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Phase Equilibrium Engr 2110 – Chapter 9 Dr. R. R. Lindeke.

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1 Phase Equilibrium Engr 2110 – Chapter 9 Dr. R. R. Lindeke

2 Topics for Study Definitions of Terms in Phase studies Binary Systems  Complete solubility (fully miscible) systems  Multiphase systems Eutectics Eutectoids and Peritectics Intermetallic Compounds The Fe-C System

3 Some Definitions Component of a system: Pure metals and or compounds of which an alloy is composed, e.g. Cu and Ag or Fe and Fe 3 C. They are the solute(s) and solvent System: A body of engineering material under investigation. e.g. Ag – Cu system, NiO-MgO system (or even sugar-milk system) Solubility Limit: The maximum concentration of solute atoms that may dissolve in the Solvent to form a “solid solution” at some temperature.

4 Phases: A homogenous portion of a system that has uniform physical and chemical characteristics, e.g. pure material, solid solution, liquid solution, and gaseous solution, ice and water, syrup and sugar. Microstructure: A system’s microstructure is characterized by the number of phases present, their proportions, and the manner in which they are distributed or arranged. Factors affecting microstructure are: alloying elements present, their concentrations, and the heat treatment of the alloy. Single phase system = Homogeneous system Multi phase system = Heterogeneous system or mixtures Definitions, cont

5 Figure 9.3 (a) Schematic representation of the one-component phase diagram for H 2 O. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with the familiar transformation temperatures for H 2 O (melting at 0°C and boiling at 100°C).

6 Figure 9.4 (a) Schematic representation of the one-component phase diagram for pure iron. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with important transformation temperatures for iron. This projection will become one end of important binary diagrams, such as that shown in Figure 9.19

7 Phase Equilibrium: A stable configuration with lowest free-energy (internal energy of a system, and also randomness or disorder of the atoms or molecules (entropy). Any change in Temperature, Composition, and Pressure causes an increase in free energy and away from Equilibrium thus forcing a move to another ‘state’ Equilibrium Phase Diagram: It is a “map” of the information about the control of microstructure or phase structure of a particular material system. The relationships between temperature and the compositions and the quantities of phases present at equilibrium are represented. Definition that focus on “Binary Systems” Binary Isomorphous Systems: An alloy system that contains two components that attain complete liquid and solid solubility of the components, e.g. Cu and Ni alloy. It is the simplest binary system. Binary Eutectic Systems: An alloy system that contains two components that has a special composition with a minimum melting temperature. Definitions, cont

8 With these definitions in mind: ISSUES TO ADDRESS... When we combine two elements... what “equilibrium state” would we expect to get? In particular, if we specify... --a composition (e.g., wt% Cu - wt% Ni), and --a temperature (T ) and/or a Pressure (P) then... How many phases do we get? What is the composition of each phase? How much of each phase do we get? Phase B Phase A Nickel atom Copper atom

9 Gibb’s Phase Rule: a tool to define the number of phases and/or degrees of phase changes that can be found in a system at equilibrium For any system under study the rule determines if the system is at equilibrium For a given system, we can use it to predict how many phases can be expected Using this rule, for a given phase field, we can predict how many independent parameters (degrees of freedom) we can specify Typically, N = 1 in most condensed systems – pressure is fixed!

10 Looking at a simple “Phase Diagram” for Sugar – Water (or milk)

11 Effect of Temperature (T) & Composition (C o ) Changing T can change # of phases: D (100°C,90) 2 phases B (100°C,70) 1 phase See path A to B. Changing C o can change # of phases: See path B to D. Adapted from Fig. 9.1, Callister 7e. A (20°C,70) 2 phases Temperature (°C) CoCo =Composition (wt% sugar) L (liquid solution i.e, syrup) L (liquid) + S (solid sugar) water- sugar system

12 Phase Diagram: A Map based on a System’s Free Energy indicating “equilibuim” system structures – as predicted by Gibbs Rule Indicate ‘stable’ phases as function of T, P & C omposition, We will focus on: -binary systems: just 2 components. -independent variables: T and C o (P = 1 atm is almost always used). Phase Diagram -- for Cu-Ni system 2 phases are possible: L (liquid)  (FCC solid solution) 3 ‘phase fields’ are observed: L L +   wt% Ni T(°C) L (liquid)  (FCC solid solution) L +  liquidus solidus An “Isomorphic” Phase System

