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PHASE TRANSFORMATIONS Nucleation Growth APPLICATIONS Transformations in Steel Precipitation Solidification & crystallization Glass transition Recovery,

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Presentation on theme: "PHASE TRANSFORMATIONS Nucleation Growth APPLICATIONS Transformations in Steel Precipitation Solidification & crystallization Glass transition Recovery,"— Presentation transcript:

1 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)

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

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

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

5 Liquid Solid phase transformation Solid (G S) Liquid (G L ) TmTm T G T G Liquid stableSolid stable T - Undercooling t For sufficient Undercooling On cooling just below T m solid becomes stable But solidification does not start E.g. liquid Ni can be undercooled 250 K below T m G ve G +ve

6 Nucleation 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 Homogenous Heterogenous Nucleation Solidification + Growth = Liquid solid walls of container, inclusions Solid solid inclusions, grain boundaries, dislocations, stacking faults

7 Homogenous nucleation r2r2 r3r3 1 Neglected in L S transformations

8 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 r 0 is obtained Trivial As G v is ve, r * is +ve r G Supercritical nucleiEmbryos

9 The bulk free energy reduction is a function of undercooling r G Increasing T Decreasing r * Decreasing G * TmTm Turnbull approximation

10 No. of critical sized particles Rate of nucleation x Frequency with which they become supercritical = Critical sized nucleus s * atoms of the liquid facing the nucleus Critical sized nucleus Jump taking particle to supercriticality nucleated (enthalpy of activation = H d ) No. of particles/volume in L lattice vibration frequency (~10 13 /s)

11 I T (K) Increasing T TmTm 0 T = T m G * = I = 0 G * I T I T = 0 I = 0

12 Heterogeneous nucleation Consider the nucleation of from on a planar surface of inclusion A lens A circle Created Lost Surface tension force balance Interfacial Energies V lens = h 2 (3r-h)/3A lens = 2 rhh = (1-Cos )rr circle = r Sin

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

14 = f(number of nucleation sites) ~ = f(number of nucleation sites) ~ BUT the exponential term dominates I hetero > I homo

15 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

16 Nucleation of phase Trasformation + Growth till is exhausted = H d – v atom G v H d phase 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 Growth

17 I, U, T T (K) Increasing T TmTm 0 U T I Maximum of growth rate usually at higher temperature than maximum of nucleation rate

18 t X

19 Time – Temperature – Transformation (TTT) diagrams A type of phase diagram T (rate sec 1 ) T (K) T TmTm 0 t (sec) T (K) TmTm 0 Time for transformation Small driving force for nucleation Growth sluggish Replot

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

21 T G Turnbulls approximation TmTm Solid (G S) Liquid (G L ) T G

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

23 Phase Transformations in Steel

24 %C T Fe Fe 3 C Peritectic L + Eutectic L + Fe 3 C Eutectoid + Fe 3 C L L + + Fe 3 C 1493ºC 1147ºC 723ºC Fe-Cementite diagram %C 0.1 %C + Fe 3 C

25 Austenite Pearlite Pearlite + Bainite Bainite Martensite Eutectoid temperature Not an isothermal transformation MsMs MfMf Coarse Fine t (s) T Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation Eutectoid steel (0.8%C)

26 Austenite Pearlite Pearlite + Bainite Bainite Martensite Eutectoid temperature MsMs MfMf t (s) T Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation Eutectoid steel (0.8%C) + Fe 3 C

27 Continuous Cooling Transformation (CCT) Curves Eutectoid steel (0.8%C) Austenite Martensite Eutectoid temperature MsMs MfMf t (s) T Original TTT lines Cooling curves Constant rate Pearlite

28 Eutectoid steel (0.8%C) t (s) T Water quench Oil quench Normalizing Full anneal Different cooling treatments M = Martensite P = Pearlite Coarse P P M M + Fine P

29 Pearlite Nucleation and growth Heterogeneous nucleation at grain boundaries Interlamellar spacing is a function of the temperature of transformation Lower temperature finer spacing higher hardness + Fe 3 C [1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962 [1]

30 Bainite 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 + Fe 3 C ** Bainite formed at 348 o C Bainite formed at 278 o C [1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962 [1]

