EQUILIBRIUM PHASE DIAGRAMS

Transcription

1 EQUILIBRIUM PHASE DIAGRAMS ANANDH SUBRAMANIAM Materials Science and Engineering INDIAN INSTITUTE OF TECHNOLOGY KANPUR Kanpur Ph: (+91) (512) , Lab: (+91) (512) MATERIALS SCIENCE & A Learner ENGINEERING A Learner s s Guide Learner s Guide AN INTRODUCTORY E-BOOKE 19 Oct Alloy Phase Equilibria, A. Prince, Elsevier Publishing Company, Amsterdam (1966)

2 Phase Diagrams Phase diagrams are an important tool in the armory of an materials scientist In the simplest sense a phase diagram demarcates regions of existence of various phases. This is similar to a map which demarcates regions based on political, geographical, ecological etc. criteria. Phase diagrams are maps* Thorough understanding of phase diagrams is a must for all materials scientists Phase diagrams are also referred to as EQUILIBRIUM PHASE DIAGRAMS This usage requires special attention: though the term used is Equilibrium, in practical terms the equilibrium is NOT GLOBAL EQUILIBRIUM but MICROSTRUCTURAL LEVEL EQUILIBRIUM (explanation of the same will be considered later) This implies that any microstructural information overlaid on a phase diagram is for convenience and not implied by the phase diagram. The fact that Phase Diagrams represent Microstructural Level equilibrium is often not stressed upon. * there are many other maps that a material scientist will encounter like creep mechanism maps, various kinds of materials selection maps etc.

3 Broadly two kinds of phase diagrams can be differentiated* those involving time and those which do not involve time (special care must be taken in understanding the former class- those involving time). In this chapter we shall deal with the phase diagrams not involving time. This type can be further sub-classified into: Those with composition as a variable (e.g. T vs %Cu) Those without composition as a variable (e.g. P vs T) Temperature-Composition diagrams (i.e. axes are T and composition) are extensively used in materials science and will be considered in detail in this chapter. Also, we shall restrict ourselves to structural phases (i.e. phases not defined in terms of a physical property)** Time-Temperature-Transformations (TTT) diagrams and Continuous-Cooling- Transformation (CCT) diagrams involve time. These diagrams are usually designed to have an overlay of Microstructural information (including microstructural evolution). These diagrams will be considered in the chapter on Phase Transformations. * this is from a convenience in understanding point of view ** we have seen before that phases can be defined based either on a geometrical entity or a physical property (sometimes phases based on a physical property are overlaid on a structural phase diagram- e.g. in a Fe-cementite phase diagram ferromagnetic phase and curie temperatures are overlaid)

4 Let us start with some basic definitions: DEFINITIONS Components of a system Independent chemical species which comprise the system: These could be: Elements, Ions, Compounds E.g. Au-Cu system : Components Au, Cu (elements) Ice-water system : Component H 2 O (compound) Al 2 O 3 Cr 2 O 3 system : Components Al 2 O 3, Cr 2 O 3 Note that components need not be only elements This is important to note that components need not be just elements!!

5 Phase This is the typical textbook definition which one would see!! Physically distinct, chemically homogenous and mechanically separable region of a system (e.g. gas, crystal, amorphous...). Gases Gaseous state always a single phase mixed at atomic or molecular level Liquids Liquid solution is a single phase e.g. NaCl in H 2 O Liquid mixture consists of two or more phases e.g. Oil in water (no mixing at the atomic/molecular level) Three immiscible liquids Solids In general due to several compositions and crystals structures many phases are possible For the same composition different crystal structures represent different phases. E.g. Fe (BCC) and Fe (FCC) are different phases For the same crystal structure different compositions represent different phases. E.g. in Au-Cu alloy 70%Au-30%Cu & 30%Au-70%Cu are different phases

