# PHASE TRANSFORMATIONS

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PHASE TRANSFORMATIONS
Nucleation Growth APPLICATIONS  Transformations in Steel  Precipitation  Solidification & crystallization  Glass transition  Recovery, Recrystallization & Grain growth Phase Transformations in Metals and Alloys David Porter & Kenneth Esterling Van Nostrand Reinhold Co. Ltd., New York (1981)

PHASE TRANSFORMATIONS PHASE TRANSFORMATIONS
Based on Mass transport PHASE TRANSFORMATIONS Diffusional Martensitic Based on order PHASE TRANSFORMATIONS 1nd order nucleation & growth 2nd order Entire volume transforms

Bulk Gibbs free energy ↓
Energies involved Interfacial energy ↑ Strain energy ↑ Solid-solid transformation New interface created Volume of transforming material The concepts are illustrated using solidification of a metal

1nd order nucleation & growth
Growth till  is exhausted Nucleation of  phase Trasformation  →  = +

Liquid → Solid phase transformation
On cooling just below Tm solid becomes stable But solidification does not start E.g. liquid Ni can be undercooled 250 K below Tm ↑ t Solid stable Liquid stable G Solid (GS) G → ve G → Liquid (GL) T G → +ve “For sufficient Undercooling” Tm T → T - Undercooling

Solidification Nucleation Growth = + Nucleation Homogenous Nucleation Liquid → solid walls of container, inclusions Solid → solid inclusions, grain boundaries, dislocations, stacking faults Heterogenous The probability of nucleation occurring at point in the parent phase is same throughout the parent phase In heterogeneous nucleation there are some preferred sites in the parent phase where nucleation can occur

Neglected in L → S transformations Homogenous nucleation r3 r2 1

Reduction in free energy is obtained only after r0 is obtained
By setting dG/dr = 0 the critical values (corresponding to the maximum) are obtained (denoted by superscript *) Reduction in free energy is obtained only after r0 is obtained As Gv is ve, r*is +ve Trivial G → Embryos Supercritical nuclei r →

The bulk free energy reduction is a function of undercooling
Turnbull approximation Tm Increasing T Decreasing G* Decreasing r* G → r →

No. of critical sized particles
Frequency with which they become supercritical x Rate of nucleation = No. of particles/volume in L  → lattice vibration frequency (~1013 /s) s* atoms of the liquid facing the nucleus Critical sized nucleus Jump taking particle to supercriticality → nucleated (enthalpy of activation = Hd) Critical sized nucleus

I → G* ↑  I ↓ T ↑  I ↑ Tm T = Tm → G* =  → I = 0 Increasing T
T (K) → T = 0 → I = 0 I →

Heterogeneous nucleation
Consider the nucleation of  from  on a planar surface of inclusion  Interfacial Energies  Alens  Created   Acircle  Created Acircle  Lost Surface tension force balance Vlens = h2(3r-h)/3 Alens = 2rh h = (1-Cos)r rcircle = r Sin

G*hetero / G*homo →  (degrees) →
G*hetero (0o) = 0 no barrier to nucleation G*hetero (180o) = G*homo no benefit G*hetero / G*homo → G*hetero (90o) = G*homo/2 Complete wetting Partial wetting No wetting  (degrees) →

BUT the exponential term dominates
= f(number of nucleation sites) ~ 1042 = f(number of nucleation sites) ~ 1026 BUT the exponential term dominates Ihetero > Ihomo

Choice of heterogeneous nucleating agent
Small value of  Choosing a nucleating agent with a low value of  (low energy  interface) (Actually the value of (  ) will determine the effectiveness of the heterogeneous nucleating agent → high  or low ) low value of  → Crystal structure of  and  are similar and lattice parameters are as close as possible Seeding rain-bearing clouds → AgI or NaCl → nucleation of ice crystals Ni (FCC, a = 3.52 Å) is used a heterogeneous nucleating agent in the production of artificial diamonds (FCC, a = 3.57 Å) from graphite

Growth till  is exhausted
Nucleation of  phase Trasformation  →  + = Growth At transformation temperature the probability of jump of atom from  →  (across the interface) is same as the reverse jump Growth proceeds below the transformation temperature, wherein the activation barrier for the reverse jump is higher Hd – vatom Gv Hd  phase  phase

I, U, T → Tm U Increasing T T I T (K) →
Maximum of growth rate usually at higher temperature than maximum of nucleation rate U Increasing T T I T (K) → I, U, T →

t → X → 1.0 0.5

Small driving force for nucleation
Time – Temperature – Transformation (TTT) diagrams A type of phase diagram Small driving force for nucleation Tm Tm Replot T Time for transformation T (K) → T (K) → T (rate  sec1) → t (sec) → Growth sluggish

TTT diagram  →  phase transformation
Increasing % transformation T (K) → 99% = finish 1% = start t (sec) →

