The University of Michigan

Structural Dynamics Laboratory

Thermodynamics of High and Ultra-

high Temperature Ceramics

- Phase diagrams, Chemical reactions,

Computational thermodynamic database -

Department of Materials Science and Engineering

Professor In-Ho Jung

Tel : 82-2-880-7077

E-mail: in-ho.jung@snu.ac.kr

http://in-ho-group.snu.ac.kr/

In-Ho Jung

Seoul National University, Seoul, South Korea

Content

2

Review of Engineering Thermodynamics

Computational thermodynamic database

– Development of CALPHAD thermodynamic database

– Application to high temperature refractories

– Application to ultra-high temperature ceramics

3

REVIEW OF

ENGINEERING THERMODYNAMICS

COMPUTATIONAL THERMODYNAMIC

DATABASE

G = H – TS; G: Gibbs Energy, H: Enthalpy, S: Entropy

1. For pure element or pure compound (Al, O2, Al2O3, etc.)

o

T

o

T

o

T TSHG

T

K

po

K

o

T dTT

CSS

298

298

Enthalpy for compound at 298 K with

reference of pure stable elemental species

at 298 K and 1 atm ( , unknown)

: Cp = a + bT + cT-2

+ dTlnT + · · ·

is known (measurable)

Standard reference state for H :

Fe(bcc), Fe(fcc), Fe(l), H2O(l), H2O(g), H2(g),

O2(g), O(g), CaO, FeO, C(s), CO2, CO,.

0ΔH o

298K

Standard entropy at 298 K

( )00 oKS00 o

KH

* In FactSage compound database,

, , are stored to

calculate Gibbs energy of solid, liquid

and gas species

o

298KΔHo

KS298 pC

Gibbs Energy

4

T

K

p

o

K

o

T dTCHH298

298

5

2. Chemical reaction between pure compounds (No solution)

nA + mB = AnBm

o

rxn

o

rxn

o

B

o

A

o

BArxn

STH

mGnGGGmn

)(

In many thermo books, these , are given. These values are

not absolute values, but dependent on each chemical reaction.

In the FactSage, absolute Gibbs energy of each species (relative to

elemental species) is stored. Then, any reaction Gibbs energy can be

automatically calculated from the Gibbs energy of each species.

o

rxnH o

rxnS

Gibbs Energy

∆𝐺𝑟𝑥𝑛𝑜

6

3. Chemical reaction involving gas

nA + mO2(g) = AnO2m

At Equilibrium state

)(22 O

oA

oOArxn mGnGGG

n

ioii PRTGG ln

for gas species i

2ln O

o PmRTG

0 rxnG

)ln(2

1m

OP

o RTG

Gibbs Energy

= ∆𝐺𝑟𝑥𝑛𝑜

∆𝐺𝑟𝑥𝑛𝑜

7

3. Chemical reaction involving gas (continue)

In general, for aA + bB(g) = cC + dD(g)

At Equilibrium

)ln( bB

dD

P

Po RTG

Keq: Equilibrium constant

Gibbs Energy

∆𝐺𝑟𝑥𝑛𝑜

∆𝐺𝑟𝑥𝑛𝑜 = -RT ln Keq

8

4. Chemical reaction involving solid or liquid solution

)ln()(ln)( io

pureisoini aRTGG a: activity

change of Gibbs energy of i in solution

by interacting with surrounding species

Definition of activity

o

Ap

Pure Liquid A

Pure Gas A

A in solution

ApGas Mixture

AAo

A

AA x

P

Pa

∴ activity is movement of species in solution

Gibbs Energy

9

Definition of activity

ii

o

iii xppa )/(

0 x i1

ia

(+) deviation

(-) deviation

ideal

1

4. Chemical reaction involving solid or liquid solution

(+) deviation: repulsion between i and other species

: more active chemical reaction of i

(-) deviation: attraction between i and other species

: less active chemical reaction of i

ii xa

ii xa

In general, for aA + bB(g) = cC + dD(g)

At Equilibrium

)ln( bB

aA

dD

cC

Pa

Pao RTG

reactantsproductsrxn GGG

* FactSage solution database contains

the model and model parameters to

calculate and eventually get ia

iG

Gibbs Energy

∆𝐺𝑟𝑥𝑛𝑜

10

In most of thermodynamic book, we always calculate equilibrium condition

0 rxnG eq

o KRTG ln

But in reality, we want to first know the direction of reaction

mA + nB

many possible outputs

A2B

Inputs (initial condition)

Tfinal, Pfinal

(m-2)A

(n-1)B

AB2

(m-1)A

(n-2)B

A2B (m-3)A

(n-3)BAB2

(m-x)A

(n-y)B

(xA-yB)soln

Final equilibrium state?

