Phase Diagrams & Phase Tranformation

Transcription

1 ep-16 Phase Diagrams & Phase Tranformation Microstructure - Phases Ferrite Cementite EM micrograph x magnification Plain C steel containing.44 wt. % C Basic Definitions Alloy: A metallic substance that is composed of two or more elements. Component: A chemical constituent (element or compound) of an alloy, which may be used to specify its composition. Phase: A homogeneous portion of a that has uniform physical and chemical characteristics. Equilibrium: The state of a where the phase characteristics remain constant oer indefinite time periods. At equilibrium the free energy is a minimum. When we combine two elements What equilibrium state do we get? If we specify... --a composition (e.g., wt% Cu - wt% Ni), and --a temperature (T ) then... How many yphases do we get? What is the composition of each phase? How much of each phase do we get? Phase A Nickel atom Copper atom Phase B Phase Diagram Three externally controllable parameters that affect phase fraction and composition Temperature Pressure Composition Unary (One component) phase diagram Phase diagram is constructed when arious combinations of these parameters are plotted against one another 1

2 ep-16 Phase Equilibria: olubility imit Introduction olutions solid solutions, single phase Mixtures more than one phase olubility imit: Max concentration for which h only a single phase solution occurs. Question: What is the solubility limit at C? Temperature ( C) Answer: 65 wt% sugar. If Co < 65 wt% sugar: syrup If Co > 65 wt% sugar: syrup + sugar. Pure Water ucrose/water Phase Diagram olubility imit (liquid solution i.e., syrup) (liquid) + (solid sugar) C o =Composition (wt% sugar) Pure ugar Effect of T & Composition (C o ) Changing T can change # of phases: path A to B. Changing Co can change # of phases: path B to D. watersugar Temperature ( C C) 1 B (1 C,7) 1 phase 8 (liquid) 6 + (liquid solution 4 (solid i.e., syrup) sugar) A ( C,7) phases D (1 C,9) phases C o =Composition (wt% sugar) Phase Equilibria imple solution (e.g., Ni-Cu solution) Crystal electroneg r (nm) tructure Ni FCC Cu FCC Phase Diagrams Indicate phases as function of T, Co, and P. For this course: -binary s: just components. -independent ariables: T and C o (P = 1 atm is almost always used). Phase Diagram for Cu-Ni (liquid) 14 phases: (liquid) (q (FCC solid solution) Both hae the same crystal structure (FCC) and hae similar electronegatiities and atomic radii (W. Hume Rothery rules) suggesting high mutual solubility. Ni and Cu are totally miscible in all proportions (FCC solid solution) wt% Ni Phase Diagrams: # and types of phases Rule 1: If we know T and C o, then we know: --the # and types of phases present. Examples: A(11 C, 6): 1 phase: B(15 C, 5): phases: (liquid) B (15 C C,5) (FCC solid solution) A(11 C,6) Cu-Ni phase diagram wt% Ni Phase Diagrams: composition of phases Rule : If we know T and C o, then we know: --the composition of each phase. Examples: Co = 5 wt% Ni At T A = 1 C: Only iquid () C = Co ( = 5 wt% Ni) At T D = 119 C: Only olid ( ) C = Co ( = 5 wt% Ni) TA 1 TB 1 TD At T B = 15 C: Both and C = Cliquidus ( = wt% Ni here) C = Csolidus ( = 4 wt% Ni here) (liquid) Cu-Ni A tie line B D (solid) C C o C wt% Ni

3 ep-16 Gibbs Phase Rule F=C-P+ Degrees of Number of Number of Freedom components phases How many number of intensie ariables we hae to specify to completely define/ specify the How many number of intensie ariables that can be independently changed without changing the number of phases Intensie ariables of the : Temperature of each phase Pressure of each phase Composition of each phase = Relatie concentration of each component in that phase Temperature of each phase is equal and is equal to the temperature of the Pressure of each phase is equal and is equal to the pressure of the To completely define the means: specifying temperature, pressure and relatie concentrations of each component in each phase of the Application of Gibbs Phase Rule: Unary phase diagram Gibbs Phase Rule when Pressure is constant F =? F=C-P+ F=C-P+1 If Pressure is fixed at a particular alue Degrees of Freedom Number of components Number of phases Phase diagrams for metals and ceramics are drawn at 1 atm. fixed pressure F=1-1+1=1 Only T F =? F=-1+1= Both T and w l (or, w s ) can be aried without changing the number of phases F=-+1=1 Either T or w l or w s Can ary only one of these without changing the number of phases Phase Diagrams: weight fractions of phases Rule : If we know T and C o, then we know: --the amount of each phase (gien in wt%). Examples: Co = 5 wt% Ni TA At T A: Only iquid () W = 1 wt%, W = 1 (liquid) At T D: Only olid ( ) TB W =, W = 1 wt% 1 At T B: Both and TD Cu-Ni A tie line B R D (solid) F=1-+1= Inariant point W R wt% C C o C wt% Ni W R R + = 7 wt%