6 What kinds of Phases exist? We have already seen the official definition of a phase: Physically distinct, chemically homogenous and mechanically separable region of a system. However, the term phase is used in diverse contexts and we list below some of these. Based on state Gas, Liquid, Solid Based on atomic order Amorphous, Quasicrystalline, Crystalline Based on Band structure Insulating, Semi-conducting, Semi-metallic, Metallic Based on Property Paraelectric, Ferromagnetic, Superconducting,.. Based on Stability Stable, Metastable, (also- Neutral, unstable) Also sometimes- Based on Size/geometry of an entity Nanocrystalline, mesoporous, layered,

7 Phase transformation Phase Transformation is the change of one phase into another. E.g.: Water Ice - Fe (BCC) - Fe (FCC) - Fe (FCC) - Fe (ferrite) + Cementite (this involves change in composition) Ferromagnetic phase Paramagnetic phase (based on a property) Grain The single crystalline part of polycrystalline metal separated by similar entities by a grain boundary Microstructure An alternate definition based on magnification (Phases + defects + residual stress) & their distributions Structures requiring magnifications in the region of 100 to 1000 times OR The distribution of phases and defects in a material Again this is a typical textbook definition which has been included for!!

8 Phase diagram Map demarcating regions of stability of various phases. or Map that gives relationship between phases in equilibrium in a system as a function of T, P and composition (the restricted form of the definition sometime considered in materials textbooks) Variables / Axis of phase diagrams The axes can be: Thermodynamic (T, P, V), Other possibilities include magnetic field intensity (H), electric field (E) etc. Kinetic (t) or Composition variables (C, %x) (composition is usually measure in weight%, atom% or mole fraction) In single component systems (unary systems) the usual variables are T & P In phase diagrams used in materials science the usual variables are:t& %x In the study of phase transformation kinetics Time Temperature Transformation (TTT) diagrams or Continuous Cooling Transformation (CCT) diagrams are also used where the axis are T & t

9 Important points about phase diagrams (Revision + extra points) Phase diagrams are also called Equilibrium Phase Diagrams. Though not explicitly stated the word Equilibrium in this context usually means Microstructural level equilibrium and NOT Global Equilibrium. Microstructural level equilibrium implies that microstructures are allowed to exist and the system is not in the global energy minimum state. This statement also implies that: Micro-constituents* can be included in phase diagrams Certain phases (like cementite in the Fe-C system) maybe included in phase diagrams, which are not strictly equilibrium phases (cementite will decompose to graphite and ferrite given sufficient thermal activation and time) Various defects are tolerated in the product obtained. These include defects like dislocations, excess vacancies, internal interfaces (interphase boundaries, grain boundaries) etc. Often cooling lines/paths are overlaid on phase diagrams- strictly speaking this is not allowed. When this is done, it is implied that the cooling rate is very slow and the system is in ~equilibrium during the entire process. (Sometimes, even fast cooling paths are also overlaid on phase diagrams!) * will be defined later

10 The GIBBS PHASE RULE The phase rule connects the Degrees of Freedom, the number of Components in a system and the number of Phases present in a system via a simple equation. To understand the phase rule one must understand the variables in the system along with the degrees of freedom. We start with a general definition of the phrase: degrees of freedom Degrees of Freedom: A general definition In response to a stimulus the ways in which the system can respond corresponds to the degrees of freedom of the system For a system in equilibrium The phase rule F = C P + 2 or F C + P = 2 F Degrees of Freedom C Number of Components P Number of Phases The Phase rule is best understood by considering examples from actual phase diagrams as shown in some of the coming slides

11 Variables in a Phase Diagram C No. of Components P No. of Phases F No. of degrees of Freedom Variables in the system = Composition variables + Thermodynamic variables Composition of a phase specified by (C 1) variables (e.g. If the composition is expressed in %ages then the total is 100% there is one equation connecting the composition variables and we need to specify only (C1) composition variables) No. of variables required to specify the composition of all Phases: P(C 1) (as there are P phases and each phase needs the specification of (C1) variables) Thermodynamic variables = P + T (usually considered) = 2 (at constant Pressure (e.g. atmospheric pressure) the thermodynamic variable becomes 1) Total no. of variables in the system = P(C 1) + 2 F < no. of variables F < P(C 1) + 2

