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Understanding Ternary Phase Diagrams in Material Science

Learn about Gibbs triangle, lever rule, and tie-triangle to analyze ternary phase diagrams for material composition. Explore binary and ternary systems, mixed phase diagrams, and phase solubility.

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Understanding Ternary Phase Diagrams in Material Science

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  1. Chapter 6 of Bergeron & RisbudChapter 5 of HummelTernary systems

  2. L a b L a+L b+L L L a+L b+L L • A-B binary system : const P potential phase diagram mB xB : mixed phase diagram a, b phases having some solubility mB xB : mixed phase diagram a, b phases having no solubility

  3. xC=1 xC=1 xB=1 xA=1 xB=1 xA=1 ③ C ① comps (on A’B’) parallel with AB : xC ② comps on a line perpendicular to AB : xA - xB = ③ comps on a line (CC’) drawn straight from C to the opposite side AB : xA / xB = A’ B’ ① A B ② C’ • Gibbs ternary triangle xA + xB + xC = 1 (xi ≥ 0)

  4. Fig. 1.40. The Gibbs triangle. • how to read comps in the Gibbs triangle ? xA = UX = SX = US xB = TX = QX = TQ = SC xC = RX = PX = PR = BU ∴ xA + xB + xC = US + SC + BU = =%

  5. how to use lever rule in the Gibbs triangle ? P, a mixture of alloy S and alloy O %S = PO/SO and %O = SP/ SO ∵ O is a mixture of alloy R and alloy L ∴ %R = SP/SO x OL/RL %L = SP/SO x RO/RL how to obtain %R and %L in a different way? Fig. 13-1. Analysis of a tie-trianlge.

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