MM-231: Phase Equilibria & MicrostructureCourse OutlineSpring 2013Course AimTo understand the basics of phase equilibria, Phase diagram and evolution of microstructure in different processing conditions. These are the bases for the development of advanced engineering materials. Course ContentsPhase rule and Phase diagramsMicrostructuresDiffusionNucleation & growthSolidificationAnnealingTransformationsNote: Contents of the course may change according to the circumstances.

Text BookPhysical Metallurgy Principles by Reza Abbaschian, Robert E. Reed-Hill, 4th edition, (2009).Phase

MM-231: Phase Equilibria & MicrostructureCourse OutlineSpring 2013Course AimTo understand the basics of phase equilibria, Phase diagram and evolution of microstructure in different processing conditions. These are the bases for the development of advanced engineering materials. Course ContentsPhase rule and Phase diagramsMicrostructuresDiffusionNucleation & growthSolidificationAnnealingTransformationsNote: Contents of the course may change according to the circumstances.

Text BookPhysical Metallurgy Principles by Reza Abbaschian, Robert E. Reed-Hill, 4th edition, (2009).Phase Diagrams and Heterogeneous Equilibriua: A Practical Introduction by B. Predel, M. Hoch, (2004).

Reference Books

An introduction to Materials Engineering and Science by Brian S. Mitchell, A John Wiley & Sons, Inc., (2004).Essentials of Materials Science and Engineering, 2nd Edition, Donald R. Askeland, CL-Engineering, (2010).Phase Diagrams in Metallurgy, Their Development and Application by Frederick N. Rhines, (1956).Grading Policy

Quizzes (Un-announced): 20%, Assignments: 5%, Mid Term: 30%, Final Exam: 45%Attendance: Minimum 80% for appearing in the final exam.

PHASESA phase is a homogeneous portion of a system with uniform physical and chemical characteristics, in principle separable from the rest of the system

A difference in either physical or chemical properties constitutes a phase

gaseous state seemingly only one phase occurs (gases always mix)

liquid state often only one phase occurs (homogeneous solutions), e.g., salt water, molten Na2O-SiO2 two immiscible liquids (or liquid mixtures) count as two phasessolid state crystalline phases: e.g., ZnO and SiO2 = two phases polymorphs: e.g., wurtzite and sphalerite ZnS are different phases solid solutions = one phase (e.g., Al2O3-Cr2O3 mixtures)

Note: metastable phases do not appear on equilibrium phase diagrams.

First AssignmentDefinitions and understanding of basic terms of thermodynamics

Internal EnergyEntropyEnthalpy Laws of thermodynamics Free energyGibbs Free energyHelmholtz Free Energy

Note: Not only, you should make a written assignment but you must have a clear idea of these terms and all this will be asked and discussed in the class.

Reference book: Introduction to the thermodynamics of materials, 4th Edition by David R. Gaskell, Taylor & Francis group (2003)

DEFINITION A Phase Diagram describes the state of a materials system in thermodynamic equilibrium as a function of temperature, pressure and composition.Phase Diagrams are maps of the equilibrium phases associated with various combinations of temperature, pressure, and composition. One-component (unary) phase diagramTwo-component (binary) phase diagramThree-component (ternary) phase diagram (partial isothermal section)

Why Do We Need Phase Diagrams?For example: to understand solidification processes ( microstructure properties) metallurgy, geology, to characterize compounds and phases CrTe (actually Cr1-xTe) YbInCu4 (valence transition; transition temp. different due to nonstoichiometry)to understand reactions welding soldering contacting of semiconductors surface layers (hardening, e.g.)

First Fe-C Phase Diagram(1897)

Sir William Chandler Roberts-Austen

Number of Metallic Phase Diagrams(Assumption: 80 metallic elements)approximately 1023 40-component systems!