12 F = C P + 2 A way of understanding the Gibbs Phase Rule: The degrees of freedom can be thought of as the difference between what you (can) control and what the system controls F = C + 2 P Degrees of Freedom = What you can control Can control the no. of components added and P & T What the system controls System decided how many phases to produce given the conditions

13 Single component phase diagrams (Unary) Let us start with the simplest system possible: the unary system wherein there is just one component. Though there are many possibilities even in unary phase diagrams (in terms of the axis and phases), we shall only consider a T-P unary phase diagram. Let us consider the Fe unary phase diagram as an illustrative example. Apart from the liquid and gaseous phases many solid phases are possible based on crystal structure. (Diagram on next page). Note that the units of x-axis are in GPa (i.e. high pressures are needed in the solid state and liquid state to see any changes to stability regions of the phases). The Gibbs phase rule here is: F = C P + 2. (2 is for T & P). Note that how the phase fields of the open structure (BCC- one in the low T regime () and one in the high T regime ()) diminish at higher pressures. In fact - phase field completely vanishes at high pressures. The variables in the phase diagram are: T & P (no composition variables here!). Along the 2 phase co-existence lines the DOF (F) is 1 i.e. we can chose either T or P and the other will be automatically fixed. The 3 phase co-existence points are invariant points with F = 0. (Invariant point implies they are fixed for a given system).

14 F = C P + 2 Gas Single phase regions F = = 2 T and P can both be varied while still being in the single phase region Temperature (ºC) Liquid (BCC) (FCC) (BCC) (HCP) Two phase coexistence lines F = = 1 we have only one independent variable (we can chose one of the two variables (T or P) and the other is automatically fixed by the phase diagram) Triple points: 3 phase coexistence F = = 0 triple points are fixed points of a phase diagram (we cannot chose T or P) Pressure (GPa) Note the P is in GPa Very High pressures are required for things to happen in the solid state The maximum number of phases which can coexist in a unary P-T phase diagram is 3

15 Understanding aspects of the iron unary phase diagram The degrees of freedom for regions, lines and points in the figure are marked in the diagram shown before The effect of P on the phase stability of various phases is discussed in the diagram below It also becomes clear that when we say iron is BCC at RT, we mean at atmospheric pressure (as evident from the diagram at higher pressures iron can become HCP) Temperature (ºC) Gas Liquid (BCC) (FCC) Increase P and gas will liquefy on crossing phase boundary This line slopes upward as at constant T if we increase the P the gas will liquefy as liquid has lower volume (similarly the reader should draw horizontal lines to understand the effect of pressure on the stability of various phases- and rationalize the same). Phase fields of non-close packed structures shrink under higher pressure Phase fields of close packed structures expand under higher pressure (BCC) (HCP) These lines slope downward as: Under higher pressure the phase with higher packing fraction (lower volume) is preferred Pressure (GPa) Usually (P = 1 atm) the high temperature phase is the loose packed structure and the RT structure is close packed. How come we find BCC phase at RT in iron?

16 Binary Phase Diagrams Binary implies that there are two components. Pressure changes often have little effect on the equilibrium of solid phases (unless ofcourse we apply huge pressures). Hence, binary phase diagrams are usually drawn at 1 atmosphere pressure. The Gibbs phase rule is reduced to: Variables are reduced to: F = C P + 1. (1 is for T). T & Composition (these are the usual variables in Materials Phase Diagrams) Phase rule for condensed phases F = C P + 1 For T In the next page we consider the possible binary phase diagrams. These have been classified based on: Complete Solubility in both liquid & solid states Complete Solubility in both liquid state, but limited solubility in the solid state Limited Solubility in both liquid & solid states.

17 Overview of Possible Binary Phase diagrams Liquid State Solid State analogue Complete Solubility in both liquid & solid states Isomorphous Isomorphous with ordering Isomorphous with phase separation Solid state analogue of Isomorphous Complete Solubility in both liquid state, but limited solubility in the solid state Eutectic Peritectic Eutectoid Peritectoid Limited Solubility in both liquid & solid states Monotectic Syntectic Monotectoid

18 What are the variables/dof in a binary phase diagram? We have already seen that the reduced phase rule at 1Atm pressure is: F = C P + 1. The one on RHS above is T. The other two variables are: Composition of the liquid (C L ) and composition (C S ) of the solid. In a fully solid state reaction: Composition of one solid (C S1 ) and composition of the other solid (C S2 ). The compositions are defined with respect to one of the components (say B): C LB, C S B The Degrees of Freedom (DOF, F) are defined with respect to these variables.