13 wt% Ni T(°C) L (liquid)  (FCC solid solution) L +  liquidus solidus Cu-Ni phase diagram Phase Diagrams: Rule 1: If we know T and C o then we know the # and types of all phases present. Examples: A(1100°C, 60): 1 phase:  B(1250°C, 35): 2 phases: L +  B (1250°C,35) A(1100°C,60)

14 wt% Ni T(°C) L (liquid)  (solid) L +  liquidus solidus L +  Cu-Ni system Phase Diagrams: Rule 2: If we know T and C o we know the composition of each phase Examples: T A A 35 C o 32 C L At T A = 1320°C: Only Liquid (L) C L = C o ( = 35 wt% Ni) At T B = 1250°C: Both  and L C L = C liquidus ( = 32 wt% Ni here) C  = C solidus ( = 43 wt% Ni here) At T D = 1190°C: Only Solid (  ) C  = C o ( = 35 wt% Ni) C o = 35 wt% Ni adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, B T B D T D tie line 4 C  3

15 Figure 9.31 The lever rule is a mechanical analogy to the mass- balance calculation. The (a) tie line in the two-phase region is analogous to (b) a lever balanced on a fulcrum.

16 Tie line – a line connecting the phases in equilibrium with each other – at a fixed temperature (a so-called Isotherm) The Lever Rule How much of each phase? We can Think of it as a lever! So to balance: MLML MM RS wt% Ni T(°C) L (liquid)  (solid) L +  liquidus solidus L +  B T B tie line C o C L C  S R

17 Rule 3: If we know T and C o then we know the amount of each phase (given in wt%) Examples: At T A : Only Liquid (L) W L = 100 wt%, W  = 0 At T D : Only Solid (  ) W L = 0, W  = 100 wt% C o = 35 wt% Ni Therefore we define wt% Ni T(°C) L (liquid)  (solid) L +  liquidus solidus L +  Cu-Ni system T A A 35 C o 32 C L B T B D T D tie line 4 C  3 R S At T B : Both  and L = 27 wt% WLWL  S R+S WW  R R+S Notice: as in a lever “the opposite leg” controls with a balance (fulcrum) at the ‘base composition’ and R+S = tie line length = difference in composition limiting phase boundary, at the temp of interest

18 wt% Ni L (liquid)  (solid) L +  L +  T(°C) A 35 C o L: 35wt%Ni Cu-Ni system Phase diagram: Cu-Ni system. System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another;  phase field extends from 0 to 100 wt% Ni. Adapted from Fig. 9.4, Callister 7e. Consider C o = 35 wt%Ni. Ex: Cooling in a Cu-Ni Binary  :43 wt% Ni L: 32 wt% Ni L: 24 wt% Ni  :36 wt% Ni B  : 46 wt% Ni L: 35 wt% Ni C D E 24 36

19 C  changes as we solidify. Cu-Ni case: Fast rate of cooling: Cored structure Slow rate of cooling: Equilibrium structure First  to solidify has C  = 46 wt% Ni. Last  to solidify has C  = 35 wt% Ni. Cored vs Equilibrium Phases First  to solidify: 46 wt% Ni Uniform C  : 35 wt% Ni Last  to solidify: < 35 wt% Ni

20 Cored (Non-equilibrium) Cooling Notice: The Solidus line is “tilted” in this non- equilibrium cooled environment

21 : Min. melting T E 2 components has a ‘special’ composition with a min. melting Temp. Binary-Eutectic (PolyMorphic) Systems Eutectic transition L(C E )  (C  E ) +  (C  E ) 3 single phase regions (L,  ) Limited solubility:  : mostly Cu  : mostly Ag T E : No liquid below T E C E composition Ex.: Cu-Ag system Cu-Ag system L (liquid)  L +  L+    CoCo,wt% Ag T(°C) CECE TETE °C

22 L+  L+   +  200 T(°C) 18.3 C, wt% Sn L (liquid)  183°C  For a 40 wt% Sn-60 wt% Pb alloy at 150°C, find... --the phases present: Pb-Sn system EX: Pb-Sn Eutectic System (1)  +  --compositions of phases: C O = 40 wt% Sn --the relative amount of each phase (by lever rule) : CoCo 11 CC 99 CC S R C  = 11 wt% Sn C  = 99 wt% Sn W  = C  - C O C  - C  = = = 67 wt% S R+SR+S = W  = C O - C  C  - C  = R R+SR+S = = 33 wt% = Adapted from Fig. 9.8, Callister 7e.

