Thermodynamics of High Temperature Materials Systems

Freiberg University of Mining and
Technology, Germany
Thermodynamics of High Temperature
Materials Systems
Hans Jürgen Seifert
Summer School
Advanced Thermostructural Materials
Santa Barbara, August 9, 2006

Thermodynamics of High Temperature Materials Systems
Outline
Hans Jürgen Seifert
1. Introduction and motivation for thermodynamic calculations
- Computational thermodynamics
- CALPHAD approach (CALculation of PHAse Diagrams)
- Thermodynamic databases and software
2. Thermodynamic optimization of the Ce-O system
- Thermodynamic modeling of solution phases
3. Precursor-derived Si-(B-)C-N ceramics
- High temperature reactions of silicon carbide and silicon
nitride ceramics
- Crystallization and high temperature stability of
Si-(B-)C-N ceramics

Thermodynamics of High Temperature Materials Systems
Outline
Hans Jürgen Seifert
4. Computational thermodynamics in heat shield
engineering
- The Y-Si-C-O system database
- Active / passive oxidation of SiC
- Phase reactions of Yttrium silicates and C/C-SiC
composites
- High temperature stability issues in the
engineering of heat shields
5. Conclusions

Combined Approach
Computational
Thermodynamics and
Modeling
+
Experiments, Analysis
Fundamental Research
Materials Engineering,
Processing

Computational Thermodynamics
Theory
Quantum Mechanics,
Statistical
Thermodynamics
Estimates
Experiments
DTA, Calorimetry,
EMF, Knudsen Effusion,
Metallography,
X-ray Diffractometry, ...
CALPHAD
Optimization
Ab-initio
Calculation
Models
with adjustable
Parameters
Adjustment of
Parameters
CALculation
of PHAse Diagrams
Thermodyn. Functions
G, H, S, C p
Storage in
Databases
Equilibrium
Calculations
Application
Equilibria
Phase Diagrams
Kinetics
Graphical
Representation

CALPHAD (CALculation of PHAse Diagrams)
• Development of Optimized Thermodynamic Datasets
stored in Computer Databases
• Calculation of :
- Thermodynamic Functions
- Liquidus Surface
- Isothermal Sections
- Isopleths
- Potential Phase Diagrams
- Phase Fraction Diagrams
- Phase Compositions
- Scheil Solidification
…
Requires Modeling of Stoichiometric and Solution Phases
Taking into Account the (Crystal-) Structures and Site
Occupancies

CALPHAD (CALculation of PHAse Diagrams)
Software
• LUKAS (BINGSS, BINFKT, TERGSS, TERFKT)
• THERMO-CALC
• FACTSAGE
• PANDAT
• MALT, MALT2
• MTDATA
• JMATPRO
• GEMINI
• ...

CALPHAD (CALculation of PHAse Diagrams)
Databases
• SGTE, Scientific Group Thermodata Europe
- SSOL2, SSOL4
- SSUB3
- Noble Metals
• Thermo-Calc: Steels, Ni-base, slags, ...
• ThermoTech: Ni-base, Al-, Mg-, ...
• PML: Al-, Ceramics
• ...

Calculated Ce–O System in Solid State from 60 to 67 mol. % O
in comparison with experimental data.

Phases in the Partial Ce – O System
Related Crystal Structures:
CeO 2-x (ss) CaF 2 - type (Strukturbericht C1)
Compound Energy Formalism:
(Ce +3 , Ce +4 ) 1 (O -2 ,Va) 2
C-Ce 2 O 3 (ss) Mn 2 O 3 - type (Strukturbericht D5 3 , Ordered State of C1)
Unit Cell: composed of 8 CaF 2 -type cells. ¼ of O-ions removed,
remaining atoms re-arrange towards these vacancies.
Compound Energy Formalism:
(Ce +3 , Ce +4 ) 2 (O -2 ) 3 (O -2 ,Va) 1
Contains more O atoms than the ideal formula of the Mn 2 O 3 .
Ce 2 O 3 Stoichiometric phase description (Strukturbericht D5 2 )

