solidification of metals - faculty of mechanical engineering –nhayati/chapter 3 crystal defect...

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33

Learning Objectives

� Study the principles of solidification as they apply topure metals.

� Examine the mechanisms by which solidificationoccurs.

2-2

Chapter Outline

� Importance of Solidification

� Nucleation and Growth

� Cooling Curves

� Cast Structure

2-3

Solidification of Metals

� Solidification of metals and their alloys is animportant industrial process:

� Metals and alloys start with the casting of ingotsfor processing into semi-finished or finishedproducts (bars, rods, and other shapes)

� During welding, a small region of the metal nearthe weld melts and resolidify

� During soldering, the whole solder alloy melts andresolidify

� Other processes which involve solidification:casting, glass forming

2-4


� Solidification of metals is a phase transformationfrom liquid to solid

� It occurs because the original state of the metal isunstable relative to the final state

But how is phase stability measured?

� The answer is provided by thermodynamicsthermodynamics.

2-5 2-6

GGL

GS

GS < GL

GL < GS

Liquid is stable

TmT

GL

GS

∆G

Solid is stable

TSolidification

Solid phase will form when a liquidmetal is cooled below Tm.

The driving force promoting thistransformation is the differencebetween the free energy of thesolid and liquid phases ∆G

2


� Solidification proceeds in 2 steps:

�� NucleationNucleation ofof aa newnew phasephase (formation of smallclusters (embryos or nuclei) in the melt and reach acritical size)

�� GrowthGrowth ofof thethe newnew phasephase:: growth of the stable nuclei

� Thermal gradients define the shape of eachgrain

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2-8

Stages of solidification of a pure metal

� Nucleation - The physical process by which a new phaseis produced in a material.

� Critical radius (r*) - The minimum size that must be formedby atoms clustering together in the liquid before the solidparticle is stable and begins to grow.

� Undercooling - The temperature to which the liquid metalmust cool below the equilibrium freezing temperaturebefore nucleation occurs.

� Homogeneous nucleation - Formation of a critically sizedsolid from the liquid by the clustering together of a largenumber of atoms at a high undercooling (without anexternal interface).

� Heterogeneous nucleation - Formation of a critically sizedsolid from the liquid on an impurity surface.

2-9

Nucleation

There are 2 types of nucleation:

�� HomogeneousHomogeneous: the solid nuclei appears spontaneously within the undercooled liquid

�� HeterogeneousHeterogeneous: the new solid phase nucleates at themould wall, impurities etc…

2-10

Homogeneous Nucleation

2-11

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� First and simplest case� Metal itself will provide atoms to form nuclei.� Metal, when significantly undercooled, has several

slow moving atoms which bond each other to formnuclei.

� Cluster of atoms below critical size (r*) is calledembryo.

� If the cluster of atoms reach critical size, they growinto crystals. Else get dissolved.

� Cluster of atoms that are greater than critical size arecalled nucleus

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herein under license.

Heterogeneous Nucleation

� Heterogeneous nucleationoccurs when there areforeign or special objectsinside a phase which cancause nucleation

� Such objects include:mould wall, impurities,other metal additions(grain refiner)

2-14

Liquid

Solid

Mould wall


� During solidification, nucleation involves the formation ofsmall solid particles surrounded by liquid

2-15

Liquid

Liquid

Solid

Liquid

Solid

Undercooled Liquid Homogeneous nucleation

Heterogeneous Nucleation

2-16

Nucleation Growth

Stages in the formation of a grain structure during solidification

Growth Grain boundaries

Cooling Curves

a) Cooling curve of a pure metal

with undercooling (metal iswell inoculated)

b) without undercooling (no

inoculation)

2-17

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Cooling Curves

� Recoalescence - The increase in temperature of anundercooled liquid metal as a result of the liberationof heat during nucleation.

� Thermal arrest - A plateau on the cooling curve duringthe solidification of a material caused by the evolutionof the latent heat of fusion during solidification.

