# Phase Equilibria & Phase Diagrams

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1 Phase Equilibria & Phase Diagrams Week7 Material Sciences and Engineering MatE271 1 Motivation Phase diagram (Ch 9) Temperature Time Kinematics (Ch 10) New structure, concentration (mixing level) (at what temperature? for how long? ) Material Sciences and Engineering MatE271 Week 7 2

2 Goals for this unit Learn definitions and basic concepts of phase equilibria and phase diagrams Interpret equilibrium phase diagrams binary isomorphous (complete ss) binary eutectic (limited ss or no ss) Intermediate compounds/phases phases present their compositions and amounts (i.e., the phase assemblage of the system) ss: solid solution Material Sciences and Engineering MatE271 Week 7 3 Phase Diagrams - Introduction Many materials systems can exist in a variety of forms depending on the temperature, pressure and overall composition (allotropy) phase diagram is a graphical representation which details the form(s) the material takes under specific conditions ssumes the system has achieved chemical equilibrium ( equilibrium diagrams ) Material Sciences and Engineering MatE271 Week 7 4 aterial Sciences and Engineering,

3 Definitions and asic Concepts Equilibrium thermodynamic definition: a system is at equilibrium if its free energy is at a minimum characteristics of the system do not change with time, i.e., the system is stable If you change the temperature, pressure, or composition, the free energy will change the specific phase(s) present may (or may not) change but the phase assemblage will! Material Sciences and Engineering MatE271 Week 7 5 Definitions Component (elements or compounds) pure substance(s) required to express composition of phases in the system Phase (solid, liquid, gas) Homogeneous portion of a system uniform chemical and physical properties several phases may be present simultaneously in principal, phases are recognizable and separable System variables Composition (in terms of components), temperature T and pressure p Material Sciences and Engineering MatE271 Week 7 6

4 Phase Equilibria o Most systems we work with are solid systems: o Sometimes (usually) the kinetics (rate of reaction) of the system will not allow a phase change to take place completely, or instantly, under certain conditions example: glass of ice water in the sun when it s 75 F outside (stays at 32 F until all ice is melted) o Consider glass, stable form is quartz This is a metastable state - persists indefinitely Same with diamond and graphite Material Sciences and Engineering MatE271 Week 7 7 Definitions & asic Concepts: Solubility o Solubility limit - Sugar in Water One phase present Two phases present Phase Diagram Material Sciences and Engineering MatE271 Week 7 8 aterial Sciences and Engineering,

5 Phase composition particular phase can have variable composition (i.e., can be a solution) Solute and solvent Solvent (component present in greatest amount) Solute (present in minor concentration) Solubility Limit maximum allowed concentration of solute in solvent depends on species, temperature and pressure Material Sciences and Engineering MatE271 Week 7 9 Definition Phases This phase diagram is a two-component system, sugar(dextrose) and water. Q. What are the phases in this system?. liquid ( syrup or sugar -in-water sol n) and a solid (pure crystalline sugar) Note: Solution vs. Mixture! - mixture is heterogeneous (more than one phase present) - solution is a single homogeneous phase of variable composition. two-phase mixture is present in the system ( syrup +sugar) Material Sciences and Engineering MatE271 Week 7 10

6 Phases Phase Characteristics: phase does not have to be OTH physically and chemically distinct Q. What is an example of a physically, but not chemically distinct phase? -. Water, ice, steam or Diamond, graphite Q. What is an example of a chemically, but not physically distinct phase? -. Oil and water (both are liquids) Material Sciences and Engineering MatE271 Week 7 11 Equilibrium Diagrams Represents phase relationships as a function of temperature, pressure and composition (equilibrium phases and microstructure) - ut many useful diagrams are constructed for constant pressure of 1 atmosphere, so only composition and temperature are variables Phase diagrams provides us with information needed for the control of phase and microstructure in the materials we make Material Sciences and Engineering MatE271 Week 7 12 aterial Sciences and Engineering,

