# Phase Transformation Chapter 9

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Phase Transformation Chapter 9

Shiva-Parvati, Chola Bronze
Q: How was the statue made? A: Invest casting Liquid-to-solid transformation An example of phase transformation Shiva-Parvati, Chola Bronze Ball State University

Czochralski crystal pulling technique
How does one produce single crystal of Si for electronic applications? Czochralski crystal pulling technique

Quenching of steel components a solid->solid phase transformation
How does one harden a steel component? Quenching of steel components a solid->solid phase transformation

Solid state phase transformation Solid 1 Solid 2 melting solidification sublimation condensation gas Liquid evaporation

Thermodynamic driving force for a phase transformation?
Decrease in Gibbs free energy Liquid-> solid gs - gl = g = -ve

g Gibbs free energy as a function of temperature, Problem 2.3 gL gS g gL < gS Solid is stable Liquid is stable gS < gL gS gL T Tfreezing Tm Fig. 9.1

How does solidification begins?
Usually at the walls of the container Heterogeneous nucleation. Why? To be discussed later.

Spherical ball of solid of radius R in the middle of the liquid at a temperature below Tm
Homogeneous nucleation r gL = free energy of liquid per unit volume gS = free energy of solid per unit volume g = gS - gL

Change in free energy of the system due to formation of the solid ball of radius r :
p 2 4 r + +ve: barrier to nucleation r r r*

Solid balls of radius r < r
Solid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!! g p 2 4 r + Solid balls of radii r > r* will grow r r* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION r*

g p 2 4 r + Eqn. 9.4 r r* Eqn. 9.5

Driving force for solidification
Tm gL gS T g (T) Eqn. 9.7 T

g p 4 r + g p 4 r + f Fig. 9.3 f1* f2* r r2* r1* Eqn. 9.7 T2 <

Critical particle Fig. 9.4 Atoms surrounding the critical particle
Formation of critical nucleus by statistical fluctuation Critical particle Diffuse jump of a surrounding atom to the critical particle makes it a nucleation Fig. 9.4

The Nucleation Rate Nt=total number of clusters of atoms per unit volume N* = number of clusters of critical size per unit volume By Maxwell-Boltzmann statistics

Eqn. 9.9 s*= no. of liquid phase atoms facing the critical sized particle Hd = activation energy for diffusive jump from liquid to the solid phase  = atomic vibration frequency The rate of successful addition of an atom to a critical sized paticle Eqn. 9.10

1. Driving force increases 2. Atomic mobility decreases
Rate of nucleation, I , (m3 s-1) = No. of nucleation events per m3 per sec = number of critical clusters per unit volume (N*) x rate of successful addition of an atom to the critical cluster (’) T Eqn. 9.11 Tm With decreasing T 1. Driving force increases 2. Atomic mobility decreases I

Growth Increase in the size of a product particle after it has nucleated T U

Overall Transformation Kinetics
I : Nucleation rate T U U : Growth rate dX/dt Overall transformation rate (fraction transformed per second) I X=fraction of product phase

Fraction transformed as a function of time
X Slow due to final impingement Slow due to very few nuclei t ts tf

TTT Diagram for liquid-to-solid transformation
X log t ts tf 1 TTT Diagram for liquid-to-solid transformation dX/dt T T Stable liquid Tm C- curves Crystallization begins L+ Crystallization ends crystal Under Cooled liquid log t

TTT Diagram for liquid-to-solid transformation
Stable liquid Under Cooled liquid log t Tm Fine grained crystals Coarse grained crystals glass

SiO2: low hm, high viscosity
ts metals ts SiO2 Metallic glass Silica glass log t Eqn. 9.11 SiO2: low hm, high viscosity Eqn. 9.8 Metals: high hm, low viscosity Hd ∝ log (viscosity)

Melt Spinning for metallic glass ribbons
u M o l y H c i Q z b R d m J f Melt Spinning for metallic glass ribbons Cooling rate 106 ºC s-1 F r o m P r i n c i p l e s o f E l e c t r o n i c M a t e r i a l s a n d D e v i c e s , S e c o n d E d i t i o n , S . O . K a s a p ( M c G r a w - H i l l , 2 2 ) h t t p : / / M a t e r i a l s . U s a s k . C a

T Log (viscosity Pa-s) crystal 30 log t glass 18 Fig. 9.17 12
Tm Log (viscosity Pa-s) L+ crystal 30 log t glass 18 Fig. 9.17 12 Undercooled liquid Stable liquid Tg T Tm

Specific volume Stable liquid Undercooled liquid Fast cool Fig. 9.18 Slow cool crystal Tgf Tgs T Tm

Glass ceramics T log t T T U TU Very fine crystals TI Fig. 9.16 I time
Stable liquid Tm Undercooled liquid L+ devitrification glass crystal log t U I T T Liquid growth TU Very fine crystals nucleation TI Fig. 9.16 glass Glass ceramic time

Corningware PyroceramTM heat resistant cookware
Corning’s new digital hot plates with PyroceramTM tops. ROBAX® was heated until red-hot. Then cold water was poured on the glass ceramic from above - with NO breakage.

