The Pennsylvania State University
The Graduate School
College of Earth and Mineral Sciences
THERMODYNAMIC INVESTIGATION OF TRANSITION METAL OXIDES VIA
CALPHAD AND FIRST-PRINCIPLES METHODS
A Thesis in
Materials Science and Engineering
by
Lei Zhang
2013 Lei Zhang
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
August 2013
The thesis of Lei Zhang was reviewed and approved* by the following:
Zi-Kui Liu
Professor of Materials Science and Engineering
Thesis Advisor
Suzanne Mohney
Professor of Materials Science and Engineering
Roman Engel-Herbert
Professor of Materials Science and Engineering
Gary L. Messing
Distinguished Professor of Materials Science and Engineering
Head of the Department of Materials Science and Engineering
*Signatures are on file in the Graduate School
iii
ABSTRACT
This thesis describes the thermodynamic modeling of the La2O3-TiO2 system, SrCoO3-δ
perovskite with extension to Sr-doped LaCoO3-δ. By using CALPHAD (CALculation of PHAse
Diagram) method, the thermochemical properties gained by first-principles calculations are put
together with phase equilibrium data for the optimization and phase stability prediction.
Thermodynamic modeling of oxides, especially transition metal oxides are not as
common as metallic systems. In the CALPHAD approach for oxides, the ionic compound energy
formalism is adopted for thermodynamic model construction. In first-principles calculations,
GGA+U method is used to account for the strong-correlation of d electrons in transition metal
ions. By fitting energy-volume curve for a certain oxide, the 0 K enthalpy is obtained. The fitting
parameters in energy-volume curve can then be utilized in the Debye-Grüneisen model to further
predict the Gibbs energy at finite temperature, which can be optimized in CALPHAD method to
predict the phase stability.
In the La2O3-TiO2 system, the thermodynamic properties of ternary oxides are calculated
by first-principles along with Debye- Grüneisen model. The phase diagram is then predicted with
an optimized liquid phase thermodynamic description. The thermodynamic database constructed
is crucial for ceramic processing involving lanthanum titanates.
The SrCoO3-δ, when doped into the LaCoO3-δ, can be applied as the ionic transport
membrane for gas separation and purification. The defect behavior in Sr-doped LaCoO3-δ along
with phase stability in the service condition then becomes significant. The defect calculations in
cubic SrCoO3-δ provide precious thermochemical data for the phase stability and defect
concentration predictions.
Key words: CALPHAD, transition metal oxides, phase stability, first-principles, defect
iv
TABLE OF CONTENTS
LIST OF FIGURES ................................................................................................................. vi
LIST OF TABLES ................................................................................................................... viii
ACKNOWLEDGEMENTS ..................................................................................................... ix
Chapter 1 Introduction ............................................................................................................. 1
1.1 Transition metal oxides ............................................................................................ 1 1.2 Motivation and objectives ........................................................................................ 2 1.3 Outline ...................................................................................................................... 2
Chapter 2 Computational methodology ................................................................................... 4
2.1 Introduction .............................................................................................................. 4 2.2 Density Functional Theory ....................................................................................... 4 2.3 CALPHAD ............................................................................................................... 6 2.4 Conclusion ................................................................................................................ 9
Chapter 3 Thermodynamic modeling of the La2O3-TiO2 pseudo-binary system aided by
first-principles calculations .............................................................................................. 11
3.1 Introduction .............................................................................................................. 11 3.2 Review of experimental data in the literature .......................................................... 12 3.3 First-principles calculations ..................................................................................... 13 3.4 Thermodynamic modeling ....................................................................................... 16 3.5 Results and discussions ............................................................................................ 18 3.6 Conclusions .............................................................................................................. 21
Chapter 4 First-principles investigation and thermodynamic modeling of oxygen
vacancies in cubic SrCoO3-δ perovskite ........................................................................... 32
4.1 Introduction .............................................................................................................. 32 4.2 Review of published data ......................................................................................... 33 4.3 First-principles calculations ..................................................................................... 35 4.4 CALPHAD modeling ............................................................................................... 36 4.5 Results and discussion .............................................................................................. 38 4.6 Conclusion ................................................................................................................ 40
Chapter 5 Conclusions and future work ................................................................................... 53
5.1 Conclusions .............................................................................................................. 53 5.2 Future work .............................................................................................................. 53
Appendix A SrCoO3-δ perovskite sublattice model ................................................................. 55
v
Appendix B La2O3-TiO2 Thermo-Calc database .................................................................... 60
Appendix C Cubic SrCoO3-δ Thermo-Calc database .............................................................. 71
Bibliography ............................................................................................................................ 83
vi
LIST OF FIGURES
Figure 3. 1.0 K enthalpy of formation of ternary oxides with respect to the ground state
La2O3 and TiO2 by PBE (dark red, solid line) and LDA (grey, dotted line). ................... 25
Figure 3. 2.Finite temperature properties of hp5- La2O3 (entropy (a), enthalpy (b) and
heat capacity (c)) and tp6- TiO2 (entropy (d), enthalpy (e) and heat capacity (f)):
black, dotted lines from SSUB4 database and red, solid lines from current first-
principles calculations. ..................................................................................................... 26
Figure 3. 3.Calculated La2O3-TiO2 phase diagram in comparison with experimental data
by Ŝkapin et al. [45], Petrova et al. [69], Nanamats et al. [50] and MacChesney et al.
[39]. .................................................................................................................................. 27
Figure 3. 4. Enlarged La2O3-TiO2 phase diagram showing the phase relation around TiO2-
rich side with experimental data by Ŝkapin et al. [45] and MacChesney et al. [39]. ....... 28
Figure 3. 5. Finite temperature properties of LT (entropy (a), enthalpy (b) and heat
capacity (c)), L2T3 (entropy (d), enthalpy (e) and heat capacity (f)) and LT2_Cmcm
(entropy (g), enthalpy (h) and heat capacity (i)): with black, dotted lines from current
database and red, solid lines from current first-principles calculations. .......................... 29
Figure 3. 6.Enthalpy of formation from first-principles calculations (symbols) and model
parameters (curve) at 298.15 K with reference states of tP6 structure for TiO2 and
hP5 structure for La2O3. ................................................................................................... 30
Figure 3. 7.Entropy of formation from first-principles calculations (symbols) and model
parameters (curve) at 298.15 K with reference states of the tP6 structure for TiO2
and hP5 structure for La2O3. ............................................................................................ 31
Figure 4. 1 (Top) Electrochemical potential from brownmillerite to SrCoO3 from Le
Toquin et al. [87] (red solid lines), Nemudry et al. [103] (blue dashed lines), and
Bezdika et al. [102] (green circles) and (Bottom) converted to Gibbs energy by
Nernst equation. First-principles calculations from the present work are given as
purple triangles. ................................................................................................................ 46
Figure 4. 2 PO2 vs. temperature phase diagram of Sr:Co ratio 1:1 with experimental phase
boundary data from Vashook et al. [88] (circles and triangles), Takeda et al. [99]
(diamond), and Rodriguez et al. [97] (square). ................................................................ 47
Figure 4. 3 Gibbs energy of SCO as a function of δ from CALPHAD at 298 K with
experimental data (triangles) [87]. The units are in kJ/mol-form for SrCoO3- δ. The
vii
reference state for the top figure is 3.25 moles of brownmillerite at corresponding
temperature and ambient pressure. ................................................................................... 48
Figure 4. 4 Temperature and PO2-dependence of δ, top and bottom, respectively,
calculated from model parameters in the current work and compared to experiments
[82, 99-101]. Numbers in the legends refer to fixed PO2 for the top figure and
temperature for the bottom figure. ................................................................................... 49
Figure 4. 5 Site occupancies of the SCO sublattice model as a function of temperature in
air (top) and PO2 at 1273 K (bottom). 1for Sr+2
, 2 for Va in A-site, 3 for Co+2
, 4 for
Co+3
, 5 for Co+4
, 6 for Va in B-site, 7 for O-2
, 8 for Va in oxygen site. ........................... 50
Figure 4. 6 Schematic projection of the composition space of the sublattice model and the plane defining possible
electrically neutral compositions. Red points correspond to the neutral compounds
chosen for the current work.............................................................................................. 51
Figure 4. 7 The formation enthalpy of defect SCO with respect to O2 and brownmillerite
at 0 K, obtained from the defect energy calculations. The y axis is the formation
enthalpy in eV/formula SCO, x axis is the δ. ................................................................... 52
viii
LIST OF TABLES
Table 3. 1.Fitted equilibrium properties from EOS by LDA and PBE potentials at 0 K
compared with previous experimental studies, including equilibrium volume, ,
bulk modulus, , and first derivative of bulk modulus with respect to pressure, , for phases in the La2O3-TiO2 system. ............................................................................... 22
Table 3. 2.Thermodynamic parameters evaluated in the La2O3-TiO2 system (all in S. I.
