\pi}\int_0^x\text{exp}(-y^2)dy$

Limitations in Error-Function Solution
- It is assumed that D is independent of the concentration of the diffusing species
- The surface concentration of the diffusing species (c~s~) is always constant

### Importance of Diffusion

Diffuision is imortant when materials are processed and used at elevated temperature

- Melting and casting - Solidification of metals and alloys , inorganic glasses
- Sintering - removes pores between powder particles
- Grain growth
- Diffusion bonding

## Phase Transformation

Solid State transformation
Phase Diagram (Binary)
Motivation - To strengthen metallic materials

### Solid State Transformation

From phase α -> ß

$\Delta G = \frac 43\pi r^3 \Delta G_{v(\alpha\rightarrow\beta)} + 4\pi r^2 σ_{\alpha\beta}+\frac 43 \pi r^3 ε$

Strain is produces between solid precipitates and surrounding matrix - last term

Growth of precipitates require long range diffusion

#### Nucleation

Nucleation occurs most easily on surface already present in the strucure, thereby minimizing the surface energy term

#### Growth

Growth of precipitates require long range diffusion and redistribution of atoms

#### Kinetics

- Depends on intital nucleation and growth
- Transformation to be completed in shorter time
- Higher the temperature, growth rate is rapid (D is higher)
- Fraction of transformation is related to "time" (at particular time)

Avrami Equation
$f = 1 - \text{exp}(-ct^n)$


#### Effect of tempertature

Rate of Transformation depends on undercooling ($\Delta = T_m - T$)

T_m - Equvilibrium temperature

Rate of nucleation is low for small undercooling
Rate of nucleation increases with large undercooling

Growth rate decreases as undercooling increases

Growth rate follows Arrhenius relation

$r^* = \displaystyle\frac{2\sigma_{sl}T_m}{\Delta H_f\Delta T}$

$\text{Growth Rate} = A \text{ exp}(\frac {-Q}{RT})$

### Micro-structural evolution

- Sequence of phase transformation
- Al-4%Cu - age hardenable alloy
- Age hardening is also called precipitation hardening - leads to uniform distribution of precipitates in ductile matrix

Application - Increase yield strength

Step 1 - Solution Treatment

- Alloy is heated above solvus temperature
- Held until a Homogeneous solid solution α is produced
- θ phase precipitate is dissolved and any microchemical segregation is reduced

For Al-4%Cu - 500°C to 548°C

Step 2 - Quench

- The alloy is rapidly cooled
- Atoms do not have time to diffuse to potential nucleation sites so θ does not form
- The structure is supersaturated solid solution α~ss~ - Metastable structure

Step 3 - Age

- The supersaturated α is heated at a temperature below the solvus temperature
- At aging temperature - atoms diffuse only short distances
- If we hold the alloy for a sufficient time at the aging temperature the equlibrium α + θ structure is produced
- Morphology is different from slow cooling

θ phase in the form of ultra-fine uniformly dispersed second-phase precipitate particles

#### Non-equilibrium precipitates during aging

Solution treatment -> Quenching -> Aging

This sequence does not show intermediate phases - a continous series of other precursor precipitate phases forms prior to the formation of the equilibrium θ phase

At the start of aging - the copper atom concentrate on {100} planes int the α matrix and produce very thin precipitates called Guinier-Preston (GP) Zones

Higher aging temperature gives lower peak strength and makes strength more sensitive to aging time

#### Effect of aging temperature and time

Higher aging temperatur gives lower peak strength and makes strength more sensitive to aging time

Benefits of using lower temperature
- Maximum strength increases
- The alloy maintains its maximum strength over a longer period of time
- The properties are more uniform

#### Requirements for Age Hardening

- Alloy must display decreasing solid solubility with decreasing temperature - must form single phase on heating above solvus line and enter two phase region on cooling
- The matrix should be relatively soft and ductile, and the precipitate should be hard, brittle intermetallic compound
- Alloy must be quenchable - Minimize residual stresses
- A coherent precipitate must form