“Compound Energy” Formalisms –
Reference Compounds
(A,B) k (D,E) l
Solution phase with
two sublattices and 4 species
Four compounds defined:
A : D
A : E
B : D
B : E
Gibbs free energy for every compound to be determined
Here:
(Ce +3 , Ce +4 ) 1 (O -2 ,Va) 2

“Compound Energy” Formalism –
Surface of Reference
(A,B) k (D,E) l
Solution phase with
two sublattices and 4 species

Modeling of solution phases; sublattice model described in
the Compound Energy Formalism
(A,B) k (D,E) l
Solution phase with
two sublattices and 4 species
Stochiometric coefficient (s: sublattice)
Site fraction of spezies A on
sublattice s

Compound Energy Formalism –
Excess term of Gibbs free energy
(A,B) k (D,E) l
Solution phase with
two sublattices and 4 species

Compound Energy Formalisms –
Gibbs free energy of solution phases
Mixing Gibbs Energy

Phases in the Partial Ce – O System
CeO 2-x (ss) CaF 2 - type (Strukturbericht C1)
Compound Energy Formalism:
(Ce +3 , Ce +4 ) 1 (O -2 ,Va) 2
Cubic close pack of Ce ions, where all the tetrahedral voids form the
sublattice on which the 2-x O-ions are statistically distributed.
Electroneutrality condition determines that site fractions on the two
sublattices are not independent: Single variable y is equal 2·x.
'
y Ce
+ 3 =
'
y Ce
+
y
4 = (1 − y)
''
y Va
=
''
y O
−2
y
4
1−
y
=
4

No.
Paper
Experimental
Technique
Measured
Quantity
Composition
Temperature
(K)
Remark
1.
Bevan &
Kordis
(1964)
Experiment
with CO 2
/CO
& H 2
O/H 2
Partial
pressures
O 2
CeO 1.5-
CeO 2
909 - 1442
+
2.
Ackerman &
Rauh
(1971)
Mass
Spectroscopy
& Mass
Effusion
Partial
pressures
CeO, CeO 2,
Ce(g), CeO
CeO 1.51 -
-
CeO 1.53
CeO 1.5
-
CeO 1.34
2000 - 3000
1600 - 2000
1825 - 2320
1550 – 2040
+
3.
Iwasaki &
Katsura
(1971)
Experiment
with CO 2
&
CO 2
/H 2
mixture
Partial
pressures
O 2
CeO 2.00
900, 1000,
1100, 1227,
1300
+
4.
Campserveux
& Gerdanian
(1978)
Micro-
Calorimetry
Partial
pressures
O 2
CeO 2
1353, 1296,
1244
+
5.
Kitayama
et al.
(1985)
Thermogravimetry
Partial
pressures
O 2
CeO 2
,
Ce 2
O 3
Ce 3
O 5
1000 – 1330
+

6.
Marushkin
et al. (2000)
Knudsen cell,
Mass
spectrometry
Partial
pressures,
CeO 2
, Ce 2
O 3
CeO 1.99,
Ce 2
O 2.96
1900-2150
1850-2050
-
7.
Kuznetzov&
Rezukhina
(1960)
Calorimetry
Heat capacity,
CeO 2
608-1172
-
8.
Westrum &
Beale Jr.
(1961)
Adiabatic
Calorimetry
Heat capacity,
CeO 2
5-300
+
9.
Justice &
Westrum
(1969)
Cryogenic
Calorimetry
Heat capacity
Ce 2
O 3.02
5-350
+
10.
Basily & El-
Sharkawy
(1979)
Plane
temperature
wave method
Heat capacity
Ce 2
O 3
400-1000
+
11.
Ricken et al.
(1984)
Calorimetry
Specific heat,
∆H trans.
CeO 1.72
–
CeO 2
320-1200
-
12.
Kuznetzov, et
al. (1960)
Bomb
calorimetry
∆H for Ce 2
O 3
Ce 2
O 3.00
298
+

