sign in sign up
<<
Home , Eutectic system, Lever rule, Phase diagram, Solid solution

Eutectic Systems • The simplest kind of system with two phases is called a . • A eutectic system contains two solid phases at low . These phases may have different structures, or the same with different lattice parameters. •Examples: – Pb (FCC) and Sn (tetragonal) - systems – Fe (BCC) and C ( - hexagonal) -cast – Al (FCC) and Si ( cubic) - cast aluminum alloys – Cu(FCC) and Ag(FCC) – high temperature solder

Cu/Ag Eutectic System • and are both FCC, but their lattice parameters and atomic radii are very different, so they have limited in the solid state. • There are two solid stable phases α and β, and at high there is a eutectic reaction where the α, β and the coexist. ← ⎯⎯Heating⎯ L(CE) α(CαE) + β(CβE) ⎯ Coolin⎯→⎯g Cu – Ag System Cu: α Ag: β phase Eutectic means “easily melted” in Greek Point E: invariant point (eutectic point) BG line: isotherm line

AB: line FG: BC: Solvus line GH: AE: line EF: BEG: Solidus line, isotherm line

TE: eutectic isotherm Eutectic isotherm Invariant or eutectic point Eutectic Reaction: Cooling L(CE) α(CαE) + β(CβE) Heating For copper-silver system: Cooling L(71.9wt%Ag) α(8.0wt%Ag) + β(91.2wt%Ag) Heating

Eutectic or invariant point - Liquid and two solid phases co-exist in equilibrium at the eutectic composition CE and the eutectic temperature TE.

Eutectic isotherm - horizontal solidus line at TE. Binary Eutectic System Eutectic reaction – transition from liquid to of two solid phases,

α + β at eutectic CE. At most two phases can be in equilibrium. Three phases (L, α, β) may be in equilibrium only at a few points along the eutectic isotherm. Single- phase regions are separated by 2-phase regions. Binary Eutectic System Compositions and relative amounts of phases are determined from the same tie lines and , as for isomorphous alloys- -demonstrate

• A

• B

• C Example For Point C: 40wt%Sn-60wt%Pb at 150oC a) What are the phases present? b) What are the compositions of the phases present? c) Mass fraction? d) at 150oC? Knowing that the of Pb and Sn are 11.23 and 7.24g/cm3, respectively a) At C, α and β phases coexist b) Draw Tie Line at 150oC: For α-phase:

Cα = 10% →10wt%Sn–90wt%Pb For β-phase:

Cβ = 98% →98wt%Sn–2wt%Pb • C c) Mass fraction:

β − CC 1 − 4098 Wα = = = 66.0 − CC αβ −1098 − CC −1040 W = 1 α = = 34.0 β − CC −1098 αβ . Wα d) volume fraction: v ρ V = α = α α + vv W W βα α + β Where: α ρρβ

100 100 −3 ρα = = = .64.10 cmg Sn α )( CC Pb α )( 10 90 + −3 + −3 Sn ρρPb .24.7 cmg .23.11 cmg

100 100 −3 ρβ = = = .29.7 cmg Sn β )( CC Pb β )( 98 2 + −3 + −3 Sn ρρPb .24.7 cmg .23.11 cmg

Wα 66.0 v ρ V = α = α = 64.10 = 57.0 α + vv W W 66.0 34.0 βα α + β + α ρρβ 64.10 29.7

β VV α =−=−= 43.057.011 L Development of microstructure in ⇓ eutectic alloys (I) L+α ⇓ α Several types of microstructure formed in slow cooling an different compositions. Cooling of liquid / system at different compositions.

In this case of lead-rich alloy (0-2 wt% of tin) solidification proceeds in the same manner as for isomorphous alloys (e.g. Cu- Ni) that we discussed earlier. Development of microstructure L in eutectic alloys (II)

α +L At compositions between room temperature solubility α limit and the maximum solid solubility at the eutectic α +β temperature, β phase nucleates as the α solid solubility is exceeded at solvus line. Development of microstructure in eutectic alloys (III) Solidification at the eutectic composition (I) No changes above eutectic temperature, TE. At TE liquid transforms to α and β phases (eutectic reaction).

L →α +β Development of microstructure in eutectic alloys (IV) Solidification at the eutectic composition (II) Compositions of α and β phases are very different → eutectic reaction involves redistribution of Pb and Sn atoms by atomic diffusion. Simultaneous formation of α and β phases results in a layered (lamellar) microstructure:called eutectic structure. Formation of eutectic structure in lead-tin system. Dark layers are lead-reach α phase. Light layers are the tin-reach β phase. Development of microstructure in eutectic alloys (V) Compositions other than eutectic but within the range of the eutectic isotherm

Primary α phase is formed in the α + L region, and the eutectic structure that includes layers of α and β phases (called eutectic α and eutectic β phases) is formed upon crossing the eutectic isotherm. L ⇓ α+L ⇓ α+β Development of microstructure in eutectic alloys (VI)

Microconstituent – element of microstructure having a distinctive structure. For case described on previous page, microstructure consists of two microconstituents, primary α phase and the eutectic structure.

Although the eutectic structure consists of two phases, it is a microconstituent with distinct lamellar structure and fixed ratio of the two phases. Compositions of α and β phases are very different → eutectic reaction involves redistribution of Pb and Sn atoms by atomic diffusion. Simultaneous formation of α and β phases results in a layered (lamellar) microstructure:called eutectic structure. Formation of eutectic structure in lead-tin system. Dark layers are lead-reach α phase. Light layers are the tin-reach β phase.

Relative amounts of microconstituents?