Gibbs Energy

∆𝐺𝑟𝑥𝑛𝑜

11

(continue)

We have to find out which phase assemblage is the most stable at given Tf

and Pf with respect to the mass balance.

Gibbs energy minimization routine: ChemSage, Solgas-mix, etc.

The most stable phase assemblage has the lowest Gibbs energy.

In FactSage

i) Put inputs amount

ii) Select all possible phases (solid compounds, solid solutions,

liquid solutions, gases)

iii) Set Tfinal and Pfinal

iv) Calculation (Gibbs energy minimization routine)

v) Equilibrium phase assemblage

Gibbs Energy Minimization

Ellingham Diagram

12

Ellingham Diagram

13

ΔG

o(k

J /

mole

of O

2)

T (K)

(A)

(B)

- Collection of ΔGo for oxidation reaction

mA + O2 = AmO2 (reference: 1 mol of O2)

- Only consider for pure species.

(No solutions are considered.)

TpRG

pRTG

pa

aRTGG

O

o

O

o

OA

AOo

)ln(

ln

)()(

)(ln

2

2

2

2 ):0(, mEquilibriuG

A + O2 = AO2

Solution thermodynamics

14

A-B solution, (Solid or Liquid solution)

iisolution GxG

i

o

ii aRTGG ln Gi: partial Gibbs energy of i in solution

)lnln()( BBAA

o

BB

o

AA axaxRTGxGx

XB

mixgΔ

solutiong

o

Ag

o

Bg

AAg

BBg A

o

AA aRTgg ln

AaRT ln

: Chemical potential of ii

Solution thermodynamics

15

A-B solution (Solid or Liquid solution)

1. Ideal solution:

)lnln()( BBAA

o

BB

o

AAsoln axaxRTGxGxG

1,1 BA

)lnln()( BBAA

o

BB

o

AAsoln xxxxRTGxGxG

2. Regular solution:2ln BABA xRT

BAABBBAA

o

BB

o

AAsoln xxxxxxRTGxGxG )lnln()(

Ω: Regular solution parameter

Solution thermodynamics

16

3. General solution: ),( TxfA

1, ji

j

B

i

A

ij

AB

ex xxG

A-B solution, (Solid or Liquid solution)

)lnln()( BBAA

o

BB

o

AAsoln axaxRTGxGxG

ex

BBAA

o

BB

o

AAsoln GxxxxRTGxGxG )lnln()(

* FactSage supports many complex solution models.

Solution database (FToxid, FTSalt, ....) contains optimized

model parameters reproducing Gibbs energy of solution.

17

Gibbs Energy vs. Phase Diagram

Phase diagram is the collection of minimum Gibbs energy

assemblage of given system with temperature.

T2

Porter, D.A., and Easterling, K.E., Phase Transformation in Metals and Alloys, 2nd Ed. CHAMAN & HALL (1992)

18

10

20

30

40

50

60

70

80

90

102030405060708090

10

20

30

40

50

60

70

80

90

SiO2

CaO MgOmass percent

2018-10-22 7 secs

CaO - MgO - SiO2

1600oC, 1 atm

Ternary phase diagram: isothermal phase diagram

Liquid

Mg2SiO4

Ca2SiO4

60%SiO2-10%CaO-30%MgO

19

Ternary phase diagram: Liquidus projection

CaO

1507

1438 1429

1438

1516

1382

1331

1366

(1454)

1576

1369

1464

2400

2300

22002100

2000

1900

1800170016001500

1600

MgOCaO

P-Woll

2 liquids

Diop ppx

Aker

MerwMont

Wo

ll

2000

1923

opxPig

2500

2500

2600

MgO

2700

2400

Crist

1409

SiO2

Fors

1361

1395

Trid

Ca3Si2O7

14001366

a -Ca2SiO4

Ca3SiO5

1410

1336

mole fraction

CaSiO3

Mg2SiO4

18631962

2017

139213911461

1411

1453

(1723)

(2825)(2572)

1463

(1888)

1558

1548

1687

13631370

(2154)

1370

1388

(1392)

1370

2374

(1799)

a

(1540)

14371465

1689

2100

MgSiO3

• Primary crystalline phase

• Univariant line

• Pseudo-binary phase diagram

• Solidification pass

2

2ln

0,

22

OA

AOo

pa

aRTG

GmEquilibriuat

AOOA

Advantage of thermodynamic database

Ellingham Diagram FactSage calculations

• Ellingham diagram : Reaction between pure stoichiometric oxide phases.