No. of components nNo. of possible systemsApproximate No. of investigated systems

1808023 1602 500382 1603 00041 581 580200524 141 016206300 500 200-73 176 716 400-

Phase DiagramsStructure of the LectureBasics (Phase rule, lever rule, )Unary (one-component) systemsBinary systems types of phase diagrams -x diagrams invariant reactions complex systems possible errorsTernary systems types of phase diagrams types of representations (isotherms, isopleths, liquidus projections, Scheil diagrams) invariant reactions complex systemsQuaternary systemsp-T diagrams for higher-order systems

Books on Phase EquilibriaB. Predel: Heterogene Gleichgewichte: Grundlagen und Anwendungen; Steinkopf (Darmstadt), 1982B. Predel, M. Hoch, M. Pool: Phase Diagrams and Heterogeneous Equilibria; Springer (Berlin), 2004F.N. Rhines: Phase Diagrams in Metallurgy: Their Development and Application; McGraw-Hill (New York), 1956P. Gordon: Principles of Phase Diagrams in Materials Systems; McGraw-Hill (New York), 1968A. Prince: Alloy Phase Equilibria; Elsevier (Amsterdam), 1966J. Zernike: Chemical Phase Theory; N.V. Uitgevers-Maatschappij Ae.E. Kluwer (Deventer), 1955Collections of Phase DiagramsT.B. Massalski et al. (Ed.): Binary Alloy Phase Diagrams (3 Volumes); ASM International (Materials Park, OH), 1995.P. Villars, A. Prince, H. Okamoto (Ed.): Handbook of Ternary Alloy Phase Diagrams (10 Volumes) , ASM International (Materials Park, OH), 1995.Journals on Phase DiagramsJournal of Phase Equilibria and Diffusion; SpringerCALPHAD - Computer Coupling of Phase Diagrams and Thermochemistry; Elsevier

GIBBS PHASE RULEP + F = C + 2orF = C + 2 PP = number of phasesC = number of componentsF = degrees of freedom (number of variables that can be varied independently)

If the pressure is kept constant:P + F = C + 1orF = C + 1 P

PHASE EQUILIBRIA IN UNARY SYSTEMS221 bar1.01325 bar6.1 mbarABCF = C - P + 2A, B: C = 1, P = 1F = 1 1 + 2 = 2 C:C = 1, P = 2F = 1 2 + 2 = 1Triple Pt.: C = 1, P = 3F = 1 3 + 2 = 0 Example: H2O

Example: H2O

1 MPa = 106 Pa = 10 barExample: CO2

ALLOTROPYElements can exist in more than one (crystalline) formsPOLYMORPHISMA substance can exist in more than one crystalline formsTRANSFORMATIONS(Principle)Both stable formsOnly one stable form

TRANSFORMATIONSGibbs Energy vs. Temperature(p = const.)Phase stable (enantiotropic transformation)Phase metastable (monotropic transformation possible )Metastable into stable phase, irreversibleStable into stable phase, reversible

UNARY PHASE DIAGRAMS: EXAMPLES Fe (enantiotropic transformations)SiO2 (schematic) (series of monotropic transformations)[Pa]

TRIPLE POINTS OF METALS*) As: 1 atm (sublimation) at 610C

MetallT (C)p (atm)p (Pa)

Ag9600.000 11.01101As81436 *)3.65106Ba7040.0011.01102Ca8500.000 11.01101Cu10830.000 000 787.910-2Fe()15350.000 055.1Hg-390.000 000 001 31.3210-4Mn12400.0011.01102Ni14550.000 11.01101Pb3270.000 000 11.0110-2Pt17730.000 0011.0110-1Sr7700.000 11.01101Zn4190.055.07103

Isomorphous Systems

p-T-x DiagramT-x diagramp-x diagramp-T diagram of pure Bp-T diagram of pure A

GGibbs Energy of Mixingp = constant !tie line (Konnode)Basis of the CALPHAD-Method to calculate phase diagrams

LEVER RULETCabN(1-y)NyN = total number of atomsy = fraction of atoms in phase (1-y) = fraction of atoms in phase Ly : (1-y) = a : b

