phase diagrams 1

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Presentation Transcript

Slide1: 

Phase Diagrams

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Why do cocktail ice served in expensive restaurants are clear whereas the ice formed in your refrigerator is cloudy? What is a solder alloy? What is the best composition for solder? How is ultrpure Si for computer chips produced?

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Melting point of an alloy Cu Ni Wt% Ni 1085ºC 1453ºC Liquid, L Solid solution,  Liquidus solidus L + 

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A diagram in the space of relevant thermodynamic variables (e.g., T and x) indicating phases in equilibrium is called a phase diagram. Equilibrium phase diagram or Equilibrium diagram or Phase diagram

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The independent chemical species (element or compound) in terms of which the composition of the system is described are called components. H2O Water +ice liquid solution  + Fe3C components Water liquid H2O Liquid+solid nimbu, chini and pani shikanji Fe + C Mild steel phases System Components

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A single component phase diagram: Unary diagram A two-component phase diagram: Binary diagram A three-component phase diagram: Ternary diagram

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Cu-Ni binary phase diagram Callister, Fig. 9.2 Any given point (x,T) on the phase diagram represents an alloy of composition x held at equilibrium at temperature T Point A: 60 wt% Ni at 1100ºC Point B: 35 wt% Ni at 1250ºC

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Phase Diagrams For any given point (x,T) the phase diagram can answer the following: What phases are present? What are the phase compositions? What are the relative amounts of the phases (phase proportions or phase fractions)?

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Point A: 60 wt% Ni at 1100ºC Q: Phase present? Ans:  Q: Phase composition ? Ans: 60 wt%Ni Q: Phase amount ? Ans: 100%

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Point B: 35 wt% Ni at 1250ºC Q: Phases present? Ans:  + L Q: Phase compositions ? Tie Line Rule Q: Phase amounts ? Lever Rule

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Composition of phases in the two-phase region Tie Line CL= 31.5 wt% Ni C= 42.5 wt% Ni Tie Line Rule

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Amount of phases in the two-phase region Tie Lever Rule Tie-Line: A lever Alloy composition C0: Fulcrum fL: weight at liquidus point f: weight at solidus point The lever is balanced

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The Lever Rule: A Mass balance Proof Prob. 7.6 f + fL = 1 Wt of Ni in alloy = W C0/100 Wt of Ni in  = fWC/100 Wt of Ni in L = fL WCL/100 C f + CL fL = C0 Wt of alloy = W Wt of  in alloy = fW Wt of L in alloy = fLW Wt of Ni in alloy = Wt of Ni in  + Wt of Ni in L

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Development of Microstructure during solidification

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Solder alloy? An alloy of Pb and Sn What is best composition of the solder alloy? Requirements: 1. should melt easily 2. should give a strong joint

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L    Pb Sn Solder alloy Wt % Sn 327 232 183 L L 1-2-1 rule Eutectic horizontal Eutectic diagram Liquidus Liquidus solidus solidus solvus solvus

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: Pb rich substitutional solid solution of Pb and Sn crystal structure: monatomic FCC : Sn rich substitutional solid solution of Pb and Sn crystal structure: monatomic BCT Pb: monatomic fcc Sn: monatomic bct

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Woods metal tea party Bi 50.0 wt% Pb 25.0 wt% Cd 12.5 wt% Sn 12.5 wt% An eutectic alloy with m.p. of 70ºC 100 g US$ 181 Anti-Fire Sprinklers

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Eutectic reaction Invariant reaction Callister Figs. 9.11, 12

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Microstructure of hypoeutectic alloy

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Amount of total  and total  at a temperature just below 183ºC Tie line just below 183ºC (red) Eutectc mixture  Proeutectic or Primary 

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Amount of proeutectic  at a temperature just below 183ºC Tie line just above 183ºC (green) Eutectc mixture  Proeutectic or Primary  = Amount of  at a temperature just above 183ºC