� Total solidification time - The time required for thecasting to solidify completely after the casting hasbeen poured.

� Local solidification time - The time required for aparticular location in a casting to solidify oncenucleation has begun.

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Cast Structure

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Development of the ingot

structure of a casting duringsolidification:

(a) Nucleation begins,(b) Chill zone forms,

(c) Preferred growth produces

the columnar zone,(d) Additional nucleation

creates the equiaxed zone

Cast Structure

2-20

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Cast ingot

Cast Structure: Dendrites

2-21

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Learning Objectives

� Introduce the three basic types ofimperfections: point defects, line defects (or

dislocations), and surface defects.

� Explore the nature and effects of differenttypes of defects.

2-2

Crystal Defects

� An ideal crystalline material is described in terms of a 3-D periodic arrangement of lattice points and an atom orgroup of atoms associated with each lattice point calledbasis

� However, when there is deviation from this ideality, thematerial is said to have crystal defects

2-3

Types of Crystal Defects & their Scale

2-4

Vacancies,

impuritiesdislocations Grain and twin

boundaries

Voids

Inclusions

precipitates

Point, Line, Surface (Planar), and volumetric defects

From Chawla and Meyers, Mechanical Behavior of Materials

Crystal Defects

� Point defects - Imperfections, such as vacancies, that are located

typically at one (in some cases a few) sites in the crystal.

� Extended (Line) defects - Defects that involve several atoms/ions

and thus occur over a finite volume of the crystalline material (e.g.,

dislocations, stacking faults, etc.).

� Vacancy - An atom or an ion missing from its regular

crystallographic site.

� Interstitial defect - A point defect produced when an atom is placed

into the crystal at a site that is normally not a lattice point.

� Substitutional defect - A point defect produced when an atom is

removed from a regular lattice point and replaced with a different

atom, usually of a different size.

2-5

Importance of Defects

2-6

� Effect on Mechanical Properties via Control of the Slip Process

� Strain Hardening

� Solid-Solution Strengthening

� Grain-Size Strengthening

� Effects on Electrical, Optical, and Magnetic Properties

2

Types of Crystal Defects

2-7

• Vacancy atoms• Interstitial atoms• Substitutional atoms

• DislocationsEdges, Screws, Mixed

• Grain Boundaries• Stacking Faults• Twin Boundaries

Point defects

Line defects

Area/Planar defects

We need to describe them and understand their effects.

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Point defects: (a) vacancy, (b) interstitial atom, (c) small substitutional

atom, (d) large substitutional atom, (e) Frenkel defect, (f) Schottkydefect. All of these defects disrupt the perfect arrangement of the

surrounding atoms.

� The fact is there MUST be vacancies in a crystal !!!! 2-9

vacancy Interstitialimpurity

Substitutionalimpurity

1.Point Defects

2-10

Frenkel defect

Schottky defect

Defects in ionic solids/crystalsDefects in ionic solids/crystals

Cation vacancy

+cation interstitial

Cation vacancy

+anion vacancy

2. Line Defects: Dislocations

2-11

� Dislocation - A line imperfection in a crystalline material.

� Screw dislocation - A dislocation produced by skewing a crystal

so that one atomic plane produces a spiral ramp about thedislocation.

� Edge dislocation - A dislocation introduced into the crystal by

adding an ‘‘extra half plane’’ of atoms.

� Mixed dislocation - A dislocation that contains partly edge

components and partly screw components.

� Slip - Deformation of a metallic material by the movement ofdislocations through the crystal.