units). ............................................................................................................................... 23
Table 3. 3.Calculated and experimental reaction temperatures and compositions for the
La2O3-TiO2 system. .......................................................................................................... 24
Table.4. 1 Current experimental measurements of δ in SrCoO3- δ. .......................................... 41
Table.4. 2 Lattice parameters, enthalpies of formation, and anti-ferromagnetic magnetic
moments of Sr2Co2O5 brownmillerite from first-principles calculations compared to
experiments. Results are shown for Sr2Co2O5 in the Pnma (62) and Ima2 (46)
structures, with and without the GGA+U correction. Experimental lattice parameters
[85] are taken at 10 K from the same neutron powder-diffraction data under the two
space group settings. ........................................................................................................ 42
Table.4. 3 Gibbs energy functions of Sr2Co2O5 and Sr6Co5O15 fitted to first-principles
calculations with and without GGA+U, in J/mol-form. ................................................... 43
Table.4. 4 Gibbs energy functions for the phases modeled in the current work, in J/mol-
form. Gibbs energy functions for the pure elements and the (Va) (Va) (Va)3 SrCoO3-
δ neutral compound can be found in the database file as supplementary material. .......... 44
Table.4. 5 Enthalpies of formation and entropies at 298 K of Sr2Co2O5 and Sr6Co5O15
with respect to the elements from first-principles calculations with GGA+U and
from the current CALPHAD modeling. Note that direct comparison between the two
phases is not possible as their compositions are different. ............................................... 45
ix
ACKNOWLEDGEMENTS
I would like to thank Prof. Zi-Kui Liu for his everlasting support, advice and
encouragement during my three years academic research. Your tutelage makes me an expert in
thermodynamic modeling.
I would like to thank Prof. Suzanne Mohney and Prof. Roman Engel-Herbert for serving
as my master defense committee.
I would like to thank the PRL group members for all your help and discussions that
sweep the obstruction ahead of me and inspire my scientific thinking.
I would like to thank Mr. Michael Carolan from Air Products and Chemicals, Inc. for his
financial support and data providing on our research.
Special thanks are given to Prof. Zi-Kui Liu, Prof. Long-Qing Chen and Dr. Yi Wang for
your support on my graduate school applications.
Finally, I would like to show my gratefulness to my parents. Without your
encouragement and suggestions, I cannot make through ups and downs during my graduate years.
Chapter 1 Introduction
1.1 Transition metal oxides
Transition metal oxides have gained great interest and intense research in recent years [1-
28]. Due to their intrinsic electronic structure, generally with strong correlation effect of d
electrons of transition metal ions and p electrons of oxygen ions, they have a large spectrum of
unique properties which normal oxides or metals do not have. To name a few, the unpaired d
electrons in transition metal ions induce spin magnetic moment for the oxides; besides, the
complex correlation effect mentioned above can induce structural distortion, oxygen cage
rotation, etc. The so-called ferroelectric property is among one of the most interesting properties
they have. When ferroelectricity is coupled with magnetism, magneto-electric or multiferroic
properties are the research focus in recent publications [1-19]. More generally speaking, the
oxides as the ceramics have dielectric response with respect to external electric field. Another
significant property of transition metal oxides, in their deficient structures, is their fast ionic and
electronic transport, due to the multi-valence of transition metal ions, which can be applied to the
cathode material of fuel cell or ion transport membrane.
In conclusion, the transition metal ions play an important role in determining the
functional properties of transition metal oxides. This kind of material has a promising future in
electric device, spintronics, electrode of cells, catalyst and so on.
2
1.2 Motivation and objectives
Instead of focusing on the functional properties of transition metal oxides, this work
focuses on the thermodynamic properties and phase stability of them. The thermodynamic
properties have a huge impact on the synthesis window of those oxides and the appropriate choice
of service conditions of those oxides. Experimental investigation takes a lot trials and errors,
while computational prediction is more time-saving and less expensive. By introducing the first-
principles ab-initio method into the thermodynamic investigation, it gives the atomic-level
explanation on why a certain crystal structure on a certain magnetic arrangement is stable. The
valuable data gained by first-principles are usually unavailable in experiments. The first-
principles data can be made use of in another method called CALPHAD (CALculation of PHAse
Diagram). CALPHAD method is another effective way of constructing the phase diagram and
predicting the phase stability with all the other thermodynamic-related properties. Although it is a
semi-empirical method, which taking consideration of all the existing experiments and
calculations into its optimization, it shows an advantage in predicting thermodynamic properties
in a consistent way and can be easily extrapolated to multi-component systems.
Due to the convenience of first-principles calculations and CALPHAD method, the
thermodynamic databases of three transition metal oxide systems are built: La2O3-TiO2 and
SrCoO3-δ. The goal is to predict the phase stability and oxygen defect concentration, which
provides important information on the ceramic sintering process, service condition design and
thin film growth condition choice of them.
1.3 Outline
This thesis is constructed as follows: Chapter 2 introduces the computational
methodology, including CALPHAD method and first-principles calculations. In Chapter 3,
Chapter 4, the first-principles calculations and thermodynamic investigation of La2O3-TiO2 and
SrCoO3-δ are demonstrated in order. Chapter 5 is the conclusion and future work. Appendix A is
the thermodynamic model for SrCoO3-δ, appendix B and C are database of those systems.
Chapter 2 Computational methodology
2.1 Introduction
Basically, first-principles method in this work is based on Density Functional Theory
[29], which describes properties of a crystal structure as a functional of charge-density in this
crystal structure. This method is also taken as ab-initio due to its parameter-free character,
although in dealing with strong-correlation materials, the parameters are inevitably introduced.
The electronic structures are the basic output of this calculation, together with other properties
such as energy we need.
CALPHAD, abbreviated from CALculation of PHAse Diagram, uses all the existing
experimental and calculation data including phase equilibrium data and thermochemical data to
perform an overall optimization [30-32]. It parameterizes all the discrete data into a Gibbs
function which describes the Gibbs energy of a certain phase as a function of composition and
temperature. This consistent way of building database is easily extrapolated to other components.
2.2 Density Functional Theory
The basic ideas of Density Functional theory are contained in the two original papers of
Hohenberg, Kohn and Sham and also referred to as Honhenberg-Kohn-Sham theorem [29].
Instead of dealing with the many-body Schrödinger equation, which involves the many-body
wavefunctions , one deals with a formulation of the problem that involves the total density
of electrons , which is a function of the electron position . This huge simplification ignores
5
the details of the many-body wavefunction. Instead, it describes the behavior of the system with
the appropriate single-particle equation as a functional of the charge density.
The energy of the system is considered as the sum of several components:
Equation 2.1
where is the kinetic energy of the electrons summed up, is the potential
energy of the electrons with respect to the external potential induced by ions or lattice,
is the electron-electron Coulombic interactions, while accounts for the
many-body effect of electrons and stands for the exchange-correlation energy of electrons.
When the three terms are all treated as an
effective external potential, the Kohn-Sham equation is then the Schrödinger equation of a
fictitious system of non-interacting electrons that generate the same density as any given system
of interacting particles. The equation is shown below:
Equation 2.2
where is the total energy of the system.
Since the exchange-correlation term depends on , which depends on ,
which in turn depends on , the solving procedure of the Kohn-Sham equation has to be
done in a self-consistent way.
In dealing with transition metal oxides, the strong-correlated d electrons cannot be well
captured without a correction. An efficient correction is adding the intra-atomic Coulomb
interaction energy, U. The formulation employed in the current work by Dudarev et al. [21]
requires an effective U as input, with Ueff =U-J where J is a separate exchange interaction energy.
6
The effective U is a fitting value. It usually fits to the band gap, magnetic moment, lattice
parameter etc. However, it is not guaranteed that all of them can be simultaneously fitted well.
Thus, this fitting value gives limitations to the prediction of transition metal oxides. In the
literature [27, 33-34], people have to compare their first-principles predictions with experimental
values to validate their U value is reasonable.
2.3 CALPHAD
The CALPHAD method is based on Gibbs energy functions within a certain model,
which is structure sensitive.
The energy obtained by first-principles is a major input for CALPHAD evaluation of
Gibbs functions of each phase. The total energy from first-principles is converted to the enthalpy
through the following equation:
Equation 2.3
The total energy from first-principles is equal to the Helmholtz energy. Since the first-principles
calculation is essentially at zero Kelvin and equilibrium pressure, the enthalpy is the Helmholtz
energy plus a constant.