19 System with complete solid & liquid solubility: ISOMORPHOUS SYSTEM Let us start with an isomorphous system with complete liquid and solid solubility Pure components melt at a single temperature, while alloys in the isomorphous system melt over a range of temperatures*. I.e. for a given composition solid and liquid will coexist over a range of temperatures when heated.

20 Model Isomorphous phase diagram We mention some important points here (may be/have been reiterated elsewhere!): Such a phase diagram forms when there is complete solid and liquid solubility. The solid mentioned is crystalline. The solid + liquid region is not a semi-solid (like partly molten wax or silicate glass). It is a crystal of well defined composition in equilibrium with a liquid of well defined composition. Both the solid and the liquid and the solid (except pure A and pure B) have both A and B components in them. A and B components could be pure elements (like in the Ag-Au, Au-Pd, Au-Ni, Ge-Si) or compounds (like Al 2 O 3 -Cr 2 O 3 ). At low temperatures the picture may not be ideal as presented in the diagram below and we may have phase separation (Au-Ni system) or have compound formation (for some compositions) (Au-Pd system). These cases will be considered later. Each solid, with a different composition is a different phase. The area marked solid in the phase diagram is a phase field. If heated further the liquid will vaporize, this part of the phase diagram is usually not shown in the diagrams considered. T Note that between two single phase regions there is a two phase region (for the alloy) (except for special cases) A Liquid (solution) Solid + Liquid Solid (solution) %B B

21 Now let us map the variables and degrees of freedom in varions regions of the isomorphous phase diagram C = 1 P = 2 F = 0 M.P. of A For pure components all transformation temperatures (BCC to FCC, etc.) are fixed (i.e. zero F ) T in the two phase region, if we fix T (and hence exhaust our DOF), the composition of liquid and solid in equilibrium are automatically fixed (i.e. we have no choice over them). Alternately we can use our DOF to chose C L then T and C S are automatically fixed. Variables T, C LB 2 Variables T, C LB, C SB 3 Solid Variables T, C SB 2 Liquid Solid + Liquid Disordered (substitutional) solid solutions C = 2 P = 2 F = 1 C = 2 P = 1 (liquid) F = 2 C = 2 P = 1 F = 2 F = C P + 1 T and Composition can both be varied while still being in the single phase region M.P. of B A B F = 2 P For pure components at any T F= 3 P For alloys %B F = 2 P

22 Gibbs free energy vs composition plot at various temperatures: Isomorphous system As we know at constant T and P the Gibbs free energy determines the stability of a phase. Hence, a phase diagram can be constructed from G-composition (G mixing -C) curves at various temperatures. For an isomorphous system we need to chose 5 sample temperatures: (i) T 1 > T A, (ii) T 2 =T A, (iii) T A >T 3 >T B, (iv) T 4 =T B, (v) T 5 <T B. G of L lower than for all compositions and hence L is stable G of L lower than for all compositions except for pure A. For compositions between X 1 and X 2 the common tangent construction gives the free energy of the L+ mixture How to get G versus composition curves Click here to to know more. 5

23 Isomorphous Phase Diagram: an example A and B must satisfy Hume-Rothery rules for the formation of extended solid solution. Examples of systems forming isomorphous systems: Cu-Ni, Ag-Au, Ge-Si, Al 2 O 3 -Cr 2 O 3. Note the liquidus (the line separting L & L+S regions) and solidus (the line separating L+S and S regions) lines in the figure. L 2200 Liquidus L + S T (ºC) Solidus S Note that the components in this case are compounds Al 2 O Cr 2 O 3 %Cr 2 O 3 Schematics

