Phase Diagrams Di g 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? d d Melting M ng point p n of f an n alloy y Liquid, Liquid L 1453ºC L+ 1085 C 1085ºC Solid solution, Cu Wt% Ni Ni E ilib i h di Equilibrium phase diagram or Equilibrium diagram E ilib i di or Ph Phase diagram di A diagram di in i th the space of f relevant l t thermodynamic variables (e.g., T and d x)) iindicating di ti phases h iin equilibrium is called a phase diagram. di Components The independent chemical species (element or compound) in terms of which the composition of the system is described are called components. components S System components phases h Water H2O liquid Water +ice H2O Liquid+solid shikanji nimbu, chini and pani liquid solution Mild steel Fe + C + Fe3C A single component phase diagram: Unary diagram A two-component phase diagram: y diagram g Binary A three-component three component phase diagram: Ternary diagram Cu-Ni binary phase diagram 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 Callister, Fig. 9.2 Phase Diagrams D g m For any given g ven po nt (x, point (x,T)) the phase diagram can answer the following: 1 What 1. Wh t phases h are present? t? 2.. What ar are the th phase phas compositions? compos t ons? 3. What are the relative amounts of th phases the h (phase ( h proportions ti or phase fractions)? Point A: 60 wt% Ni at 1100ºC Q Q: Phase p present? Ans: Q: Phase composition ? Ans: 60 wt%Ni Q: Phase amount ? Ans: 100% Point B: 35 wt% Ni at 1250ºC Q Q: Phases p present? Ans: + L Q: Phase compositions ? Tie Line Rule Q: Phase amounts ? Lever Rule Composition of phases in the two-phase region Tie Line Rule L Tie Line CL= 31 31.5 5 wt% t% Ni C= 42.5 wt% Ni Amount of phases in the two-phase region L Tie-Line: A lever Alloy composition C0: Fulcrum fL: weight at liquidus point f: weight at solidus point fL f The lever is balanced f L (C0 C L ) f (C C0 ) f L f 1 Tie Lever Rule C C0 opposite pp lever arm fL C C L total lever arm The Lever Rule: A Mass balance Proof L Prob. 7.6 Wt of alloy = W Wt of in alloy = fW Wt of L in alloy = fLW W of Wt f Ni in i alloy ll = W C0/100 Wt of Ni in = fWC/100 Wt of Ni in L = fL WCL/100 Wt of Ni in alloy = Wt of Ni in + Wt of Ni in L C f + CL fL = C0 f + fL = 1 C C0 opposite arm it lever l fL total lever arm C C L Development of Microstructure during lidifi ti solidification 35 32 3 0.273 43 32 11 f L 1 f 0.727 f Single phase polycrystalline Solder alloy? An alloy of Pb and Sn What is best composition of the solder alloy? Requirements: 1. should melt easily 2 should 2. h ld give i a strong jjoint i Solder alloy 1-2-1 rule 327 183 Eutectic diagram L L L Eutectic horizontal Eutectic temperature Eutectic point Pb 232 62 Wt % Sn Sn Eutectic composition Pb: monatomic fcc Sn: monatomic bct : Pb rich substitutional solid solution of Pb and Sn crystal structure: monatomic FCC : Sn n rrich ch substitutional su st tut ona so solid solution of Pb and Sn crystal st l structure: st t monatomic t i BCT Woods metal tea W m party Bi B 50.0 50 0 wt% % Pb 25.0 wt% Cd 12.5 12 5 wt% % Sn 12.5 wt% An eutectic alloy with m m.p. p of 70ºC 70 C 100 g US$ 181 Anti-Fire Sprinklers Eutectic ti reaction Invariant reaction L 62 wt%Sn cooll 183ºC 18 wt%Sn % 97 wt%Sn % Eutectic mixture Callister Figs. 9.11, 12 375 X L (40 wt% Sn) L L 18 wt% Sn L+ L (62 wt% Sn) Eutectic mixture + Primary 18 wt% t% Sn Eutectic (18 wt % Sn) Eutectic (97 wt % Sn) Hypoeutectic alloy Microstructure of hypoeutectic alloy Eutectc mixture Proeutectic or Primary 18 62 97 f total 1 0.72 0.28 Amount of total and total at a temperature just below 183ºC Tie lline just below b l 1 º (red) 183ºC ( d) f total 97 40 57 0 . 