2-12

Missing half plane� A Defect

3

2-13

An extra half plane…

…or a missing half plane 2-14

Edge dislocation

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1234568 79101112131415

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S

b 16F

⊥⊥⊥⊥Map the same Burgers circuit on a

real crystal

2-16

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A closed Burgers Circuit

in an ideal crystal

SF

14 15 16

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Burgers Vector

2-17

Johannes Martinus BURGERS

Burgers vector

Burger’s vector

2-18

b

t

b || t

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3

4

Line Defects: Dislocations

2-19

Comparison between EDGE and SCREW Dislocations:

• Edge Dislocation: dislocation line (t) is normal to the burgers vector (b)

• Screw dislocation: dislocation line (t) is parallel to the Burgers vector (b)


2-20


2-21

Dislocations are formed

• solidification• plastic deformation• thermal stresses from cooling

Movement of Edge Dislocation

2-22

Movement of an edge dislocation across the crystal lattice under a shearstress. Dislocations help explain why the actual strength of metals inmuch lower than that predicted by theory.

2-23

Burger’s

Vector = b

3. Planar Defects

2-24

• All defects increase energy (energy is higher than perfect crystal)Surfaces, grains, interphase and twin boundaries, stacking faults

• Planar Defect Energy is Energy per Unit Area(J/m2)

• Surfaces: missing or fewer number of optimal or preferred bonds.

5

Planar Defects: Grain Boundaries

2-25

GB: missing or fewer number of optimal or preferred bonds.

Planar Defects: Twinning

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Application of a stress to the perfect crystal (a) may cause a

displacement of the atoms, (b) causing the formation of a twin. Note thatthe crystal has deformed as a result of twinning.

Planar Defects: Twinning

2-27

• Occurs in metals with BCC or HCP crystal

structure

• Occurs at low temperatures and high rates

of

shear loading (shock loading)

• Occurs in conditions in which there are fewpresent slip systems (restricting the possibility

of slip)

• Small amount of deformation when

compared

with slip.

4. Volume Defects

2-28

• Volume defects include undesirable

defects such as:

• voids or porosity found in casting

• Inclusions or foreign particles

• But, they also include precipitates or

second phase particles whichcontribute to strengthening of the

material

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Learning Objectives

� Explain what is diffusion and why is it an importantpart of metal processing?

� How does diffusion in metals occur?

� How can the diffusion rate can be predicted

� Factors affecting diffusion (rate of diffusion)

2-2

Chapter Outline

� Diffusion: definition, importance of diffusion in metal processing

� Types of Diffusion

� Mechanisms of diffusion

� Steady-state diffusion: Fick’s First Law

� Example of metal processing using diffusion

2-3

DiffusionWhat is diffusion?

� Diffusion is the atom movement (migration) in materials (solids,liquids, or gases)

Why is diffusion important?

� Diffusion plays an important role in many areas of materialsscience

� It is important in processes such as:� Heat treatment (phase transformation from solid to solid)� Solidification (liquid to solid)

� Surface hardening of steel (carburising, nitriding, carbo-nitridingetc…)

� Corrosion and oxidation� Coatings (galvanising, electroplating, anodising)

2-4

Types of Diffusion�� ThereThere areare 22 typestypes ofof diffusiondiffusion inin crystallinecrystalline solidssolids::

1.1. ImpurityImpurity diffusiondiffusion alsoalso calledcalled interinter--diffusiondiffusion

�� OccursOccurs inin aa solidsolid materialmaterial withwith moremore thanthan oneone typetype ofofelementelement (such(such asas anan alloy)alloy)

22.. SelfSelf--diffusiondiffusion

�� OccursOccurs inin chemicallychemically purepure materialsmaterials (only(only oneone typetype ofofatoms)atoms)

� For diffusion to occur pointpoint defectsdefects (vacancy) must be present in acrystal (atomic diffusion is in a way the migration of these defects)

2-5

Different Types of flows in materials

� Electrical Current : flow of electric charge

� Heat transfer : flow of temperature

� Diffusion : flow of matter

2-6

2

Mechanisms of Diffusion

� Self-diffusion - The random movement of atoms within an essentially pure material.

� Vacancy diffusion (also called Substitutional diffusion)-Diffusion of atoms when an atom leaves a regular lattice position to fill a vacancy in the crystal.

� Interstitial diffusion - Diffusion of small atoms from one interstitial position to another in the crystal structure.