24 ISOMORPHOUS PHASE DIG. Points to be noted: Pure components (A,B) melt at a single temperature. (General) Alloys melt over a range of temperatures (we will see some special cases soon). Isomorphous phase diagrams form when there is complete solid and liquid solubility. Complete solid solubility implies that the crystal structure of the two components have to be same and Hume-Rothery rules have to be followed. In some systems (e.g. Au-Ni system) there might be phase separation in the solid state (i.e. the complete solid solubility criterion may not be followed) these will be considered later in this chapter as a variation of the isomorphous system (with complete solubility in the solid and the liquid state). Click here to know more about HUME ROTHERY RULES Both the liquid and solid contain the components A and B. In Binary phase diagrams between two single phase regions there will be a two phase region In the isomorphous diagram between the liquid and solid state there is the (Liquid + Solid) state. The Liquid + Solid state is NOT a semi-solid state it is a solid of fixed composition and structure, in equilibrium with a liquid of fixed composition. In the single phase region the composition of the alloy is the composition. In the two phase region the composition of the two phases is different and is NOT the nominal composition of the alloy (but, is given by the lever rule). Lever rule is considered next.

25 Tie line and Lever Rule Given a temperature and composition- how do we find the fraction of the phases present along with the composition? Say the composition C 0 is cooled slowly (equilibrium) At T 0 there is L + S equilibrium Solid (crystal) of composition C 1 coexists with liquid of composition C 2 We draw a horizontal line (called the Tie Line) at the temperature of interest (say T 0 ). Tie line is XY. Note that tie lines can be drawn only in the two phase coexistence regions (fields). Though they may be extended to mark the temperature. To find the fractions of solid and liquid we use the lever rule.

26 We draw a horizontal line (called the Tie Line) at the temperature of interest (say T 0 ). The portion of the horizontal line in the two phase region is akin to a lever with the fulcrum at the nominal composition (C 0 ). The opposite arms of the lever are proportional to the fraction of the solid and liquid phases present (this is the lever rule). T 0 Arm of the lever proportional to the liquid Cooling Fulcrum of the lever Note: strictly speaking cooling curves cannot be overlaid on phase diagrams Arm of the lever proportional to the solid L + S L At T 0 The fraction of liquid (f l ) is (C 0 C 1 ) The fraction of solid (f s ) is (C 2 C 0 ) Tie line C C f liquid att 0 C C C C solid att f 0 C C Note that tie line is drawn within the two phase region and is horizontal. T A C 0 C 1 C 2 %B S B

27 Expanded version At T 0 The fraction of liquid (f l ) is proportional to (C 0 C 1 ) AC The fraction of solid (f s ) is proportional to (C 2 C 0 ) CB T 0 Arm of the lever proportional to the liquid A C Fulcrum of the lever Arm of the lever proportional to the solid B Extended tie line AC C C 0 1 f liquid AB C 2 C1 f solid CB C AB C C C C 1 C 0 C 2

28 Points to be noted For a composition C 0 At T 0 Both the liquid and the solid phases contain both the components A and B To reiterate: The state is NOT semi-solid but a mixture of a solid of a definite composition (C 1 ) with a liquid of definite composition (C 2 ) If the alloy is slowly cooled (maintaining ~equilibrium) then in the two phase region (liquid + solid region) the composition of the solid will move along the brown line and the composition of the liquid will move along the blue line. The composition of the solid and liquid are changing as we cool!

29 Isomorphous Phase Diagrams Note that Ag & Au are so similar that the phase diagram becomes a thin lens (i.e. any alloy of Au & Ag melts over a small range of temperatures as if it were nearly a pure metal!!). Any composition melts above the linear interpolated melting point. Any composition melts above the linearly interpolated melting point Note here that there is solid solubility, but it is not complete at low temperatures (below the peak of the phase field dome) (we will have to say more about that soon) Below T 1 (820C) for some range of compositions the solid solubility of Au in Ni (and vice-versa) is limited. T 1

30 Extensions of the simple isomorphous system: Congruently melting alloys We have seen that a pure metal melts at a single temperature (Why?!!). An alloy typically melts over a range of temperatures. However, there are special compositions which can melt at a single temperature like a pure metal. One of these is the congruent melting compositionin a variation of the isomorphous phase diagram. Some systems show this type of behaviour. Intermediate compounds also have this feature as we shall see later. Case A Elevation in MP Variables T, C LB, C SB 3 Depression in MP Case B C = 2 P = 2 F = 1?? (see below) Congruently melting alloys just like a pure metal Is the DOF 1? No: in requiring that C LB = C SB we have exhausted the degree of freedom. Hence T is automatically fixed DOF is actually zero! Tie line has shrunk to a point!

