Chapter 9

Chapter 9

Phase Diagrams 1 What is Phase? The term phase refers to a separate and identifiable state of matter in which a given substance may exist. Applicable to both crystalline and non-crystalline materials An important refractory oxide silica is able to exist as three crystalline phases, quartz, tridymite and cristobalite, as well as a non-crystalline phase, silica glass, and as molten silica Every pure material is considered to be a phase, so also is every solid, liquid, and gaseous solution For example, the sugarwater syrup solution is one phase, and solid sugar is another 2 Introduction to Phase Diagram There is a strong correlation between microstructure and mechanical properties, and the development of microstructure of an alloy is related to the characteristics of its phase diagram It is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium Provides valuable information about melting, casting, crystallization, and other phenomena 3 ISSUES TO ADDRESS... When we combine two elements... what equilibrium state do we get? In particular, if we specify... --a composition (e.g., wt% Cu - wt% Ni), and --a temperature (T )

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 4 Solubility Limit At some specific temperature, there is a maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution, which is called as Solubility Limit The addition of solute in excess of this solubility limit results in the formation of another compound that has a distinctly different composition This solubility limit depends on the temperature 5 Solubility Limit Sugar-Water 6 Microstructure the structure of a prepared surface of material as revealed by a microscope above 25 magnification The microstructure of a material can strongly influence properties such as strength, toughness, ductility, hardness, corrosion resistance, high/low temperature behavior, wear resistance, etc 7

Components and Phases Components: The elements or compounds which are present in the mixture (e.g., Al and Cu) Phases: The physically and chemically distinct material regions that result (e.g., and ). AluminumCopper Alloy (lighter phase) (darker phase) 8 Effect of T & Composition (Co) Changing T can change # of phases: path A to B. Changing Co can change # of phases: path B to D. B (100C,70) D (100C,90) 1 phase watersugar system Temperature (C) 100 L 80 (liquid) 60

L (liquid solution 40 i.e., syrup) + S (solid sugar) A (20C,70) 20 0 2 phases 2 phases 0 20 40 60 70 80 100 Co =Composition (wt% sugar) 9 PHASE EQUILIBRIA Free Energy -> a function of the internal energy of a system, and also the disorder of the atoms or molecules (or entropy) A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition A change in temperature, pressure, and/or composition for a system in equilibrium will result in an increase in the free energy

And in a possible spontaneous change to another state whereby the free energy is lowered 10 Unary Phase Diagram Three externally controllable parameters that will affect phase structure: temperature, pressure, and composition The simplest type of phase diagram to understand is that for a one-component system, in which composition is held constant Pure water exists in three phases: solid, liquid and vapor 11 Pressure-Temperature Diagram (Water) Each of the phases will exist under equilibrium conditions over the temperaturepressure ranges of its corresponding area The three curves (aO, bO, and cO) are phase boundaries; at any point on one of these curves, the two phases on either side of the curve are in equilibrium with one another Point on a PT phase diagram where three phases are in equilibrium, is called a triple point 12 Binary Phase Diagrams A phase diagram in which temperature and composition are variable parameters, and pressure is held constantnormally 1atm Binary phase diagrams are maps that represent the relationships between temperature and the compositions and quantities of phases at equilibrium, which influence the microstructure of an alloy. Many microstructures develop from phase transformations, the changes that occur when

the temperature is altered 13 Phase Equilibria Simple solution system (e.g., Ni-Cu solution) Crystal Structure electroneg r (nm) Ni FCC 1.9 0.1246 Cu FCC 1.8 0.1278 Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume Rothery rules) suggesting high mutual solubility. Ni and Cu are totally miscible in all proportions. 14 Phase Diagrams Indicate phases as function of T, Compos, and Press. For this course: -binary systems: just 2 components. -independent variables: T and Co (P = 1 atm is almost always used).

T(C) Phase Diagram for Cu-Ni system 2 phases: 1600 1500 L (liquid) 1400 us d i u liq + s L lidu so 1300 1200 (FCC solid solution) 1100 1000 L (liquid) (FCC solid solution) 0

20 40 60 80 3 phase fields: L L+ 100 wt% Ni 15 Phase Diagrams: # and types of phases Rule 1: If we know T and Co, then we know: --the number and types of phases present. A(1100C, 60): 1 phase: B(1250C, 35): 2 phases: L + 1600 L (liquid) 1500 B (1250C,35) Examples: T(C)

1400 1300 1200 us d i u liq us d i l so L (FCC solid solution) 1100 1000 + Cu-Ni phase diagram A(1100C,60) 0 20 40 60 80 100

wt% Ni 16 Phase Diagrams: composition of phases Rule 2: If we know T and Co, then we know: --the composition of each phase. Examples: T(C) Cu-Ni system A TA Co = 35 wt% Ni 1300 L (liquid) At T A = 1320C: Only Liquid (L) B T B CL = Co ( = 35 wt% Ni) At T D = 1190C: + L 1200 D Only Solid ( ) TD C = Co ( = 35 wt% Ni) 20 3032 35 At T B = 1250C: CLCo Both and L

