Lecture06and07S_Oct12 (1)

CHE 211 ADVANCED THERMODYNAMICS Lecture 06 / 07 Week 8 (10/12) Lilian Chang

Source: Gaskell D. R., Introduction to the Thermodynamics of Materials

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Fixed p liquidus

solidus

Liquidus Boundary: xB(l) vs. T as given by common tangent construction for Tm(B) < T < Tm(A) Solidus Boundary: xB(s) vs. T as given by common tangent construction for Tm(B) < T < Tm(A)

Ideal solid and liquid 2-component mixtures (“lens” phase diagram)

Examples: Cu – Ni Si – Ge Roughly same size crystal structure, chemically not so different

3 Eutectic Phase Diagrams Solid don’t like to mix

•  Liquid mixtures stable for all compositions above elemental melting

temperatures

•  Liquid mixtures stable over some composition range below lowest

elemental melting temperature

•  Lowest temperature where single phase liquid is stable is the eutectic

temperature (TE)

è composition of eutectic liquid is xBE

•  Below TE, we have homogeneous solids (α) and (β) and regions

where 2-phase equilibrium between solids exists (α+β)

α è A-rich solid

β è B-rich solid

4 Regular Eutectics α and β have some crystal structure and are separated by solid-state miscibility gap

Tm(A) Tm(B)

α β

α + β

liquid

α+l β+l

TC

TE

xB xB

E A B xBα

(s)(TE) xBβ

(s)(TE)

Stable phase boundaries Metastable extension of solid miscibility gap

Source: Gaskell D. R., Introduction to the Thermodynamics of Materials

5 Eutectic Phase Diagrams Solid don’t like to mix

Source: Gaskell D. R., Introduction to the Thermodynamics of Materials

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Features: •  3 single

phase regions α, β, and liquid

•  Limited solubility: α: Mostly Cu β: Mostly Ag

•  3 two phase regions (α + L), (β + L), (α + β)

Callister & Rethwisch 9th ed. Wiley, 2013.

Binary Eutectic Phase Diagram

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Features: •  3 single

phase regions α, β, and liquid

•  Limited solubility: α: Mostly Cu β: Mostly Ag

•  3 two phase regions (α + L), (β + L), (α + β)

•  No liquid below TE

Ag é, Tm(Cu) ê

Cu é, Tm(Ag) ê

CE = 71.9

TE = 779°C Eutectic Reaction:

Callister & Rethwisch 9th ed. Wiley, 2013.

Binary Eutectic Phase Diagram

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Features: •  3 single

phase regions α, β, and liquid

•  Limited solubility: α: Mostly Cu β: Mostly Ag

•  3 two phase regions (α + L), (β + L), (α + β)

CE = 71.9

Eutectic Reaction:

8.0 wt% 91.2 wt%

Eutectic Isotherm

Callister & Rethwisch 9th ed. Wiley, 2013.

Binary Eutectic Phase Diagram

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• Binary •  2 components

• Eutectic (Greek for “easily melted”) •  Has a special composition with minimum melting temperature, Tm

• Examples: •  Cu (FCC) – Ag (FCC) •  Pb (FCC) – Sn (tetragonal) •  Fe (BCC) – C (graphite – hexagonal)

Binary Eutectic Phase Diagram

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Example: Pb - Sn

α + β

L + α

L + β

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α + β

L + α

L + β

For 40 wt% Sn – 60 wt% Pb alloy at 150°C, determine: (a) The phases present (b) The phase compositions (c)  The relative amount of each phase

Example: Pb - Sn 12

α + β

L + α L + β

For 40 wt% Sn – 60 wt% Pb alloy at 150°C: a)  The phases present

α + β

Example: Pb - Sn 13

α + β

L + α L + β

For 40 wt% Sn – 60 wt% Pb alloy at 150°C: a)  The phases present

α + β

b)  The phase

compositions

Cα = 11 wt% Sn

Cβ = 99 wt% Sn Cα Cβ

R S

Example: Pb - Sn 14

α + β

L + α L + β

For 40 wt% Sn – 60 wt% Pb alloy at 150°C: a)  The phases present

α + β

b)  The phase

compositions

Cα = 11 wt% Sn

Cβ = 99 wt% Sn

c)  The relative amount of each phase

Cα Cβ

R S

W α = Cβ - C0 Cβ - Cα

= 99 - 40 99 - 11

= 59 88

= 0.67

S R+S

= W β = C0 - Cα Cβ - Cα

= R R+S

= 29 88

= 0.33 = 40 - 11 99 - 11

Example: Pb - Sn 15

Example Problem: SiO2 melts at 1723°C, and TiO2 melts at 1842°C. SiO2 and TiO2 are immiscible in the solid state, and the SiO2-TiO2 binary system contains a monotectic equilibrium at 1794°C, at which essentially pure TiO2 is in equilibrium with 2 liquids containing mole fractions of SiO2 of 0.04 and 0.76. Assume that the compositions of the two liquids are XSiO2 = 0.24 and XSiO2 = 0.76 and the liquid solutions are regular in behavior, What is the value of Ωl and at what temperature does the liquid immiscibility gap disappear?

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Example Problem: Gold and silicon are mutually insoluble in the solid state and form a eutectic system with a eutectic temperature of 636 K and a eutectic composition of Xsi = 0.186. Calculate the Gibbs free energy of the eutectic melt relative to (a)  Unmixed liquid Au and liquid Si, and (b)  Unmixed solid Au and solid Si Given: Tm,Au = 1338 K, ΔH°m,Au = 12600 J

Tm,Si = 1658 K, ΔH°m,Si = 12600 J

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Development of Microstructure: Case 1 Cooled slowly from 350°C at composition C1 point a : liquid point b: solidification of the α phase point c: complete solidification At room temperature: polycrystalline

Pb – Sn system

Callister & Rethwisch 9th ed. Wiley, 2013.

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Development of Microstructure: Case 2 Cooled slowly at composition C2 point d : liquid point e: solidification of the α phase point f: α grains point g: formation of small β-phase particles

Pb – Sn system

Callister & Rethwisch 9th ed. Wiley, 2013.

Cα CL

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Development of Microstructure: Case 3

Eutectic Structure

Callister & Rethwisch 9th ed. Wiley, 2013.

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Development of Microstructure: Case 3

Callister & Rethwisch 9th ed. Wiley, 2013.

Photomicrograph of Pb-Sn alloy of eutectic composition

α-phase is Pb-rich (dark) β-phase is Sn-rich (light)

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Eutectic Structure example (Organic System)

Source: https://www.youtube.com

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