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Let the fraction of proeutectic  in micrograph fpro = 0.25 Tie line just above 183ºC (green) Eutectc mixture  Proeutectic or Primary  Let the composition (wt% Sn) of the alloy be C0 EXPERIMENT 5

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Optimum composition for solders For electronic application Eutectic solder 62 wt% Sn For general application Minimum heating Hypoeutectic solder Cheaper Allows adjustment of joint during solidification in the L range

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Modern Trend Lead-free solders Phase diagrams can help in identification of such solders Sn-Ag-Cu

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Please collect your Minor I answer books from Lab in the afternoon Those who can, do. Those who can’t teach G.B. Shaw

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Gibbs Phase Rule Thermodynamic variables: P, T, Phase Compositions (overall composition is not considered) If there are C components then C-1 compositions have to be specified for each phase Therefore total number of composition variables: P (C-1) With Pressure and Temperature, total number of variables = P (C-1) + 2

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Degrees of Freedom F: No. of thermodynamic variables that can be specified independently Gibbs phase rule states that one cannot specify all of the above P (C-1) + 2 variables independently in a system at equilibrium

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Gibbs Phase Rule F = C – P + 2 F = Degrees of freedom C = No. of components in the system P = No. of phases in equlibrium If pressure and temp both are variables F = C – P + 1 If pressure is held constant

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F = C – P + 1 F =2 F =1 C=2 F=3-P At eutectic reaction P=3 (L, , ) F=0 Invariant reaction

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steel Cast iron The Iron-carbon system Mild steel 0-0.3 wt% C Bicycle frame Ship hull Car body Medium C steel 0.4-0.7 wt% C Rail wheel rail axle rails High C steel 0.8-1.4 wt% C Razor blades scissors, knives

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Phases in Fe-C system Phase Symbol Description Liquid L Liquid solution of Fe and C -Ferrite  Interstitial solid solution of C in -Fe (high temperature bcc phase) Austenite  Interstitial solid solution of C in -Fe (FCC phase of Fe) Ferrite  Interstitial solid solution of C in -Fe (room temperature bcc phase) Soft and Ductile Cementite Fe3C Intermetallic compound of Fe and C (orthorhombic system) Hard and Brittle

Slide33: 

Ferrite Austenite

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Invariant Reactions in Fe-C system Peritectic Reaction A horizontal line always indicates an invariant reaction in binary phase diagrams Eutectic Reaction Eutectoid Reaction

Slide35: 

Eutectoid Reaction Pearlite

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Ammount of Fe3C in Pearlite Red Tie Line below eutectoid temp

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Development of Microstructure in a hypoeutectoid steel

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Proeutectoid Ferrite Pearlite Microsructure of a hypoeutectoid steel, 0.38 wt% C EXPERIMENT 5

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fpearlite below TE = faustenite above TE Tie-Line above the eutectoid temperature TE

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Development of Microstructure in a hypereutectoid steel

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Microsructure of a hypereutectoid steel, 1.4 wt% C Proeutectoid cementite on prior austenite grain boundaries Pearlite

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Fproeutectoid cementite=fcementite above TE

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Phase vs. microconstituents A phase or a mixture of phases which has a distinct identity in a microstructure is called a microconstituent Pearlite is not a phase. It is microconstituent which is a mixture of two phases  and Fe3C.

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Eutectoid steel +Fe3C Pearlite Hypoutectoid steel +Fe3C Pearlite + proeutectoid ferrite Hypereutectoid steel +Fe3C Pearlite + proeutectoid cementite

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A Wt % B C0 T TmA L  +L C CL C < CL Principle of Zone Refining T

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SemiconductorTransistor was invented by Bardeen, Brattain and Shockley At AT&T Bell Labs One needs ultrapure Si (impurity level few ppm) Zone Refining was invented by Pfann at Bell Labs as a process to obtain ultrapure Si Basis for modern Si technology