MATERIALS SCIENCE AND

BITSPilaniPilani Campus

MATERIALS SCIENCE AND ENGINEERING

Dr. Subrata Bandhu Ghosh

Department of Mechanical Engg.

Vacancy atoms

Interstitial atoms

Substitutional atomsPoint defects

1-2 atoms

Types of Imperfections

Dislocations Line defects

1-dimensional

Dislocations

The strength of a material with no

dislocations is 20-100 times greater than

the strength of a material with a high

dislocation density.

So, materials with no dislocations may be

very strong, but they cannot be deformed.

The dislocations weaken a material, but

make plastic deformation possible.

are line defects,

slip between crystal planes result when dislocations

move,

produce permanent (plastic) deformation.

Dislocations:

Schematic of Zinc (HCP): after tensile elongation

Line Defects

4

before deformation after tensile elongation

slip steps

Line Defects (Dislocations) Are one-dimensional defects around which atoms

are misaligned

Edge dislocation: extra half-plane of atoms inserted in a crystal

structure

b (the Bergers vector) is (perpendicular) to dislocation line

Screw dislocation: Screw dislocation: spiral planar ramp resulting from shear deformation

b is || (parallel) to dislocation line

Burgers vector, b: is a measure of lattice distortion

and is measured as a distance along the close

packed directions in the lattice

Imperfections in Solids

Linear defects are associated primarily with mechanical deformation.

Types of dislocations: edge, screw

Edge dislocation:

extra half-plane of atoms inserted in a crystal structure; the edge

of the plane terminates within the crystal.

Around the dislocation line there is some localized distortion.

b perpendicular () to dislocation line b perpendicular () to dislocation line

Bonds across the slipping planes are broken and

remade in succession.

The (plastic) permanent deformation of most

crystalline materials is by dislocation movement.

Most contain some dislocations that were introduced

Motion of Edge Dislocation

7

during solidification, plastic deformations, and rapid

cooling (thermal stresses).

To deform plastically means to slide atomic planes

past each other.

Imperfections in Solids

Screw dislocation:

Named for the spiral stacking of crystal planes around the

dislocation line; results from shear deformation

b parallel (||) to dislocation line

8

Characteristics of Dislocations

During plastic deformation, the number of dislocations

increase dramatically to densities of 1010 mm-2.

Grain boundaries, internal defects and surface

irregularities serve as formation sites for dislocations

during deformation.

The number of dislocations in a material is expressed The number of dislocations in a material is expressed

as the dislocation density- the total dislocation

length per unit volume or the number of

dislocations intersecting a unit area. Dislocation

densities can vary from 105 cm-2 in carefully solodified

metal crystals to 1012 cm-2 in heavily deformed metals.

Dislocations During Cold Working

Ti alloy after cold working.

Dislocations entangle with one

another during cold work.

Dislocation movement

10

Dislocation movement

becomes more difficult.

Dislocations are visible in

electron micrographs

Vacancy atoms

Interstitial atoms

Substitutional atomsPoint defects

1-2 atoms

Types of Imperfections

Dislocations Line defects1-dimensional

Grain Boundaries

twins, twists

Area/Planar defects

2-dimensional

The free or external surface of any material is the most

common type of planar defect!

Polycrystalline Materials

Grain Boundaries regions between crystals

transition from lattice of one

region to another

(a) The atoms near the boundaries of

12

(a) The atoms near the boundaries of

the 3 grains do not have an

equilibrium spacing or

arrangement; slightly disordered.

(b) Grains and grain boundaries in a

stainless steel sample. low density

in grain boundaries

Planar Defects in Solids - Twinning

A shear force that causes atomic displacements such that the atoms on one side of a plane (twin boundary) mirror the atoms on the other side. A reflection of atom positions across the twin plane.

Displacement magnitude in the twin region is proportional to the atoms distance from the twin plane.

Takes place along defined planes and directions depending Takes place along defined planes and directions depending upon the system.

Ex: BCC twinning occurs on the (112)[111] system

Slip Systems

Usually there are preferred slip planes and

directions in crystal systems.

The combination of both the slip plane and

direction form the slip system.

Slip plane is generally taken as the closest Slip plane is generally taken as the closest

packed plane in the system

Slip direction is taken as the direction on the

slip plane with the highest linear density.

Slip Systems

FCC and BCC materials have large numbers of slip systems (at

least 12) and are considered ductile.

HCP systems have few slip systems and are quite brittle.

Slip Systems

Twinning

Applied stress to a perfect crystal (a) may cause a displacement of the atoms,

(b) causing the formation of a twin. Note that the crystal has deformed as a

result of twinning.

Properties of Twinning

Of the three common crystal structures BCC, FCC and

HCP, the HCP structure is the most likely to twin.

FCC structures will not usually twin because slip is

more energetically favorable.

Twinning occurs at low temperatures and high rates of

shear loading (shock loading) conditions where there are

few present slip systems (restricting the possibility of few present slip systems (restricting the possibility of

slip)

Small amount of deformation when compared with slip.

