MAT_101_Winter08_Lecture_14

MAT_101_Winter08_Lecture_14 - Gibbs Phase Rule P F=C 2 P of...

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Gibbs Phase Rule P + F = C + 2 P: # of phases F: Degrees of freedom C: # of components Normally, pressure = 1 atm P + F = C + 1 or F = C - P + 1 Apply to eutectic phase diagram 1 phase field: F = 2 – 1 + 1 = 2 Change T and C independently in phase field 2 phase field: F = 2 – 2 + 1 = 1 C depends on T – not independent 3 phase point: F = 2 – 3 +1 = 0 C and T defined only at one point (Eutectic point) (no degrees of freedom)
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Phase Diagrams with Intermediate Phases/Compounds Example: Mg-Pb binary phase diagram Terminal phases/solid solutions: α and β Intermediate compound: Mg 2 Pb (line compound)
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Phase Diagrams with Intermediate Phases/Compounds Example: Sn-Au binary phase diagram Terminal phases/solid solutions: α and η Intermediate compounds: β , γ , δ , ζ
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Phase Diagram: Precipitation Strengthening System Al-Cu Alloys – 1 st Precipitation-Hardenable Alloys Homogenize Heat Precipitation of Θ or related phases Cool Quickly Supersaturated α -phase
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Precipitation Strengthening In Al-Cu Precipitation in Al-4%Cu (aged at 180 °C, 6 h) GP-Zones Precipitation in Al-4%Cu (aged at 200 °C, 2 h) θ ’ Phase Precipitation in Al-4%Cu (aged at 450 °C, 45 min.) θ Phase
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Ceramic Phase Diagrams Example – Continuous Solid Solution Components: Al 2 O 3 and Cr 2 O 3 (both have same crystal structure) Ceramic alloy: random occupancy of Al 3+ and Cr 3+ on cation sites
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Ceramic Phase Diagrams Identify Components Identify invariant points Identify compound formation
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Ceramic Phase Diagrams Identify Components Identify invariant points Identify compound formation
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Ceramic Phase Diagrams
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Chapter 10: Phase Transformations ISSUES TO ADDRESS . .. • Transforming one phase into another takes time. • How does the rate of transformation depend on time and T? Fe γ± (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) • How can we slow the transformation so that we can engineer non-equilibrium structures? • Are the properties of non-equilibrium structures improved?
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Fraction of Transformation Fraction transformed depends on time. Adapted from Fig. 10.1, Callister 6e. y log (t) Fixed T 0 0.5 1 t 0.5 fraction transformed time y = 1 e k t n Avrami Eqn. Transformation rate depends on T. 11 01 0 2 10 4 0 50 100 1 3 5 ° C 9 0 2 8 4 y (%) log (t) min Ex: recrystallization of Cu r = 1 t 0.5 = Ae Q/RT activation energy r often small: equil not possible! Adapted from Fig. 10.2, (Fig. 10.2 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME , 188, 1950, p. 888.)
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Transformations and Undercooling • Can make it occur at: ...727ºC (cool it slowly) ...below 727ºC (“undercool” it!) Eutectoid transf. (Fe-C System): α± ferrite 1600 1400 1200 1000 800 600 400 0 123456 6.7 L γ± austenite γ +L γ +Fe 3 C Fe 3 C cementite α +Fe 3 C α + γ L+Fe 3 C (Fe) C
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MAT_101_Winter08_Lecture_14 - Gibbs Phase Rule P F=C 2 P of...

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