13.
Baker &
Holley
(1968)
Oxygen
Bomb
Calorimetry
Heat of
combustion
Ce 2
O 3
Ce 2
O 3
298.15
-
14.
Baker, Huber,
Holley &
Krikorian
(1971)
Bomb
calorimetry
Heat of
formation
CeO 2
, CeC 1.5
,
CeC 2
CeO 2
298.15
-
15.
Campserveux
& Gerdanian
(1974)
Micro
Calorimetry
Partial molal
enthalpy
∆H soln.
(O 2
)
CeO 1.5
–
CeO 2
1353
+
16.
Panlener,
Blementhal &
Garnier(1975)
Thermogravimetry
∆W/W
CeO 2-x
1023-1773
+
17
Riess,
Koerner &
Noelting
Dilatometry
Thermal
expansion
coefficient
CeO 1.79
–
CeO 2
320-1200
+
(1988)

Calculated Ce–O System in Solid State from 60 to 67 mol. % O
in comparison with experimental data.

Heat capacities of Ce 2
O 3
and CeO 2
.
Enthalpy increment (heat contents) of
CeO 2
.
H.J. Seifert, P. Nerikar, H.L. Lukas, Int. J. Mater. Res. 97 [6] (2006) 744-752.

Chemical potentials of oxygen for ceria as a function of composition
and temperature.

Chemical potentials of oxygen for ceria as a function of composition
and temperature.

Chemical potentials of oxygen for ceria as a function of composition
and temperature.

Chemical potentials of oxygen for ceria as a function of composition
and temperature.

Chemical potentials of oxygen for ceria as a function of composition
and temperature.

Chemical potentials of oxygen in the two-phase areas.

Partial Enthalpies of Oxygen in CeO 2
kJ/mol
HH CeO 2 CeO2
O O
Mole fraction O

Thermodynamics of High Temperature Materials Systems
Outline
Hans Jürgen Seifert
1. Introduction and motivation for thermodynamic calculations
- Computational thermodynamics
- CALPHAD approach (CALculation of PHAse Diagrams)
- Thermodynamic databases and software
2. Thermodynamic optimization of the Ce-O system
- Thermodynamic modeling of solution phases
3. Precursor-derived Si-(B-)C-N ceramics
- High temperature reactions of silicon carbide and silicon
nitride ceramics
- Crystallization and high temperature stability of
Si-(B-)C-N ceramics

Precursor-derived Si-B-C-N Ceramics
• Produced by thermolysis (1323 K, Ar) of
polymer precursors
• Amorphous, purely homogeneous inorganic materials
• NCP200: 40.1Si 23C 36.9N (at.%)
- Starts to crystallize at 1700 K (N 2 )
- Thermal stability up to 1800 K (N 2 )
• T2-1: 29.1Si 41.7C 19.4N 9.8B (at.%)
- X-ray amorphous, nanocrystalline
- Thermal stability up to 2300 K

Process for Precursor-derived Si-(B-)C-N Ceramics
Monomer
Polymer
Synthesis
Monomer Unit
Precursor Polymer
Preceramic Network
Crosslinking (200-400°C)
Thermolysis (1000-1400°C)
Amorphous Solid
Amorphous Ceramic
Polycrystalline Ceramic
Crystallization ( > 1400°C)
Crystalline Ceramic
Novel ceramics with high
temperature stability and with
good resistance to oxidation
can be obtained from
molecular units without
sintering aid.

J. Gröbner, PhD thesis, 1994
Si-C binary subsystem

Si-N binary subsystem
Gas
Si(l) + Gas
Si 3
N 4
2114 K
Gas + Si 3 N 4
Si 3 N 4 + Si(l)
1687 K
Si 3 N 4 + Si(s)
Si(l)
Si(s)

Isopleth from Carbon to Si 3 N 4 in the Si-C-N System

Isothermal Section of the Ternary System Si-C-N
T = 3000 K
(2727 °C)

Isothermal Sections of the Ternary System Si-C-N
Si 1 N 1.6 C 1.33 (VT50, Polyvinysilazane, Hoechst AG, Frankfurt, Germany)
Si 1 N 0.6 C 1.02 (NCP200, Polyhydridomethylsilazane, Nichimen Corp., Tokyo, Japan)
N
Si 3 N 4 + 3C = 3SiC +2N 2
(1)
N
Si 3 N 4 = 3Si + 2N 2
(2)
N
Si 3 N 4
Si 3 N 4
C
SiC
Si
C
SiC
Si
C
SiC
Si
T < 1484°C
(1757 K)
1484°C < T < 1841°C T > 1841°C
(2114 K)
P = 1 bar