The Gibbs energy, , can be expressed in terms of enthalpy, , and entropy, :
Equation 2.4
where is the temperature. However, and can also be dependent on temperature, so a Gibbs
function with temperature as the variable is employed:
7
Equation 2.5
where , , , and are model parameters. This temperature polynomial has been tested on
numerous phases (including pure metals, gas molecules, ionics and covalent compounds) of their
thermochemical behavior experimentally, including most of the elements. In order to determine
the model parameters of a given phase, usually the three chemical properties are calculated
through first-principles or measured experimentally: the temperature dependent heat capacity ,
the temperature dependent entropy , and the enthalpy of formation at room temperature .
They can also be written as a function of temperature through a simple thermodynamic
derivation:
Equation 2.6
Equation 2.7
Equation 2.8
To fit the model parameters, the heat capacity data is used to fit the , and terms.
Then the entropy can be fitted by adjusting the parameter and formation enthalpy is used to fix
parameter . The Gibbs function cannot be applied to predict the thermochemical properties
lower than the room temperature 298.15 K because the polynormial is fitted to the experiments
above the room temperature.
The Gibbs energy function of a certain phase can also be written as the energy
combination of its component with the formation enthalpy and entropy:
8
Equation 2.9
where is the molar Gibbs energy of the phase , and
are the molar Gibbs
energies of components A and B, respectively, in their stable state at 298.15 K. and are the
mole fractions of A and B for the phase, and are model parameters corresponding
to the enthalpy and entropy of formation.
For solution phases, a specific model should be assigned to them. Depending on the
property of a specific phase, a certain model is chosen to best describe the property with fewest
fitting parameters.
For oxide systems, the liquid phase is usually described within the ionic liquid model
[35], written as
, where
is the cation in the first sublattice with
positive charge ,
is anion in the second sublattice with negative charge , Va is
hypothetical vacancy to describe the metallic behavior of the oxide liquid phase, is the neutral
species indicating a stable associate in the liquid instead of tending to be ionized. and are the
number of sites in cation and anion sublattice, defined as:
Equation 2.10
where denotes the site fraction of constitute . This equation simply means the and are
equal to the average charge on the opposite sublattice.
The Gibbs energy of a solution phase is composed of several parts, each with a specific
meaning:
Equation 2.11
9
Equation 2.12
Equation 2.13
where is the gas constant, is the interaction parameter indicating interactions between two
species in one sublattice.
is the molar Gibbs energy indicating mechanical mixing between
available end members,
is the random configurational entropy on each sublattice, is
the excess Gibbs energy.
Interaction parameter is written as a Redlich-Kister polynormial:
Equation 2.14
where is an integer number, is the mole fraction. is the fitting parameter which usually a
linear function of temperature.
The solid ionic sublattice models have very similar formula as the ones shown above.
The one shown above is a general representation of liquid ionic sublattice model for oxide phases.
2.4 Conclusion
When first-principles method is introduced to assist the CALPHAD modeling, the non-
existing thermochemical data which is expensive or even impossible to get from experiments can
be calculated and used to predict the Gibbs energy of individual phases. By combining the Gibbs
10
energy of individual phases, thermodynamic properties and phase stability can be easily predicted
based on a consistent mathematical model. In this way, the database of La2O3-TiO2 and SrCoO3-δ
are built.
11
Chapter 3 Thermodynamic modeling of the La2O3-TiO2 pseudo-binary
system aided by first-principles calculations
3.1 Introduction
An accurate thermodynamic database of the La2O3-TiO2 pseudo-binary system is
desirable for understanding and designing the processing of ceramic materials with lanthanum
titanates. The phase diagram predicted by the thermodynamic database can provide useful
information on phase transformations during sintering or thin film growth. The thermodynamic
properties of each oxide in this system provide basis for further investigations of their physical
properties, such as the dielectric permittivity. In addition, the first-principles calculations based
on density functional theory provide bulk modulus information as a preliminary indication of
mechanical properties of those oxide crystallites.
In the La2O3-TiO2 pseudo-binary system, the following lanthanum titanates have been
reported in the literature: La2TiO5, La2Ti2O7, La2/3TiO3, La4Ti3O12, and La4Ti9O24 with La2Ti2O7
having three polymorphs. For convenience, L and T are used to represent La2O3 and TiO2 in the
present work, and the above five ternary oxides are denoted by LT, LT2, LT3, L2T3 and L2T9
accordingly. These lanthanum titanates exhibit interesting electrical related properties and have
been recently extensively investigated as microwave frequency dielectrics [36]. Specially,
La2Ti2O7 exhibits an unusually high Curie temperature and was reported to be a promising
candidate for high temperature piezoelectric and electro-optical devices [37]. In the present work,
the thermochemical properties of La2O3, TiO2, LT, LT2, and L2T3 are predicted by first-
principles calculations and Debye-Grüneisen model [38], due to the lack of thermochemical data.
12
The Gibbs energy functions of all phases are modeled by means of the CALculation of PHAse
Diagram (CALPHAD) method using both phase equilibrium data in the literature and the results
from first-principles calculations in the present work [31].
3.2 Review of experimental data in the literature
MacChesney et al. [39] measured the stable phase regions, invariant temperatures and
congruent melting points in this La2O3-TiO2 system using quenching technique followed by X-
ray diffraction (XRD) and metallographic analysis. In their paper, three compounds LT, LT2, and
L2T9 were reported. The compound L2T9 was found to melt incongruently at 1728 K, and LT
and LT2 melt congruently at 1973 K and 2063 K, respectively. They also reported a possible
miscibility gap of liquid phase near TiO2. Later on, Ismailzade et al. [40] found the fourth
compound in the system, L2T3. Fedorov et al. [41] determined that L2T3 has a perovskite-like
hexagonal crystal structure and decomposes to LT and LT2 at 1723 K. The existence of L2T3
was confirmed by German et al. [42] and Saltikova et al. [43], but not by Jonker et al. [44].
Based on previous experimental work, Ŝkapin et al. [45] reinvestigated the phase
relations and transition temperatures by XRD and scanning electron microscope (SEM) equipped
with electron probe wavelength (WDS) and energy-dispersive X-ray (EDS) analyzers. They
prepared the LT3 monocrystalline and indicated its stability between 1933 K and 1728 K.
However, the authors also pointed out that LT3 is stabilized by Ti+3
and oxygen vacancy from the
electrical resistivity and dielectric permittivity data. Based on this defect mechanism, LT3 should
be slightly away from the pseudo-binary plane of the La2O3-TiO2 system.
The L2T9 phase has an orthorhombic crystal structure measured by synchrotron X-ray
[46]. The LT2 phase has three polymorphs above room temperature under ambient condition. The
room temperature structure is monoclinic (space group: P21, Pearson symbol: mP44) [47-48]. At
13
~1053K and 1773K, it becomes orthorhombic (space group: Cmc21, Pearson symbol: oS44) [49]
and paraelectric (space group: Cmcm, Pearson symbol: oS44) [50], respectively. The enthalpy of
formation for LT2_P21 was measured in calorimetric method as around -206.0 kJ/mol-formula
[51]. For the binary oxide La2O3, three polymorphs are included in the current database, i.e.
hexagonal (space group: P-3m1, Pearson symbol: hP5) [52-53], hexagonal (space group:
P63/mmc, Pearson symbol: hP10) [53] and cubic (space group: Im-3m, Pearson symbol: cI26)
[54] with increasing temperature. On the other hand, the binary oxide TiO2 keeps a tetragonal
structure (space group: P42/mnm, Pearson symbol: tP6) [55] in the whole temperature range
under ambient pressure and in air until melting. All the ternary oxides in the La2O3-TiO2 system
are thermodynamically stable at room temperature [56].
3.3 First-principles calculations
First-principles calculations based on the density functional theory (DFT) can predict
thermodynamic properties of solid phases [31]. In the present work, the Vienna ab-initio
Simulation Package (VASP) [57] is used to calculate the total energies of oxides, with the
projector augmented wave (PAW) [58-59] method. In the pseudo-potentials used, the following
electrons are treated as valence electrons with core electrons frozen. Those valence electrons are
2s22p
4 for O, 5s
25p
65d
16s
2 for La and 2p
63d
34s
1 for Ti. Both the local density approximation
(LDA) [60] and the generalized gradient approximation (GGA) as implemented by Perdew,
Burke, and Erzhenfest [61] are used for the exchange-correlation energy functional. A plane-
wave cutoff energy of 520 eV is used, together with 12×12×7 -centered k-points for La2O3,
10×2×7 k-points for LT2_Cmc21, 5×7×3 k-points for LT2_P21, 12×8×4 k-points for LT2_Cmcm,
4×10×4 k-points for LT, 7×7×7 k-points for L2T3, 9×9×14 k-points for TiO2 for the Brilliouin-
zone integrations [62] in order to ensure the evenly arranged K-mesh and energy accuracy as 1e-4
14
eV/cell. The cell shapes and ionic positions are fully relaxed followed by the static calculations
using the linear tetrahedron method with Blöchl’s correction [63] for an accurate total energy
calculation.