CoringSolidificationfor case of coringFrozen firstFrozen lastDendritic solidificationAssumption: homogeneous equilibrium in the liquid phase is always retained

Minima and MaximaPbTl xTlAuCu xCuMiscibility GapSuperstructuresSpecial Cases:

Eutectic SystemsMetastable extension into two-phase field!AxBAxBT

The Boundary Rule: Any p-phase region can be bounded only by regions containing p +/- 1 phases, where p denotes the number of phases.The Boundary Curvature Rule: Boundaries of one-phase regions must meet with curvatures such that the boundaries extrapolate into the adjacent two-phase regions.The Solubility Rule: All components aresoluble to some degree in all phases

Eutectic ReactionOften: lamellar microstructure of eutectic alloys

G-xbinary eutectic

Eutectic Systems: ExamplesAl-SiPb-BiAg-CuAl-Sn

Eutectic Systems:

Primary Crystallization and MicrostructureHypereutectic Al-Si 14% alloy: primary crystallizationHypereutectic Al-Si 14% alloy: final microstructure

Eutectic Systems:

Solidification and Non-equilibriumxBNo eutectic mixture should be detected in this case, however ...

Eutectic Systems:

Isothermal Diffusion / Diffusion Couples700C900C

Eutectic Systems:

Limiting Casesdegenerateeutectic

Eutectic Systems:

Errors(from a customer journal of the company METTLER)

Eutectoid SystemsEutectoid Reaction: + TtTLTSTTecoolheat

Eutectoid

Fe Fe3C(Pearlite) + Fe3C: bcc (Ferrite): fcc (Austenite): bcc

Fe3C: cementitehypoeutectoid: 0.3 % Ceutectoid: 0.8 % Chypereutectoid: 1.2 % C

Eutectoid ReactionsExamplesFe-TeNi-Zn

Monotectic SystemsMonotectic Reaction: L1 L2 + ... the phase field L1+L2 can be regarded as being made up of an infinite number of tie-lines ...

Monotectic SystemsSolidification

Monotectic SystemsExamplesCuPbBiFeCu-PbBi-Fe (limiting case with virtually no solubility in the solid and very limited solubility in the liquid state)

Monotectic SystemsExamples

upper critical solution temperature (UCST

Phases that are separated from the composition extremes (0% and 100%) are called intermediate phases.

Intermediate phases could be either compounds or intermediate solid solutions.

Peritectic Reaction

A very rare example. Peritectic reactions are frequent components of complex phase diagrams with many phases, but they rarely occur as the only feature of a phase diagram.

Three stages of peritectic reaction in a directionally solidified high-speed steel. (a) First-stage structure. Dark gray is austenite; white is ferrite. The mottled structure is quenched liquid. (b) Subsequent peritectic transformation of (a). (c) Further peritectic transformation of (b). Dark gray in the middle of the white ferrite is newly formed liquid. Source: ASM Handbook, Vol. 9, Metallography and Microstructures, 2004, p 100

Peritectoid SystemsAgAl +

Complex Binary SystemsExamplesAgOsCuSnReaction e:L2 G + (Os)Reaction r:G + (Os) L1Reaction l (Metatectic or Catatectic Reaction): + L

Complex Binary SystemsPossible Errors

Complex Binary SystemsTechnically Important SystemsCuZnCu-Zn = BrassFeMartensiteFe-C = Steel

Complex Binary SystemsDiffusion Couple

Tie line

Solid Solutions

A solid-state solution: a crystalline material with variable composition

Two types:Substitutional (solute atom/ion replaces solvent atom/ion)Interstitial (solute atom/ion occupies interstitial site)

Formation of solid solutions favored by:similar atomic/ionic radii (15%)Same crystal structureSimilar electronegativitiesSame valencyExample:Al2O3-Cr2O3 (substitutional, complete)Si-Ge (substitutional, complete)Fe-C (interstitial, partial)

Substitutional (a) and interstitial (b)