Calculated Phase Fraction Diagrams of Precursor Derived Ceramics
Si 3 N 4 + 3C = 3SiC +2N 2
Si 1 N 1.6 C 1.33
(VT50)
1484°C

Thermogravimetrical (TG) analysis of precursor-derived Si-C-N ceramics
Mass Loss (%)
5
0
-5
-10
-15
-20
-25
-30
-35
NCP200
VT50
1000 1200 1400 1600 1800 2000
Temperature (°C)

Calculated Phase Fraction Diagram of Precursor Derived Ceramics
NCP200, Polyhydridomethylsilazane (Nichimen Corp., Tokyo, Japan)
Ceramics:
Si 1 N 0.6 C 1.02
Phase Fraction Diagram
Reaction Path
N
1484°C
Si 3 N 4
1841°C
C
SiC
Si

Thermogravimetrical (TG) analysis of precursor-derived Si-C-N ceramics
Mass Loss (%)
5
0
-5
-10
-15
-20
-25
-30
-35
NCP200
VT50
1000 1200 1400 1600 1800 2000
Temperature (°C)

Thermogravimetrical (TG) analysis of precursor-derived Si-B-C-N ceramics
Mass Loss (%)
5
0
-5
-10
-15
-20
-25
-30
-35
T2-1
Si 3 N 4 + 3C = 3SiC + 2N 2 MW36 MW33
(Si-B-C-N)
NCP200
VT50
Si 3 N 4 = 3Si + 2N 2
(Si-C-N)
-40
1200 1400 1600 1800 2000 2200
Temperature (°C)

Calculated Phase Fraction Diagram of
T2-1- Derived Ceramic Si 3.0 B 1.0 C 4.3 N 2.0
Si 3.0 B 1.0 C 4.3 N 2.0
1484°C
( T2-1 precursor, PML,
Max-Planck-Institut,
Stuttgart, Germany )

B
SiB n SiB 6
B 4+ δ C
BN
SiB 3
B 2 CN 2
mol-% B
mol-% B
BC 3 N
BC 4 N
BC 2 N
mol-% C
SiC
N
“C 3 N 4 “ SiC 2 N 4 Si 2 CN 4
Si 3 N 4
mol-% B
mol-% N
C
mol-% Si
Si

Isothermal Section at 1500 K in the Ternary System Si-B-C
T = 1500 K
(1227 °C)

B
SiB n
B 4+δ C
SiB 6
SiB 3
BN
N
Si 3 N 4
C
SiC
Si

Calculated Potential Phase Diagram
10 bar
1 bar
Si 3
N 4

Calculated Potential Phase Diagram
1484°C
1700°C
1841°C
2034°C
10 bar
1 bar

Carbon activity - temperature diagram
(2034°C)
I0 bar pressure:
ac. = 1 1973 K (1700°C)
ac. = 0.17 2307 K (2034°)
(1700°C)
Estimating a pressure of 10
bar and a carbon activity of
0.17, it can be concluded
that the thermal stability of
precursor-derived Si-B-C-N
ceramics remains up to
2000°C.

B
N
C
Si

Isopleth from B to Si 1 C 1.6 N 1.33 (VT50) in the Si-B-C-N System
B
N
C
Si

Isopleth from B 0.1 C 0.65 Si 0.25 to B 0.1 N 0.65 Si 0.25 in the Si-B-C-N System
(at 10 mol-% B and 25 mol-% Si)
X (N)
B 0.1 C 0.65 Si 0.25 B 0.1 N 0.65 Si 0.25
X (Si)