72 97 18 79 Eutectc mixture Proeutectic or Primary 18 62 97 f eut 1 0.5 0.5 Amount of proeutectic at a temperature just below 183ºC = Amount of at a temperature just above 183ºC Tie line just above 183ºC (green) f pro 62 40 22 0 .5 44 62 18 EXPERIMENT 5 Eutectc mixture Proeutectic or Primary 18 62 C0 51 wt % Sn Let the fraction of proeutectic in micrograph fpro = 0.25 Let the composition (wt% Sn) of the alloy be C0 Tie line just above 183ºC (green) f pro 62 C 0 0 . 25 62 18 97 Optimum composition for solders F electronic l t i application li ti For Eutectic solder 62 wt% Sn 18 62 97 Mi i Minimum h heating i For general application Hypoeutectic solder Cheaper Allows adjustment j of jjoint during g solidification in the L range Modern Trend Lead-free solders Phase diagrams g m can help p 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 h can’t ’t teach t h G B Sh G.B. Shaw Gibbs Phase Rule Thermodynamic variables: P, P T, 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) (C 1) With Pressure and Temperature Temperature, total number of variables = P (C-1) + 2 Gibbs phase rule p u states that one n cannot specify all of the above p y in P ((C-1)) + 2 variables independently a system at equilibrium Degrees of Freedom F: No. of thermodynamic variables that can be specified independently Gibbs Phase Rule F = Degrees of freedom C = No. of components in the system P = No. No of phases in equlibrium F=C–P+2 If pressure and temp both are variables F=C–P+1 If pressure is held constant F=C–P+1 C=2 F=3-P F =2 At eutectic u reaction P=3 (L, , ) F =1 F=0 Invariant reaction The Iron-carbon system Bicycle frame Ship hull Car C body b d 1410 Medium C steel 0.4-0.7 wt% C 1150 910 steel Cast iron 725 0.8 0 02 0.02 Mild steel 0-0.3 wt% C Rail wheel rail axle rails High C steel 0.8-1.4 wt% C Razor bl R blades d 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 Fe (high temperature bcc phase) Austenite Interstitial solid solution of C in -Fe ((FCC p 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 ( th h bi system) (orthorhombic t ) Hard and Brittle Ferrite Austenite Invariant Reactions in Fe-C system i t l li l iindicates di t an iinvariant i t reaction ti Ah horizontal line always in binary phase diagrams Peritectic Reaction (0.1 wt % C ) L (0.5 wt % C ) (0.18 wt % C ) 1493o C Eutectic Reaction L (4.3 wt % C ) (2.1 wt % C ) Fe3C (6.67 wt % C ) 1150 o C Eutectoid Reaction (0.8 wt % C ) (0.02 wt % C ) Fe3C (6.67 wt % C ) 725o C E t t id Reaction R ti Eutectoid Fe 3 C 0.8 725 o C cool 0.02 6.67 Pearlite Eutectoid Reaction Fe F 3C 0.8 725 o C cool 0.02 6.67 Pearlite Ammount of Fe3C in Pearlite Red Tie Line below eutectoid temp f pearlite F3C 0.8 0.02 0.78 0.117 6.67 0.02 6.65 Development of Microstructure in a hypoeutectoid st l steel Proeutectoid Ferrite EXPERIMENT 5 Pearlite Microsructure of a hypoeutectoid steel, 0.38 wt% C f pearlite 0.8 0.38 0.42 0.54 0.8 0.02 0.78 fpearlite below TE = faustenite above TE Tie-Line above the eutectoid temperature TE f pearlite 0.8 0.38 0.42 0.54 0.8 0.2 0.78 Development of Microstructure in a hypereutectoid steel Pearlite Proeutectoid cementite on prior austenite grain boundaries Microsructure of a hypereutectoid steel, 1.4 wt% C Fproeutectoid cementite=fcementite above TE f proeutectoid cementite 1.4 0.8 0.6 0.10 6.67 0.8 5.87 Phase vs. microconstituents fp Ap 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 steell Hypoutectoid steell Hypereutectoid steell +Fe3C +Fe3C +Fe3C Pearlite Pearlite + proeutectoid ferrite Pearlite + proeutectoid cementite T Principle of Zone Refining L TmA C < CL T +L L A C C0 CL Wt % B 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 B i for Basis f modern d Sii technology h l