31 Extensions of the simple isomorphous system: What does this imply w.r.t the solid state phases? Elevation in the MP means that the solid state is more stable (crudely speaking the ordered state is more stable ) ordering reaction is seen at low T. Depression in MP means the liquid state (disordered) is more stable phase separation is seen at low T. (Phase separation can be thought of as the opposite of ordering. Ordering (compound formation) occurs for ve values of H mix, while phase separation is favoured by +ve values of H mix. AB bonds stronger than AA and BB bonds Solid stabilized Ordered solid formation Case A AA and BB bonds stronger than AB bonds Liquid stabilized Phase separation in the solid state Case B E.g. Au-Ni

32 Examples of isomorphous systems with phase separation and compound formation Au-Ni: model system to understand phase separation Au-Pt system with phase separation at low temperatures Au-Pd system with 3 compounds Phase separation in a AlCrFeNi alloy (with composition Al 28.5 Cr 27.3 Fe 24.9 Ni 19.3 ) into two BCC phases

33 Congruent transformations We have seen two congruent transformations (transformations which occur without change in composition). The list is as below. Melting point minimum Melting point maximum Order disorder transformation Formation of an intermediate phase Melting point maximum Formation of an intermediate phase Order disorder transformation

34 Eutectic Phase Diagram Very few systems exhibit an isomorphous phase diagram (usually the solid solubility of one component in another is limited). Often the solid solubility is severely limited- though the solid solubility is never zero (due to entropic reasons). In a simple eutectic system (binary), there is one composition at which the liquid freezes to two solids at a single temperature. This is in some sense similar to a pure solid which freezes at a single temperature (unlike a pure substance the freezing produces a two solid phasesboth of which contain both the components). The term EUTECTIC means Easy Melting The alloy of eutectic composition freezes at a lower temperature than the melting points of the constituent components. This has important implications e.g. the Pb-Sn * eutectic alloy melts at 183C, which is lower than the melting points of both Pb (327C) and Sn (232C) can be used for soldering purposes (as we want to input least amount of heat to solder two materials). In the next page we consider the Pb-Sn eutectic phase diagram. As noted before the components need not be only elements. E.g. in the A-Cu system a eutectic reaction is seen between (Solid solution of Cu in Al) and (Al 2 Cu- a compound). * Actually - eutectic alloy (or (Pb)-(Sn) eutectic alloy)

35 327C Liquidus L T (ºC) D Solidus + L Eutectic reaction L + E 183C L + F 232C T eutectic = T E T E 100 Solvus + Pb Eutectic reaction (the proper way of writing the reaction) 18% 62% %Sn C E L Cool 62% Sn 18% Sn 97% Sn C E 183C C E C E C eutectic = C E Note that Pb is CCP, while Sn at RT is Tetragonal (ti4, I4 1 amd) therefore complete solid solubility across compositions is ruled out!! C E 97% Sn

36 Note the following points: and are terminal solid solutions (usually terminal solid solutions are given symbols ( and )); i.e. is a solid solution of B (Sn) in A (Pb). (In some systems the terminal solid solubility may be very limited: e.g. the Bi-Cd system). has the same crystal structure as that of A (Pb in the example below) and has the same crystal structure as B (Sn in the example below). Typically, in eutectic systems the solid solubility increases with temperature till the eutectic point (i.e. we have a sloping solvus line ). In many situations the solubility of component B in A (and viceversa) may be very small. The Liquidus, Solidus and Solvus lines are as marked in the figure below. 327C Liquidus L T (ºC) Solidus + L Eutectic reaction L + 183C L + 232C Solvus Pb 18% 62% 97% Sn %Sn

