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3-D Representation of Phase Diagrams and other Property Diagramsand other Property Diagrams for Multi-component Systems

K Hack1 P Cerfontaine2 E Fried2 T Kuhlen2K. Hack1, P. Cerfontaine2, E. Fried2, T. Kuhlen2,D. Senk3, A. Babich3, S. Geimer3

RCCM-GTT Tokyo Workshop 2006

1GTT-Technologies2 VR Group RWTH Aachen University3Institut für Eisenhüttenkunde RWTHRCCM GTT Tokyo Workshop 2006

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Wh ill 3 D t ti h l ?Where will 3-D representation help?

- From Gibbs energy to phase diagram

- Thermodynamic properties in ternaries, e.g. isothermal activities

- Liquidus projections

- Quaternary phase diagrams

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Phase diagrams j ti f Gibb E l tas projections from Gibbs Energy plots

1.0

0.5

0 00.0

-0.5

-1.0

G

300

400

500

600

7001.0 0.8 0.6 0.4 0.2 0.0

T

CuxNiNi

Binary system: projection in G-T-x diagram, p = const.

CuNi

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Phase diagrams j ti f Gibb l tas projections from Gibbs energy plots

Ternary system: projection in G-x1-x2 diagram,T = const and p = constp

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Perspective Representation of Isothermal Activity Plotsy

for the System Ti-Si-C

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1: Si+SiC + TiSi1: Si+SiC + TiSi22: TiSi2 + SiC + Ti3SiC23: SiC + Ti3SiC2 + TiC1-x4: SiC + TiC + C4: SiC + TiC1-x + C

5: TiC1-x + Ti3SiC2 + Ti5Si3Cx6: TiBCC + TiC1-x + Ti5Si3Cx7: TiSi + Ti Si + Ti Si C7: TiSi + Ti5Si4 + Ti5Si3Cx8: TiSi + TiSi2 + Ti5Si3Cx

Carbon activity in system Ti-Si-C for T = 1200° C

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Silicon activity in system Ti-Si-C for T = 1200° C

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Liquidus Projectionfor the System

MgO-Al2O3-SiO2

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FromFrom Slag atlas

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Quaternary Phase DiagramsQuaternary Phase Diagrams

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From Slag atlasMnO

1: SiO22 2C O SiO2

5

2: 2CaO.SiO23: 3CaO.SiO24: (Ca Mn)O5

4

4: (Ca,Mn)O5: (Mn,Ca)O

1

42

FeO SiO2

3

FeO SiO2

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From Slag atlas

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From Slag atlasFrom Slag atlas

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Wire Models

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Wire model for thefor thesystemAl-Li-Si

(R.Schmid-Fetzer, TU-Clausthal)

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Wire model for the system Co-Fe-Mo-Ni, T=1373K

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Intermediate SummaryIntermediate Summary

The routine 3D-visualisation of phase diagrams and also property diagrams would contributeand also property diagrams would contribute considerably to the understanding of multi-dimensional relationships in material systems. p y

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Results of thermochemical calculationsResults of thermochemical calculationsPart 1

I h l i b i i l h iIsothermal isobaric isopleth sections

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Fe - Cr - V - C SystemT 850°C t % C 0 3 P 1 t

– fcc + M23C6

– fcc + M7C3 + M23C6

– bcc + fcc + M7C3 + M23C6

T = 850°C, wt.% C = 0.3, Ptot = 1 atm<F*A*C*T>0.05

MCfccbcc

MCfccbcc7 3 23 6

– bcc + MC + M7C3 + M23C6

V

0.04

bccM7C3M23C6

bccM7C3

M23C6

bcc + MC+ M23C6

bcc + MC

frac

tion

V

0.03

bcc+ fcc+ MC

bcc + MC + M7C3

bcc + fcc + MC

+ M 23

C 6mas

s f

0.02

fcc + MC

f + M C

bcc + M23C6

fcc + bcc

fcc + bccfcc + MC + M7C3

C+ M7C3 bcc + M7C3

+ M7C3

bcc +

M7C

3 +

0.01

fccfcc + M7C3 fcc + bcc

+ M23C6

mass fraction Cr0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0.00

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Results of thermochemical calculationsResults of thermochemical calculationsPart 2

Liquidus projectionsLiquidus projections

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MgO - CaO - ZrO2Polythermal projection 2200 - 3500

09.07.06D:\FSage541\Teach\CMZO-Aux\CMZO.LiqSurf

0.9 0

MgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgOMgO

0.7

0.8

0.

0.1

0.2

03

05

0.6

0. .3

0.4

03

0.4

0.

0.5

0.6

01

0.2

0.3 0.7

0.8

0

2218.02 K

2253.18 K Tmax=2311.54

0.1

0.10.20.30.40.50.60.70.80.9

0.9

ZrO2 CaOmole fraction


























ZrO2 CaOmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fractionmole fraction

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Results thermochemical calculationsPart 3

Binary composition-temperature-pressurecube

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Th Pb S T P Ph DiThe Pb-Sn T-P-x Phase Diagramleft: from low to high pressure

right: from high to low pressure

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Results of thermochemical calculationsPart 4Part 4

Ternary composition-temperature prism

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ZPF linesf C C Ffor Co-Cr-FeT = 1400 K

Sigma

BCC

FCCFCC

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ZPF surfacesfor Co-Cr-Fe

iin range1000<T/K<1400

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Results of thermochemical calculationsPart 5

Quaternary composition tetrahedron

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The ZPF surfaces ofCorundum,

Monoxidd Li idand Liquid

in the systemCaO-MnO-Al2O3-SiO2CaO MnO Al2O3 SiO2

T = 1973 K

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All phasesT = 1973 KT = 1973 K

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Results of thermochemical calculationsP t 6Part 6

4D: Quaternary composition tetrahedron with variable temperaturep

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Summary

- Gibbs Energy thermodynamics (Software and Databases) permit quantitative calculation of systems with arbitrarily“ high number ofsystems with „arbitrarily“ high number of components.

- Regarding time (animation) as an additional parameter it is even possible to generate four dimensional representations.

Up to date graphics soft and hardware provides- Up-to-date graphics soft- and hardware provides tools for real 3D-representation.

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Thank you for your attention !a you o you atte t o

We would be happy to welcome You in the 3D cave of

RWTH computer center, Aachen !!!

Polarisation glasses will be made available.

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