Turnbull’s approximation
Solid (GS) G G → T Liquid (GL) Tm T →

APPLICATIONS Phase Transformations in Steel Precipitation
Solidification and crystallization Glass transition Recovery recrystallization & grain growth

Phase Transformations in Steel

Fe-Cementite diagram Eutectic L →  + Fe3C Peritectic L +  →  L 1493ºC L +  0.1 %C 1147ºC 2.06 Eutectoid  →  + Fe3C  + Fe3C 723ºC 0.025 %C  + Fe3C T → Fe Fe3C 0.16 0.8 4.3 6.7 %C →

Not an isothermal transformation
Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation Eutectoid steel (0.8%C) 800 Eutectoid temperature 723 Austenite Coarse Pearlite 600 Fine 500 Pearlite + Bainite 400 T → Bainite 300 Austenite Ms Not an isothermal transformation 200 Mf 100 Martensite 0.1 1 10 102 103 104 105 t (s) →

Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation
Eutectoid steel (0.8%C) 800 Eutectoid temperature 723 Austenite Pearlite 600  + Fe3C 500 Pearlite + Bainite 400 T → Bainite 300 Ms 200 Mf 100 Martensite 0.1 1 10 102 103 104 105 t (s) →

Cooling curves Constant rate
Continuous Cooling Transformation (CCT) Curves Eutectoid steel (0.8%C) 800 Eutectoid temperature 723 Austenite 600 Pearlite 500 Original TTT lines 400 T → 300 Ms Cooling curves Constant rate 200 Mf 100 Martensite 0.1 1 10 102 103 104 105 t (s) →

Different cooling treatments
Eutectoid steel (0.8%C) 800 723 M = Martensite 600 P = Pearlite 500 Water quench Full anneal 400 T → Normalizing 300 Oil quench 200 Coarse P 100 Fine P M M + P 0.1 1 10 102 103 104 105 t (s) →

Heterogeneous nucleation at grain boundaries
Pearlite [1] [1]  →  + Fe3C Nucleation and growth Heterogeneous nucleation at grain boundaries Interlamellar spacing is a function of the temperature of transformation Lower temperature → finer spacing → higher hardness [1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962

Acicular, accompanied by surface distortions
Bainite [1] [1] Bainite formed at 348oC Bainite formed at 278oC  →  + Fe3C** Nucleation and growth Acicular, accompanied by surface distortions ** Lower temperature → carbide could be ε carbide (hexagonal structure, 8.4% C) Bainite plates have irrational habit planes Ferrite in Bainite plates possess different orientation relationship relative to the parent Austenite than does the Ferrite in Pearlite [1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962

C along the c-axis obstructs the contraction
Martensite Possible positions of Carbon atoms Only a fraction of the sites occupied FCC Austenite Bain distortion C along the c-axis obstructs the contraction FCC Austenite Alternate choice of Cell Tetragonal Martensite In Pure Fe after the Matensitic transformation c = a 20% contraction of c-axis 12% expansion of a-axis Austenite to Martensite → 4.3 % volume increase Refer Fig.9.11 in textbook

Martensite The martensitic transformation occurs without composition change The transformation occurs by shear without need for diffusion The atomic movements required are only a fraction of the interatomic spacing The shear changes the shape of the transforming region → results in considerable amount of shear energy → plate-like shape of Martensite The amount of martensite formed is a function of the temperature to which the sample is quenched and not of time Hardness of martensite is a function of the carbon content → but high hardness steel is very brittle as martensite is brittle Steel is reheated to increase its ductility → this process is called TEMPERING

Harness of Martensite as a function of Carbon content Hardness (Rc) →
60 Harness of Martensite as a function of Carbon content Hardness (Rc) → 40 20 % Carbon → 0.2 0.4 0.6 Properties of 0.8% C steel Constituent Hardness (Rc) Tensile strength (MN / m2) Coarse pearlite 16 710 Fine pearlite 30 990 Bainite 45 1470 Martensite 65 - Martensite tempered at 250 oC 55 1990

Tempering Heat below Eutectoid temperature → wait→ slow cooling The microstructural changes which take place during tempering are very complex Time temperature cycle chosen to optimize strength and toughness Tool steel: As quenched (Rc 65) → Tempered (Rc 45-55)

To avoid residual stresses generated during quenching
MARTEMPERING To avoid residual stresses generated during quenching Austenized steel is quenched above Ms for homogenization of temperature across the sample The steel is then quenched and the entire sample transforms simultaneously Tempering follows Austenite Pearlite Pearlite + Bainite Bainite Martensite 100 200 300 400 600 500 800 723 0.1 1 10 102 103 104 105 Eutectoid temperature Ms Mf t (s) → T →  + Fe3C Martempering Austempering AUSTEMPERING To avoid residual stresses generated during quenching Austenized steel is quenched above Ms Held long enough for transformation to Bainite