7 Single Component Systems (fixed composition) Note:, p Pressure, atm Ice II Ice Water H 2 O polymorphism triple point Steam Temperature, C 100 Variables: - Pressure p - Temperature T Material Sciences and Engineering MatE271 Week 7 13 Two Component Systems (P=1 atm) o o o o Melting temp of ice changes with % salt Four phase fields Liquid (rine) Solid and Liquid (Ice & rine) Solid and Liquid (Salt & rine) Solids (Ice and Salt) Composition of brine changes Questions What is min temp at which salt works? t any given temp is there an optimal amount of salt? Temperature, C 0 C -21 C Solid + Liquid (Ice + rine) NaCl and Water Liquid solution (rine-saltdissolved in water) Solid Solution (Frozen rine) 23.3 % NaCl H 2O 76.7 % Composition, wt% (Salt + rine) Material Sciences and Engineering MatE271 Week 7 14 aterial Sciences and Engineering,

8 The Phase Rule Gibbs Phase Rule fter J. W. Gibbs - 19th century physicist ased on thermodynamics Predicts the number of phases that will coexist within a system at EQUILIRIUM Does not apply in non-equilibrium situations! Material Sciences and Engineering MatE271 Week 7 15 The Phase Rule P + F = C + N P = number of phases present C = the number of components (minimum # needed to describe system) N = number of noncompositional variables N = 1 or 2 for T (temperature) and p (pressure) N = 1 If p=const or T=const (HINT: p is usually constant so N is usually 1) Material Sciences and Engineering MatE271 Week 7 16

9 The Phase Rule P + F = C + N P = Phases C = Number of components N = 1 (usually for temperature) F = number of degrees of freedom No. of externally controllable variables (e.g. T, p, and composition of a phase), which can be changed independently without altering the number and kinds of phases which coexist at equilibrium. Material Sciences and Engineering MatE271 Week 7 17 Phase Rule - Example + Liquid Liquid + β Liquid + β β C C o Point: P + F = C +1 (N = 1, p = const.) C = 2 ( and ) P = 1 (liquid) F =C+1-P = 2+1-1=2 To completely describe the characteristics of this alloy: - you must describe 2 parameters T and composition - you can change 2 variables without changing the # of phases at equilibrium Material Sciences and Engineering MatE271 Week 7 18 aterial Sciences and Engineering,

10 Phase Rule - Example + Liquid Liquid Liquid + β β C + β Point: C o P + F = C +1 (N = 1, p = const.) C = 2 ( and ) P = 2 (liquid and ) F = C+1-P = = 1 To completely describe the characteristics of this alloy: - you must describe 1 parameter (T or composition of one of the phases) - you can change 1 variable without changing the # of phases at equilibrium (note only the nature of the phases is important - not relative amount) Material Sciences and Engineering MatE271 Week 7 19 Phase Rule - Example + Liquid Liquid Liquid + β β C + β Point: C C o P + F = C +1 (N = 1, p = const.) C = 2 ( and ) P = 3 (liquid and and β) F = C+1-P = = 0 To completely describe the characteristics of this alloy: - you do not need to describe T or composition - you cannot change any variables without changing the number of phases present Material Sciences and Engineering MatE271 Week 7 20

11 Equilibrium phase diagrams -binary systems I. inary isomorphous (complete ss) II. inary eutectic with no ss III. inary eutectic with limited ss IV. Eutectoid V. Peritectic VI. Intermediate Phase VII. General Material Sciences and Engineering MatE271 Week 7 21 I. inary Isomorphous Systems complete ss Complete liquid and solid solubility of both components Common in some alloy systems e.g. Ni-Cu Seen in some salt systems KCl- Kr Solid phase is a solid solution it s like a liquid solution e.g. water and alcohol not like a liquid mixture e.g. oil and water Material Sciences and Engineering MatE271 Week 7 22