37 At the eutectic point E (fig. below) 3 phases co-exist: L, & The number of components in a binary phase diagram is 2 the number of degrees of freedom F = 0. This implies that the Eutectic point is an Invariant Point for a given system it occurs at a fixed composition and temperature. For a binary system the line DF is a horizontal line. Any composition lying between D and F will show eutectic solidification at least in part (for composition E the whole liquid will solidify by the eutectic reaction as shown later). The percentage of and produced by eutectic solidification at E is found by considering DF* as a E lever with fulcrum at E. D F 300 L Eutectic reaction L T (ºC) 100 A D + L Increasing solubility of B in A with T %B C = 2 P = 3 F = 0 L E F B * Actually just below DF as tie lines are drawn in a two phase region

38 Examples of Eutectic microstructures As pointed out before microstructural information is often overlaid on phase diagrams. These represent microstructures which evolve on slow cooling. (Al) Al-Al 2 Cu lamellar eutectic Sn Pb-Sn lamellar eutectic Al 2 Cu (note that one of the components is a compound!) 2 μm Though we label the microstructure as Pb-Sn lamellar eutectic it is actually a - eutectic. Composition plot across lamellae Pb

39 C 2 C 1 C 4 The solidification sequence of C 4 will be similar to C 2 except that the proeutectic phase will be C 3 Pb-Sn eutectic

40 Funda Check What is meant by microstructural level equilibrium? let us understand the concept using an example considered before. During the eutectic reaction (during slow cooling) a lamellar micro constituent is obtained. Fig.1: Al-Al 2 Cu eutectic This results in a huge amount of interfacial area between the two phases (Al, Al 2 Cu), which will result in a high value of interfacial energy. 2 μm The equilibrium state would correspond to the schematic as shown below. Polyhedral crystals Since we tolerate the microstructure as in Fig.1 (and do not take the system to the global energy minimum state), the equilibrium considered in typical phase diagrams are microstructural level equilibrium.

41 Peritectic Phase Diagram Like the eutectic system, the peritectic reaction is found in systems with complete liquid solubility but limited solid solubility. In the peritectic reaction the liquid (L) reacts with one solid () to produce another solid (). L +. Since the solid forms at the interface between the L and the, further reaction is dependent on solid state diffusion. Needless to say this becomes the rate limiting step and hence it is difficult to equilibrate Peritectic reactions (as compared to say eutectic reactions). Figure below. In some peritectic reactions (e.g. the Pt-Ag system- next page), the (pure) phase is not stable below the peritectic temperature (T P = 1186C for Pt-Ag system) and splits into a mixture of ( + ) just below T P.

42 Pt-Ag Peritectic system Peritectic reaction L + Melting points of the components vastly different. Pt-Ag is perhaps not a good example of a peritectic system obvious looking at the phase field (not stable below the peritectic composition). T P Note that below T P pure is not stable and splits into ( + ) C P C P L C P Formal way of writing the peritectic reaction L Cool 66.3% Ag 10.5% Ag 42.4% Ag C L P C P 1186C C P

43 Funda Check Components need not be only elements- they can be compounds like Al 2 O 3, Cr 2 O 3. Phase diagrams usually do not correspond to the global energy minimum- hence often microstructures are tolerated in phase diagrams. Phase diagrams give information on stable phases expected for a given set of thermodynamic parameters (like T, P). E.g. for a given composition, T and P the phase diagram will indicate the stable phase(s) (and their fractions). Phase diagrams do not contain microstructural information- they are often overlaid on phase diagrams for convenience. Metastable phases like cementite are often included in phase diagrams. This is to extend the practical utility of phase diagrams. Strictly speaking cooling curves (curves where T changes) should not be overlaid on phase diagrams. (Again this is done to extend the practical utility of phase diagrams assuming that the cooling is slow ).