4 ep-16 Phase Diagrams: # and types of phases Rule 1: If we know T and C o, then we know: --the # and types of phases present. Examples: A(11 C, 6): 1 phase: B(15 C, 5): phases: (liquid) B (15 C C,5) (FCC solid solution) A(11 C,6) Cu-Ni phase diagram wt% Ni Ex: Cooling in a Cu Ni Binary Phase diagram: Cu-Ni. Consider C o = 5 wt%ni. (liquid) 1 : 5 wt% Ni : 46 wt% Ni 1 11 A 5 B C 4 D 6 (solid) E : 5wt%Ni Co wt% Ni Cu-Ni : wt% Ni : 4 wt% Ni : 4 wt% Ni : 6 wt% Ni Non equilibrium/ Fast Cooling Cored s Equilibrium Phases C changes as we solidify. Cu-Ni case: First to solidify has C = 46 wt% Ni. ast to solidify has C = 5 wt% Ni. Fast rate of cooling: Cored structure low rate of cooling: Equilibrium structure Uniform C: First to solidify: 46 wt% Ni 5 wt% Ni ast to solidify: < 5 wt% Ni Binary Eutectic ystems components Ex.: Cu-Ag single phase regions (, ) imited solubility: : mostly Cu : mostly Ag T E : No liquid below T E C E : Min. melting T E composition Eutectic transition (C E ) (C E ) + (C E ) has a special composition with a min. melting T. Cu-Ag 1 (liquid) C + T 8 E C E 8 1 C o, wt% Ag EX: Pb n Eutectic ystem (1) For a 4 wt% n-6 wt% Pb alloy at 15 C, find... --the phases present: + --compositions of phases: C O = 4 wt% n C = 11 wt% n C = 99 wt% n + --the relatie amount of each phase: 18. C -C O 15 W= R R+ = C -C 1 = W = = R R+ = C O -C = C -C = 9 88 = 67 wt% = wt% (liquid) Pb-n 18 C C C o C, wt% n C 4

5 ep-16 EX: Pb n Eutectic ystem () For a 4 wt% n-6 wt% Pb alloy at C, find... --the phases present: + --compositions of phases: C O = 4 wt% n C = 17 wt% n C = 46 wt% n + --the relatie amount of each phase: R W = C -C O 46-4 = C -C = 6 9 = 1 wt% W = C O -C = C -C 9 = 79 wt% (liquid) 18 C + Pb-n C C o C C, wt% n Microstructures in Eutectic ystems: I Co < wt% n Result: --at extreme ends --polycrystal of grains i.e., only one solid phase. 4 : C o wt% n T E 1 : C o wt% n C o C o, wt% n (room T solubility limit) (Pb-n ystem) Microstructures in Eutectic ystems: II wt% n < Co < 18. wt% n Result: 4 Initially liquid + then alone finally two phases polycrystal fine -phase inclusions T E : C o wt% n : C o wt% n Pb-n 1 C o C o, wt% n (sol. limit at Troom) 18. (sol. limit at T E ) Microstructures in Eutectic ystems: III Co = CE Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of and crystals. Pb-n + 18 C T E 1 : C o wt% n : 97.8 wt% n : 18. wt%n C E C, wt% n Micrograph of Pb-n eutectic microstructure 16m amellar Eutectic tructure Eutectic Phase Diagram Apply Gibbs Phase Rule 9 5

6 ep-16 Microstructures in Eutectic ystems: III If the iquid composition is Euctectic composition Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of and crystals. Pb-n + 18 C T E 1 : C o wt% n : 97.8 wt% n : 18. wt%n C E C, wt% n Micrograph of Pb-n eutectic microstructure 16m Microstructures in Eutectic ystems: IV 18. wt% n < Co < 61.9 wt% n Result: crystals and a eutectic microstructure : C o wt% n Pb-n + R + T E R 1 + primary eutectic eutectic C o, wt% n Just aboe T E : C = 18. wt% n C = 61.9 wt% n W= = 5 wt% R + W = (1- W) = 5 wt% Just below T E : C = 18. wt% n C = 97.8 wt% n W= = 7 wt% R + W = 7 wt% Hypoeutectic & Hypereutectic You can draw Eutectic phase diagram stating from the eutectic reaction T E (Pb-n ystem) C o,wt%n eutectic hypoeutectic: C o = 5 wt% n 61.9 hypereutectic: (illustration only) α iquid α+β β 175 m eutectic: C o=61.9 wt% n 16 m eutectic micro-constituent Other Phase Diagrams Peritectoid Phase diagram Eutectoid + Peritectic ti + Peritectoid α+ 6