• FactSage calc.: Multicomponent phase equilibria including many solid/liquid/gas solutions.

- for example, Spinel/Slag/Monoxide/Corundum/Fe-steel/Gas/etc….

20

FactSage 7.3

(gram) 40 CaO + 30 SiO2 + 10 Al2O3 + 20

MgO + (gram) 5 Cr2O3 =

93.310 gram ASlag-liq

(93.310 gram, 1.6394 mol)

(1600 C, 1 atm, a=1.0000)

( 9.6948 wt.% Al2O3

+ 32.151 wt.% SiO2

+ 42.862 wt.% CaO

+ 14.359 wt.% MgO

+ 4.7413E-04 wt.% CrO

+ 0.93357 wt.% Cr2O3

+ 5.9255 gram ASpinel

(5.9255 gram, 3.3221E-02 mol)

(1600 C, 1 atm, a=1.0000)

( 2.4413 wt.% Al3O4[1+]

+ 8.7136E-07 wt.% Al1O4[5-]

+ 13.954 wt.% Mg1Al2O4

+ 0.84280 wt.% Al1Mg2O4[1-]

+ 4.8139 wt.% Mg3O4[2-]

+ 4.9251E-06 wt.% Mg1O4[6-]

+ 66.331 wt.% Mg1Cr2O4

+ 5.2307E-02 wt.% Cr1Cr2O4[1+]

+ 3.9894E-03 wt.% Cr1Mg2O4[1-]

+ 11.549 wt.% Al1Cr2O4[1+]

+ 5.7638 gram AMonoxide#1

(5.7638 gram, 0.13398 mol)

(1600 C, 1 atm, a=1.0000)

( 0.10016 wt.% CaO

+ 91.310 wt.% MgO

+ 0.18976 wt.% Al2O3

+ 8.3998 wt.% Cr2O3

Development of Thermodynamic Database

A BGibbs energy between A-B = f (X, T, P)

in multicomponent system

Thermodynamic Database

Phase diagram data• Phase diagram

• S/L/G phase equilibria

Crystal Structural data

Thermodynamic data• Calorimetric data: Heat capacity,

H of mixing, H of melting, etc.

• Vapour pressures

• Chemical Potentials: activity

21

CALPHAD

Thermodynamic Database

22

Pure compound

Solution

Calorimetry

emf

Knudsen cell

Vapor pressure

emf (activity)

Knudsen cell (activity)

Vapor pressure (activity)

Solution calorimetry (enthalpy)

Phase diagram

o

T

o

T

o

T TSHG

T

K

p

o

K

o

T dTCHH298

298

T

K

po

K

o

T dTT

CSS

298

298

K

K

po

K dTT

CS

298

0

298

1, ji

j

B

i

A

ij

AB

ex xxG

Commercial database and software: CALPHAD

23

F*A*C*T + ChemSage: CRCT, Canada + GTT Tech., Germany

www.crct.polymtl.ca, www.factsage.com

TD: Oxide (slag, inclusion, refractory), Salt, Steel, Light alloy (very good)

Fully Window Interface

KTH, Sweden, www.thermocalc.se

TD: Steel, Light Alloy (very good) + poor Oxide

DICTRA (Diffusion Process)

DOS Interface, Window Interface

NPL, UK, www.npl.co.uk/npl/cmmt/mtdata

TD: Oxide, Salt, Steel, Light alloy (good)

Window Interface

SGTE (Europe + Canada + US), www.sgte.org

Orginazation of Database Development

Slag/Refractory/

Inclusions/Flux/

Steel

Slag:Viscosity,

Molar volume,

Thermal

Conductivity, etc.