23 L+   +  200 T(°C) C, wt% Sn L (liquid)   L+  183°C For a 40 wt% Sn-60 wt% Pb alloy at 220°C, find... --the phases present: Pb-Sn system EX: Pb-Sn Eutectic System (2)  + L --compositions of phases: C O = 40 wt% Sn --the relative amount of each phase: W  = C L - C O C L - C  = = 6 29 = 21 wt% W L = C O - C  C L - C  = = 79 wt% 40 CoCo 46 CLCL 17 CC 220 S R C  = 17 wt% Sn C L = 46 wt% Sn

24 C o < 2 wt% Sn Result: --at extreme ends --polycrystal of  grains i.e., only one solid phase. Microstructures In Eutectic Systems: I 0 L +  200 T(°C) CoCo,wt% Sn 10 2% 20 CoCo L  30  +  400 (room Temp. solubility limit) TETE (Pb-Sn System)  L L: C o wt% Sn  : C o wt% Sn

25 2 wt% Sn < C o < 18.3 wt% Sn Result:  Initially liquid  Then liquid +   then  alone   finally two solid phases   polycrystal  fine  -phase inclusions Microstructures in Eutectic Systems: II Pb-Sn system L +  200 T(°C) CoCo,wt% Sn CoCo L  30  +  400 (sol. limit at T E ) TETE 2 (sol. limit at T room ) L  L: C o wt% Sn    : C o wt% Sn

26 C o = C E Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of  and  crystals. Microstructures in Eutectic Systems: III 160  m Micrograph of Pb-Sn eutectic microstructure Pb-Sn system LL  200 T(°C) C, wt% Sn L   L+  183°C 40 TETE 18.3  : 18.3 wt%Sn 97.8  : 97.8 wt% Sn CECE 61.9 L: C o wt% Sn 45.1%  and 54.8%  -- by Lever Rule

27 Lamellar Eutectic Structure

28 18.3 wt% Sn < C o < 61.9 wt% Sn Result:  crystals and a eutectic microstructure Microstructures in Eutectic Systems: IV SR 97.8 S R primary  eutectic   WLWL = (1-W  ) = 50 wt% C  = 18.3 wt% Sn CLCL = 61.9 wt% Sn S R +S W  = = 50 wt% Just above T E : Just below T E : C  = 18.3 wt% Sn C  = 97.8 wt% Sn S R +S W  = = 72.6 wt% W  = 27.4 wt% Pb-Sn system L+  200 T(°C) C o, wt% Sn L   L+  40  +  TETE L: C o wt% Sn L  L 

29 L+  L+   +  200 C o, wt% Sn L   TETE 40 (Pb-Sn System) Hypoeutectic & Hypereutectic Compositions 160  m eutectic micro-constituent hypereutectic: (illustration only)       from Metals Handbook, 9th ed., Vol. 9, Metallography and Microstructures, American Society for Metals, Materials Park, OH,  m       hypoeutectic: C o = 50 wt% Sn T(°C) 61.9 eutectic eutectic: C o = 61.9 wt% Sn

30 “Intermetallic” Compounds Mg 2 Pb Note: an intermetallic compound forms a line - not an area - because stoichiometry (i.e. composition) is exact. Adapted from Fig. 9.20, Callister 7e. An Intermetallic Compound is also an important part of the Fe-C system!

31 Eutectoid: solid phase in equilibrium with two solid phases S 2 S 1 +S 3   + Fe 3 C (727ºC) intermetallic compound - cementite cool heat Peritectic: liquid + solid 1 in equilibrium with a single solid 2 (Fig 9.21) S 1 + L S 2  + L  (1493ºC) cool heat Eutectic: a liquid in equilibrium with two solids L  +  Eutectoid & Peritectic – some definitions cool heat

32 Eutectoid & Peritectic Cu-Zn Phase diagram Adapted from Fig. 9.21, Callister 7e. Eutectoid transition   +  Peritectic transition  + L 