### Eutectoid Reaction

Solid State reaction

$S_1 \rightarrow S_2 + S_3$

Phase transformation to control microstructure and properties

At 727°C -
γ(0.77%C) → α(0.0218%C) + Fe~3~C(6.67%C)

γ - Austenite
α - Ferrite
Fe~3~C - Cementite

Above 727°C - only austenite grains

In the reaction
- the two phases that form have different compositions so atoms must diffuse
- Most of carbon in asutenite diffuses to the Fe~3~C
- The redistribution is easier if the diffusion distances are short - thin lamellae

Pearlite - The lamellar structure of α and Fe~3~C tat develops in the iron-carbon system is called pearlite

#### Controlling the eutectoid reaction

- Amount of the eutectoid
- By changing composition - we can change amount of hard second phase
- As the carbon content increases towards the eutectoid compositon - the amount of Fe~3~C and Pearlite increases - Strength increases
- This strengthening effect peaks
- Austenite Grain Size
- Number of pearlite colonies can be increased - reducing the prior austenite grin size - Low temp
- Increase the strength of the alloy by increasing the number of colonies of Pearlite
- Cooling Rate
- Increase in cooling rate - reduction in distance that atoms are able to diffuse - Finer Lamellar
- Fine Pearlite - high strength
- Transformation Temperature
- Eutectoid reaction - slow - steel may cool below equilibrium eutectoid temp before transformation - Austenite phase can be undercooled
- Lower transformation temp - finer, stronger structure
- Time-Temperature-Transformation(TTT) Diagram - Isothermal transformation

#### Nucleation and Growth

Pearlite
- Quench just below eutectoid temperature - Austenite is only slightly undercooled
- Long times are required before stable nuclei for ferrite and cementite form
- After phases that form pearlite nucleate - atoms rapidly diffuse and coarse pearlite is produced
- Austenite quenched at lower temperature is highly undercooled - nucleation occurs more rapidly and the P~s~ is shorter - slow and short diffusion - fine pearlite

Bainite (Arrangement of ferrite and cementite)
- Below the nnose of the TTT diagram - diffusion is very slow and total tranformation time increases
- Lamellae in pearlite would have to be extremely thin and the boundary area between the ferrite and Fe~3~C lamellae would be very large
- The internal energy of the steel will be very high - permitting the cementite to precipitate as discrete, rounded particles in ferrite matrix energy can be reduced
- Times required for austenite to finish its trasnformation to bainite increase and the bainite becomes finer as thke transformation temperature continues to decrease
- Bainite that forms just below the nose of the curve is called coarse bainite, upper bainite, or feathery bainite
- Bainite that forms at lower temperature is called fine bainite, lower baininte, pr acicular bainite

As temperature decreases - general trend towards higher strength and lower ductility

Design heat treatment to produce Pearlite structure
- 1 - Heatl steel to 750°C for 1hr
- 2 - Quench to 700°C and hold for 10^5^s
- 3 - Cool to RT

Design heat treatment to produce Bainite structure
- 1 - Austenzie an eutectoid steel to 750°C for 1hr
- 2 - Quench to 250°C and hold for 10^4^s (250°C for 15min -> Bainite + Martensite)
- 3 - Cool to RT

## Thermal Conductivity

Thermal Properties

- Response of materials to the application of heat
- Heat Capacity - Ability of material to absorb heat from the externa surrounding
- Mathematically C = dQ/dT
- Vibrational Heat Capacity - With increase in thermal energy there is increase in vibrational energy of atoms
- Vibrational waves are termed as phonons
- Elastics waves - Shoer

### Temperature dependence on heat capacity

$C_v = AT^3$
- C~v~ becomes indepentent of therature at value 3R
- Essentially with increase in temperature no change in C~v~, termed as $\theta_D$Debye temperature