Thermodynamic

database

Physical Property

database

Kinetic Process

Simulation models

(EERZ Concept)

- Secondary Refining Units

- Continuous Casting Process

Overall Goal of FactSage Steelmaking Consortium Project

(2009~2020)

Combining Thermodynamics

& Mass transfer based on

numerical analysis and plant

sampling data24

Available Thermodynamic Database – Refractories

25

Steelmaking, Non-ferrous and Cement industry

MgO-C, Al2O3-MgO, MgO-Cr2O3, Mullite, Olivine,

ZrO2-based, Al2O3-SiC type refractories:

• Reaction with slags, atmosphere, liquid metals

• Refractory mineral phases

Monoxide: MgO-FeO-MnO-CaO ….

Spinel: (Mg,Mn,Fe,..)[Al,Cr,Fe,..]2O4

Olivine: (Mg,Mn,Ca,Fe,..)2SiO4

(CaO)x(Al2O3)y…..

Si-C-N-O..

Cr6+ : in progress

• Slag phase:

CaO-MgO-Al2O3-SiO2-FeO-Fe2O3-MnO-Ti2O3-TiO2-CrO-Cr2O3-ZrO2-P2O5…-S-F

• Liquid metallic phase

Fe, Ferro-alloy, Al, Mg, Si, Cu, …

Glass, Biomass combustion, and Coal combustion industry

• K2O, Na2O, Li2O containing slags: Glass and Biomass application

• V oxide containing slags: Coal combustion – in progress

• Sulphate containing slags: Coal combustion – in progress

Since 1976

Applications of phase diagram: Case Study

26

MgO solubility in slags

• CaO-MgO-SiO2 Phase diagram vs. MgO solubility

• BOF slag, LF slag

• Multicomponent slag with CaF2

Melting temperature of MgO and MgCr2O4

• Impurity

• Oxygen partial pressure

Other Slag – Refractory Interactions

• Ladle glaze

• Purging plug – cleaning process

Non-metallic inclusions – Stopper

Nozzle refractory

• Carbothermal reduction process

• Inclusion formation

27

MgO solubility in slags

• CaO-MgO-SiO2 Phase diagram vs. MgO solubility

• BOF slag

• Multicomponent slag with CaF2

• LF slag

CaO-MgO-SiO2 phase diagram

28

10

20

30

40

50

60

70

80

90

102030405060708090

10

20

30

40

50

60

70

80

90

SiO2

CaO MgOmass percent

2018-10-22 7 secs

CaO - MgO - SiO2

1600oC, 1 atm

Liquid (L)

L+MgO

L+Mg2SiO4s.s.L+Ca2SiO4s.s.

Decreasing Slag basicity (CaO/SiO2)

Increasing MgO solubility

Molten

CaO-SiO2

MgO

Refractory: CaO-FetO-SiO2-5wt%MgO system with Fe saturation10

20

30

40

50

60

70

80

90

102030405060708090

10

20

30

40

50

60

70

80

90

SiO2

CaO FeO

SiO2

CaO FeO

SiO2

CaO FeOmass %

1500 o

C

1600

1700

150s / 1437oC

300 / 1521

450 / 1551

600 / 1667

750 / 1607

900 / 1648

initial carried over slag

final slag (1695oC)

CaO - SiO2 - FeO - Fe

Fe/(CaO+SiO2+FeO) (g/g) = 1E-9, 1700

oC, 0.1 atm

Overall slag chemistry change

during BOF process

Refractory reaction with F containing slag/flux

30

Liquid (L)

MgO + L

C2S + L

CaO + MgO + Ca3SiO5

MgO

+ C

2S

+ C

a3 S

iO5

MgO

+ C

2S

+ L

CaO + Ca3siO5

wt% SiO2

wt%

Mg

O

0 10 20 30 40 50

0

5

10

15

20

25

30

Phase diagram of the CaO-MgO-SiO2

system at 1600 oC

10%

CaF

2+1

5%Al2O

3

CaO

MgO 2

0%

Ca

F2

MgO

CaO

C2S

MgO

15%

CaF

2

MgO

10%

CaF

2

C2S

10%

CaF2+20

%Al2O

3

MgO

CaO C

2S

10%

CaF2

+10

%Al2O

3

MgO

CaO

C2S

wt% SiO2

wt%

Mg

O

10 20 30 40

0

5

10

15

20

25

30

Influences of CaF2 and Al2O3 on the

liquidus of the CaO-MgO-SiO2 system

at 1600 oC

MgO solubility in CaO-SiO2 and CaO-Al2O3 based slags

31

CaO-SiO2-15%Al2O3 slag with MgO CaO-Al2O3-15%SiO2 slag with MgO

MgO solubility in the CaO-Al2O3 based slags is much lower

than that in the CaO-SiO2 based slags

BOF slag (SiO2 containing slag)

Source of SiO2 in LF slag (earlier stage)

Al deoxidation: reduction of SiO2 in slag

Can change MgO solubility in LF slag

Ladle Furnace (LF) slag

32

10

20

30

10203040506070

70

80

90MgAl2O4 s.s.