12 Solid Solutions How do they form: Usually by introducing solute atoms into the solvent lattice Why are solid solutions important? tailor mechanical, electrical, magnetic properties Complete solid solution sometimes occurs when solute and solvent have: same crystal structure and similar atomic radii Material Sciences and Engineering MatE271 Week 7 23 Solid Solution Phase Diagram What is this point? Temperature Liquid Liquid +Solid Solution Solid Solution Liquid: SS: Composition - Complete Solid Solubility note that solid and liquid are each homogenous - Q: Number of phases in each phase field Material Sciences and Engineering MatE271 Week 7 24 aterial Sciences and Engineering,

13 Solid Solution Phase Diagram Temperature L + L Liquidus Line Solidus Line Composition o Note solid solution phase is called o Liquidus line- First solid appears on cooling o Solidus line- Last liquid disappears on cooling Material Sciences and Engineering MatE271 Week 7 25 Interpretation of Phase Diagrams To determine phases present: 1. Locate Temperature Composition Isomorphous system 2. Phase Field is labeled Liquid Liquid and S.S. () Solid Solution, Only Temperature L +SS Solid Solution Composition % Material Sciences and Engineering MatE271 Week 7 26 aterial Sciences and Engineering,

14 Phase Compositions What is the phase assemblage For a composition of 35% at a temperature of T 1? Temperature T 1 Liquid L + Phases present (by inspection) solid solution a and liquid Phase compositions (ends of the tie line) -- 45%, 55% liquid -- 10%, 90% C C C L o liquid solid composition Material Sciences and Engineering MatE271 Week 7 27 Phase mounts- Inverse Lever law How much liquid and how much solid? Use Inverse Lever Law Temperature T 1 Liquid amount solid liquid L + t T 1 and C o : C C C L o C o C Fraction of liquid = Fraction of solid = C L -C - Valid for two phase region only C L - C o C L -C Material Sciences and Engineering MatE271 Week 7 28

15 Phase mounts- Inverse Lever law C o = 35% C L = 10 % C = 45% Temperature T 1 Liquid amount solid liquid L + Phase mount C C C L o Calculate length of tie line and length of each segment e.g. For an overall composition of 35% at T 1 liquid amount =(45-35)/(45-10) = (28.6%) solid amount =(35-10)/(45-10) = (71.4%) Material Sciences and Engineering MatE271 Week 7 29 Common Mistakes Mixing up phase composition and phase amount Taking the fraction of the tie line for the wrong phase (take the length opposite the phase you are interested in) Weight fraction vs. mole fraction note how the composition axis is labeled! you may have to convert from weight to mole fraction or even to volume fraction Material Sciences and Engineering MatE271 Week 7 30

16 Example w% Cu-Ni Cooling from 1400 C - What T does 1st solid form? - What is the comp. of the solid phase? - t what T does the last liquid solidify? - What is the composition of the liquid phase? Material Sciences and Engineering MatE271 Week 7 31 Example - 1st solid at 1320 C - Composition of solid 62w% Ni, 38w% Cu - Last liquid at 1275 C - Composition of liquid: 37% Ni, 63% Cu - Ni rich solid forms leaving Cu rich liquid Material Sciences and Engineering MatE271 Week 7 32 aterial Sciences and Engineering,

17 Microstructure Development Cu-Ni phase diagram (49 wt%ni) L (35 wt%ni) 23 wt%ni 30 wt%ni 43 wt%ni 49 wt%ni Cu Material Sciences and Engineering MatE271 Week 7 33 Ni Microstructure Development Cu-Ni phase diagram 23 wt%ni 30 wt%ni 43 wt%ni L (30 wt%ni) (49 wt%ni) (35 wt%ni) L (23 wt%ni) (35 wt%ni) Cu Material Sciences and Engineering MatE271 Week 7 34 Ni aterial Sciences and Engineering,