Czochralski crystal pulling technique for single crystal Si
J. Czochralski, ( ) Polish Metallurgist SSPL: Solid State Physics Laboratory, N. Delhi

TABLE 9.2 Hardness Rockwell C Wt% C Micro-structure Heat treatment Steel Coarse pearlite A 15 0.8 Annealing fine pearlite B 30 0.8 normalizing C 45 0.8 bainite austempering Tempered martensite D 55 0.8 tempering E 65 0.8 martensite quenching

HEAT TREATMENT Heating a material to a high temperature, holding it at that temperature for certain length of time followed by cooling at a specified rate is called heat treatment

holding T heating AT A Q T N time Annealing Furnace cooling RC 15 Normalizing Air cooling RC 30 Quenching Water cooling RC 65 Tempering Heating after quench RC 55 Austempering Quench to an inter- RC mediate temp and hold

Ammount of Fe3C in Pearlite
Eutectoid Reaction 0.8 0.02 6.67 cool Pearlite Ammount of Fe3C in Pearlite Red Tie Line below eutectoid temp

austenite-> pearlite
Phase diagrams do not have any information about time or rates of transformations. We need TTT diagram for austenite-> pearlite transformation

TTT diagram for eutectoid steel
Stable austenite start finish unstable austenite

TTT diagram for eutectoid steel
Stable austenite unstable austenite start finish Annealing: coarse pearlite Normalizing: fine pearlite

Callister

TTT diagram for eutectoid steel QUENCHING
Stable austenite Hardness RC 65 start finish ’: martensite (M) Extremely rapid, no C-curves unstable austenite Ms : Martensite start temperature Ms A+M Mf : Martensite finish temperature Mf M

Martensitic transformation
Amount of martensite formed does not depend upon time, only on temperature. Atoms move only a fraction of atomic distance during the transformation: 1. Diffusionless (no long-range diffusion) 2. Shear (one-to-one correspondence between  and ’ atoms) BCT 3. No composition change

Martensitic transformation (contd.)
Problem 3.1 Contract ~ 20% BCT unit cell of  (austenite) Expand ~ 12% BCT unit cell of ’ (martensite) 0% C (BCC) 1.2 % C Fig. 9.12

Martensitic transformation (contd.)
Hardness of martensite as a function of C content 60 40 Hardness, RC Fig. 9.13 20 0.2 0.4 0.6 Wt % Carbon → Hardness of martensite depends mainly on C content and not on other alloying additions

T heating AT A Q T N

TEMPERING Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling. T<TE ?

Tempering (contd.) +Fe3C PEARLITE A distribution of fine particles of Fe3C in  matrix known as TEMPERED MARTENSITE. Hardness more than fine pearlite, ductility more than martensite. Hardness and ductility controlled by tempering temperature and time. Higher T or t -> higher ductility, lower strength

Tempering Continued Callister

Austempering Bainite Short needles of Fe3C embedded in plates of ferrite

Quench Cracks Problems in Quenching High rate of cooling: surface cooler than interior Surface forms martensite before the interior Austenite martensite Volume expansion When interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses

Solution to Quench cracks
Shift the C-curve to the right (higher times) More time at the nose Slower quenching (oil quench) can give martensite But how to shift the C-curve to higher times?

By alloying All alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right. Exception: Co Substitutional diffusion of alloying elements is slower than the interstitial diffusion of C

Alloy steel Plain C steel Alloying shifts the C-curves to the right. Fig. 9.10 Separate C-curves for pearlite and bainite

Hardenability Ability or ease of hardening a steel by formation of martensite using as slow quenching as possible Alloying elements in steels shift the C-curve to the right Alloy steels have higher hardenability than plain C steels.