In order to obtain a thermodynamic description for a specific phase at finite temperature,
the Helmholtz energy F as a function of volume V and temperature T includes additional energy
terms besides the first-principles calculated 0 K energy [38], defined as
Equation 3.1
where is the static energy at 0 K without the zero-point vibrational energy, the
vibrational contribution, and the thermal electronic contribution. At zero pressure,
the Helmholtz energy equals to the Gibbs energy. In the present work, is calculated via
first-principles directly. is obtained from the empirical Debye-Grüneisen model [38,
64] for the sake of simplicity and efficiency, and the thermal electronic contribution
is ignored due to band gaps of oxides in the system [65].
In the Debye-Grüneisen model [38], the vibrational contribution to Helmholtz energy is
described as
Equation 3.2
where is the Debye temperature, Boltzmann’s constant. The Debye function, , is
defined as follows:
Equation 3.3
15
In order to solve the equation above, the Debye temperature, , must be calculated. In
the present work, the Debye-Grüneisen approximation is used to describe as
Equation 3.4
where is a constant, viz., , the ground state volume, the atomic mass, the
Grüneisen parameter, the bulk modulus, and a parameter that scales the Debye temperature
to be discussed in detail in the section of results and discussion. The Grüneisen parameter can be
expressed as , where
is the first derivative of the bulk modulus with
respect to pressure. The temperature-dependent term, , is chosen as 2/3 for thermodynamic
properties above the Debye temperature of all the phases [64].
The equilibrium properties used in the Debye model are obtained from energy versus
volume equation of state (EOS) calculated from first-principles using at least five volumes for
each compound. A four-parameter Birch-Murnaghan EOS [66] is adopted herein to fit the energy
versus volume data points.
Equation 3.5
where the parameters a, b, c and d are fitted to the 0 K first-principles calculations of the structure
at a series of fixed volumes around the equilibrium volume.
The enthalpy of formation for compound LxTy is obtained as follows:
Equation 3.6
16
where ,
and
are the enthalpies of the ternary oxides LxTy, La2O3 and TiO2
with their stable structures at room temperature, respectively.
3.4 Thermodynamic modeling
The CALPHAD technique parameterizes Gibbs energy of individual phases as a function
of temperature and composition using thermochemical data of individual phases and phase
equilibrium data between phases. In this work, the Gibbs energy descriptions of La2O3 and TiO2
are taken from the SGTE substance (SSUB4) database [67], and the Gibbs functions of ternary
oxides and the interaction parameters of the liquid phase are evaluated.
For ternary oxides, the Gibbs energy per mole of unit formula used in the present work is
of the form:
Equation 3.7
where , , , and are model parameters determined from enthalpy of formation with
respect to La2O3 and TiO2, heat capacity, and entropy of the ternary oxide.
Gibbs energies of LT2 polymorphs are written as follows by assuming no heat capacity
of transition between different structures due to their similar crystal structure and atomic
environment:
Equation 3.8
17
where is the Gibbs energy, is the temperature, and are the transition enthalpy and
entropy between the adjacent phases of LT2. The neglected heat capacity of transition would
have little effect on the Gibbs energy since heat capacity is the second derivative of the Gibbs
energy. This approximation could make thermodynamic modeling much easier.
The two sublattice ionic liquid model [35] is used to describe the liquid phase with the
formula (La3+
, Ti4+
)P(O2-
)Q. To maintain neutrality, P and Q vary with the composition of liquid
according to the model,
Equation 3.9
The Gibbs energy of liquid per mole formula,
, is given as
Equation 3.10
where and are the site fractions of La3+
and Ti4+
in the first sublattice, respectively;
and
are the Gibbs energies of La2O3 and TiO2 in the liquid state, respectively;
and
is the excess Gibbs energy. The first two terms represent the contributions from the
components La2O3 and TiO2, and the third term represents the ideal mixing between La3+
and
Ti4+
. The excess Gibbs energy is modeled with a Redlich-Kister polynomial [68]:
Equation 3.11
where
represents the non-ideal interactions between La
3+ and Ti
4+ and is usually
defined as
18
Equation 3.12
where and
are model parameters to be evaluated.
The model parameters are evaluated using the PARROT module of the Thermo-Calc
software [30] with thermochemical data from the present work and phase equilibrium data from
the literature [45, 50, 56, 69]. It should be pointed out that the model parameters evaluated from
thermochemical data alone do not have enough accuracy to reproduce the phase equilibrium data
and need to be refined using phase equilibrium data [31].
3.5 Results and discussions
To validate the first-principles methodology, the cell volumes V, bulk moduli B0 and first
derivative of bulk moduli to pressure B’0 of binary and ternary oxides calculated in the system are
listed in Table 3. 1. to compare with available experimental data.
The volumes are underestimated by LDA while overestimated by PBE in comparison
with experimental data. The largest deviation of calculated and experimental volumes is from
La2O3, which is due to the self-interaction errors of valence electrons. The bulk moduli of TiO2
and LT2_P21 are better predicted by LDA than by PBE. Specifically, the bulk modulus of each
oxide in this system predicted by LDA is always larger than that predicted by PBE, while the first
derivative of bulk modulus predicted by LDA is generally smaller than that predicted by PBE,
which indicates that LDA gives a stiffer description of oxides than PBE does. In Figure 3. 1, the
convex hulls of ternary oxides in the La2O3-TiO2 system predicted by LDA and PBE are plotted
together. It shows that LDA gives a correct thermodynamic stability prediction of the ternary
oxides while PBE does not. One ternary oxide, L2T3 is predicted rather unstable by PBE
19
potential in this system, which contradicts to the experimental observation [56]. First-principles
results obtained by LDA are thus chosen in this work, for the CALPHAD modeling.
The parameters in the Debye-Grüneisen model come from the values in Table 3. 1. The
scaling parameter s can be derived from the Debye temperature which is obtained from phonon
density of states. For rutile TiO2 at room temperature, the scaling parameter is obtained as 0.759
based on previous experimental and calculated Debye temperatures [65, 70]. For room
temperature stable La2O3, the scaling parameter is a fit value to the entropy from experiments.
The obtained scaling parameter is 0.85 for ground state La2O3. The predicted finite temperature
properties of La2O3 and TiO2 are compared with the data from SSUB4 database [67, 71] in Figure
3. 2. It can be seen that all thermodynamic data at room temperature are well matched between
the predictions from the Debye-Grüneisen model and the SSUB4 database. For entropy, the
agreement is within the range of 10 J/mol-formula, and for enthalpy, the agreement is within the
range of 20 kJ/mol-formula. The larger discrepancy of heat capacities at high temperatures is
probably due to the anharmonic vibrations [72], which cannot be captured by the Debye-
Grüneisen model [73]. Nevertheless, the comparison shows the reasonable values of scaling
parameters chosen for La2O3 and TiO2, and the agreement of thermodynamic properties between
predictions and the literature data, particularly at room temperatures. It demonstrates that this
approach can be used to predict the thermodynamic properties of ternary oxides reasonably well,
at least at room temperature, with their high temperature properties to be further refined by phase
equilibrium data at high temperatures [31]. For the CALPHAD modeling, the thermodynamic
properties of three polymorphs of La2O3 and rutile TiO2 are taken from the SSUB4 database in
order to be compatible with other modeling in the literature involving these two oxides.
The thermodynamic model parameters of the La2O3-TiO2 system are listed in Table 3. 2.
The parameters are evaluated based on invariant reactions by Ŝkapin et al. and Nanamats et al.
[45, 50] and phase boundary data by MacChesney et al. [39] along with the finite temperature
20
thermodynamic properties from the present first-principles calculations. The calculated phase
diagram is shown in Figure 3. 3 and enlarged in Figure 3. 4 around L2T9. It is noted in Table 3. 2
that three interaction parameters for liquid phase are required to well reproduce the asymmetric
liquid phase boundary. The invariant reactions are listed in Table 3. 3, showing that both
experimental temperatures and liquid compositions are well reproduced by the present
thermodynamic models. It is noted that the liquidus boundaries in the original paper by
MacChesney et al. [39] were drawn by hand, they are treated with lower weight in the modeling
process.
The enthalpy, entropy, and heat capacity of L2T3, LT and LT2_Cmcm from the Debye-
Grüneisen model are compared with those from current thermodynamic model in Figure 3. 5. The
comparison shows an excellent agreement in enthalpy (disagreement is much less than 10 kJ/mol-
component) and entropy (disagreement is much less than 10 J/mol-component), although
discrepancies occur at the high temperature part of heat capacity, further demonstrating the
success of the Debye-Grüneisen model with the chosen scaling parameters in predicting finite
temperature thermodynamic properties of oxides. Figure 3. 6 and Figure 3. 7 show the enthalpy
and entropy of formation at 298.15 K with respect to La2O3 and TiO2 calculated by first-
principles (symbols) and the current CALPHAD modeling (curves). As shown in Figure 3. 6, the
enthalpies of formation from first-principles calculations are well re-produced comparing with the
current database. The experimental value of formation enthalpy for LT2_P21 is -68.7 kJ/mol-
component [51], comparing with our first-principles calculated value -56.0 kJ/mol-component.