Comparison

Slip Twinning

orientation of atomsremains the same

reorientation of atomicdirection across twin planeremains the same direction across twin plane

displacements take placein exact atomic spacings

atomic displacement is lessthan interatomic spacing

Microscopic Examination

Applications

To Examine the structural elements and defects that

influence the properties of materials.

Ensure that the associations between the properties and

structure (and defects) are properly understood.structure (and defects) are properly understood.

Predict the properties of materials once these

relationships have been established.

Structural elements exist in macroscopic and

microscopic dimensions

Microscopic Examination

Metallography sample preparation is necessary to examine the surface of materials (metals, ceramics, polymers).

A smooth mirror-like finish is obtained by grinding and polishing using successively finer abrasive papers and powder mixed with water.abrasive papers and powder mixed with water.

The microstructure (grain size, shape, orientation) is revealed using a chemical reagent (etching solution) on a polycrystalline sample.

Etching characteristics vary from grain to grain.

Microscopy

Optical (light) resolution (0.1 m = 100 nm = 10-7 m)

For higher resolution need higher frequency

X-Rays are difficult to focus.

Electrons

wavelengths are roughly 3 pm (0.003 nm) wavelengths are roughly 3 pm (0.003 nm)

(Magnification - 1,000,000X)

Atomic resolution possible

Electron beam focused by magnetic lenses.

Useful up to 2000X magnification.

Polishing removes surface features (e.g., scratches)

Etching changes reflectance, depending on crystal

orientation.

Optical Microscopy

Micrograph of

brass (a Cu-Zn alloy)

0.75mm

crystallographic planes

Grain boundaries...

are imperfections,

are more susceptible

Optical Microscopy

grain boundary

surface groove

polished surface

are more susceptible

to etching

may be revealed as

dark lines

change in crystal

orientation across

boundary.

grain boundary(a)

Polycrystalline Deformation

The grain size is often determined when the properties of

a polycrystalline material are under consideration. The

grain size has a significant impact of strength and

response to further processing

Linear Intercept method

Straight lines are drawn through several

photomicrographs that show the grain

Grain Size Determination

photomicrographs that show the grain

structure.

The grains intersected by each line segment are

counted

The line length is then divided by an average

number of grains intersected.

The average grain diameter is found by dividing this

result by the linear magnification of the

photomicrographs.

ASTM (American Society for Testing and Materials)

VISUAL CHARTS (@100x) each with a number

Quick and easy used for steel

ASTM has prepared several standard comparison charts, all having different

average grain sizes. To each is assigned a number from 1 to 10, which is

termed the grain size number; the larger this number, the smaller the grains.

Quick and easy used for steel

N = 2 n-1No. of grains/square inch

Grain size no.

NOTE: The ASTM grain size is related a grain area

AT 100x MAGNIFICATION

Determining Grain Size, using a Micrograph

taken at 300x

We count 14 grains

in a 1 in2 area on the

image

To report ASTM

2

12100

M is mag. of image

N is measured grain count at M

now solve for n:

n

M

M

MN

=

To report ASTM

grain size we need N

at 100x not 300x

We need a

conversion method!

( ) ( )( ) ( ) ( )

( ) ( )( )

( ) ( )

now solve for n:

log( ) 2 log log 100 1 log 2

log 2log 41

log 2

log 14 2log 300 41 7.98 8

0.301

M

m

N M n

N Mn

n

+ =

+ = +

+ = + =

For this same material, how many Grains

would I expect /in2 at 100x?

1 8 1 22 2 128 grains/in

Now, how many grain would I expect at 50x?

nN

= =

2 2

8 1

2 2

100 100N 2 128*

50

N 128*2 512 grains/in

M

M

M

= =

= =

300

400

500

600

N

u

m

b

e

r

o

f

G

r

a

i

n

s

/

i

n

2

At 100x

0

100

200

0 2 4 6 8 10 12

Grain Size number (n)

N

u

m

b

e

r

o

f

G

r

a

i

n

s

/

i

n

2

Electron Microscopes

beam of electrons of

shorter wave-length

(0.003nm) (when

accelerated across large

voltage drop)

Image formed with

Magnetic lenses

High resolutions and

magnification (up to

50,000x SEM); (TEM up

to 1,000,000x)

Uses a moveable Probe of very small diameter

to move over a surface

Atoms can be arranged and imaged!

Photos produced from

the work of C.P. Lutz,

Zeppenfeld, and D.M.

Eigler.

Scanning Tunneling Microscopy (STM)

Carbon monoxide

molecules arranged on

a platinum (111)

surface.

Eigler.

Iron atoms arranged

on a copper (111)

surface. These Kanji

characters represent

the word atom.

Summary

Point, Line, and Area defects exist in solids.

The number and type of defects can be varied and controlled

T controls vacancy conc.

amount of plastic deformation controls # of dislocations

Weight of charge materials determine concentration of Weight of charge materials determine concentration of substitutional or interstitial point defects

Defects affect material properties (e.g., grain boundaries control crystal slip).

Defects may be desirable or undesirable

e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.

Inclusions can be intention for alloy development