ENGR-45_Lec-21_PhasrDia-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 45 Phase Diagrams (1)

ENGR-45_Lec-21_PhasrDia-1.ppt 2 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals – Phase Diagrams  When Two Elements Are Combined, Determine the Resulting MicroStructural Equilibrium State  For Example Specify –a composition (e.g., wt%Cu - wt%Ni), and –a temperature (T) –a pressure (P)  almost ALWAYS assume ROOM Pressure Determine Structure

ENGR-45_Lec-21_PhasrDia-1.ppt 3 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals.2 – Phase Dia. Cont: Determine Structure –HOW MANY phases Result –The COMPOSITION of each phase –Relative QUANTITY of each phase Phase A Phase B

ENGR-45_Lec-21_PhasrDia-1.ppt 4 Bruce Mayer, PE Engineering-45: Materials of Engineering Definitions – Phase Systems  Component  Pure Constituent of a Compound Typcially an ATOM, but can also be a Molecular Unit  Solvent/Solute Solvent  Majority Component in a Mixture Solute  Minority Component in a Mixture  System  Possible Alloys Formed by Specific Components (e.g. C-Fe Sys)

ENGR-45_Lec-21_PhasrDia-1.ppt 5 Bruce Mayer, PE Engineering-45: Materials of Engineering The Solid Solubility Limit  Solubility Limit  Max Concentration of Solute that will actually DISSOLVE in a Solvent to form a SOLUTION  Example: Water-Sugar Add Sugar (Solute) to Water (Solvent) –Initially ALL the Sugar Dissolves –But after a Certain Amount, SOLID Sugar Starts to Collect on the bottom of the Vessel Sucrose/Water Phase Diagram Pure Sugar Temperature (°C) CoCo =Composition (wt% sugar) L (liquid solution i.e., syrup) Solubility Limit L (liquid) + S (solid sugar) PureWater

ENGR-45_Lec-21_PhasrDia-1.ppt 6 Bruce Mayer, PE Engineering-45: Materials of Engineering The Solid Solubility Limit cont.  Sol-Sol Quantitative Example At What wt% Sugar does the Sugar NO Longer Dissolve for –20 °C –80 °C  For 20 °C Cast Right from 20C –Find Solid Sugar in Vessel at C 0 = 63 wt% For 80C, Again Cast Rt –Find Solid Sugar in Vessel at C 0 = 75 wt% INcreased Temp INcreases Sol-Sol Limit Sugar Pure Temperature (°C) CoCo =Composition (wt% sugar) L (liquid solution i.e., syrup) Solubility Limit L (liquid) + S (solid sugar) PureWater 63 75

ENGR-45_Lec-21_PhasrDia-1.ppt 7 Bruce Mayer, PE Engineering-45: Materials of Engineering Components & Phases  Components  The elements or compounds which are mixed initially (e.g., Al and Cu)  Phases  The PHYSICALLY and CHEMICALLY DISTINCT material regions that result from mixing (e.g.,  and  below) Aluminum Copper Alloy

ENGR-45_Lec-21_PhasrDia-1.ppt 8 Bruce Mayer, PE Engineering-45: Materials of Engineering Effect of T & Composition (C 0 ) Water Sugar System  Changing T can change No. of phases: path A to B.  Changing C 0 can change No. of phases: path B to D

ENGR-45_Lec-21_PhasrDia-1.ppt 9 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Equilibria  Consider the Cu-Ni Alloy System Crystal Structure electroneg r (nm) NiFCC CuFCC  Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (c.f. Hume – Rothery rules) suggesting high mutual solubility.  Copper and Nickel are, in fact, totally miscible in all Proportions

ENGR-45_Lec-21_PhasrDia-1.ppt 10 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Diagrams –The Cu-Ni Phase Diagram  Describes Phase Formation as a Function of T, C 0, P  This Course Considers binary systems: 2 components independent variables: T & C 0 (P = 1atm in all Cases) 2 phases: L (liquid)  (FCC solid soln) 3 phase fields: L L+   wt% Ni T(°C) L (liquid)  (FCC solid solution) L +  liquidus solidus