The relative stability of three LT2 polymorphs is also clearly illustrated. In Figure 3. 7, the
entropies of formation predicted by the Debye-Grüneisen model are much less negative than
those from the current thermodynamic modeling evaluated from experimental phase equilibrium
data at high temperatures. The intrinsic imperfection in pseudo-potential of La and the
21
approximation of the Debye-Grüneisen model give the uncertainty of our first-principles
thermodynamic predictions. The entropy of La2O3 predicted by first-principles directly affects the
prediction of formation entropy of ternary oxides in the La2O3-TiO2 system.
3.6 Conclusions
The finite temperature thermodynamic properties for phases of interest in the La2O3-
TiO2 system are predicted by first-principles calculations together with the Debye-Grüneisen
model. The thermochemical data of binary oxides obtained in this work are reasonable and in
good agreement with the experimental data. The thermochemical data of ternary oxides in this
work ankers the thermodynamic properties of each phase. Combined with the experimental phase
equilibrium data in the literature, the thermodynamic description of the La2O3-TiO2 system is
obtained by means of the CALPHAD method with the experiments and first-principles data both
well re-produced. This work demonstrates the significance of first-principles thermochemical
data in assisting thermodynamic modeling.
The methodology demonstrated in this paper can be used in obtaining other pseudo-
binary systems. More accurate thermodynamic properties of oxides can be obtained through
phonon spectrum calculations, although it is computational consuming and can only be applied to
the ground state structures. Phonon spectrum provides a more accurate vibration property
comparing with the Debye-approximated vibrations.
22
Table 3. 1.Fitted equilibrium properties from EOS by LDA and PBE potentials at 0 K compared
with previous experimental studies, including equilibrium volume, , bulk modulus, , and first
derivative of bulk modulus with respect to pressure, , for phases in the La2O3-TiO2 system.
Phase Space group ( /atom) (GPa)
LDA PBE Exp. LDA PBE Exp. LDA PBE
La2O3 P-3m 15.54 16.63 16.54 [52] 123.84 108.73 3.48 3.73
TiO2 P42/mnm 10.13 10.73 10.4 [74] 242.07 199.49 235 [75] 4.93 5.25
LT Pnma 14.79 15.76 15.13 [76] 131.98 114.48 2.94 2.89
LT2 P21 12.17 13.11 12.64 [77] 129.69 100.27 121.0 [78] 7.28 7.58
Cmc21 12.13 13.05 13.08 [49] 150.60 106.95 4.56 6.81
Cmcm 12.28 13.13 140.02 119.79 3.55 4.42
L2T3 R-3 11.77 12.59 12.27 [79] 177.65 143.13 4.72 5.01
23
Table 3. 2.Thermodynamic parameters evaluated in the La2O3-TiO2 system (all in S. I. units).
Phases Sublattice model Evaluated descriptions
Liquid
L2T9 (La2O3)2(O2Ti1)9
LT2_Cmcm (La2O3)1(O2Ti1)2
LT2_P21 (La2O3)1(O2Ti1)2
LT2_Cmc21 (La2O3)1(O2Ti1)2
L2T3 (La2O3)2(O2Ti1)3
LT (La2O3)1(O2Ti1)1
24
Table 3. 3.Calculated and experimental reaction temperatures and compositions for the La2O3-
TiO2 system.
Reactions Temperatures (K) by
Cal.
at. % TiO2 by
Cal.
Exp. [45, 50,
69]
Liquid→Rutile+L2T9 1718 0.845 1718
Liquid+LT2_Cmc21→L2T9 1728 0.830 1728
Liquid→LT2_Cmcm 2063 0.667 2063
LT2_Cmcm→LT2_Ccmc21 1773 0.667 1773
LT2_Cmc21→LT2_P21 1053 0.667 1053
Liquid→LT2_Cmcm+LT 1947 0.551 1948
LT2_Cmcm+LT→L2T3 1872 0.6 1873
Liquid→LT 1965 0.5 1963
Liquid→LT+La2O3_S 1902 0.412 1903
25
Figure 3. 1.0 K enthalpy of formation of ternary oxides with respect to the ground state La2O3 and
TiO2 by PBE (dark red, solid line) and LDA (grey, dotted line).
26
Figure 3. 2.Finite temperature properties of hp5- La2O3 (entropy (a), enthalpy (b) and heat
capacity (c)) and tp6- TiO2 (entropy (d), enthalpy (e) and heat capacity (f)): black, dotted lines
from SSUB4 database and red, solid lines from current first-principles calculations.
27
Figure 3. 3.Calculated La2O3-TiO2 phase diagram in comparison with experimental data by
Ŝkapin et al. [45], Petrova et al. [69], Nanamats et al. [50] and MacChesney et al. [39].
28
Figure 3. 4. Enlarged La2O3-TiO2 phase diagram showing the phase relation around TiO2-rich
side with experimental data by Ŝkapin et al. [45] and MacChesney et al. [39].
29
Figure 3. 5. Finite temperature properties of LT (entropy (a), enthalpy (b) and heat capacity (c)),
L2T3 (entropy (d), enthalpy (e) and heat capacity (f)) and LT2_Cmcm (entropy (g), enthalpy (h)
and heat capacity (i)): with black, dotted lines from current database and red, solid lines from
current first-principles calculations.
30
Figure 3. 6.Enthalpy of formation from first-principles calculations (symbols) and model
parameters (curve) at 298.15 K with reference states of tP6 structure for TiO2 and hP5 structure
for La2O3.
31
Figure 3. 7.Entropy of formation from first-principles calculations (symbols) and model
parameters (curve) at 298.15 K with reference states of the tP6 structure for TiO2 and hP5
structure for La2O3.
32
Chapter 4 First-principles investigation and thermodynamic modeling of
oxygen vacancies in cubic SrCoO3-δ perovskite
4.1 Introduction
The development of CALPHAD-based thermodynamic models for complex oxide
systems has quickened in recent years, which allows the in-depth understanding of their defect
mechanism [31, 80-82]. Perovskites, in particular, are ripe for such development, featuring the
possibility of wide solid solution ranges for a multitude of dopants and large defect
concentrations. Experimental tailoring of desired properties in such a complex system would be
greatly aided by a comprehensive thermodynamic database for perovskite solid solutions.
To that end, the thermodynamic modeling of SrCoO3-δ cubic perovskite (SCO) is
presented in the current work using the CALPHAD technique [31] with the assistance from first-
principles calculations. SCO and other strontium cobaltate oxides have garnered great interest for
their unique defect properties and complex phase equilibria [83-88]. SCO has notably large
oxygen mobility, attributable to large oxygen vacancy concentrations, and is a promising dopant
in La1-xSrxCoO3-δ perovskites for use as cathodes in solid oxide fuel cells and gas separation
membranes [89]. Recently, SCO has been found to be an endmember for a perovskite solid
solution developed as one of the most effective catalysts for water splitting [25]. Sr2Co2O5
brownmillerite, the room-temperature metastable form of SCO, also exhibits many of these
properties [85, 87]. SCO is not stable at room temperature in air, decomposing instead into
Sr6Co5O15 and Co3O4 [90]. Sr6Co5O15 has also received attention for thermoelectric applications
[84, 86]. Other compounds have been reported in the Sr-Co-O ternary system [91-96] but are not
33
considered in the current work as they have not been observed to be in equilibrium with
perovskite phase and may not be stable equilibrium phase.
The CALPHAD modeling of SCO is performed using experimental data from the
literature. Phase equilibrium data between the perovskite and two neighbouring phases is used,
and first-principles calculations were employed to predict the thermochemical properties of these
two phases and defect energetic of perovskite. An appendix is also provided, detailing the
development of the SCO model functions.
4.2 Review of published data
Several studies have probed the properties of SrCoO3-δ due to varying reports of stable
structures and its importance as an endmember of several perovskite solid solutions [88, 97-101].