MgOs.s.

CaO LiquidCaAl4O7

Al2O3CaO

MgO

CaO-MgO-Al2O3

CaO-MgO-Al2O3-5%SiO2

wt.% CaO/(CaO+MgO+Al2O3)

CaO-MgO-Al2O3-10%SiO2

CaO - MgO - Al2O3 - SiO2

SiO2/(CaO+MgO+Al

2O

3+SiO

2)

(g/g)=0.05, 1600oC, 1 atm

3(SiO2) + 4Al = 3Si + 2(Al2O3)

Initial LF slag: 39.2CaO-39.2Al2O3-11.6MgO-10SiO2 (open circle)

Al deoxidation

Final LF slag: 38.7CaO-50.1Al2O3-11.2MgO (open triangle)

(0.6 wt.% lower than the MgO saturation)

Contents

33

Other Slag – Refractory Interactions

• Ladle glaze

• Purging plug – cleaning process

Ladle Glaze

Ladle Glaze

• Reactions with Ladle refractory lining

• Formation of non-metallic Inclusions

steel

slag

teeming

Slag adheres to

the ladle wallLadle glaze

formationErosion of the

ladle glaze

by the steel melt

Purpose of the present study

• Glaze formation mechanism / Glazed refractory

• Influence on melt cleanliness (inclusion): Al, Al/Ca

34

Glaze (Reaction product of slag and refractory)

Slag

Spinel

CaAl12O19

CaAl4O7

Al2

O3

x slag + (1-x) refractory

ph

ase

dis

trib

uti

on

(w

t%)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

10

20

30

40

50

60

70

80

90

100

Al2O3

CaO

SiO2

MgO

x slag + (1-x) refractory

sla

g c

om

po

siti

on

(w

t %

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

10

20

30

40

50

60

70

spinel islands

Glaze composition

CaO SiO2 Al2O3 MgO

35.8 6.6 51.1 6.5

35

Corrosion of Ladle purging plug by Fe oxides

36

Purging plug: Low- or ultra-low-cement castable (LCC or ULCC)

in the Al2O3-MgO-CaO system: Corundum + Spinel

Corrosion during frequent cleaning operations of the

clogged purging plug surface by “oxygen lancing”

Ca(Al,Fe)12O19 + Cors.s.

Ca(Al,Fe)12O19 + Spinel

Liquid + Spinel

Liquid

Ca(Al,Fe)12O19 + Cors.s. + Spinel

2 Cors.s. + Ca(Al,Fe)12O19 + Spinel

+ Spinel

matrix weight percent Fe 2O3

Tem

per

atu

re,

oC

0 10 20 30 40 50 60 70 80 90 100

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

Spinel

Liquid + Spinel

Liquid

Cors.s. + Spinel

2 Cors.s. + Spinel

Cors.s. + Spinel

matrix weight percent Fe 2O3

Tem

per

atu

re,

oC

0 10 20 30 40 50 60 70 80 90 100

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

Conventional CaO containing castable:

92.8Al2O3-5.7MgO-1.5CaO (in wt%)CaO-free castable:

94.3Al2O3-5.7MgO (in wt%)

CaO free castable is better against chemical corrosion by high Fe oxide slag

O2

2Fe + 3/2O2 = Fe2O3

Slag + refractory rxn

37

Melting temperature of MgO and MgCr2O4

• Impurity

• Oxygen partial pressure

T = 1500 oC

Melting temperature of MgO

38

Melting temperature of

(1) pure MgO = 2825 oC

(2) impure MgO ?

MgO ore – impurity of CaO and SiO2

<99.5-A> MgO + <A> CaO + 0.5 SiO2

<A> impurity amount of CaO

T(C

)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

1500

1550

1600

1650

1700

1750

1800

1850

1900

1950

Ca3MgSi2O8Ca2SiO4

CaM

gS

iO4

<A> CaO

am

ou

nt

of

imp

uir

ty p

ha

se

, w

t%

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

0

1

2

Solidus (initial melting)

T = 1500 oC

Melting temperature of MgO

39

Melting temperature of

(1) pure MgO = 2825 oC

(2) impure MgO ?