### Thermal Expansion

$\displaystyle\frac {l_f - l_0}{l_0} = \alpha_l(T_f - T_0)$

$\displaystyle \frac {\Delta l}{l_0} = \alpha_l\Delta T$

$\displaystyle\frac {\Delta V}{V_0} = \alpha_v\Delta T$

### Ptnetial Enerygy vs Interatomic Distances

Assymetric curvature

### Thermal Behaviour of material

- For metal - α~l~ - 5x10^-6^ to 25x10^-6^ /°C
- Ceramic - α~l~ - 0.5x10^-6^ to 15x10^-6^/°C
- For polymer - α~l~ - 50x10^-6^ to 400x10^-6^/°C
- Brittle material may experience fracture due to no uniform dimesional change - Thermal shock
- In Polymer - Secondary intermolecular bonds

Kovar
54 wt% - Fe
29 wt% - Ni
17 wt% - Co

Invar
64 wt% - Fe
36 wt% - Ni

Supar-invar
63 wt% - Fe
32 wt% - Ni
5 wt% - Co

### Thermal Stress

Stress induced in body as a result of changes in temperature in body as a result of charges in temperature

The magnitude of stress(σ)
σ = E α~l~(T~0~-T~f~) = Eα~l~$\Delta T
$\frac {I_f - I_0}{I_0} = \alpha_l(T_f - T_0)$
E - Elastic modulus
α~l~ - Linear Coefficient of thermal Expansion

T~f~ > T~0~ - σ < 0 - Compressive

Isotropic Material - stress free

### Thermal Shock Resistance

The capacity of material to withstand failure due to rapid cooling is termed as thermal shock resistance

Depends on Mechanical and thermal properties of materials

TSR = $\displaystyle\frac{\sigma_f k}{E \alpha_l}$

σ~f~ - Fracture strength
k - Thermal conductivity
E - Elastic moduli
α~l~ - Linear coefficient of thermal expansion

Soda-lime glass vs Pyrex Glass

- $\alpha_l$ is $9\times10^{-6}°C^{-1}$ for soda-lime glass - susceptible to thermal shock
- B~2~O~3~ and reduce CaO and Na~2~O to form borosilicate glass (Pyrex glass)
- $\alpha_l$ is $3\times10^{-6}°C^{-1}$ for Pyrex glass

## Optical Properties

Material response to electromagnetic radiation

### Intensity of non absorbed readiation (I'~T~)

- Continously decreases with distance inside the transparent material
$\quad I'_T = I'_0e^{-\beta x}$
x - Thickness of the material
$\beta$ - Linear absorption coefficient

### Luminescence

- Abosorbing energy and reemitting visible light
- Photon are emitted due to electron transition
- Fluorescence - re-emission occurs for less than 1s
- Phosphorescence - re-emmistion occurs for more than 1s

> Tutorial 10
>>Q1. Gallium arsenide GaAs - 1.42eV and gallium phosphide - 2.25eV
>>A. Proportional
>
>>Q2. Visible spectrum energy
>A.
>
>>Q3. GaAs - 1.47eV - wavelength?
>>A. Wavelength and colour
>
>>Q4. CdS - 2.59eV - wavelength?
>>A.
>
>>Q5.

### Optical Fibres in communitcation

Encoder -> Electrical/Optical Converter -> Reppeater -> Optical/Electrical Coverter -> Decoder

# Magnetic Material

Magnetic Field (H)
Magnetic induction (B)
$H = \frac {NI}l$

Relative permeability

$\mu_r = \displaystyle \frac {\mu}{\mu_0}$

$B = \mu_0H+\mu_0M$

M - Magnetization - extentt to which material can be magnetized

B is also termed as magnetic flux density
Alignemnt of magnetic moment by virture of M

$M = \chi_mH$
$\chi_m$ - Magnetic Susceptibility

Net magnetic moment comes from orbital and spin contribution

If cancellation of both orbital and spin moments happens, no magnetization can happen - He, Ne, Ar

## Diamagnetism

- Weak
- Non Permanent
- only under application of external magnetic field
- Induce change in orbital motion of election - due to applied magnetic field
- Magnetic moment is very small
- Under strong magnetic field, diamagnetic materials attracted toward regions