SCO’s oxygen nonstoichiometry has been measured by several authors. Takeda et al. [99]
measured δ in air from 473 to 1473K. They synthesized SCO samples by solid state reaction,
determining the absolute value of δ from iodometric titration. Two studies by Vashook et al. [88,
100] also used solid state reaction synthesis, using both iodometric titration and full reduction of
the samples to determine the absolute value of δ. Thermogravimetric analysis [101] and
coulometric titration [100] were used to measure the relative change in δ. In their first study
[101], δ was measured from 321 to 1370K across a range of reducing atmospheres. Their later
study [100], a narrower window of temperatures and oxygen partial pressure were explored. New
measurements were also performed by the current authors, using solid state reactions to produce
the samples, thermograviemtric analysis to measure δ, and thermal reduction to determine the
absolute value of δ. Details of these measurements can be found in forthcoming paper [82]. The
measured values can be found in Table.4. 1 by [82], with δ typically larger than 0.5 in air. For this
reason, it was shown that the point defect model, based on the dilute concentration limit, is not
34
appropriate to describe the defect mechanism of SCO, as there is now more than one type of
defect and defect-defect interactions can be significant. Through a statistical cluster analysis, the
review [82] suggests which published δ datasets are more reliable, and the results for SCO are
used in the current work.
SCO exhibits two perovskite-type structures: fully disordered cubic perovskite at high
temperatures and the brownmillerite structure with ordered oxygen vacancies below around
1275K in air [99]. A third reported structure was a rhombohedral/hexagonally distorted
perovskite, which appears below 1180 K in air, but this has been confirmed as a separate, two-
phase mixture of Sr6Co5O15 and Co3O4 [90]. Vashook et al. [88] mapped these phase
transformation temperatures at various oxygen partial pressures (PO2). They reported that the
cubic perovskite to brownmillerite transformation is second-order and brownmillerite to
Sr6Co5O15 and Co3O4 is first-order.
Stoichiometric SCO (with δ = 0) has been created by electrochemically intercalating
oxygen into Sr2Co2O5 at room temperature. Bezdika et al. [102] produced stoichiometric SCO
using a Hg/HgO reference electrode in 1M KOH under a potential of 0.598 V with respect to the
standard hydrogen electrode (SHE). Nemurdy et al. [103] also oxidized SCO with a Hg/HgO
reference in 1 M KOH, reporting the potentials for δ from 0.5 to 0 with the presence of vacancy
ordering at intermediate values of δ and a potential of 0.678 V SHE to achieve stoichiometric
SCO. Le Toquin et al. [87] performed a similar study using a Ag/AgCl reference in 1 M KOH,
also reporting intermediate vacancy ordering and stoichiometric SCO at 0.635 V SHE. The
potentials of Hg/HgO and Ag/AgCl with respect to SHE are taken to be 0.108 V [104] and 0.235
V [105], respectively. The potential of Ag/AgCl reference electrodes with respect to SHE is more
precise than that for Hg/HgO due to uncertainty in the activity coefficients at concentrated
electrolyte solutions [104]. For this reason, the potentials from Le Toquin et al. [87] are used in
the current work to describe the Gibbs energy of the perovskite with respect to brownmillerite.
35
However, only those potentials near stoichiometric SCO are used (δ < 0.15) since this is the only
region of δ where distorted cubic perovskite was observed. Recently, Ichikawa, etc. [106] have
studied the lattice stability of SrCoO3-δ by intercalating oxygen ions and taking the XRD. They
found the SCO thin film at around 200 oC would become amorphous when δ is larger than 0.5.
High-pressure studies have also examined the properties of highly oxidized SCO [99,
107-108], reaching values of δ as small as 0.05 with PO2’s as high as nearly 2000 atm. All high-
pressure samples exhibited cubic perovskite symmetry. However, to achieve such large oxygen
contents, the experiments had to be performed at low temperatures (between 473-673 K).
Therefore, this data will not be employed in the current work, preferring the electrochemical data
to describe the properties of near-stoichiometric SCO.
4.3 First-principles calculations
Spin-polarized density functional theory are performed with the Vienna Ab-initio
Simulation Package (VASP) [109]. The pseudopotentials supplied with VASP are used with the
projected augmented wave methos and the generalized gradient approximation of Perdew, Burke,
and Ernzerhof [61]. Calculations for the enthalpies of formation and equation of state employ the
GGA+U correction with Dudarev’s approach [21], which requires as input the difference (Ueff) of
the on-site Coulomb interaction energy, U, and a separate exchange interaction energy, J. The
previously determined Ueff value 3.3 for Co is used [27]. Calculations for the 0 K ground states
are carried out by relaxing all degrees of freedom.
Equation 4. 1
36
The defect structure of SrCoO3-δ is built by taking one oxygen atom out of a series of
supercells. The supercells are built based on the primitive cell of SrCoO3, which
doubles the lattice parameter of the primitive cell in [001], [010] and [100] directions. The
calculated energetic are shown in Figure 4. 7.
4.4 CALPHAD modeling
The evaluation of the model parameters was performed with the PARROT module of
ThermoCalc software [30]. In this section, the Gibbs energy functions employed for the phases in
this work are detailed. The development of their models, when applicable, will also be discussed.
The Gibbs energy functions for CoO, Co3O4, SrO and SrO2 are taken from the modelings of the
Co-O [110] and Sr-O systems [111]. No phase equilibria data or intermetallic compounds for the
Co-Sr system have been reported [112]. The description for elemental Co, Sr, and O are taken
from the SGTE SSUB4 database in ThermoCalc software [67].
The modeling of the Sr-Co-O system in the current work is limited to the perovskite
phase and those phases that are in equilibrium with the perovskite, Sr6Co5O15 and Sr2Co2O5. The
low-temperature Sr6Co5O15 phase uses the sublattice model to
describe the phase’s multivalence nature [84]. Oxygen nonstoichiometry in Sr6Co5O15 is ignored
in the sublattice model, and its Gibbs energy function is taken from previous first-principles
calculations using the GGA+U correction with Ueff=3.3 [73]. The second term of the function is
fitted to reproduce the experimental phase equilibria data between Sr2Co2O5 and Sr6Co5O15 +
Co3O4 [88].
The brownmillertite phase, Sr2Co2O5, is modeled as ,
following EELS and STEM measurements showing distinct and ions [113].
Variability in the oxygen content of brownmillerite is ignored. The last three terms of the Gibbs
37
energy function for brownmillerite are fitted using the first-principles predicted heat capacity.
The first two terms are determined by reproducing the phase equilibria data between Sr2Co2O5
and Sr6Co5O15 + Co3O4 and between Sr2Co2O5 and SCO [88].
SCO perovskite is described as . The
development of the model functions are detailed in the appendix, with five neutral compounds
referenced in the functions of the sublattice model’s endmembers, also shown as a figure in
Figure 4. 6. The first neutral compound is and its function parameters are
evaluated with the electrochemical oxidation potentials from Le Toquin et al [87]. The parameters
of the next two neutral compounds,
and
, are evaluated with the phase equilibria between Sr2Co2O5 and
SCO [88], the corrected oxygen nonstoichiometry data [82] and the first-principles defect
energetic data. The function for the last neutral compound,
, is taken from the modeling of the La1-xSrxMnO3-δ system [80], so as to be
consistent for the eventual merging of the two system models.
The experimental electrochemical potentials [87] were converted to the Gibbs energy
difference between Sr2Co2O5 and SCO through the Nernst equation:
Equation 4. 2
where is the number of electrons transferred (related to by
), F is Faraday’s constant
(96,485 C/mol), is the measured potential with respect to the reference electrode, and is the
potential of the reference electrode with respect to SHE. for Hg/HgO and Ag/AgCl are taken
to be 0.108 V [104]and 0.235 V [105], respectively. The measured potentials with respect to SHE
and the converted is shown in Figure 4. 1.
38
The parameters describing the non-ideal interactions between species within a sublattice
is defined with the Redlich-Kister polynomial [68]. Which parameters to employ was determined
by the defect mechanism responsible for charge balance when oxygen vacancies are introduced.
In the case of LaCoO3-δ, this mechanism was determined by analyzing the PO2-dependence of δ
with the point defect model [81]. Specifically, transforms into and charge
disproportionation occurs, where two transform into a and a . Although the point
defect model, in the case of Sr-doped LaCoO3-δ, was able to reveal trends in the thermochemical
properties of oxygen vacancy formation , the use of the model to deduce the defect mechanism in
SCO fails since the relationship between and is no longer linear [82]. This is
indicative of defect-defect interations due to a large defect concentration, a violation of the
assumption of the point defect model that defects are isolated from one another in a dilute
solution. Therefore, the fitted interaction parameters in SCO are assumed to be similar to
LaCoO3-δ [81], describing the nonideal mixing of oxygen ions and oxygen vacancies in the third
sublattice. Indeed, this interaction should be even stronger than that in LCO since more oxygen
vacancies are present.