CL = C liquidus ( = 32 wt% Ni here) C = C solidus ( = 43 wt% Ni here) tie line dus i liqu + L id so l us (solid) 4043 50 C wt% Ni 17 Phase Diagrams: weight fractions of phases Rule 3: If we know T and Co, then we know: Cu-Ni system --the amount of each phase (given in wt%). Examples: Co = 35 wt% Ni At T A: Only Liquid (L) W L = 100 wt%, W = 0 At T D: Only Solid ( ) W L = 0, W = 100 wt%

At T B: Both and L S 43 35 73 wt % WL R + S 43 32 W T(C) TA 1300 A L (liquid) B R S TB 1200 TD 20 tie line dus i liqu L + D 3032 35 CLCo +

L us d i l so (solid) 40 43 50 C wt% Ni R = 27 wt% R +S 18 The Lever Rule Tie line connects the phases in equilibrium with each other - essentially an isotherm T(C) 1300 tie line dus i l i qu L (liquid) 1200 20 + L

B TB s L + R How much of each phase? Think of it as a lever (teeter-totter) S (solid) 30C C 40 C L o R 50 wt% Ni WL M ML us d i l

o C C0 ML S ML M R S C CL S M S M L R W C CL R 0 R S C CL 19 Ex: Cooling in a Cu-Ni Binary Phase diagram: Cu-Ni system. System is: --binary i.e., 2 components: Cu and Ni. T(C) L (liquid) 1300 L: 35 wt% Ni : 46 wt% Ni i.e., complete solubility of one component in another; phase field extends from

0 to 100 wt% Ni. Consider Co = 35 wt%Ni. A 32 --isomorphous L: 35wt%Ni 35 B C 46 43 D 24 1200 L+ L: 32 wt% Ni 36 L+ : 43 wt% Ni E

L: 24 wt% Ni : 36 wt% Ni (solid) 1100 20 30 Cu-Ni system 35 Co 40 50 wt% Ni 20 Cored vs Equilibrium Phases C changes as we solidify. Cu-Ni case: First to solidify has C = 46 wt% Ni. Last to solidify has C = 35 wt% Ni. Fast rate of cooling: Cored structure Slow rate of cooling: Equilibrium structure First to solidify: 46 wt% Ni Last to solidify: < 35 wt% Ni

Uniform C : 35 wt% Ni 21 Mechanical Properties: Cu-Ni System Effect of solid solution strengthening on: --Ductility (%EL,%AR) 400 TS for pure Ni 300 TS for pure Cu 200 0 20 40 60 80 100 Cu Ni Composition, wt% Ni --Peak as a function of Co Elongation (%EL) Tensile Strength (MPa) --Tensile strength (TS) 60 %EL for pure Cu %EL for pure Ni 50 40 30

20 0 20 Cu 40 60 80 100 Ni Composition, wt% Ni --Min. as a function of Co 22 Eutectic System A eutectic system is a mixture of chemical compounds or elements that has a single chemical composition that solidifies at a lower temperature than any other composition 23 Binary-Eutectic Systems has a special composition with a min. melting T. Cu-Ag T(C) system 2 components Ex.: Cu-Ag system 1200 3 single phase regions L (liquid)

1000 (L, ) L + 779C Limited solubility: L+ 800 TE : mostly Cu 8.0 71.9 91.2 : mostly Ag 600 TE : No liquid below TE 400 CE : Min. melting TE composition 200 Eutectic transition L(CE) 0 20 40 60 CE 80 100 Co , wt% Ag (CE) + (CE) 24 EX: Pb-Sn Eutectic System (1) For a 40 wt% Sn - 60 wt% Pb alloy at 150C, find... --the phases present: +

T(C) --compositions of phases: CO = 40 wt% Sn C = 11 wt% Sn C = 99 wt% Sn --the relative amount of each phase: C - CO S = W = R+S C - C 300 200 150 100 99 - 40 59 = = = 67 wt% 99 - 11 88 C - C W = R = O C - C R+S = Pb-Sn system 40 - 11 29

= = 33 wt% 99 - 11 88 L (liquid) L+ 18.3 183C 61.9 R L+ 97.8 S + 0 11 20 C 40 Co 60 80 C, wt% Sn 99100 C 25

EX: Pb-Sn Eutectic System (2) For a 40 wt% Sn - 60 wt% Pb alloy at 220C, find... --the phases present: + L T(C) --compositions of phases: CO = 40 wt% Sn C = 17 wt% Sn CL = 46 wt% Sn --the relative amount of each phase: CL - C O 46 - 40 = W = CL - C 46 - 17 6 = = 21 wt% 29 Pb-Sn system 300 L+ 220 200 R L (liquid) L+ S

183C 100 CO - C 23 = WL = = 79 wt% CL - C 29 + 0 17 20 C 100 40 46 60 80 Co CL C, wt% Sn 26 Microstructures in Eutectic Systems: I Co < 2 wt% Sn Result: --at extreme ends --polycrystal of grains i.e., only one solid phase. T(C) L: Co wt% Sn 400 L

