Phase Diagrams

A general overview

Hume Rothery Seminar

Derby, Jan. 17th 2017

Klaus Hack

GTT-Technologies

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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

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Practical cases of phase

diagram applications

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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

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Precipitation Hardening in

Noble Metal Alloy Systems

Alloy compositions and Vickers hardness

Au Pd Pt Ag Sn Ir Härte (HV)

81,5 - 16 - 2 0,5 85

81,8 15 - - 3 0,2 200

63 - 15 20 2 - 87

62 15 - 20 3 - 138

80,2 13,5 4 - 2,1 0,2 180

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Precipitation Hardening in

Noble Metal Alloy Systems

micro graph for alloy 1: phase diagram near for alloy 1:

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Precipitation Hardening in

Noble Metal Alloy Systems

micro graph for alloy 2: phase diagram near for alloy 2:

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Reduction of Refractory Wear

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Reduction of Refractory Wear

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Reduction of Refractory Wear

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Unary System

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Example: Fe

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Binary System

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Example: Pb-Sn

Liquid

FCC_a1 BCT_a5

FCC_a1 + BCT_a5

FCC_a1 + Liquid Liquid + BCT_a5

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Example: Pb-Sn

Liquid

FCC_a1 BCT_a5

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Example: Pb-Sn

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Example: Pb-Sn

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Example: Pb-Sn

LIQ

UID

FC

C_a1

BC

T_a5

(1-x) Pb + x Sn

Phase composition

mole fract. Sn

T(K

)

0 0.20 0.40 0.60 0.80 1.00

300

350

400

450

500

550

600

650

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A more complex case: Fe-Ni

L12_FCC

FCC_A1

BCC_A2

BCC_A2

LIQUID

TC

molefraction Ni

T /

[K

]

0 .2 .4 .6 .8 1

300

600

900

1200

1500

1800

Chemical and magnetic ordering !

GTT-Technologies Printed Compilations

• Early compilations by M. Hansen,

R.P. Elliott, F.A. Shunk, W.G.

Moffat

• Succeeded by

„Massalski“

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Ternary System

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Example: Fe-Co-Cr (isotherm)

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Example: Fe-Co-Cr (isotherm)

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Example: Fe-Co-Cr (isotherm)

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Printed Compilations

SGTE Landolt-

Börnstein Volumes

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Family of Phase Diagrams

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0i i i iSdT VdP n d q d Gibbs-Duhem:

i i i idU TdS PdV dn dq

N-Component System (A-B-C-…-N)

S

V

nA

nB

nN

T

-P

µA

µB

µN

Extensive

variables Corresponding

potentials

jqi

iq

U

iq

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- Type 1 or Potential Diagrams:

Two potentials, Φi vs Φj.

- Type 2 or Mixed Diagrams:

One potential and one ratio of conjugate extensive properties, Φi vs QΦ

j/QΦ

k.

- Type 3 or Extensive Property Diagrams:

Two ratios of conjugate extensive properties,

QΦi/Q

Φk vs QΦ

j/QΦ

k

Only three types of phase diagrams

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Interrelationship of corresponding type 1, type 2, type 3 phase

diagrams. (Φ4, Φ5 , ... are held constant; Φ3 is unspecified)

Pelton and Schmalzried, 1973

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Phase diagram family for the binary system Fe-C, P=const.

Type 1 Type 2

Type 3 Type 2

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Isopleth sections

and

Zero Phase Fraction lines

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How to handle such a diagram ?

The method of Zero Phase Fraction lines John Morall et al., since 1984

, rest Fe

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A simple ternary with three terminal solutions

C

A

B

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… including tie-lines

A

C B

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… including 10%-lines

A

C B

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… showing zero-phase fraction lines

A

C B

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Some generalisations

The inside-outside

feature

The crossover

feature

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More generalisations

The number

of phases

feature

NOTE: n must NOT be ZERO !

n

n + 1

n + 2

n + 1

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ZPF-lines are a set of phase boundaries,

that mark the appearance of the same phase

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ZPF-lines start and end on coordinate axes

or else form a closed loop

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Phase Diagrams

with

additional information

GTT-Technologies The Fe-C diagram

0.001

0.001

0.01

0.01

0.1

0.1

1

1

Liquid

FCC_A1

BCC_A2

BCC_A2Liquid + C_Graphit

FCC_A1 + C_Graphit

BCC_A2 + C_Graphit

Fe - C

1 atm, C(s) iso-activities

C/(Fe+C) (mol/mol)

T(C

)

0 0.05 0.1 0.15 0.2 0.25

300

500

700

900

1100

1300

1500

1700

1900

Liquid

FCC_A1

BCC_A2

BCC_A2Liquid + C_Graphit

FCC_A1 + C_Graphit

BCC_A2 + C_Graphit

Fe - C

C/(Fe+C) (mol/mol)

T(C

)

0 0.05 0.1 0.15 0.2 0.25

300

500

700

900

1100

1300

1500

1700

1900

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1e-25 1e-25

1e-201e-20

1e-15

1e-15

1e-10

1e-10

1e-5

1e-5

1e.-4

1e-3

1e-3

1e-2

0.21

0.21

1

1

1e-9

1e-9

1e-8

1e-7

1e-6

1e-6

1e-5

1e-5

1e-7

1e-8

1e-6

1e-2

Fe - O

1 atm, O2(g) isobars (atm)

O/(Fe+O) (mol/mol)

T(C

)

0 0.1 0.2 0.3 0.4 0.5 0.6

300

500

700

900

1100

1300

1500

1700

1900

The Fe-O diagram

liq metal + liq slag

BCC_a2 + liq slag

BCC_a2 + Wustite

BCC_a2 + Magnetite

FCC_a1 + Wustite

Hem

atit

e

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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