2-7


2-8

VacancyInterstitial

impurity

Substitutional

impurity


2-9

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Diffusion mechanisms in a material: (a) vacancy or substitutional atom

diffusion and (b) interstitial diffusion

Activation Energy for Diffusion

2-10

� Diffusion couple - A combination of elements involved in

diffusion studies

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A high energy is required to

squeeze atoms past oneanother during diffusion.

This energy is theactivation energy Q.

Generally more energy isrequired for a substitutional

atom than for an interstitial

atom

Vacancy Diffusion

� Occurs in substitutional solid solutions� Requires vacancies and activation energy� A substitutional atom will only be able to move if there is

a vacancy� Vacancy moves in opposite direction of atomic

movement

Rate of vacancy diffusion (fast or slow) depends on:� Concentration of vacancies (number of vacancies increases as

the temperature increases)

� Activation energy for atom migration

� Example of vacancy diffusion: Ni in Cu alloy

2-11

Interstitial Diffusion

� Migration of an interstitial atom to an adjacent vacant interstitial site

� Occurs in interstitial solid solutions

Rate of diffusion depends on:

� Concentration of interstitial atoms

� Interstitial diffusion is faster than vacancy diffusion because:

� more empty interstitials are present � no vacancy is required

� Example of interstitial diffusion: C in Fe (steel)

2-12

3

Driving Force for Diffusion

� The driving force (whydiffusion occurs) for diffusionis a “concentration gradient”

� Atoms will diffuse only if thereis a “concentrationconcentration gradientgradient.”

� Atoms can diffuse fromregions of high concentrationtowards regions of lowconcentration and vice versa.

2-13

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2-14

T oC

Time

Cu Ni

NiCu

Distance (x)

Co

nc

en

tra

tio

n o

f C

u

0

100

Distance (x)

Co

nc

en

tra

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f C

u

0

100

Rate of Diffusion: Fick’s First Law

2-15

� Fick’s first law - The equation relating the flux ofatoms by diffusion to the diffusion coefficient and theconcentration gradient.

� Diffusion coefficient (D) - A temperature-dependentcoefficient related to the rate at which atoms, ions, orother species diffuse.

� Concentration gradient - The rate of change ofcomposition with distance in a nonuniform material,typically expressed as atoms/cm3.cm or at%/cm.

Rate of Diffusion: Fick’s First Law

−=

RT

QDD exp0

2-16

• The diffusion rate follows the Arrhenius equation (valid for anythermally activated process)

• Where:

� D: is the diffusivity, which is proportional to the diffusion rate

� Do: is the temperature – independent constant (m2 .s-1)

� Q: is the activation energy (J. mole-1)

� R: is the gas constant (8.314 J. mole-1 K-1)

� T: is the absolute temperature (K)

Fick’s First Law: Steady-State Diffusion

−=

dx

dCDJ

2-17

1829-1901

• Steady-state diffusion means that the diffusion fluxdoes not vary with time

• The negative sign indicates that the direction of diffusion flux is “down” the concentration gradient from high to low concentration

� J: is the diffusion flux (atoms/ m2/ s or kg / m2 / s)� D: is the diffusivity (or diffusion coefficient) (m2 s-1)

� C: is the concentration� X: is the distance

� dC/ dx: concentration gradient

Factors Affecting Diffusion

2-18

1. Temperature

The diffusion rate increases with increase in temperature

2. Diffusing species (substitutional or interstitial atom) and host material (size, bonding)

Smaller atoms diffuse faster than bigger atoms

3. Microstructure

Diffusion at defects such as grain boundaries and dislocations is

much faster than in perfect crystals

Vacancy concentrations are also higher near these defects

4

Example of Processing using Diffusion

2-19

Case Hardening of gears:• Diffuse carbon atoms into the host iron atoms at the surface.

• Result is the case (surface) is harder and so is difficult to deform

and crack

solidification of metals - faculty of mechanical engineering –nhayati/chapter 3 crystal defect...

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