4.5 Results and discussion
The first-principles calculations on the formation energy of SCO from brownmillerite and
O2 gas shows an overestimation (~80 kJ/mol-form) comparing with the experimental values
(60~65 kJ/mol-form), shown in Figure 4. 1. The reason is mainly the limitation of GGA+U
method in predicting accurate enough energy for transition metal oxide, especially when this
oxide is deficient. Another reason is the intrinsic limitation of pseudo-potentials in VASP in
calculating accurate energy for the O2 gas molecule. The evaluated model parameters can be
found in Table.4. 4. Following the relative stability issues with the Gibbs energy functions of
39
Sr6Co5O15 and Sr2Co2O5 derived from first-principles calculations shown in Table.4. 3, the
function for Sr2Co2O5 is evaluated with the first-principles and phase equilibria data. The
temperature-PO2 phase diagram for a 1:1 ratio of Sr:Co is reproduced well with the evaluated
Gibbs energy functions, shown in Figure 4. 2. To achieve this, the enthalpy of formation and
entropy at 298 K for Sr2Co2O5 and the entropy at 298 K for Sr6Co5O15 were changed from their
first-principles predicted values, as shown in Table.4. 5.
The parameters of the SCO Gibbs energy were also evaluated using the experimental
phase equilibria, reproducing the SCO- Sr2Co2O5 phase boundary. Under further reducing
conditions, all ternary phases are predicted to decompose into SrO and CoO. The model also
accurately reproduces the Gibbs energy of SCO with respect to brownmillerite at 298 K from
electrochemical oxidation, shown in Figure 4. 3 as a function of δ. It is worth noting that although
the oxygen contents of SCO and Sr2Co2O5 are different at each value of δ, their energies can be
directly compared as the excess oxygen is in the gas phase, which is taken as the reference state
in this plot. The first-principles calculations on defect energetic also support the CALPHAD
modeling predictions, shown in Figure 4. 7, where the GGA+U predict the very similar energy
profile. The SCO non-stoichiometry data is shown in Figure 4. 4 as a function of temperature and
of PO2. The model reproduces the general trend amongst the scattered data.
From the consistent fitting of the experimental data described above, the predicted defect
mechanism of the CALPHAD model for SCO is a mixture of all three cobalt valences in the
region where experimental oxygen nonstoichiometry data is available. This is shown in Figure 4.
5 as plots of the concentration of each species in the three sublattices as a function of temperature
and oxygen partial pressure. In air at 1273 K, SCO is predicted to contain about 30% . The
presence of in SCO is consistent with interpretations of XANES and XAS studies of LSCO
[114-116] and can be considered physically equivalent to electron holes. The presence of is
a consequence of the consistent modeling of the Gibbs energy data near δ=0 from the
40
electrochemical oxidation of SCO and the oxygen nonstoichiometry around δ=0.5. However, the
absolute amount of can change by an order of magnitude with the addition of more model
parameters. To fix the quantity requires more data related to the concentration of the various
cobalt valences, either from experiments or first-principles calculations. Regardless, to reproduce
the experimental oxygen nonstoichiometry behavior, the presence of was required.
4.6 Conclusion
First-principles defect calculations on SCO have been performed to give an indication on
the Gibbs curve of SCO with respect to δ. The first-principles calculated properties on Sr6Co5O15
and Sr2Co2O5 have been remodeled in the CALPHAD approach to give a correct phase stability.
A thermodynamic model has been developed for SrCoO3-δ cubic perovskite using the CALPHAD
method, as well as its neighboring phases. The defect mechanism for SCO required the presence
of to reproduce the experimental oxygen nonstoichiometry data, enabling the interpretation
of experimental observations.
41
Table.4. 1 Current experimental measurements of δ in SrCoO3- δ.
PO2 [atm] Temperature [K] δ
0.005 1223 0.4929
0.005 1273 0.5040
0.209 1223 0.4816
0.209 1273 0.4947
1 1223 0.4480
1 1273 0.4610
42
Table.4. 2 Lattice parameters, enthalpies of formation, and anti-ferromagnetic magnetic moments
of Sr2Co2O5 brownmillerite from first-principles calculations compared to experiments. Results
are shown for Sr2Co2O5 in the Pnma (62) and Ima2 (46) structures, with and without the GGA+U
correction. Experimental lattice parameters [85] are taken at 10 K from the same neutron powder-
diffraction data under the two space group settings.
a [Å] %
error
b [Å] %
error
c [Å] %
error
ΔfH [kJ/mol-
atom]
Moments
[µB]
Pnma
GGA+U
5.519 1.12 15.772 0.85 5.659 1.70 -9.098 2.90, 2.85
Pnam GGA 5.525 1.22 15.694 0.35 5.674 1.96 -5.569 2.53, 2.47
Pnma Exp. 5.458 15.639 5.564 3.21, 2.88
Ima2
GGA+U
15.888 1.60 5.658 1.68 5.474 0.29 -8.592 2.90, 2.88
Ima2 GGA 16.145 3.25 5.615 0.90 5.384 -1.35 -5.245 2.52, 2.35
Ima2 Exp. 15.6388 5.564 5.458 3.21, 2.88
43
Table.4. 3 Gibbs energy functions of Sr2Co2O5 and Sr6Co5O15 fitted to first-principles calculations
with and without GGA+U, in J/mol-form.
Phases Function
Sr2Co2O5 GGA+U -1967816+1301*T-213.7345*TlnT-0.0237988*T2+1635410*T
-1
Sr2Co2O5 GGA -1936053+1301*T-213.7345*TlnT-0.0237988*T2+1635410*T
-1
Sr6Co5O15 GGA+U -5599516+3694*T-602.2313*TlnT-0.08952871*T2+4863524*T
-1
Sr6Co5O15 GGA -5887576+3694*T-602.2313*TlnT-0.08952871*T2+4863524*T
-1
44
Table.4. 4 Gibbs energy functions for the phases modeled in the current work, in J/mol-form.
Gibbs energy functions for the pure elements and the (Va) (Va) (Va)3 SrCoO3- δ neutral
compound can be found in the database file as supplementary material.
Phases Parameter Function
SrCoO3- δ
-453305
206048
358786
Sr2Co2O5 -1744533+1112.8*T-213.7345*TlnT-
0.0237988*T2+1635410*T
-1
Sr6Co5O15 -5887997+3804*T-602.2313*TlnT-
0.08952871*T2+4863524*T
-1
45
Table.4. 5 Enthalpies of formation and entropies at 298 K of Sr2Co2O5 and Sr6Co5O15 with respect
to the elements from first-principles calculations with GGA+U and from the current CALPHAD
modeling. Note that direct comparison between the two phases is not possible as their
compositions are different.
[kJ/mol-atom] [J/mol-atom/K]
Sr6Co5O15 FP -206.90 17.35
Sr6Co5O15 CALPHAD -217.99 13.12
Sr2Co2O5 FP -210.11 18.25
Sr2Co2O5 CALPHAD -185.30 39.17
46
Figure 4. 1 (Top) Electrochemical potential from brownmillerite to SrCoO3 from Le Toquin et al.
[87] (red solid lines), Nemudry et al. [103] (blue dashed lines), and Bezdika et al. [102] (green
circles) and (Bottom) converted to Gibbs energy by Nernst equation. First-principles calculations
from the present work are given as purple triangles.
47
Figure 4. 2 PO2 vs. temperature phase diagram of Sr:Co ratio 1:1 with experimental phase
boundary data from Vashook et al. [88] (circles and triangles), Takeda et al. [99] (diamond), and
Rodriguez et al. [97] (square).
48
Figure 4. 3 Gibbs energy of SCO as a function of δ from CALPHAD at 298 K with experimental
data (triangles) [87]. The units are in kJ/mol-form for SrCoO3- δ. The reference state for the top
figure is 3.25 moles of brownmillerite at corresponding temperature and ambient pressure.
49
Figure 4. 4 Temperature and PO2-dependence of δ, top and bottom, respectively, calculated from
model parameters in the current work and compared to experiments [82, 99-101]. Numbers in the
legends refer to fixed PO2 for the top figure and temperature for the bottom figure.
50
Figure 4. 5 Site occupancies of the SCO sublattice model as a function of temperature in air (top)
and PO2 at 1273 K (bottom). 1for Sr+2
, 2 for Va in A-site, 3 for Co+2
, 4 for Co+3
, 5 for Co+4
, 6 for
Va in B-site, 7 for O-2
, 8 for Va in oxygen site.
51
Figure 4. 6 Schematic projection of the composition space of the
sublattice model and the plane defining possible
electrically neutral compositions. Red points correspond to the neutral compounds chosen for the
current work.
52
Figure 4. 7 The formation enthalpy of defect SCO with respect to O2 and brownmillerite at 0 K,
obtained from the defect energy calculations. The y axis is the formation enthalpy in eV/formula
SCO, x axis is the δ.