L 300 200 L+ (Pb-Sn System) : Co wt% Sn TE 100 + 0 Co 10 20 30 Co , wt% Sn 2 (room T solubility limit) 27 Microstructures in Eutectic Systems: II L: Co wt% Sn

T(C) 2 wt% Sn < Co < 18.3 wt% Sn 400 Result: Initially liquid + then alone finally two phases polycrystal fine -phase inclusions L L 300 L+ 200 : Co wt% Sn TE 100 + 0 10 20 Pb-Sn system 30

Co Co , wt% 2 (sol. limit at T room ) 18.3 (sol. limit at TE) Sn 28 Microstructures in Eutectic Systems: III Co = CE Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of and crystals. T(C) L: Co wt% Sn 300 Pb-Sn system L+ 200 L 100 0 L 183C

TE 20 18.3 40 Micrograph of Pb-Sn eutectic microstructure : 97.8 wt% Sn : 18.3 wt%Sn 60 CE 61.9 80 160 m 100 97.8 C, wt% Sn 29 Lamellar Eutectic Structure 30 Microstructures in Eutectic Systems (Pb-Sn): IV 18.3 wt% Sn < Co < 61.9 wt% Sn Result: crystals and a eutectic microstructure T(C)

L: Co wt% Sn 300 L L Pb-Sn system L L+ 200 R TE S R 100 L+ S primary eutectic eutectic

20 18.3 40 60 61.9 C = 18.3 wt% Sn CL = 61.9 wt% Sn W = S = 50 wt% R+S WL = (1- W) = 50 wt% Just below TE : + 0 Just above TE : 80 Co, wt% Sn 100 97.8 C = 18.3 wt% Sn C = 97.8 wt% Sn W = S = 73 wt% R+S W = 27 wt% 31 Hypoeutectic & Hypereutectic 300 L

T(C) 200 L+ L+ TE + 100 0 20 40 hypoeutectic: Co = 50 wt% Sn 60 80 100 eutectic 61.9 (Pb-Sn System)

Co, wt% Sn hypereutectic: (illustration only) eutectic: Co = 61.9 wt% Sn 175 m 160 m eutectic micro-constituent 32

Recently Viewed Presentations

  • The Triangulation of Value and the Cost of Capital

    The Triangulation of Value and the Cost of Capital

    Julian Wentzel of Cazenove The Errunza-Miller Study December 2000 "Market Segmentation and the Cost of Capital in International Equity Markets." Findings: Capital market theory suggests that the removal of barriers to capital flows reduces companies' cost of capital and investors'...
  • Top worries of 1975

    Top worries of 1975

    Of Mice and Men Not Does and Women Graham Seibert October 20, 2017
  • Development of a High-Speed Multi-Channel Analog Data Acquisitioning

    Development of a High-Speed Multi-Channel Analog Data Acquisitioning

    Analog Data Acquisitioning Architecture L. Björk, S. Persyn, B. Walls, M. Epperly Southwest Research Institute September 2005 Introduction As the measurement techniques in the space science community rapidly evolve, the demand for multi-channeled, high-speed, radiation tolerant data acquisitioning systems get...
  • Jonesboro Middle School Mr. Corey Stephens, Principal

    Jonesboro Middle School Mr. Corey Stephens, Principal

    the georgia milestones assessment system (georgia milestones) is a comprehensive summative assessment pro gram spanning grades 3 through high school. georgia milestones measures how well students have learned the knowledge and skills outlined in the state-adopted content standards in english...
  • Spelling for Older Students

    Spelling for Older Students

    Slide 3 Rhyming words. Slide 4 Hearing long ie sound. Slide 5- knowing vowels and consonants is vital for learning spelling rules. Multisensory learning (feeling the formation of a sound) is useful for many students. Rule 1: If the short...
  • Heat, Temperature, Heat Transfer, Thermal Expansion ...

    Heat, Temperature, Heat Transfer, Thermal Expansion ...

    Heat, Temperature, Heat Transfer, Thermal Expansion & Thermodynamics Heat vs. Temperature Heat A form of energy Measured in calories or Joules There is no "coldness" energy Any object with temperature above zero Kelvin has heat energy Temperature Avg. Kinetic Energy...
  • Electric Potential - McMaster University

    Electric Potential - McMaster University

    Review Example 1 Two charges of equal magnitude and opposite sign separated by a distance 2a, are placed on the x axis at ( a, 0) and (+a, 0).
  • SCHEDULE OF PRESENTATIONS (11AM  2PM) 6 MARCH 2013

    SCHEDULE OF PRESENTATIONS (11AM 2PM) 6 MARCH 2013

    Mr Roger Clark, Managing Director 11.30 - 11.45am ... Dr Claudia Anselmi, Director of Sales and Operation 12.30 - 12.45pm ... Pacific 11.45am - 12.00pm Comparing the P4 and the TPP approaches to intellectual property - Consumers International Dr Jeremy...