ALLOY STEELS Various elements like Cr, Mn, Ni, W, Mo etc are added to plain carbon steels to create alloy steels The alloys elements move the nose of the TTT diagram to the right → this implies that a slower cooling rate can be employed to obtain martensite → increased HARDENABILITY The ‘C’ curves for pearlite and bainite transformations overlap in the case of plain carbon steels → in alloy steels pearlite and bainite transformations can be represented by separate ‘C’ curves

ROLE OF ALLOYING ELEMENTS
Interstitial Segregation / phase separation Solid solution Substitutional Element Added Compound (new crystal structure) + Simplicity of heat treatment and lower cost  Low hardenability  Loss of hardness on tempering  Low corrosion and oxidation resistance  Low strength at high temperatures Plain Carbon Steel ↑ hardenability Provide a fine distribution of alloy carbides during tempering ↑ resistance to softening on tempering ↑ corrosion and oxidation resistance ↑ strength at high temperatures Strengthen steels that cannot be quenched Make easier to obtain the properties throughout a larger section ↑ Elastic limit (no increase in toughness) Alloying elements Alter temperature at which the transformation occurs Alter solubility of C in  or  Iron Alter the rate of various reactions

TTT diagram for Ni-Cr-Mo low alloy steel
800 Austenite Pearlite 600 500 400 T → 300 Bainite Ms 200 Mf 100 Martensite ~1 min t →

Precipitation

The presence of dislocation weakens the crystal → easy plastic deformation
Putting hindrance to dislocation motion increases the strength of the crystal Fine precipitates dispersed in the matrix provide such an impediment Strength of Al → 100 MPa Strength of Duralumin (Al + 4% Cu + other alloying elements) → 500 MPa

Al rich end of the Al-Cu phase diagram
600 400 T (ºC) → Sloping Solvus line  high T → high solubility low T → low solubility of Cu in Al 200 Al 15 30 45 60 % Cu →

 →  +  Slow equilibrium cooling gives rise to coarse  precipitates which is not good in impeding dislocation motion.*  +  4 % Cu *Also refer section on Double Ended Frank-Read Source in the chapter on plasticity: max = Gb/L

To obtain a fine distribution of precipitates the cycle A → B → C is used
4 % Cu  +  Note: Treatments A, B, C are for the same composition B A C A Heat (to 550oC) → solid solution  supersaturated solution B Quench (to RT) → Increased vacancy concentration C Age (reheat to 200oC) → fine precipitates

100oC 180oC Hardness → 20oC Log(t) → Higher temperature  less time of aging to obtain peak hardness Lower temperature  increased peak hardness  optimization between time and hardness required

Region of solid solution strengthening (no precipitation hardening)
Peak-aged 180oC Hardness → Coarsening of precipitates with increased interparticle spacing Dispersion of fine precipitates (closely spaced) Underaged Overaged Log(t) → Region of precipitation hardening (but little solid solution strengthening) Region of solid solution strengthening (no precipitation hardening) Tm

180oC Hardness → Log(t) → CRSS Increase → Particle radius (r) →
Peak-aged Hardness → Coherent (GP zones) In-coherent (precipitates) Log(t) → Particle shearing Particle By-pass CRSS Increase → Particle radius (r) →

Due to large surface to volume ratio the fine precipitates have a tendency to coarsen → small particles dissolve and large particles grow Coarsening  ↓ in number of particles  ↑ in interparticle spacing  reduced hindrance to dislocation motion (max = Gb/L)

Solidification and Crystallization

Enthalpy of activation for diffusion across the interface
Metals Thermodynamic ↑ Hfusion High → (10-15) kJ / mole Crystallization favoured by Kinetic ↓ Hd  Log [Viscosity ()] Low → (1-10) Poise Enthalpy of activation for diffusion across the interface Difficult to amorphize metals Very fast cooling rates ~106 K/s are used for the amorphization of alloys → splat cooling, melt-spinning.

Fine grain size bestows superior mechanical properties on the material
High nucleation rate and slow growth rate  fine grain size ↑ Cooling rate  lesser time at temperatures near Tm , where the peak of growth rate (U) lies  ↑ nucleation rate Cooling rates ~ (105 – 106) K/s are usually employed Grain refinement can also be achieved by using external nucleating agents Single crystals can be grown by pulling a seed crystal out of the melt Tm U T (K) → I I, U →

Enthalpy of activation for diffusion across the interface
Silicates Thermodynamic ↑ Hfusion low Crystallization favoured by Kinetic ↓ Hd  Log [Viscosity ()] High → (1000) Poise Enthalpy of activation for diffusion across the interface Easily amorphized Certain oxides can be added to silica to promote crystallization