Eutectic microconstituent forms from liquid having eutectic composition (61.9 wt% Sn) Treat the eutectic as if it were a separate phase and apply lever rule to find relative fractions of primary α phase (18.3 wt% Sn) and eutectic structure (61.9 wt% Sn):

We = P / (P+Q) (eutectic)

Wα’ = Q / (P+Q) (primary)

Equilibrium Diagrams Having Intermediate Phases or Compounds

Terminal solid : a that exists over a composition range extending to either composition extremity of a binary Equilibrium Diagrams Having Intermediate Phases or Compounds Intermediate solid solution: Copper-zinc α and η: two terminal solid δ solution β β, γ, δ, & ε are intermediate α γ phases ε Intermetallic Compounds

Ex: magnesium- lead phase diagram: Intermetallic compound:

Mg2Pb can exist by itself only at the precise composition of 19wt%Mg – 81wt%Pb Eutectoid Reaction (Invariant Point E at 560oC) Copper-zinc

cooling δγ+ ε Eutectoid reaction heating Peritectic Reaction (Invariant Point P at 598oC) Copper-zinc

cooling δ + L ε Peritectic reaction heating The - Iron Carbide (Fe-Fe3C) Phase Diagram Reactions Phases Present

Peritectic L + δ = γ at T=1493oC and 0.18wt%C L δ ferrite delta Eutectic L = γ + Fe3C Bcc structure o at T=1147 C and 4.3wt%C Paramagnetic

γ Eutectoid γ = α + Fe3C at T=727oC and 0.77wt%C Fcc structure Non-magnetic ductile

α ferrite Fe3C Max. solubility of C Bcc structure Orthorhombic in ferrite=0.022% Ferromagnetic Hard, brittle in austenite=2.11% Fairly ductile Phases in Fe–Fe3C Phase Diagram ¾ α-ferrite - solid solution of C in BCC Fe • Stable form of iron at room temperature. • Transforms to FCC g-austenite at 912 °C ¾ γ-austenite - solid solution of C in FCC Fe • Transforms to BCC δ-ferrite at 1395 °C • Is not stable below the eutectic temperature (727 ° C) unless cooled rapidly. ¾ δ-ferrite solid solution of C in BCC Fe • It is stable only at T, >1394 °C. It melts at 1538 °C

¾ Fe3C (iron carbide or cementite) • This intermetallic compound is metastable at room T. It decomposes (very slowly, within several years) into α-Fe and C (graphite) at 650 - 700 °C ¾ Fe-C liquid solution Comments on Fe–Fe3C system

C is an interstitial impurity in Fe. It forms a solid solution with α, γ, δ phases of iron Maximum solubility in BCC α-ferrite is 0.022 wt% at 727 °C. BCC: relatively small interstitial positions Maximum solubility in FCC austenite is 2.14 wt% at 1147 °C - FCC has larger interstitial positions

Mechanical properties: Cementite (Fe3C is hard and brittle: strengthens ). Mechanical properties also depend on microstructure: how ferrite and cementite are mixed. Magnetic properties: α -ferrite is magnetic below 768 °C, austenite is non-magnetic Classification. Three types of ferrous alloys: Iron: < 0.008 wt % C in α-ferrite at room T Steels: 0.008 - 2.14 wt % C (usually < 1 wt % )

α-ferrite + Fe3C at room T : 2.14 - 6.7 wt % (usually < 4.5 wt %) 3

1

3 Eutectoid Microstructure of eutectoid steel Alloy of eutectoid composition (0.76 wt % C) is cooled slowly: forms , layered structure of two phases: α-ferrite and cementite (Fe3C) Mechanically, pearlite has properties intermediate to soft, ductile ferrite and hard, brittle cementite. Hypoeutectoid steel Hypoeutectoid alloys contain proeutectoid ferrite (formed above the eutectoid temperature) plus the eutectoid perlite that contain eutectoid ferrite and cementite. Hypereutectoid steel Hypereutectoid alloys contain proeutectoid cementite (formed above the eutectoid temperature) plus perlite that contain eutectoid ferrite and cementite. How to calculate the relative amounts of proeutectoid phase

(α or Fe3C) and pearlite? Use the lever rule and a tie line that extends from the eutectoid composition (0.75 wt% C) to α (0.022 wt% C) for hypoeutectoid

alloys and to Fe3C (6.7 wt% C) for hypereutectoid alloys.

Example: hypereutectoid alloy, composition C1

X ()7.6 − C Fraction of Pearlite W == = 1 P ()+ XV ()− 76.07.6 V ()C − 76.0 Fraction of Proeutecto id Cementite W == = 1 Fe3C ()+ XV ()− 76.07.6 Example

For alloys of two hypothetical A and B, there exist an α, A-rich phase and a β, B-rich phase. From the mass fractions of both phases of two different alloys, which are at the same temperature, determine the composition of the phase boundary (or solubility limit) for both α and β at this temperature.

Fraction of α Fraction of β Alloy Composition phase phase

60wt%A – 40wt%B 0.57 0.43

30wt%A – 70wt%B 0.14 0.86 The problem is to solve for compositions at the phase boundaries for both α and β phases (i.e., Cα and Cβ). We may set up two independent lever rule expressions, one for each composition, in terms of Cα and Cβ as follows:

Cβ − Co1 Cβ − 60 W = 0.57 = = α1 C − C C − C β α β α

Cβ − Co2 Cβ − 30 W = 0.14 = = α2 C − C C − C β α β α In these expressions, compositions are given in weight percent A. Solving for Cα and Cβ from these equations, yield Cα = 90 (or 90 wt% A-10 wt% B) Cβ = 20.2 (or 20.2 wt% A-79.8 wt% B)