18 Microstructure Development o Notice that composition of solid changes continuously as it forms o djustments in composition is often limited by diffusion (dependent on rate of cooling) o Most cooling processes are fast nonequilibrium solidification segregation cored structures Material Sciences and Engineering MatE271 Week 7 35 Cored Microstructure o Interior is rich in higher melting component o Exterior is rich in lower melting component Material Sciences and Engineering MatE271 Week 7 36 aterial Sciences and Engineering,

19 II. Simple inary Eutectic: No Solid Solubility o Liquidus -first solid appears on cooling Melting Temp. (Pure ) Melting Temp. (Pure ) o Eutectic Line - line of 3 phase equilibrium o Invariant Point - where 2 liquidus lines and eutectic line meet + Liquid Eutectic Line + (both solids) Liquid Liquidus Invariant Point Liquid + T m(eutectic) < T m() or T m() Composition, % Material Sciences and Engineering MatE271 Week 7 37 III. Simple inary Eutectic: Limited Solid Solubility Liquid + Liquid Liquid + β β + β Composition % o o Limited Solid Solubility is solid with small amount of solid dissolved in it β is solid with small amount of solid dissolved in it Components have different solid solubilities Material Sciences and Engineering MatE271 Week 7 38

20 inary Eutectic Solidus + Liquid Liquid Liquidus Solidus o o Solvus Eutectic line + β Composition % Liquid + β Solvus Invariant Point Eutectic (occurs at eutectic temperature) Line of three-phase equilibrium Limit of solid solubility solidus (between solid and liquid and solid solution) solvus (between single solid solution and mixture of solid solutions) Material Sciences and Engineering MatE271 Week 7 39 β Interpretation of Phase Diagrams To determine phases present Locate Temperature Composition Phase field is labeled inary Eutectic + L Liquid L + β β t T 1 and C o (approx. 35%) Composition of Liquid is C L (approx. = 45% ) Composition of Solid is - (approx. = 10%) C C ο C L Composition %, amount (~ 20%), amount (~ 80%) Material Sciences and Engineering MatE271 Week 7 40

21 Microstructure Close to end-member Liquid above liquidus Solid precipitates crossing two phase boundary Solid forms completely in solid solution region No other phase forms +β L +L Material Sciences and Engineering MatE271 Week 7 41 Microstructure First solid () forms at liquidus Solid grows- changes in composition Crosses solvus - becomes pure Crosses two-phase boundary - (β precipitates) Material Sciences and Engineering MatE271 Week 7 42 aterial Sciences and Engineering,

22 Eutectic Microstructure (forms when eutectic liquid freezes) Lamellae Pb +L + β L Composition %Sn L + β β Sn L +β lternating Pb-rich -phase (dark layers) and a Sn-rich β-phase (light layers) Chk textbook P. 317 Material Sciences and Engineering MatE271 Week 7 43 IV. Eutectoid inary Diagram (γ Fe -Fe) o Eutectoid Reaction Invariant point with three phases Upon cooling, a solid phase transforms into two other solid phases e.g. γ (eutectoid) +β It s like a eutectic only involving solids L (eutectic) +β Material Sciences and Engineering MatE271 Week 7 44

23 Eutectoid inary Diagram γ Fe (FCC) austenite γ γ+l L β+l +γ γ+β eutectic β eutectoid +β -Fe (CC) ferrite β: Fe 3 C (cementite) rapid cooling β: C slow cooling Material Sciences and Engineering MatE271 Week 7 45 Unit Review Explain basic concepts of phase equilibria and phase diagrams Solubility limit, phases, microstructure Equilibrium phase diagram topics: binary isomorphous, binary invariant points phases present - their composition and amounts microstructural development The phase rule is p+f=c+n RED Class Notes & Shackelford, 2001, Ch 9, pp , Material Sciences and Engineering MatE271 Week 7 46

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