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.10.20.30.40.50.60.70.80.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

SiO2

CaO MgOmass fraction

Mg2SiO4

CaMgSiO4Ca3MgSi2O8Ca2SiO4

MgSiO3CaMgSi2O6

CaSiO3

CaO - MgO - SiO2

25oC, 1 atm

Merw

init

e

Fo

rste

rite

Mo

nti

cell

ite

Liquid

+L

a L+Forsterite

MgO+L+Forsterite

MgO+L+MgO+L

'

a

a

1718

a

1576

1507

1393

848

1678

1516

2150

1882

Ca2SiO4 mole fraction Mg2SiO4

Tem

pera

ture,

oC

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

600

800

1000

1200

1400

1600

1800

2000

2200

Melting profile with addition of CaO

Spinel + Cr2O3

PO2 = 0.21 bar

2340

2397

2234

Periclase + Spinel

Spinel

Liquid

Periclase

Alper et al., 1964

Single phase

Two phases

Phase boundary

Frenkel et al., 1960

Greskovich et al., 1966

Hering, 1971

Henriksen and Kingery,1979

MgO mole fraction Cr2O3

Tem

pera

ture,

oC

0.0 0.2 0.4 0.6 0.8 1.0

1000

1400

1800

2200

2600

3000

Periclase + Spinel

Spinel

Spinel + Cr2O3

Liquid

Periclase

Alper et al., 1964

Melted

Partly Melted

Not melted

Single phase

Two phases

Phase boundary

Frenkel et al., 1960

Greskovich et al., 1966

Hering, 1971

2225

2326

2379

log (PO2) = -1.5 (bar)

Henriksen and Kingery,1979

MgO mole fraction Cr2O3

Tem

pera

ture,

oC

0.0 0.2 0.4 0.6 0.8 1.0

1000

1400

1800

2200

2600

3000

Periclase + Spinel

Spinel

Spinel + Cr2O3

Liquid

Peri

cla

se

Alper et al., 1964

Single phase

Two phases

Phase boundary

Frenkel et al., 1960

Greskovich et al., 1966

Hering, 1971

20672162

2177

log (PO2) = -5.5 (bar)

Wilde and Rees,1943Solidus or eutectic

Henriksen and Kingery,1979

MgO mole fraction Cr2O3

Tem

pera

ture,

oC

0.0 0.2 0.4 0.6 0.8 1.0

1000

1400

1800

2200

2600

3000

Jung et al., J. Amer. Ceram. Soc.,

vol. 88, 2005, p. 1921

Decreasing

PO2

MgO-Cr2O3 phase diagram

Inc

on

gru

en

t m

elt

ing

Gee, 1940: probably carbon tube

Alper et al., 1964: N2 atmosphere

Keith, 1954: Carbon tube

Wilde and Rees, 1943: carbon tube

Panek and Kanclir, 1969: Inert gas

log (PO2), bar

Melt

ing

tem

pera

ture,

oC

-10 -8 -6 -4 -2 0

1900

2000

2100

2200

2300

2400

2500

Melting temperature of

MgCr2O4 with PO2

41

Nozzle refractory

• Carbothermal reduction process

• Inclusion formation

Nozzle clogging

42

Nozzle

ZrO2 + C = ZrC + CO(g)

Ar+CO gas formation

Carbothermic reduction of ZrO2 to ZrC

43

ZrO2

ZrC

Ar gas injection can effectively reduce CO partial pressure

Carbothermal reduction of ZrO2 to ZrC is possible.

ArLiq

uid

ste

el

ZrO

2+

C

Formation of Al2O3 in Nozzle: Al killed steel

44

Ar+CO

Al2O3+C

Ar gas

Liquid steel

(Al-killed)

2[Al] + 3CO(g) =

Al2O3 + 3[C]

Fe-liq + Al2O3

Fe-liq

Fe - Al - CO

wt% Al

log

10 p

(CO

)/atm

0 0.02 0.04 0.06 0.08 0.1

-5

-4

-3

-2

-1

0

Al2O3 formation

2Al2O3+9C = Al4C3+6CO(g)

Nozzle clogging in Al-Ti killed steel

45

Fe-liq + Al2O3

Fe-liq + Al2O3 + Slag

Fe-liq + Slag

Fe-liq + Ti3O5

Fe

-liq

+ T

i 3O

5

Fe-liq

+ Slag

Fe - Al - Ti - CO

Ti = 1000 ppm, 1550oC

wt% Al

log

10 p

(CO

)/atm

0 0.02 0.04 0.06 0.08 0.1

-5

-4

-3

-2

-1

0

Reoxidation of steel by CO gas through ceramic nozzle to form slag(Al-Ti-O) and Al2O3

Ultra High Temperature Ceramics

46

LEAP, GE9X Engine

• Ceramic Matrix Composites (CMC)

• TBC coating: ZrO2 stabilized by CaO, Y2O3, etc.)