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

32 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

33 % Carbon Hardness (R c ) Harness of Martensite as a function of Carbon content Properties of 0.8% C steel ConstituentHardness (R c )Tensile strength (MN / m 2 ) Coarse pearlite16710 Fine pearlite30990 Bainite Martensite65- Martensite tempered at 250 o C551990

34 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 (R c 65) Tempered (R c 45-55)

35 Austenite Pearlite Pearlite + Bainite Bainite Martensite Eutectoid temperature MsMs MfMf t (s) T + Fe 3 C MARTEMPERING AUSTEMPERING 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 To avoid residual stresses generated during quenching Austenized steel is quenched above M s Held long enough for transformation to Bainite Martempering Austempering

36 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

37 ROLE OF ALLOYING ELEMENTS + 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 Element Added Segregation / phase separation Solid solution Compound (new crystal structure) 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 Interstitial Substitutional

38 Austenite Pearlite Bainite Martensite MsMs MfMf t T TTT diagram for Ni-Cr-Mo low alloy steel ~1 min

39 Precipitation

40 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

41 Al % Cu T (ºC) L Sloping Solvus line high T high solubility low T low solubility of Cu in Al Al rich end of the Al-Cu phase diagram

42 4 % Cu + + Slow equilibrium cooling gives rise to coarse precipitates which is not good in impeding dislocation motion. * *Also refer section on Double Ended Frank-Read Source in the chapter on plasticity: max = Gb/L

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

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

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

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

47 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)

48 Solidification and Crystallization

49 H fusion H d Log [Viscosity ( )] Crystallization favoured by High (10-15) kJ / mole Low (1-10) Poise Metals Enthalpy of activation for diffusion across the interface Difficult to amorphize metals Thermodynamic Kinetic Very fast cooling rates ~10 6 K/s are used for the amorphization of alloys splat cooling, melt-spinning.

50 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 T m, where the peak of growth rate (U) lies nucleation rate Cooling rates ~ (10 5 – 10 6 ) 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 I, U T (K) TmTm 0 U I

51 H fusion H d Log [Viscosity ( )] Crystallization favoured by low High (1000) Poise Silicates Enthalpy of activation for diffusion across the interface Easily amorphized Thermodynamic Kinetic Certain oxides can be added to silica to promote crystallization

52 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

53 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) Glass-ceramic (pyroceram) Shaping of material in glassy state Heterogenous nucleating agents (e.g. TiO 2 ) added (dissolved) to molten glass TiO 2 is precipitated as fine particles Held at temperature of maximum nucleation rate (I) Heated to temperature of maximum growth rate

54 t T Nucleation Growth T maximum I T maximum U 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

55 Glass Transition

56 All materials would amorphize on cooling unless crystallization intervenes T Volume Or other extensive thermodynamic property S, H, E Liquid Glass Crystal TgTg TmTm Glass transition temperature

57 T Volume Change in slope TfTf Fictive temperature (temperature at which glass is metastable if quenched instantaneously to this temperature) can be taken as T g

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

59 T Log (viscosity) Glass Crystal TgTg TmTm Supercooled liquid Liquid On crystallization the viscosity abruptly changes from ~100 ~10 20 Pa s A solid can be defined a material with a viscosity > Poise

60 TgTg Heat glass Cool liquid TxTx Often metallic glasses crystallize before T g

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

62 Recovery, Recrystallization & Grain Growth

63 Cold work dislocation density point defect density Plastic deformation in the temperature range (0.3 – 0.5) T m 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

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

65 Cold work Anneal Recrystallization Recovery Grain growth

66 Cold work Hardness Strength 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 Electrical resistance Ductility

67 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

68 POLYGONIZATION Bent crystal Low angle grain boundaries Polygonization

69 Recrystallization T recrystallization (0.3 – 0.5) T m 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) T Recrystallization 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

70 Further points about recrystallization Deformation recrystallization temperature (T recrystallization ) 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 T recrystallization = strong function of the purity of the material T recrystallization (very pure materials) ~ 0.3 T m T recrystallization (impure) ~ (0.5 – 0.6) T m T recrystallization (99.999% pure Al) ~ 75 o C T recrystallization (commercial purity) ~ 275 o C 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)

71 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

72 Hot Work and Cold Work Hot Work Plastic deformation above T Recrystallization Cold Work Plastic deformation below T Recrystallization Cold Work Hot Work Recrystallization temperature (~ 0.4 T m )

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

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

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

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