Phase Diagrams. A general overview
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1 Phase Diagrams A general overview Klaus Hack GTT-Technologies Hume Rothery Seminar Derby, Jan. 17th 2017
2 Contents Practical use of Phase Diagrams Binary Systems Ternary Systems Family of Phase Diagrams Multi-component isopleth sections Zero Phase Fraction lines Phase Diagrams with additional info
3 Practical cases of phase diagram applications
4 Precipitation Hardening in Noble Metal Alloy Systems dental prosthesis based on noble metal alloys gold band bridge (Etruscan) ca. 400 bc modern dental prosthesis with ceramics coating mechanical properties are crucial for the application of noble metal alloys as dental prosthesis
5 Precipitation Hardening in Noble Metal Alloy Systems Alloy compositions and Vickers hardness Au Pd Pt Ag Sn Ir Härte (HV) 81, , , , ,2 13,5 4-2,1 0,2 180
6 Precipitation Hardening in Noble Metal Alloy Systems micro graph for alloy 1: phase diagram near for alloy 1:
7 Precipitation Hardening in Noble Metal Alloy Systems micro graph for alloy 2: phase diagram near for alloy 2:
8 Reduction of Refractory Wear
9 Reduction of Refractory Wear
10 Reduction of Refractory Wear
11 Unary System
12 Example: Fe
13 Binary System
14 Example: Pb-Sn Liquid FCC_a1 FCC_a1 + Liquid Liquid + BCT_a5 BCT_a5 FCC_a1 + BCT_a5
15 Example: Pb-Sn Liquid FCC_a1 BCT_a5
16 Example: Pb-Sn
17 Example: Pb-Sn
18 T(K) GTT-Technologies Example: Pb-Sn (1-x) Pb + x Sn Phase composition LIQUID FCC_a1 400 BCT_a mole fract. Sn
19 Example: Pb-Sn
20 T / [K] GTT-Technologies A more complex case: Fe-Ni 1800 BCC_A2 LIQUID FCC_A1 900 T C BCC_A2 600 L12_FCC molefraction Ni Chemical and magnetic ordering!
21 Printed Compilations Early compilations by M. Hansen, R.P. Elliott, F.A. Shunk, W.G. Moffat Succeeded by Massalski
22 Ternary System
23 Example: Fe-Co-Cr (isotherm)
24 Example: Fe-Co-Cr (isotherm)
25 Example: Fe-Co-Cr (isotherm)
26 Printed Compilations SGTE Landolt- Börnstein Volumes
27 Family of Phase Diagrams
28 N-Component System (A-B-C- -N) q i U i qi q j Extensive variables S V n A n B n N T -P µ A µ B µ N Corresponding potentials Gibbs-Duhem: du TdS PdV dn dq i i i i SdT VdP n d q d 0 i i i i Copyright by GTT 2016
29 Only three types of phase diagrams - Type 1 or Potential Diagrams: Two potentials, Φ i vs Φ j. - Type 2 or Mixed Diagrams: One potential and one ratio of conjugate extensive properties, Φ i vs Q Φ j/q Φ k. - Type 3 or Extensive Property Diagrams: Two ratios of conjugate extensive properties, Q Φ i/q Φ k vs Q Φ j/q Φ k Copyright by GTT 2016
30 Interrelationship of corresponding type 1, type 2, type 3 phase diagrams. (Φ 4, Φ 5,... are held constant; Φ 3 is unspecified) Pelton and Schmalzried, 1973 Copyright by GTT 2016
31 Type 3 Type 2 Type 2 Type 1 Phase diagram family for the binary system Fe-C, P=const. Copyright by GTT 2016
32 Isopleth sections and Zero Phase Fraction lines Copyright by GTT 2016
33 How to handle such a diagram?, rest Fe The method of Zero Phase Fraction lines John Morall et al., since 1984 Copyright by GTT 2016
34 A simple ternary with three terminal solutions A C B Copyright by GTT 2016
35 including tie-lines A C B Copyright by GTT 2016
36 including 10%-lines A C B Copyright by GTT 2016
37 showing zero-phase fraction lines A C B Copyright by GTT 2016
38 Some generalisations The inside-outside feature The crossover feature Copyright by GTT 2016
39 More generalisations The number of phases feature n n + 1 n + 1 n + 2 NOTE: n must NOT be ZERO! Copyright by GTT 2016
40 ZPF-lines are a set of phase boundaries, that mark the appearance of the same phase Copyright by GTT 2016
41 ZPF-lines start and end on coordinate axes or else form a closed loop Copyright by GTT 2016
42 Phase Diagrams with additional information Copyright by GTT 2016
43 T(C) GTT-Technologies The Fe-C diagram Fe - C 1 atm, C(s) iso-activities Liquid BCC_A Liquid + C_Graphit FCC_A FCC_A1 + C_Graphit BCC_A BCC_A2 + C_Graphit C/(Fe+C) (mol/mol)
44 Hematite T(C) GTT-Technologies The Fe-O diagram Fe - O 1 atm, O2(g) isobars (atm) e-9 1e-8 1e-7 1e-10 1e-6 liq metal + liq slag BCC_a2 + liq slag FCC_a1 + Wustite 1e e-3 1e-5 1e-6 1e e e-8 1e-6 1e-2 1e-9 1e-3 1e-5 1e e-15 1e-20 BCC_a2 + Wustite 1e-20 1e-15 1e-25 1e BCC_a2 + Magnetite O/(Fe+O) (mol/mol)
45 Summary Phase diagrams are of technological importance, both in materials development and application Public sources of Phase Diagrams provide information on binary and ternary systems CALPHAD type calculations are not restricted in no. of components but require new method of reading ZPF lines Isobars or isoactivity lines can be added
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