## Paramagnetism

- Some atoms posses permanent dipole moment - incomplete

### Domains

For ferromagnetic and ferrimagnetic material below T~c~

Mutual alignment of magnetic dipole moments in same region

Such regions are called domains

Domain Boundary - direction of magnetization gradually changes
For polycrystalline material - domain are of microscopic size

B vs H curve
Permeability(µ) is slope of BHcurve
At H = 0, µ~i~ is initial permeability
Domain shape and size change with H rotaion of domain, oriented with H field

## Corrosion

### Corrosion in Metals

Destructive and unintentional attack
Electrochemical in nature
Significant loss in terms of economy
Electrochemical
Corrosion
- Rusting of automotive body
- Etching procedure

Oxidation - Anodic reaction - Anode site
Reduction - Cathodic reaction - Cathod side

$M \rightarrow M^{n+} + ne^-$
$Fe \rightarrow Fe^{2+}+ 2e^-$
Electron release

Metal corrode in acidic solution that have high concentraction of H^+^ ions
2H^+^ + 2e^-^ → H~2~

If acid solution has dissolved oxygen then,
$O_2 + 4H^+ + 4e^- \rightarrow 2H_2O$

304L 316L

Corrosion of Zinc in acid solution

Zn → Zn^2+^ +2e^-^
2H^+^ + 2e^-^ → H~2~

### Galvanic Couple

Two metals electrically connect in a liquid electrolyte where one mteal becomes anode and corrodes and another metal acts as a cathode

### Standard EMF series

Compares the standar electrode potential E^0^ for each metal waith that of the hydrogen electrode under standard conditions of 25°C and a 1 M solution of ions in the electrolyte

Effect of Concentration and temperature

$\Delta V = \displaystyle(V_2^0 - V_1^0) - \frac{RT}{nF}\text{ln}\left(\frac{[M_1^{n+}][M_2]}{[M_2^{n+}][M_1]}\right)$

V^0^ - Standard Eletrode potential
RT/F - 0.0592
F - 96500 C/mol

### Glavanic Series

EMF - Highly idealized
Galvanic - realistis and practical
Measures reactivitiesof metals and commercial alloys in seawater
Top are cathodic, unreactive
Bottom are anodic, reactive
No voltage provided

### Corrosion Rates

Real corroding system are not at equilibrium

Corrosion Penetration Rates, $CPR = \displaystyle\frac{KW}{\rho tA}$

W - weight loss after exposure time t
$\rho$ - density of specimen
A - Exposed area
K - constant (K = 87.6)
For most application CPR < 0.5mm/yr

Corrosion rate, when elcetri current i is associatied with electrochemical corrosion (i - current density)

r = i/nF

n - No of electrons associated with ionization

Polarization - The displacement of each electrode from its equilibrium value

Over-voltage - Magnitude of displacement

Activation Polarization
- The reaction rate is controlled by the one step in the series that occurs at the slowest rate
- Process
- Adsorption of H^+^ ions from the solution onto the zinc surface
- Electron transfer from zinc to form hydrogen atom
- Combining 2 Hydrogen atoms to form a molecule
- Coalescence of many hydrogen molecules to form a bubble

Concentration Polarization
- Reaction is limited by diffusion

### Passivity

Active metal under particular environment condition loose their chemical reactivity and become extremely inert

Formation of very thin oxide film

Alteration in concentration of active corrosive species may cause oassive material to revert back to active state

### Corrosion Properties of Materials

Decided by corrosion enviroment

- Increase in fluid velocity - enhances the corrosion due to erosive effect
- Increase in temperature corrosion rates increases
- High concentration of corrosive species increases the corrosion rates
- Plastically deformed metals are prone to corrosion as compared to annealed state

## Corrosion Environment

- Atmosphere, Aqueous solution, soil, acid, bases, inorgainc solvents, molten salts, liquid metals, human body