• Self-healing materials

Ultra High Temperature Ceramics

47

S. V. Ushakov, A. Navrotsky, J. Am. Ceram. Soc. 95 (2012) 1463–1482.

• Melting

• Oxidation

• Evaporation

• Phase transition

Available Thermodynamic Database – Ultra high T ceramics

48

Carbides, Nitrides, Borides, Silicides

(SpMCBN database)

- All ultra high temperature ceramics

- Oxygen, all other gas species

- Oxides (solid and liquids solutions)

ZrO2-RE2O3 based Oxide

- ZrO2-CaO, MgO, ….

- ZrO2-RE2O3 are not available – in progress

Applications of phase diagram: Case Study

49

Oxidation

• Carbide Oxides

• ZrC, HfC, SiC

Evaporation

• SiO2 SiO gas

CMC

• SiC/SiCf

• Self healing CMC

ZrO2-CaO and ZrO2-RE2O3

Oxidation: HfC

50

HfC(liq)HfC

HfO2(liq) + HfC(liq)

C + HfO2(liq)

C + HfO2(s2)

C +

HfO

2(s

1)

Hf0.999C - O2

1 atm

T(C)

log

10 p

(O2)/

atm

1000 1500 2000 2500 3000 3500 4000 4500 5000

-10

-8

-6

-4

-2

0

HfO2

S3: Cubic

S2: Tetragonal

S1: Monoclinic

C+

HfO

2(s

3)

Oxidation: ZrC

51

ZrC(liq)

ZrC

ZrO2(liq) + ZrC(liq)C + ZrO2(liq)

C +

ZrO

2(s

3)

C + ZrO2(s2)C +

ZrO

2(s

1)

Zr0.999C - O2

1 atm

T(C)

log

10 p

(O2)/

atm

1000 1500 2000 2500 3000 3500 4000 4500 5000

-10

-8

-6

-4

-2

0

ZrO2

S3: Cubic

S2: Tetragonal

S1: Monoclinic

Oxidation: SiC

52

C + LIQUID LIQUID

SiC

C + SiO2(liq)

LIQUID + SiO2(liq)

C +

SiO

2(s

6)

C +

SiO

2(s

4)

SiC - O2

1 atm

T(C)

log

10 p

(O2)/

atm

1000 1500 2000 2500 3000 3500 4000 4500 5000

-10

-8

-6

-4

-2

0

Oxidation of ZrC-SiC-C (CMC)

53

Selection criteria of cubic HfO2 stabilizer(i) No melting at 2500 oC(ii) No (less) solid solution with HfC below 2000 oC – high thermal conductivity(iii) Effective stabilizer with small amount

HfC-SiC

Air (High speed + High

temperature (2500 oC))

HfC-SiCSolid HfO2

Liquid SiO2

HfC-SiCHfO2

Stress cracking

(cubic tet or mono)

Definition of problem

Solution: addition of xO, xC, yO, yC

Design the materials based on thermal stability and chemical

reactions (phase diagrams)

C C

SiO(g)

C

Evaporation: SiO2(l) SiO(g)

54

gas_ideal

SiO2(liq) + gas_ideal

Si(liq) + gas_ideal

SiC(s2)

SiO

2(s

4)

+ g

as_

ide

al

SiO

2(s

6)

+ g

as_

ide

al

SiO2 - O2 - C

SiO2/(SiO

2+C) (mol/mol) = 0.5, 1 atm

T(C)

log

10 p

(O2)/

atm

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

-15

-13

-11

-9

-7

-5

-3

-1

SiO2(l)

C

SiC(s)

SiO2(s)

GAS

SiO2 + C

T(C)

mo

le

1000 1200 1400 1600 1800 2000 2200 2400

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

SiO2 melting

SiO(g) + CO(g) formation

690 kJ !!!