Hardnenability Hardness Resistance to plastic deformation as measured by indentation Ability or ease of hardening a steel Only applicable to steels Applicable to all materials Alloying additions increase the hardenability of steels but not the hardness. C increases both hardenability and hardness of steels.

High Speed steel Alloy steels used for cutting tools operated at high speeds Cutting at high speeds lead to excessive heating of cutting tools This is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edge Alloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.

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Alfred Wilm’s Laboratory 1906-1909
Steels harden by quenching Why not harden Al alloys also by quenching?

Eureka ! Hardness has Increased !!
T Wilm’s Plan for hardening Al-4%Cu alloy Hold 550ºC Heat Quench Check hardness time Sorry! No increase in hardness. Eureka ! Hardness has Increased !! One of the greatest technological achievements of 20th century

Hardness increases as a function of time: AGE HARDENING
Property = f (microstructure) Wilm checked the microstructure of his age-hardened alloys. Result: NO CHANGE in the microstructure !!

Hardness initially increases: age hardening
Peak hardness Hardness Overaging As- quenched hardness time Hardness initially increases: age hardening Attains a peak value Decreases subsequently: Overaging

: solid solution of Cu in FCC Al +
Tsolvus : solid solution of Cu in FCC Al + : intermetallic compound CuAl2 4 supersaturated saturated  Precipitation of  in  FCC FCC Tetragonal 4 wt%Cu 0.5 wt%Cu 54 wt%Cu

TTT diagram of precipitation of  in 
Stable  Tsolvus  start unstable   finsh + As-quenched  Aging A fine distribution of  precipitates in  matrix causes hardening Completion of precipitation corresponds to peak hardness

-grains As quenched -grains +  Aged Peak aged Dense distribution of fine  overaged Sparse distribution of coarse  Driving force for coarsening / interfacial energy

Aging temperature hardness 100ºC 20ºC 180ºC Fig. 9.15 Aging time 0.1 1 10 100 (days) Peak hardness is less at higher aging temperature Peak hardness is obtained in shorter time at higher aging temperature

T U + I 1  start  finsh 180 ºC 100 ºC Aging hardness Stable 
Tsolvus  start unstable   finsh + 180 ºC 100 ºC As-quenched  Aging I 1 hardness 180ºC 100ºC 20ºC

Recovery, Recrystallization and grain growth
Following slides are courtsey Prof. S.K Gupta (SKG) Or Prof. Anandh Subramaniam (AS)

AS Plastic deformation in the temperature range above(0.3 – 0.5)
Tm → COLD WORK ↑ point defect density Cold work ↑ dislocation density Point defects and dislocations have strain energy associated with them (1 -10) % of the energy expended in plastic deformation is stored in the form of strain energy AS

↑ Strength ↑ Hardness Cold work ↑ Electrical resistance ↓ Ductility AS

Anneal Cold work Recovery Recrystallization Grain growth AS

Recovery, Recrystallization and Grain Growth
During recovery 1. Point Defects come to Equilibrium 2. Dislocations of opposite sign lying on a slip plane annihilate each other (This does not lead to substantial decrease in the dislocation density) SKG

AS POLYGONIZATION Bent crystal Polygonization
Low angle grain boundaries AS

Recrystallization Strained grains Strain-free grains
Driving force for the Process = Stored strain energy of dislocations SKG

Recrystallization Temperature:
Temperature at which the 50% of the cold-worked material recrystallizes in one hour Usually around 0.4 Tm (m.p in K) SKG

Factors that affect the recrystallization temperature:
1. Degree of cold work 2. Initial Grain Size 3. Temperature of cold working 4. Purity or composition of metal Solute Drag Effect Pinning Action of Second Phase Particle SKG

Solute Drag Effect SKG

Grain Boundary Pinning
SKG

Grain Growth Increase in average grain size following recrystallization Driving Force reduction in grain boundary energy Impurities retard the process SKG

Grain growth Globally ► Driven by reduction in grain boundary energy Locally ► Driven by bond maximization (coordination number maximization) AS

AS Bonded to 4 atoms Bonded to 3 atoms
Direction of grain boundary migration JUMP Boundary moves towards its centre of curvature

AS Hot Work and Cold Work
Hot Work  Plastic deformation above TRecrystallization Cold Work  Plastic deformation below TRecrystallization Hot Work Recrystallization temperature (~ 0.4 Tm) Cold Work AS

Annealing Temperature %CW
Electical conductivity Internal stress Ductility Tensile strength Cold work Recovery Recrystallization Grain growth Annealing Temperature %CW Fig. 9.19 AS