B - C - N B - C - Si B - C - N - Si C - N - Si B - N -Si
2722 u1
G + L = BN + B4C
2657 u2
G + L = C + B4C
2597 u3
G + B4C = C + BN
2372 u5
L + B4C = B + BN
2568 u4
L + C = B4C + SiC
2278 u6
L + B = B4C + SiBn
L + C + BN + B4C
2597 G + B4C = L + C + BN U1
G + L +
C + BN
G, L,
SiC, BN
2586 G + L = BN + SiC + C U2
L, SiC, G, SiC,
C, BN
C, BN
2568 L + C = SiC + B4C, BN U3
SiC, C, BN, B4C
2311 L + B = B4C + SiBn, BN D1
BN, B4C, SiBn, B
L, BN,
B4C, SiBn
2590 M
G = L + SiC + BN
3095 d1
L + C = SiC, G
L, SiC, BN,
B4C
G, L, SiC, BN
2310 d2
L + B = SiBn, BN
2273 K
2123 u7
L + SiBn=B4C + SiB6
2123 L + SiBn=SiB6 + B4C, BN D2
2123 d3
L + SiBn = SiB6, BN
L, BN, B4C, SiB6
BN, B4C, SiB6, SiBn
2114 G + L = Si3N4 + SiC, BN D3
G, Si3N4,
SiC, BN
L, Si3N4,
SiC, BN
2114 u8
G + L = Si3N4 + SiC
2114 d4
G + L = Si3N4, BN
1873 K
1669 u10
L + SiC = B4C + Si
1757 G + SiC = C + Si3N4, BN D4
G, Si3N4, C, BN
Si3N4, SiC, C, BN
1687 L = Si, Si3N4, BN, SiC D5
Si3N4, SiC, BN, Si
L, SiC,
BN, Si
1669 L + SiC = B4C + Si, BN D6
1757 u9
G + SiC = C + Si3N4
1687 d5
L = Si, SiC, Si3N4
1687 d6
L = Si, Si3N4, BN
1673 K
SiC, BN, Si, B4C
L, BN,
Si, B4C
1657 d7
L = Si + SiB6, B4C
1657 L = Si + SiB6,, BN, B4C D7
1657 d8
L = Si + SiB6, BN
BN, Si,
B4C, SiB6
1471 d9
Si + SiB6=SiB3, B4C
1471 Si + SiB6 = SiB3, B4C, BN D8
1471 d10
Si + SiB6 = SiB3, BN
BN, B4C, SiB3, SiB6
BN, Si, B4C, SiB3
298 K

Si-B-C-N phase diagram at 1673 K with 4 of 9 4-phase equilibria
B
SiB n
SiB 6
B 4
C
BN
N
Si 3 N 4
L
C
SiC
Si

Si-B-C-N concentration tetrahedron with indicated
plane at a constant B content of 25 at.%
T = 1400°C (1673 K)
B 4+δ
C
B
SiB n
SiB 6
SiB 3
BN
N
Si 3
N 4
C
SiC
Si

Si-B-C-N concentration tetrahedron with indicated
plane at a constant B content of 10 at.%
Si 3.0 B 1.0 C 4.3 N 2.0
( T2-1 precursor, PML,
Max-Planck-Institut,
Stuttgart, Germany )
B
SiB n
SiB
B 4+δ
C
6 SiB 3
Si
BN
N
T2-1
Si 3 N 4
C
SiC

Isothermal Section at 10 mol-% B in the Si-B-C-N System
B 4+δ C
B
SiB n
SiB 6
N
BN
T2-1
Si 3 N 4
C
SiC
Si
T = 1400°C
(1673 K)

Isothermal Sections at 10 mol-% B in the Si-B-C-N System
T = 1673 K
(1400°C)
T = 1873 K
(1600 °C)

System Si-B-C-N
- Metastable phase separation -
B
SiB n
a - Si-B-C-N
B 4+δ C
BN
SiB 6
SiB 3
a - BNC y +
a-Si 3+ x C x N 4-x
t - BNC y Si 3 N 4 SiC
1
4
N
a-BNC y Si 3
N 4
a-Si 3+ x C x N 4-x
C
1
4
Si

a - Si-B-C-N
B
SiB n
stable
a - C y (BN) +
a-Si 1 3+ x C x N 4 4-x
B 4+δ
C
SiB 6
SiB 3
not stable
t - BNC y Si 3 N 4 SiC
BN
N
Si 3
N 4
C
a-BNC y
a-Si 3+ x C x N 4-x
T2-1
SiC
1
4
Si