phase diagrams 1

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Phase Diagrams


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?


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


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


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


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


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


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)?


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


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


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


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


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


Development of Microstructure during solidification


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


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


: 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


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


Eutectic reaction Invariant reaction Callister Figs. 9.11, 12


Microstructure of hypoeutectic alloy


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


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


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


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


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


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


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


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


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


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


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


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


Ferrite Austenite


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


Eutectoid Reaction Pearlite


Ammount of Fe3C in Pearlite Red Tie Line below eutectoid temp


Development of Microstructure in a hypoeutectoid steel


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


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


Development of Microstructure in a hypereutectoid steel


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


Fproeutectoid cementite=fcementite above TE


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.


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


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


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

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