44 Precipitation

45 Precipitation Hardening The presence of dislocations weakens the crystal leading to 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 with proper heat treatment (Al + 4% Cu + other alloying elements) 500 MPa. Philosophy behind the process steps in Precipitation Hardening If a high temperature solid solution is slowly cooled, then coarse (large sized) equilibrium precipitates are produced. These precipitates have a large distance between them. These precipitates have incoherent boundaries with the matrix (incoherent precipitates). Such (coarse) precipitates, which have a large inter-precipitate distance, are not the best in terms of the increase in the hardness. Hence, we device a 3 step process to obtain a fine distribution of precipitates, which have a low inter-precipitate distance, to obtain a good increase in hardness. Not good Coarse incoherent precipitates, with large inter-precipitate distance Multi-step process used to obtain a fine distribution of precipitates (with small inter-precipitate distance) Better

46 Al-Cu phase diagram: the sloping solvus line and the design of heat treatments The Al-Cu system is a model system to understand precipitation hardening (typical composition chosen is Al-4 wt.% Cu). Primary requirement (for precipitation hardening) is the presence of a sloping solvus line (i.e. high solubility at high temperatures and decreasing solubility with decreasing temperature). In the Al rich end, compositions marked with a shaded box can only be used for precipitation hardening. Sloping Solvus line: high T high solubility low T low solubility of Cu in Al Al Cu

47 + + Slow equilibrium cooling gives rise to coarse precipitates which is not good in impeding dislocation motion. * ( FCC) ( FCC) CuAl2( Tetragonal) slow cool 4 % Cu 0.5 % Cu 52 % Cu o 550 C RT RT 4 % Cu *Also refer section on Double Ended Frank-Read Source in the chapter on plasticity: max = Gb/L

48 Heat treatment steps to obtain a fine distribution of precipitates To obtain a fine distribution of precipitates the cycle A B C is used B A C 4 % Cu + Note: Treatments A, B, C are for the same composition Assume that we start with a material having coarse equilibrium precipitates (which has been obtained by prior slow cooling of the sample). A: We heat the sample to the single phase region () in the phase diagram (550C). B: We quench (fast cooling) the sample in water to obtain a metastable supersaturated solid solution (the amount of Cu in the sample is more than that allowed at room temperature according to the phase diagram). C: We reheat the sample to relatively low temperature (~180C/200C) get a fine distribution of precipitates. We have noted before that at low temperatures nucleation is dominant over growth. A Heat (to 550 o C) solid solution B Quench (to RT) Supersaturated solution Increased vacancy concentration C Age (reheat to 200 o C) fine precipitates

49 100 o C Schematic curves Real experimental curves are in later slides Hardness 180 o C 20 o C Log(t) Higher temperature less time of aging to obtain peak hardness Lower temperature increased peak hardness optimization between time and hardness required Note: Schematic curves shown- real curves considered later

50 180 o C Peak-aged Hardness Dispersion of fine precipitates (closely spaced) Coarsening of precipitates with increased inter-precipitate spacing Underaged Overaged Not zero of hardness scale Region of solid solution strengthening Hardness is higher than that of Al (no precipitation hardening) Log(t) Region of precipitation hardening (but little/some solid solution strengthening)

51 180 o C Peak-aged In-coherent (precipitates) Coherent (GP zones) Hardness Section of GP zone parallel to (200) plane Particle shearing r r Particle radius (r) Particle By-pass Log(t) r f (t) CRSS Increase

52 GP Zones Cu rich zones fully coherent with the matrix low interfacial energy (Equilibrium phase has a complex tetragonal crystal structure which has incoherent interfaces) Zones minimize their strain energy by choosing disc-shape to the elastically soft <100> directions in the FCC matrix The driving force (G v G s ) is less but the barrier to nucleation is much less (G*) 2 atomic layers thick, 10nm in diameter with a spacing of ~10nm The zones seem to be homogenously nucleated (excess vacancies seem to play an important role in their nucleation)

53 Selected area diffraction (SAD) pattern, showing streaks arising from the zones. 5nm Bright field TEM micrograph of an Al-4% Cu alloy (solutionized and aged) GP zones. 5nm Atomic image of Cu layers in Al matrix