33 Iron-Carbon (Fe-C) Phase Diagram 2 important points -Eutectoid (B):  + Fe 3 C -Eutectic (A): L  + Fe 3 C Fe 3 C (cementite) L  (austenite)  +L+L  +Fe 3 C   +  L+Fe 3 C  (Fe) C o, wt% C 1148°C T(°C)  727°C = T eutectoid A SR 4.30 Result: Pearlite = alternating layers of  and Fe 3 C phases 120  m (Adapted from Fig. 9.27, Callister 7e.)    RS 0.76 C eutectoid B Fe 3 C (cementite-hard)  (ferrite-soft) Max. C solubility in  iron = 2.11 wt%

34 Hypoeutectoid Steel Adapted from Figs and 9.29,Callister 7e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in- Chief), ASM International, Materials Park, OH, 1990.) Fe 3 C (cementite) L  (austenite)  +L+L  + Fe 3 C  L+Fe 3 C  (Fe) C o, wt% C 1148°C T(°C)  727°C (Fe-C System) C0C proeutectoid ferrite pearlite 100  m Hypoeutectoid steel R S  w  =S/(R+S) w Fe 3 C =(1-w  ) w pearlite =w  rs w  =s/(r+s) w  =(1-w  )              

35 Hypereutectoid Steel Fe 3 C (cementite) L  (austenite)  +L+L  +Fe 3 C  L+Fe 3 C  (Fe) C o, wt%C 1148°C T(°C)  adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, (Fe-C System) 0.76 CoCo proeutectoid Fe 3 C 60  m Hypereutectoid steel pearlite RS w  =S/(R+S) w Fe 3 C =(1-w  ) w pearlite =w  s r w Fe 3 C =r/(r+s) w  =(1-w Fe 3 C )            

36 Example: Phase Equilibria For a 99.6 wt% Fe-0.40 wt% C at a temperature just below the eutectoid, determine the following: a) composition of Fe 3 C and ferrite (  ) b) the amount of carbide (cementite) in grams that forms per 100 g of steel c) the amount of pearlite and proeutectoid ferrite (  )

37 Solution: b)the amount of carbide (cementite) in grams that forms per 100 g of steel a) composition of Fe 3 C and ferrite (  ) C O = 0.40 wt% C C  = wt% C C Fe C = 6.70 wt% C 3 Fe 3 C (cementite) L  (austenite)  +L+L  + Fe 3 C  L+Fe 3 C  C o, wt% C 1148°C T(°C) 727°C COCO R S C Fe C 3 CC

38 Solution, cont: c) the amount of pearlite and proeutectoid ferrite (  ) note: amount of pearlite = amount of  just above T E C o = 0.40 wt% C C  = wt% C C pearlite = C  = 0.76 wt% C pearlite = 51.2 g proeutectoid  = 48.8 g Fe 3 C (cementite) L  (austenite)  +L+L  + Fe 3 C  L+Fe 3 C  C o, wt% C 1148°C T(°C) 727°C COCO R S CC CC Looking at the Pearlite: 11.1% Fe 3 C (.111*51.2 gm = 5.66 gm) & 88.9%  (.889*51.2gm = 45.5 gm)  total  = = 94.3 gm

39 Alloying Steel with More Elements T eutectoid changes: C eutectoid changes: Adapted from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 127.) T Eutectoid (°C) wt. % of alloying elements Ti Ni Mo Si W Cr Mn wt. % of alloying elements C eutectoid (wt%C) Ni Ti Cr Si Mn W Mo

40 Looking at a Tertiary Diagram When looking at a Tertiary (3 element) P. diagram, like this image, the Mat. Engineer represents equilibrium phases by taking “slices at different 3 rd element content” from the 3 dimensional Fe-C-Cr phase equilibrium diagram What this graph shows are the increasing temperature of the euctectoid and the decreasing carbon content, and (indirectly) the shrinking  phase field From: G. Krauss, Principles of Heat Treatment of Steels, ASM International, 1990

41 Fe-C-Si Ternary phase diagram at about 2.5 wt% Si This is the “controlling Phase Diagram for the ‘Graphite‘ Cast Irons

42 Phase diagrams are useful tools to determine: -- the number and types of phases, -- the wt% of each phase, -- and the composition of each phase for a given T and composition of the system. Alloying to produce a solid solution usually --increases the tensile strength (TS) --decreases the ductility. Binary eutectics and binary eutectoids allow for (cause) a range of microstructures. Summary


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