7 ep-16 Peritectic and Peritectoid Phase Diagrams Peritectic Peritectoid Eutectoid & Peritectic Cu Zn Phase diagram Peritectic transition + Eutectoid transition + Eutectic Eutectoid Peritectic Two Phases ingle Phase Two solid Phases Intermediate/ Intermetallic Compounds Not isomorphous with either of the components of the alloy Peritectoid ingle Phase solid Mg Pb Note: intermetallic compound forms a line - not an area - because stoichiometry (i.e. composition) is exact. Congruently melting intermediate phases Intermetallic phase Cu-Zn : Intermediate Phases Fe-Cementite Phase Diagram 7

8 ep-16 Few Principles about Phase Diagrams 1. One phase regions may touch each other only at single points (point of congruent transformation), neer along a boundary. Adjacent one phase regions are seperated from each other by phase regions inoling the same phases. Three phase regions must originate upon three phase isotherm 4. Two three phase isotherms may be connected by a phase region proided that there are phases which are common to both of the three phase equilibria 5. All boundaries of phase fields must project into phase fields when they join a three phase isotherm Fe-Cementite Phase Diagram important points -Eutectic (A): + Fe C -Eutectoid (B): +Fe C Iron Carbon (Fe C) Phase Diagram R A +Fe C 1 +Fe C 8 B 77 C = Teutectoid 6 R +Fe C Fe C (ceme entite) Growth of Pearlite colony 1 m Result: Pearlite = alternating layers of and Fe C phases (From Fig. 7.7, Callister Adapted Version.) (Fe) C o, wt% C Fe C (cementite-hard) (ferrite-soft) C eutectoid Hypoeutectoid teel (Fe-C + 1 +Fe C ystem) 1 +Fe C 8 r s 77 C R w =s/(r+s) 6 +Fe C w =(1- w) (Fe) C pearlite C o, wt% C w pearlite = w w =/(R+) 1 m Hypoeutectoid steel w Fe =(1-w) C pearlite proeutectoid ferrite.76 Fe C (ce ementite) Hypereutectoid teel Fe C 1 +Fe C Fe C 8 r s R 6 w FeC =r/(r +s) +Fe C w =(1-w FeC) 4 1 C o pearlite (Fe) C o, wt%c w pearlite = w w =/(R+) w FeC =(1-w ).76 pearlite Fe C (ce ementite) (Fe-C ystem) 6 m Hypereutectoid steel proeutectoid Fe C 8

9 ep-16 Class Work/ Class Test Do it now on your own notebook For an alloy, Fe.4 wt% C at a temperature just below the eutectoid, determine the following a) composition of Fe C and ferrite () b) the amount of carbide (cementite) in grams that forms per 1 g of steel c) the amount of pearlite and proeutectoid ferrite () Fe-Cementite Phase Diagram olution: Phase Equilibria a) composition of Fe C and ferrite () b) the amount of carbide (cementite) in grams that forms per 1 g of steel C O =.4 wt% C C =. wt% C C Fe C = 6.7 wt% C 16 Fe C C C o 14 x1 FeC CFe C C x 1 5.7g Fe C +Fe C 8 77 C R FeC 5.7 g 6 +Fe C 94. g C C O C o, wt% C C Fe C Fe C (cementite) Phase Equilibria c. the amount of pearlite and proeutectoid ferrite () Amount of pearlite = amount of just aboe T E C o =.4 wt% C C =. wt% C C pearlite = C =.76 wt% C C o C x g 1 + C C 1 +Fe C 8 77 C pearlite = 51. g proeutectoid = 48.8 g +Fe C R 6 +Fe C C C C O C o, wt% C Fe C (cementite) Recap of µstructure eolution in steel Hypoeutectoid teel (Fe-C + 1 +Fe C ystem) 1 +Fe C 8 r s 77 C R w =s/(r+s) 6 +Fe C w =(1- w) (Fe) C pearlite C o, wt% C w pearlite = w w =/(R+) 1 m Hypoeutectoid steel w Fe =(1-w) C pearlite proeutectoid ferrite.76 Fe C (ce ementite) Recap of µstructure eolution in steel Hypereutectoid teel Fe C 1 +Fe C Fe C 8 r s R 6 w FeC =r/(r +s) +Fe C w =(1-w FeC) 4 1 C o pearlite (Fe) C o, wt%c w pearlite = w w =/(R+) w FeC =(1-w ).76 pearlite Fe C (ce ementite) (Fe-C ystem) 6 m Hypereutectoid steel proeutectoid Fe C 9

