BINARY SYSTEMS. Definition of Composition: Atomic (molar) fraction. Atomic percent. Mass fraction. Mass percent (weight percent)

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1 BINARY SYSTEMS Definition of Composition: Atomic (molar) fraction Atomic percent Mass fraction Mass percent (weight percent) na =, x i n = A i i i Weight percent mainly in industry! x at % A = x 100 A w ma =, w i m 1 = A i i i wt % A = w 100 A 100 ( at% A) M A wt% A = ( at% A) M + ( at% B) M A 1 B VO Phasendiagramme Binäre Systeme Folie 1

2 Isomorphous Systems p-t-x Diagram p-t diagram of pure A T-x diagram p-t diagram of pure B p-x diagram VO Phasendiagramme Binäre Systeme Folie 2

3 p = constant! tie line (Konnode) G Gibbs Energy of Mixing Basis of the CALPHAD-Method to calculate phase diagrams VO Phasendiagramme Binäre Systeme Folie 3

4 Solidification for case of coring Coring (Kornseigerung) Assumption: homogeneous equilibrium in the liquid phase is always retained Frozen first Frozen last Dendritic solidification VO Phasendiagramme Binäre Systeme Folie 4

5 Minima and Maxima x B x B Error Special Cases: Pb x Tl Tl Superstructures Au Miscibility Gap Ni x Ni Au Cu x Cu VO Phasendiagramme Binäre Systeme Folie 5

6 Eutectic Systems Eutectic Line e: Eutectic Point T Metastable extension into two-phase field! A x B A x B VO Phasendiagramme Binäre Systeme Folie 6

7 Eutectic Reaction Invariant Reaction: Often: lamellar microstructure of eutectic alloys VO Phasendiagramme Binäre Systeme Folie 7

8 Eutectic Reaction Cooling Curves x 0 x e T T T L x 0 x e T e T e t t VO Phasendiagramme Binäre Systeme Folie 8

9 G-x binary eutectic VO Phasendiagramme Binäre Systeme Folie 9

10 Eutectic Systems: Examples Al-Si Ag-Cu Pb-Bi Al-Sn VO Phasendiagramme Binäre Systeme Folie 10

11 Eutectic Systems: Primary Crystallization and Microstructure ß Hypereutectic Al-Si 14% alloy: primary crystallization Hypereutectic Al-Si 14% alloy: final microstructure VO Phasendiagramme Binäre Systeme Folie 11

12 Eutectic Systems: Solidification and Non-equilibrium x B No eutectic mixture should be detected in this case, however... x B VO Phasendiagramme Binäre Systeme Folie 12

13 Eutectic Systems: Isothermal Diffusion / Diffusion Couples 900 C 700 C VO Phasendiagramme Binäre Systeme Folie 13

14 Eutectic Systems: Limiting Cases degenerate eutectic T x B x B VO Phasendiagramme Binäre Systeme Folie 14

15 Eutectic Systems: Errors (from a customer journal of the company METTLER) VO Phasendiagramme Binäre Systeme Folie 15

16 Eutectoid Systems Eutectoid Reaction: heat γ α + β cool T T L T S T ß T e t VO Phasendiagramme Binäre Systeme Folie 16

17 Eutectoid Fe Fe3C ( Pearlite ) γ α + Fe3C hypoeutectoid: 0.3 % C δ γ α eutectoid: 0.8 % C α: bcc (Ferrite) γ: fcc (Austenite) δ: bcc Fe3C: cementite VO Phasendiagramme Binäre Systeme hypereutectoid: 1.2 % C Folie 17

18 Eutectoid Reactions Examples Fe-Te Ni-Zn VO Phasendiagramme Binäre Systeme Folie 18

19 Monotectic Systems Monotectic Reaction: L 1 L 2 + α L 2 L 2 L 2 L 2... the phase field L 1 +L 2 can be regarded as being made up of an infinite number of tie-lines VO Phasendiagramme Binäre Systeme Folie 19

20 Monotectic Systems Solidification VO Phasendiagramme Binäre Systeme Folie 20

21 Monotectic Systems Examples Cu-Pb Cu Pb Bi-Fe (limiting case with virtually no solubility in the solid and very limited solubility in the liquid state) Bi VO Phasendiagramme Binäre Systeme Folie 21 Fe