In contrast to metals silicates, borates and phosphates tend to form glasses
Due to high cation-cation repulsion these materials have open structures In silicates the difference in total bond energy between periodic and aperiodic array is small (bond energy is primarily determined by the first neighbours of the central cation within the unit

Glass-ceramic (pyroceram)
A composite material of glass and ceramic (crystals) can have better thermal and mechanical properties But glass itself is easier to form (shape into desired geometry) Heterogenous nucleating agents (e.g. TiO2) added (dissolved) to molten glass Shaping of material in glassy state TiO2 is precipitated as fine particles Held at temperature of maximum nucleation rate (I) Heated to temperature of maximum growth rate

Tmaximum U Tmaximum I Growth Nucleation T → Glass
Partially crystallized Glass Even at the end of the heat treatment the material is not fully crystalline Fine crystals are embedded in a glassy matrix Crystal size ~ 0.1 m (typical grain size in a metal ~ 10 m) Ultrafine grain size  good mechanical properties and thermal shock resistance Cookware made of pyroceram can be heated directly on flame

Glass Transition

“All materials would amorphize on cooling unless crystallization intervenes”
Liquid Glass Volume → Crystal Tg Tm T → Or other extensive thermodynamic property → S, H, E Glass transition temperature

Change in slope Volume → T → Tf Fictive temperature (temperature at which glass is metastable if quenched instantaneously to this temperature) → can be taken as Tg

Effect of rate of cooling
As more time for atoms to arrange in closer packed configuration Volume → Slower cooling T → Lower volume Slower cooling Higher density Lower Tg

A solid can be defined a material with a viscosity > 1012 Poise
On crystallization the viscosity abruptly changes from ~100 → ~1020 Pa s A solid can be defined a material with a viscosity > 1012 Poise Crystal Glass Log (viscosity) → Supercooled liquid Liquid T → Tg Tm

Cool liquid Heat glass Tg Tx Often metallic glasses crystallize before Tg

Please read up paragraph on glassy polymers → p228 in text book

Recovery, Recrystallization & Grain Growth

Plastic deformation in the temperature range (0. 3 – 0
Plastic deformation in the temperature range (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

Material tends to lose the stored strain energy Anneal Cold work
↑ point defect density Material tends to lose the stored strain energy Anneal Cold work ↑ dislocation density Increase in strength of the material Softening of the material Low temperature Recovery Anneal Cold work Recrystallization High temperature

Anneal Cold work Recovery Recrystallization Grain growth

↑ Strength ↑ Hardness Cold work ↑ Electrical resistance ↓ Ductility Changes occur to almost all physical and mechanical properties X-Ray diffration ► Laue patterns of single crystals show pronounced asterism → due to lattice curvatures ► Debye-Scherrer photographs show line broadning → Residual stresses + deformations

Recovery Recovery takes place at low temperatures of annealing “Apparently no change in microstructure” Excess point defects created during Cold work are absorbed: ► at surface or grain boundaries ► by dislocation climb Random dislocations of opposite sign come together and annihilate each other Dislocations of same sign arrange into low energy configurations: ► Edge → Tilt boundaries ► Screw → Twist boundaries  POLYGONIZATION Overall reduction in dislocation density is small

POLYGONIZATION Bent crystal Polygonization Low angle grain boundaries

Recrystallization Trecrystallization  (0.3 – 0.5) Tm “Nucleation” and growth of new, strain free crystals Nucleation of new grains in the usual sense may not be present and grain boundary migrates into a region of higher dislocation density G (recrystallization) = G (deformed material) – G (undeformed material) TRecrystallization is the temperature at which 50 % of the material recrystallizes in 1 hour Region of lower dislocation density Region of higher dislocation density Direction of grain boundary migration

Deformation ↑  recrystallization temperature (Trecrystallization) ↓ Initial grain size ↓  recrystallization temperature ↓ High cold work + low initial grain size  finer recrystallized grains ↑ cold work temperature  lower strain energy stored  ↑ recrystallization temperature Rate of recrystallization = exponential function of temperature Trecrystallization = strong function of the purity of the material Trecrystallization (very pure materials) ~ 0.3 Tm Trecrystallization (impure) ~ (0.5 – 0.6) Tm ► Trecrystallization (99.999% pure Al) ~ 75oC Trecrystallization (commercial purity) ~ 275oC The impurity atoms segregate to the grain boundary and retard their motion → Solute drag (can be used to retain strength of materials at high temperatures)

The impurity atoms seggregate to the grain boundary and retard their
The impurity atoms seggregate to the grain boundary and retard their motion → Solute drag (can be used to retain strength of materials at high temperatures) Second phase particles also pin down the grain boundary during its migration

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

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

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

Electical conductivity Internal stress
Ductility Tensile strength Cold work Recovery Recrystallization Grain growth

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