phase transformation

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Phase Transformation Chapter 9


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


Czochralski crystal pulling technique for single crystal Si


Quenching of steel components a solid->solid phase transformation


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


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


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


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


Spherical ball of solid of radius R in the middle of the liquid at a temperature below Tm Homogeneous nucleation 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 : +ve: barrier to nucleation r r*


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


r r* Eqn. 9.5 Eqn. 9.4


T Eqn. 9.7


f r Eqn. 9.8 Eqn. 9.7 Fig. 9.3 r1* f1* f2* r2* T1 T2 <


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


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


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 Eqn. 9.9


Rate of nucleation, I , (m3 s-1) With decreasing T 1. Driving force increases 2. Atomic mobility decreases = 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 (’) Eqn. 9.11


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


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


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


TTT Diagram for liquid-to-solid transformation T Stable liquid Under Cooled liquid crystal Crystallization begins L+ Crystallization ends log t Tm C- curves


TTT Diagram for liquid-to-solid transformation Coarse grained crystals Fine grained crystals glass


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


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 0 0 2 ) h t t p : / / M a t e r i a l s . U s a s k . C a Melt Spinning for metallic glass ribbons


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


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


log t L+ T Stable liquid Undercooled liquid Tm devitrification time T Glass ceramics nucleation growth glass Glass ceramic Liquid glass crystal Very fine crystals


Corning’s new digital hot plates with PyroceramTM tops. Corningware PyroceramTM heat resistant cookware 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 SSPL: Solid State Physics Laboratory, N. Delhi J. Czochralski, (1885-1953) Polish Metallurgist


You may collect slide handouts for chapters 6, 7 and 8 from Scoops Xerox Shop no more grades, no more pencils, no more sharing/using stencils, no more reading, no more books, no more teachers dirty looks, so when we hear that final bell, we drop our books and run like hell !!


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


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


A N AT T Q heating holding time T 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 45 mediate temp and hold


Ammount of Fe3C in Pearlite Red Tie Line below eutectoid temp


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


Stable austenite unstable austenite TTT diagram for eutectoid steel start finish


Annealing: coarse pearlite Normalizing: fine pearlite TTT diagram for eutectoid steel




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


BCT 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) 3. No composition change Martensitic transformation


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


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


A N AT T Q heating T


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


Problems in Quenching Quench Cracks 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


But how to shift the C-curve to higher times? 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


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


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


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 Ability or ease of hardening a steel Resistance to plastic deformation as measured by indentation 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?


time Wilm’s Plan for hardening Al-4%Cu alloy Sorry! No increase in hardness. 550ºC T Heat Quench Hold Check 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 !!


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


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


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


Driving force for coarsening / interfacial energy


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


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


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


Cold work ↑ dislocation density ↑ point defect density Plastic deformation in the temperature range above(0.3 – 0.5) Tm → COLD WORK 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


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


Cold work Anneal Recrystallization Recovery Grain growth AS

Recovery, Recrystallization and Grain Growth: 

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


POLYGONIZATION Bent crystal Low angle grain boundaries Polygonization 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: 

Solute Drag Effect SKG

Grain Boundary Pinning: 

Grain Boundary Pinning SKG

Grain Growth: 

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


Direction of grain boundary migration Boundary moves towards its centre of curvature JUMP AS


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


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

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