ENGR-45_Lec-21_PhasrDia-1.ppt 11 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Dia.’s: Phase No.s & Types  Rule-1: Given T & C 0 (for P = 1 atm) then Find NUMBER & TYPES of Phases Present  Examples Pt- A (1100C, 60wt-%) –1 Phase →  ; the FCC Solid Solution Pt- B (1250,35) –2 Phases → L+  wt% Ni T(°C) L (liquid)  (FCC solid solution) L +  liquidus solidus A(1100,60) B (1250,35) –Cu-Ni Phase Diagram

ENGR-45_Lec-21_PhasrDia-1.ppt 12 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Dia.’s: Phase Composition  Rule-2: Given T & C 0 (for P = 1 atm) then Find The COMPOSITION (wt% or at%) for EACH Phase  Example: C 0 = 35 wt% Ni At T A : –Only Liquid –C L = C O = 35 wt% Ni –Cu-Ni Phase Diagram

ENGR-45_Lec-21_PhasrDia-1.ppt 13 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Dia.’s: Phase Comp. cont.  Example: C 0 = 35 wt% Ni At T D : –Only Solid (  -FCC) –C  = C 0 = 35 wt% Ni At T B : –BOTH  and L –C  = C solidus  43 wt% Ni –C L = C liquidus  32 wt% Ni –Cu-Ni Phase Diagram  Note the Use of the IsoThermal “Tie Line” at T B to Find C L & C 

ENGR-45_Lec-21_PhasrDia-1.ppt 14 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Dia.’s: Phase Wt Fractions  Example: C 0 = 35 wt% Ni At T A : –Only Liquid –W L = 1.00 & W  = 0.00 (wt Frac’s) At T D : –Only Solid –W L = 0.00 & W  = 1.00 (Frac’s) –Cu-Ni Phase Diagram  Rule-3: Given T & C 0 (for P = 1 atm) then Find The AMOUNT of EACH Phase in Wt-Fraction

ENGR-45_Lec-21_PhasrDia-1.ppt 15 Bruce Mayer, PE Engineering-45: Materials of Engineering Phase Dia.’s: Wt Fractions cont.  Example: C 0 = 35 wt% Ni At T B : –BOTH  and L Calc W ,B & W L,B Using the INVERSE LEVER RULE –Cu-Ni Phase Diagram WLWL  S R  S = 27wt% WW  R R  S S R

ENGR-45_Lec-21_PhasrDia-1.ppt 16 Bruce Mayer, PE Engineering-45: Materials of Engineering Lever Rule Proof  Sum of weight fractions:  Conservation of mass (Ni):  Combine These Two Equations for W L & W α  A Geometric Interpretation Balance massXdist at Tip-Pt

ENGR-45_Lec-21_PhasrDia-1.ppt 17 Bruce Mayer, PE Engineering-45: Materials of Engineering Cooling Cu-Ni Binary Phase-Sys  Phase Diagram for Cu-Ni System →  System Characteristics: BINARY → 2 components: Cu & Ni ISOMORPHOUS → Complete Solubility of one Component in Another –At least One Solid Phase-Field Extends from 0 to 100 wt% Ni

ENGR-45_Lec-21_PhasrDia-1.ppt 18 Bruce Mayer, PE Engineering-45: Materials of Engineering Ex: Cu-Ni Binary Cooling  Consider 35 wt% Ni Cooled: 1300 °C → Rm-Temp  Pt-A 1.00 Liquid 35 wt% Ni  Pt-B on Liquidus Tiny Amount of solid-  in Liq. Suspension –Liq → 35 wt% Ni –  → 46 wt% Ni

ENGR-45_Lec-21_PhasrDia-1.ppt 19 Bruce Mayer, PE Engineering-45: Materials of Engineering Ex: Cu-Ni Binary Cooling cont.  Pt-C in 2-Ph Region (43-35)/(43-32) = Liquid –Liq → 32 wt% Ni –  → 43 wt% Ni  Pt-D on Solidus Small Liq Pockets in Solid Suspension –Liq → 24 wt% Ni –  → 36 wt% Ni  Pt E 1.00 C 0

