MAT_101_Winter08_Lecture_13

MAT_101_Winter08_Lecture_13 - 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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Ex: Pb-Sn Eutectic System (1) • For a 40wt%Sn-60wt%Pb alloy at 150 °C, find. .. --the phases present: α + β --the compositions of the phases: Pb-Sn system Adapted from Fig. 9.7, Callister 6e. (Fig. 9.7 adapted from Binary Phase Diagrams , 2nd ed., Vol. 3, T.B. Massalski (Editor-in-Chief), ASM International, Materials Park, OH, 1990.) L + α L + β α + β 200 T(°C) 18.3 C o , wt% Sn 20 40 60 80 100 0 C o 300 100 β L (liquid) α 183°C 61.9 97.8 150
Ex: Pb-Sn Eutectic System (2) • For a 40wt%Sn-60wt%Pb alloy at 150 °C, find. .. --the phases present: α + β --the compositions of the phases: C α = 11wt%Sn C β = 99wt%Sn --the relative amounts of each phase: W α = 59 88 = 67±wt±% β = 29 88 = 33 wt % Pb-Sn system Adapted from Fig. 9.7, Callister 6e. (Fig. 9.7 adapted from Binary Phase Diagrams , 2nd ed., Vol. 3, T.B. Massalski (Editor-in-Chief), ASM International, Materials Park, OH, 1990.) L + α L + β α + β 200 T(°C) 18.3 C o , wt% Sn 20 40 60 80 100 0 C o 300 100 L (liquid) α 183°C 61.9 97.8 150 11 99 R S β

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Microstructures in Eutectic Systems (1) L + α 200 T(°C) C o , wt% Sn 10 2 20 0 C o 300 100 L α 30 L: C o wt%Sn α L α : C o wt%Sn α + β 400 (room T solubility limit) T E (Pb-Sn System) •C o < 2wt%Sn • Result: --polycrystal of α grains. Adapted from Fig. 9.9, Callister 6e.
Microstructures in Eutectic Systems (2) •2w t%Sn < C o < 18.3wt%Sn • Result: -- α polycrystal with fine β crystals. α : C o wt%Sn L + α 200 T(°C) C o , wt% Sn 10 18.3 20 0 C o 300 100 L α 30 L: C o wt%Sn α + β 400 (sol. limit at T E ) T E 2 (sol. limit at T room ) L α α β Pb-Sn system Adapted from Fig.

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MAT_101_Winter08_Lecture_13 - Gibbs Phase Rule P F=C 2 P of...

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