22 Monotectic Systems Examples Ni Ag VO Phasendiagramme Binäre Systeme Folie 22

23 Congruent Transformations Example: Mg-Si When one phase changes directly into another without change in composition, the phase change is said to be congruent. L β α = (Mg) β = Mg 2 Si γ = (Si) System can be divided into two independent eutectic systems VO Phasendiagramme Binäre Systeme Folie 23

24 Nomenclature Intermetallic Compounds (Phases) frequently designated by Greek letters: α, β, γ, δ, sometimes: β for bcc phases β for B2 (CsCl) phases β 1 for L1 0 phases γ for compounds with γ-brass structure (Cu 5 Zn 8 ) σ for compounds with certain tetragonal structure (as in Fe-Cr system) sometimes designated as compound, like Mg 2 Si, Cu 3 Sn, Cu 5 Zn 8, sometimes non-stoichiometry is indicated, for example: Fe 1-x S, Ni 1±x Sb, VO Phasendiagramme Binäre Systeme Folie 24

25 Congruent Transformations Example: Fe-Cr T ( C) a α γ b σ c α + α At% Cr a: melting point minimum b: congruent transformation γ α at minimum c: congruent transformation of σ-phase at maximum VO Phasendiagramme Binäre Systeme Folie 25

26 Transformations First Order Transformation: Two-phase field exists Second Order Transformation: No two-phase field; continuous transformation Cu Zn 50%Cu+50%Zn β -CuZn (CsCl-structure) Order-Disorder Transformation (Example β-brass) β-cuzn (bcc structure) First Order Transformation: First derivative of Gibbs energy is discontinuous Second Order Transformation: Second derivative of Gibbs energy is discontinuous First Order Second Order λ-transition VO Phasendiagramme Binäre Systeme Folie 26

27 Peritectic Systems Peritectic Reaction: L + α β Peritectic Composition Peritectic Point T A x B B β L+β β+γ β+γ also: incongruent melting point of β VO Phasendiagramme Binäre Systeme Folie 27

28 Peritectic Systems Solidification Peritectic Envelopment VO Phasendiagramme Binäre Systeme Folie 28

29 Peritectic Systems Examples L+(Pt) (Ag) Limiting Cases VO Phasendiagramme Binäre Systeme Folie 29

30 Peritectoid Systems α + γ β Limiting Cases VO Phasendiagramme Binäre Systeme Folie 30

31 Peritectoid Systems Examples Ag Al VO Phasendiagramme Binäre Systeme Folie 31

32 Syntectic Systems Syntectic Reaction: L I + L II β β L I L II Example: L I + L II NaZn VO Phasendiagramme Binäre Systeme Folie 32

33 consist of: Complex Binary Systems one-phase equilibria: two-phase equilibria: areas areas (consisting of tie lines) three-phase equilibria: lines eutectic type 2 > < 3 eutectic eutectoid monotectic (and others) peritectic type 1 > < 2 ^ peritectic 3 peritectoid syntectic (and others) VO Phasendiagramme Binäre Systeme Folie 33 1 v

34 Complex Binary Systems Ag-Os Cu-Sn metatectic (catatectic) Ag-Os VO Phasendiagramme Binäre Systeme Folie 34

35 Complex Binary Systems Examples Reaction e: L 2 G + (Os) Reaction r: G + (Os) L 1 Ag Os Reaction l (Metatectic or Catatectic Reaction): γ ε + L Cu Sn VO Phasendiagramme Binäre Systeme Folie 35

36 Complex Binary Systems can be constructed from invariant reactions: VO Phasendiagramme Binäre Systeme Folie 36

37 Complex Binary Systems Possible Errors VO Phasendiagramme Binäre Systeme Folie 37

38 Complex Binary Systems Technically Important Systems Cu-Zn = Brass Cu Zn Fe-C = Steel Martensite Fe VO Phasendiagramme Binäre Systeme Folie 38

39 Complex Binary Systems Diffusion Couple VO Phasendiagramme Binäre Systeme Folie 39

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