- Atmospheric corrosion accounts greatest losses due to oxygen, moisture, chloride and sulphur containing compounds

## Processing of Materials

- Metal are stiff and strong yet ductile, resistant to fracture
- Cermaic - Stiff, strong, hard, extremely brittle, susceptible to fracture
- Polymers - Not stiff but ductile and pliable(easily form complex shapes)
- Material Selection - ease with which materials can be processes

## Fabrication of Metals


### Forging Operations

#### Forging

#### Rolling

Passing piece of metal between two rolls
Compressive stress and reduction in thickness
Cold rolling - Sheet, Strip, foil (high quality surface finish)

#### Extrusion

Bar of metal forced throu

#### D

### Casting

Molten Metal is poured into mold cavity with desired

Sand, Die, Investment,

#### Sand Casting

#### Die Casting

Liquid Metal is forced into the mold with high velocity

#### Investment Casting

#### Lost Foam Casting

Variation of investing casting
Pattern is a foam forme

### Miscellaneous

#### Powder Metallurgy

Compaction of powder metal -> heat treatment for more dense piece

Diffusional process for development of non

Niche Market

#### Welding

Two or more metal parts are joined to form single piece
Similar or Dissimilar metals may be welded
Metallurgical - not mechanical (rivetting and bolting)
- Arc, Gas Welding, Brazings, Soldering

Material Alterations
- Microstuctural and property alteration
- Formation of residual stresses upon colling
- Undesirable phase may form
- Stainless steel - sensitized during welding - intergranular corrosion

Laser Beam Welding
- Filler matterials are not required
- Non contact process
- Rapid and highly automated
- Energy input is low, HAZ is minimized
- Weld is precise and small in size
- Variety of metals/alloys can be joined
- Porosity free weld

## Heat Treatment of Steels

Heat Treatment of steel to produce martensitic microstructure throughout the cross section

Factors
- Composition of alloy
- quenching media
- size and shape of specimen

### Hardenability

Ability of an alloy to form martensite as a result of given heat treatment

Quantitative measure of hardness drop with decrease in martensite content
High Hardenability means steel alloy hardens to form martensite

Jominy End Quench Test

### Influence of Composition

## Fabrication of Ceramics


### Glass Forming

#### Press and Blow Technique


#### Drawing


#### Particulate Forming Process

#### Drying

Piece obtained from Hydroplasticity and slip casting have porosity, insufficient strength and water
Removal of liquid by dying process -> green product

Rate of evaporation and rate of water removal diffusion must be balanced otherwies it will result in defects like crack and distortion

#### Firing

Density is imporved - mechanical strength is enhanced

Vitrification - formation of glassy liquid that fills the pores - for clay 900-1400°C

Role of flux - reduce temperature of vitrification

#### Powder pressing

- Filling
- Compacting
- Ejection

No plastic deformation
Use of binder to lubricate powder particles

Uniaxial - Green product - weaker
Isostatic
Hort Pressing - Introduction of heat

#### Sintering

Particle after pressing -> Sintering begins -> sintering proceeds

Mechanism of sintering is by atomic diffusion

Dricing Force - reduction in total particle surface area

#### Tape Casting

To produce thin sheet of flexible plate


## Processing Plastics

Methods depend on
- Thermoplastic (recyclable) or thermosetting
- If termoplastic, temp at which it softens
- Atmospheric stability
- Geometical size of finished product

Fabrication is fone at elevated temp + pressure

### Fabrication of Thermo setting polymers

- Preparation of linear polymer
- Curing
- chemical and structural changes occur
- thermosets are difficult to recycle
- thermosets are usable and iner at higher temperature

Methods
- Compression Molding
- Transfer Molding
- Blow Injection Molding
- Extrusion Molding

#### Compression Molding

- Appropriate amount thoroughly mixed polymers with additives


- Tranfer molding is a type of Compression molding - thermosetting polymers and complex geometrics

#### Injection Molding


- Similar to Die casting for metals
- Thermoplastics
- Rapid Rate - Solidification happens immediately