SiO2 + C

T(C)

De

lta

H,

kJ

1000 1200 1400 1600 1800 2000 2200

0

100

200

300

400

500

600

700

800

131 kJ from 25 oC to 1500oC

Evaporation: SiO2 +C SiO(g) + CO(g)

55

SiO2(l)

C

SiC(s)

SiO2(s)

GAS

SiO2 + C

T(C)

mo

le

1000 1200 1400 1600 1800 2000 2200 2400

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

SiO2 melting

SiO(g) + CO(g) formation

690 kJ !!!

SiO2 + C

T(C)

De

lta

H,

kJ

1000 1200 1400 1600 1800 2000 2200

0

100

200

300

400

500

600

700

800

131 kJ from 25 oC to 1500oC

Self healing CMC

56

SiC + (Al-B)metal // C

SiC + 2O2 SiO2 + CO2

2Al + 2B + 3O2 Al2O3 + B2O3

SiO2 + Al2O3 + B2O3

Liquid + Solid oxide

(Liquid can fill up the gap)

SiC + X(metal) or XO(oxide)

SiC + 2O2 = SiO2 + CO2

Si-X-O

+ Y or YO

Si-X-Y-O

Self healing mechanism: Al2O3-B2O3-SiO2 system

57

Slag-liq

SiO2(s2) + Slag-liq

SiO2(s4) + Slag-liq

SiO2 + Slag-liq

B2O3 + SiO2

B2O3 - SiO2

1 atm

SiO2/(B2O3+SiO2) (mol/mol)

T(C

)

0 0.2 0.4 0.6 0.8 1

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Liquid formation at low temperature

Self healing mechanism: Al2O3-B2O3-SiO2 system

58

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.10.20.30.40.50.60.70.80.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Al2O3

B2O3 SiO2mole fraction

SiO2 - B2O3 - Al2O3

1200oC, 1 atm

liquid

Liquid+Mullite

(Al2O3)9(B2O3)2

Mullite

T=1200oC

Materials Design and Structure Design• Si-B-C + Al not good at high temperature

because Liquid can be pulled out.• Si-B-C + porous Al2O3 same chemistry but

may be Good structure

Al2O3

(Al2O3)9(B2O3)2

Liquid

Mullite

0.5B2O3-0.5SiO2 mole fraction Al2O3

ph

ase

dis

trib

utio

n (

mo

le f

ract

ion

)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

T=1200oC

Increasing effective viscosity by forming

liquid+solid mixture

TBC coating: Cubic HfO2 and ZrO2 stabilization

59

Cubic HfO2 and ZrO2 stabilization by additives

ZrO2-Re2O3 phase diagram (Predicted)

60

H. Yokokawa, N. Sakai, T. Kawada. (1993), Science and technology of Zirconia V, pp. 59-68.

ZrO2-CaO

61

1622 K1530 K

1309 K1316 K

Ruff et al., 1929: XRD, QMDuwez et al., 1952: XRD, QMNoguchi et al., 1967: HTXRD, XRD, QMTraverse and Foex, 1969: HTXRD, TAStubican and Ray, 1977: HTXRD, XRD,QMHellmann and Stubican, 1983: SAD, TEM

Duran et al., 1987: XRD, QM, DTA

Yin and Argent, 1993: XRD, QM

Hannon, 1985: XRD, QM

Jacob and Waseda, 1994: EPMA, XRD, QM

ZrO2(css)

ZrO2(tss)

ZrO2(mss)

L

Ca

O(s

s)ZrO2(css)+CZ(c)

ZrO2(css)+CZ(o)

ZrO2(mss)+CZ(o)

CZ(c)+CaO(ss)

CZ(o)+CaO(ss)

Andrievskaya et al., 1988: XRD, QM, DTA

ZrO2 mole fraction CaO

Tem

pera

ture, K

0.0 0.2 0.4 0.6 0.8 1.0

500

1000

1500

2000

2500

3000

3500

4000

Summary

62

Phase diagram is one of the most fundamental

knowledge for the materials design and process

optimization

- Continuous support for the experimental phase diagram

study and thermodynamic properties measurement are

necessary.

- Computational thermodynamic database, such as

FactSage, is an useful tool for complex phase diagram

and chemical reaction analysis.

Steelmaking consortium project (2009~2020) – 2018 Annual meeting, Seoul, Korea

Acknowledgement