10 ep-16 Phase transformations (change of the microstructure) can be diided into three categories: Phase Transformation Diffusion-dependent with no change in phase composition or number of phases present (e.g. melting, solidification of pure metal, allotropic transformations, recrystallization, etc.) Diffusion-dependent with changes in phase compositions and/or number of phases (e.g. eutectic or eutectoid transformations) Diffusionless phase transformation - by cooperatie small displacements of all atoms in structure, (e.g. martensitic transformation ) Diffusion-dependent phase transformations can be rather slow and the final structure often depend on the rate of cooling/heating. The formation of a solid nucleus leads to a Gibbs free energy change of 4 G V ( G G ) A r G 4r Free energy change per unit olume. Below T m, it is -e A phase transformation occurs spontaneously only when G decreases in the course of the transformation 1

11 ep-16 Homogeneous Nucleation & Energy Effects urface Free Energy- Energy needed to make an interface) G 4r = surface tension G T = Total Free Energy = G + G V Volume (Bulk) Free Energy releases of energy due to formation of solid 4 G r V G r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy) G at r=r*, r Homogeneous nucleation G at r=r*, r 4 G V ( G G ) A r G 4r * r * 16 G G G H T T G T Tm T Undercooling Tm Tm H = is latent heat of solidification G, H Therefore, * T m 1 r G H T Both r* and G* decrease with increasing undercooling * T m 1 G G H T r G * T m 1 H T G T m H T * G Both r* and G* decrease with increasing undercooling Homogeneous nucleation in solid G V G A V G strain 4 r G Gstrain 4r * r G G strain 16 G G * 16 G strain Both r* and G* increase because of strain energy inoled in solid state transformation Rate of Homogeneous nucleation G * 1 T T T m T Rate of Homogeneous nucleation As T T G* exp(-(g*)/kt) (G d 11

12 ep-16 Heterogeneous nucleation Heterogeneous nucleation M M M M G V G A A M A M M M G V G A A M A M M M cos M M cos M M A r 1 cos 4 r V 4 G r G 4r Heterogeneous nucleation olidification: Nucleation Processes M M G het 4 r G 4r Homogeneous nucleation nuclei form in the bulk of liquid metal requires supercooling (typically 8- C max) Heterogeneous nucleation Nuclei form on mold wall or inoculants allows solidification with only.1-1ºc supercooling Nucleation rate Variation of () with hetero / G * homo G * h Complete wetting G * hetero ( o ) = no barrier to nucleation Partial wetting G * hetero (9 o ) = G * homo/ No wetting (degrees) G * hetero (18 o ) = G * homo no benefit M Cos M 1

13 ep-16 Nucleation rate: Homogeneous s. Heterogeneous I homo I homo e * Ghomo kt I hetero I hetero e * Ghetero kt = f(number of nucleation sites) = f(number of nucleation sites) ~ 1 4 ~ 1 6 BUT the exponential term dominates I hetero > I homo Rate of Phase Transformation Time Temperature Transformation (TTT) diagram phase transformation Increasing % transformation (K) T 99% = finish 1% = start t (sec) 1

14 ep-16 Transformations & Undercooling Eutectoid transformation (Fe-Fe C ): + Fe C For transformation to occur, must.76 wt% C 6.7 wt% C cool to below 77 C. wt% C Fe C ferrite 1 +Fe C Eutectoid: 8 Equil. Cooling: T transf. = 77ºC 77 C T +Fe C 6 Undercooling by T transf. < 77C (Fe) C, wt% C..76 Fe C (cementite) Isothermal Transformation Diagrams solid cures are plotted: one represents the time required at each temperature for the start of the transformation; the other is for transformation completion. The dashed cure corresponds to 5% completion. The austenite to pearlite transformation will occur only if the alloy is supercooled to below the eutectoid temperature (77 C). Time for process to complete depends on the temperature. Next class onwards Prof. umantra Mandal will teach at the same class timings olidification of pure metal: Cooling cure Concept of supercooling Homogeneous and heterogeneous nucleation processes, Microstructure of pure metals Cooling Cure for pure metal Deelopment of Thermal Dendrites Dendritic structure a) pherical Nucleus b) The interface becomes unstable c) Primary arms deelop in crystallographic directions <1> in cubic crystals d) econdary and tertiary arms deelop 14

15 ep-16 Grains can be olidification equiaxed (roughly same size in all directions) columnar (elongated grains) ~ 8 cm Typical Cast tructure Fine grain heat flow Columnar in area with less undercooling hell of equiaxed grains due to rapid cooling (greater T) near wall Columnar grain Equiaxed grain Cast Grain tructure Cast Microstructure chematic Diagram Typical Cast tructure Fine grain Columnar grain Equiaxed grain 15