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: [email protected]
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