ENGR-45_Lec-21_PhasrDia-1.ppt 20 Bruce Mayer, PE Engineering-45: Materials of Engineering NonEquilibrium Cooling  Phases Diagrams are Constructed Under the Assumption of ThermoDynamic Equilibrium i.e., All Phases have Formed Sufficiently Slowly to allow for HOMOGENOUS (same) Concentrations WITHIN ALL Phases  In the Previous Example The Solid STARTS at 46 wt%-Ni (pt-B) and ENDS at 35 wt%-Ni (Pt-E) Thus Solid particles that WERE 46Ni Had to CHANGE to 35Ni by SOLID STATE DIFFUSION  But Solid-State Diffusion Proceeds Slowly Rapid Cooling Can result in NonUniform Comp.

ENGR-45_Lec-21_PhasrDia-1.ppt 21 Bruce Mayer, PE Engineering-45: Materials of Engineering NonEquil Cool → Cored Structure  C  Changes Composition Upon Cooling First  to solidify has C  = 46 wt%Ni Last  to solidify has C  = 35 wt%Ni  Fast Cool Rate → Cored structure  Slow Cool Rate → Equil. Structure Uniform C  35wt%Ni to solidfy: First  to solidfy: 46wt%Ni Last  < 35wt%Ni

ENGR-45_Lec-21_PhasrDia-1.ppt 22 Bruce Mayer, PE Engineering-45: Materials of Engineering Mech Props → Cu-Ni System  Recall Solid-Solution Strengthening Tensile Strength, TSDuctility (%EL,%AR) Tensile Strength (MPa) Composition, wt%Ni Cu Ni TS for pure Ni TS for pure Cu Elongation (%EL) Composition, wt%Ni Cu Ni %EL for pure Ni %EL for pure Cu Max As Fcn of C 0 Min as Fcn of C 0

ENGR-45_Lec-21_PhasrDia-1.ppt 23 Bruce Mayer, PE Engineering-45: Materials of Engineering WhiteBoard PPT Work  Problems 9.[5,6] The Affect of PRESSURE on Phase Diagrams Water Ice, Has at Least TEN, yes 10, Distinct Structural Phases –Phases form in Response to the PRESSURE Above The Ice

ENGR-45_Lec-21_PhasrDia-1.ppt 24 Bruce Mayer, PE Engineering-45: Materials of Engineering Ice is Nice – Problem 9.5 Starting Point Note Typo in Book Temperature needs to be –15 °C for this to work  Given Ice-I at −15C & 10atm → Find MELTING and SUBLIMATION PRESSURES

ENGR-45_Lec-21_PhasrDia-1.ppt 25 Bruce Mayer, PE Engineering-45: Materials of Engineering Ice is Nice P9.5a – Melt Temp  At −15C Cast UPward to the Solid-LIQUID Phase Boundary Find that Ice-I, when held at −15C, MELTS at about 1000 atm (~15000 psi, ~100 Mpa) 1000

ENGR-45_Lec-21_PhasrDia-1.ppt 26 Bruce Mayer, PE Engineering-45: Materials of Engineering Ice is Nice P9.5b – Sublime Temp  At −15C Cast DOWNward to the Solid-VAPOR Phase Boundary Find that Ice-I, when held at −15C, VAPORIZES at about atm (~ psi, ~20 Pa)

ENGR-45_Lec-21_PhasrDia-1.ppt 27 Bruce Mayer, PE Engineering-45: Materials of Engineering Ice is Nice P9.6  P = 0.1 Atm  At 0.1 Atm Cast RIGHTward to intercept the Sol-Liq and Liq-Vap Phase-Boundaries 2.0 Ice-I MELTS at  2 °C Water BOILS at  75 °C –i.e., the VAPOR PRESSURE of Water at 75 °C is  10% of Atm 75