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

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270121 VO Phasendiagramme Binäre Systeme Folie 1

BINARY SYSTEMS

Definition of Composition:

Atomic (molar) fraction

Atomic percent

Mass fraction

Mass percent

(weight percent)

Weight percent mainly in industry!

1 ,

i i i i A A

∑

=

∑

=

x

n

x

100 A

%

= x

_A

⋅

at

1 ,

i i i i A A

∑

=

∑

=

w

m

w

100 A

%

= w

_A

⋅

wt

B A A

B)

%

(

A)

%

(

A)

%

(

100 A

%

M

at

M

at

M

at

wt

⋅

+

⋅

=

(2)

Isomorphous Systems

p-T-x Diagram

T-x diagram p-x diagram p-T diagram of pure B p-T diagram of pure A

(3)

∆

_G

Gibbs Energy of Mixing

p = constant !

tie line (Konnode)

Basis of the

CALPHAD-Method

to calculate

phase diagrams

(4)

Coring

(Kornseigerung)

Solidification

for case of coring Frozen first Frozen last Dendritic solidification Assumption: homogeneous equilibrium

in the liquid phaseis

(5)

Minima and Maxima

x_B x_B

Error

Pb xTl Tl Au _x Ni Ni Au xCu Cu Miscibility Gap Superstructures

Special Cases:

(6)

Eutectic Systems

Eutectic Line e: Eutectic Point Metastable extension

into two-phasefield!

A x_B

A x_B T

(7)

Eutectic Reaction

Invariant Reaction:

Often:

lamellar

microstructure

of eutectic alloys

(8)

Eutectic Reaction

Cooling Curves

x0 xe T t T_e T_L

x

₀ T t T_e

x

_e

(9)

∆

_G-x

(10)

Eutectic Systems:

Examples

Al-Si

Pb-Bi

Ag-Cu

(11)

Eutectic Systems:

Primary Crystallization and Microstructure

Hypereutectic Al-Si 14% alloy:

primary crystallization Hypereutectic Al-Si 14% alloy: final microstructure

(12)

Eutectic Systems:

Solidification and Non-equilibrium

x_B

No eutectic mixture should be detected in this case, however ...

(13)

Eutectic Systems:

Isothermal Diffusion / Diffusion Couples

700°C

(14)

Eutectic Systems:

Limiting Cases

T x_B x_B degenerate eutectic

(15)

Eutectic Systems:

Errors

(16)

Eutectoid Systems

Eutectoid Reaction:

γ  α

_{+ β}

T t T_L T_S T_ß T_e cool heat

(17)

Eutectoid

Fe – Fe

₃

C

(“Pearlite”)

γ



α

+ Fe

₃

C

γ

α

δ

α

_{: bcc (Ferrite)}

γ

_{: fcc (Austenite)}

δ

_{: bcc}

Fe

₃

C: cementite

hypoeutectoid: 0.3 % C eutectoid: 0.8 % C hypereutectoid: 1.2 % C

(18)

Eutectoid Reactions

Examples

Fe-Te

(19)

Monotectic Systems

Monotectic Reaction:

L

₁



L

₂

+ α

L₂

... the phase field L₁+L₂ can be regarded as being made up of an infinite number of tie-lines ...

L₂ L2

(20)

Monotectic Systems

(21)

Monotectic Systems

Examples

Cu Pb Bi Fe

Cu-Pb

Bi-Fe

(limiting case with virtually no solubility in the solid and very limited solubility in the liquid state)

(22)

Monotectic Systems

Examples

Ag Ni

(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.

β L

α = (Mg)

β = Mg

₂

Si

γ = (Si)

System can be divided into two

independent eutectic systems

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Nomenclature

Intermetallic Compounds (Phases)

• frequently designated by Greek letters: α, β, γ, δ, …

sometimes:  β for bcc phases

 β’ for B2 (CsCl) phases  β₁ for L1₀ phases

 γ for compounds with “γ-brass” structure

(Cu₅Zn₈)

 σ for compounds with certain tetragonal structure

(as in Fe-Cr system)

• sometimes designated as compound,

like Mg₂Si, Cu₃Sn, Cu₅Zn₈, …

• sometimes non-stoichiometry is indicated, for example:  Fe_1-xS, Ni_1±xSb, …

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Congruent Transformations

Example: Fe-Cr

At% Cr T(°C) γ α α‘ + α“ σ

a

b

c

a:

melting point minimum

b:

congruent transformation γ  α at minimum

(26)

Transformations

First Order Transformation:

Two-phase field exists

Second Order Transformation:

No two-phase field; continuous transformation

Order-Disorder Transformation (Example β-brass)

Cu

Zn

β‘-CuZn

(CsCl-structure) β-CuZn_{(bcc structure)}

50%Cu+50%Zn

First Order Transformation:

First derivative of Gibbs energy is discontinuous

Second Order Transformation:

Second derivative of Gibbs energy is discontinuous

First Order Second

Order

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Peritectic Systems

Peritectic Reaction:

L + α  β

Peritectic Point Peritectic Composition A xB B T β+γ

β

β+γ

L+β

also: “incongruent melting point of β”

(28)

Peritectic Systems

Solidification

Peritectic Envelopment

(29)

Peritectic Systems

Examples

L+(Pt)  (Ag)

(30)

Peritectoid Systems

Limiting Cases

(31)

Peritectoid Systems

Examples

(32)

Syntectic Systems

Syntectic Reaction:

L

_I

+ L

_II



β

L

_I

L

_II

β

Example:

L

_I

+ L

_II



NaZn

₁₃

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Complex Binary Systems

consist of:

• one-phase equilibria: areas • two-phase equilibria: areas

(consisting of tie lines)

• three-phase equilibria: lines

 eutectic type 2

> <

3

eutectic eutectoid

monotectic (and others)

 peritectic type 1

> <

2

peritectic peritectoid

syntectic (and others) v 1

3

(34)

Complex Binary Systems

Ag-Os

Ag-Os Cu-Sn

metatectic (catatectic)

(35)

Complex Binary Systems

Examples

Ag Os Cu Sn Reaction e: L₂  G + (Os) Reaction r: G + (Os)  L₁ Reaction l (Metatectic or Catatectic Reaction): γ  ε _{+ L}

(36)

Complex Binary Systems

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Complex Binary Systems

(38)

Complex Binary Systems

Technically Important Systems

Cu Zn

Cu-Zn = Brass

Fe

Martensite

Fe-C = Steel

(39)