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Form
atio
n e
nth
alp
y (e
V)
δ in SrCoO3-δ
Defect energetic by PBE
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
Form
atio
n e
nth
alp
y (e
V)
δ in SrCoO3-δ
Defect energetic by PBE+U
Chapter 5 Conclusions and future work
5.1 Conclusions
The CALPHAD approach has been approved effective and advantageous in predicting
the thermodynamic properties and phase stabilities of oxide systems in a consistent manner. The
prediction is based on a rational modeling of all the experimental and calculated data. The
modeled oxide system La2O3-TiO2 contains interesting dielectric phases. The phase
transformation and thermodynamic properties are recorded in our current database, as a useful
reference for future manufacturing or investigation. SrCoO3-δ is well known for its high ionic and
electronic conductivity, promising as a dope material to LaCoO3-δ for ion transport membrane,
cathode of solid oxide fuel cell, etc. The constructed database can well capture the oxygen
vacancy concentrations as a function of temperature and partial pressure of oxygen gas. The
database can be used to further predict the defect behavior and phase stability of Sr-doped
LaCoO3-δ under service conditions.
5.2 Future work
The future work can be carried out on the following directions:
The robustness of Debye model with scaling parameter as 1 in predicting the
thermodynamic properties of oxides can be validated by phonon calculations.
Test the phase stability and oxygen defect concentration of LaSrCoO3-δ database
under service conditions.
54
Continue on another system, SrTiO Ruddlesden-Popper series.
Phonon calculations on SrTiO Ruddlesden-Popper series is needed to investigate
the lattice dynamics.
Deformation charge density can be utilized to study the bond property in SrTiO
inter-layers.
The dielectric permittivity of unstable lattice is going to be further investigated.
Appendix A
SrCoO3-δ perovskite sublattice model
In this appendix, the construction of the sublattice model and related Gibbs energy
functions for SCO perovskite is detailed. The model is constructed in a manner similar to those
for the La1-xSrxMnO3-δ (LSMO) [80] and LaCoO3-δ (LCO) [81] systems for the possible merging
of all three databases. The SCO sublattice model is:
.
Despite the lack of cation vacancies in experimental observations, they are include in the
model for consistency with LSMO. With this sublattice model, the Gibbs energies of 16
endmembers must be defined, each with at least two model parameters, the enthalpies and
entropies of formation ( and , respectively), which are evaluated from experimental and
first-principles data. However, by enforcing charge neutrality conditions, the number of model
parameters is greatly reduced by defining only the Gibbs energies of neutral compounds and
describing the Gibbs energies of non-neutral endmembers with these neutral compounds via
reciprocal relations. This requires a system of 16 independent equations to describe the 16
endmembers. To minimize the number of model parameters, the number of neutral compounds
must be minimized. At most, ten independent reciprocal relations can be defined after imposing
charge and mass balance, as determined by the current sublattice model. An arbitrary reference
energy is chosen as well, providing another equation. Therefore, at least five neutral compounds
must be selected to provide the necessary 16 equations.
The composition space of the SCO sublattice model can be visualized as a cube, where
each edge corresponds to the occupation of a sublattice, as shown in Figure 4. 6. The three
character labels refer to the constituent each sublattice (i.e. S3V corresponds to
56
). It should be noted that not all compositions within the sublattice model are
shown in this cube, specifically certain compositions with more than one species in the second
sublattice, such as
. To show all possible compositions would
require a separate axis for mixing between energy species in the second sublattice, resulting in an
8-dimensional figure. Therefore, a simplified schematic of the composition space is shown in for
visualization purposes only. All 16 endmembers are found along the edges of the cube, where
each sublattice is occupied by only one species. Not every point in this composition space
satisfies charge neutrality. The compositions that are neutral, and physically capable of existing
by themselves, lie on a plane through the composition space, also shown in, which again is a
projection of a multi-dimensional hyper surface. Many endmembers lie outside this plane and are
not neutral. Indeed, only two endmembers are neutral, stoichiometric SrCoO3(S4O) and VVV.
Other neutral stoichiometric compounds can be defined, by introducing mixing between
oxygen and vacancies in the third sublattice. In this way, six more independent neutral
compounds can be generated: two with Sr and Co present
and
; three with Sr vacancies
,
, and
; and the last with Co vancacy
. Of these six, three must be chosen to complement the two neutral
endmembers.
and
are natural
choices since these compositions are closest to what is described by the experimental data. The
choice of the last compound is arbitrary since those endmembers that depend on the last neutral
compound will have their functions defined by the LCO and LSMO modelings, discussed later in
the appendix. For the purposes of the following discussion, the
compound is chosen. The Gibbs energy functions of the five neutral compounds are defined as:
57
Equation A. 1
Equation A. 2
Equation A. 3
Equation A. 4
where , and are the Gibbs energies of elemental strontium, cobalt, and oxygen,
respectively, taken from the SGTE SSUB4 database. and
are the enthalpy and entropy
of formation of compound , respectively, and T is the temperature. The final neutral compound
Gibbs energy function, is taken from the modeling of the LSMO system, described
in more detail later.
Although the 16 endmembers would have involved 32 model parameters ( and
for each endmember), the current choice of the five neutral compounds has only eight model
parameters (VVV has none as it is taken from a previous modeling without modification). The
Gibbs energies of the 16 endmembers (defined herein as GXXX where XXX is the endmember
designation, e.g. GV4O) are written in terms of the Gibbs energies of the five neutral compounds
by devising a system of 16 equations that relate the endmembers to the neutral compounds. First
there are two endmembers that are neutral compounds:
Equation A. 5
Equation A. 6
Next are three equations describing the remaining neutral compounds as ideal mixtures of
endmembers:
Equation A. 7
Equation A. 8
Equation A. 9
58
where R is the gas constant. Another equation is the choice of an arbitrary reference. In this case,
it is the assumption that VVO is equivalent to VVV plus oxygen gas:
Equation A. 10
The last ten equations consist of reciprocal relations describing charge neutral reactions between
the remaining endmembers that haven’t been included in the previous six equations:
Equation A. 11
Equation A. 12
Equation A. 13
Equation A. 14
Equation A. 15
Equation A. 16
Equation A. 17
Equation A. 18
Equation A. 19
Equation A. 20
where is the Gibbs energy of reciprocal relation j. The value of all ten are assumed to
be zero as they involve endmembers that are far from the neutral plane. By solving this system of
equations, the Gibbs energies of the 16 endmembers can be written in terms of the Gibbs energies
of the five neutral compounds. The resulting endmember functions can be found in the database
file included online as supplementary material.
To combine the LCO and SCO models into LSCO and then eventually combine LSCO
with LSMO, certain considerations of the LCO and SCO models must be made. The construction
of the sublattice model, described above, is the first ,where cation vacancies have been included.
The second consideration is to ensure that the endmembers that are common across systems have
59
the same Gibbs energy functions. For instance, the VVO and VVV endmembers are present in all
three systems. The functions for these two endmembers are taken from the LSMO modeling since
it has already been completed. Between LCO and LSMO , the LVO and LVV endmembers
overlap and their energies are taken from LSMO. Between LCO and SCO, the common
endmembers are V2O, V3O, V4O, V2V, V3V, and V4V and their Gibbs energy functions are
taken from LCO. With this consideration, the SCO system is dependent on functions from the
LCO system. Lastly, the SVO and SVV endmembers are found in both LSMO and SCO and their
Gibbs energy functions are taken from LSMO, making the choice of the last neutral compound
for SCO arbitrary (as discussed above) since all endmember functions that depend on it have been
taken from other sources.
This borrowing of endmember functions leads to counter-intuitive behavior, where now
the energy of SCO perovskite is dependent on the Gibbs energy of unrelated elements, in this
case Mn and La. Indeed, the inter-dependence of all the endmember Gibbs energy functions is an
issue with the current sublattice model approach, particularly with ionic systems, where
developing models for new systems requires explicitly considering the higher-order systems that
may be later developed. The inverse pyramid problem that currently exists within the extensive
CALPHAD databases that have been developed for metallic alloy systems is much more
pronounced for ionic solid solutions, where functions from other systems must be incorporated in
the development of the subsystem.
60
Appendix B
La2O3-TiO2 Thermo-Calc database
$ Database file written 2012- 9-19
$ From database: User data 2012. 8.16
ELEMENT /- ELECTRON_GAS 0.0000E+00 0.0000E+00 0.0000E+00!
ELEMENT VA VACUUM 0.0000E+00 0.0000E+00 0.0000E+00!
ELEMENT LA DHCP 1.3891E+02 0.0000E+00 0.0000E+00!
ELEMENT O 1/2_MOLE_O2(GAS) 1.5999E+01 4.3410E+03 1.0252E+02!
ELEMENT TI HCP_A3 4.7880E+01 4.8100E+03 3.0648E+01!
SPECIES LA+3 LA1/+3!
SPECIES LA1O1 LA1O1!
SPECIES LA2O1 LA2O1!
SPECIES LA2O2 LA2O2!
SPECIES LA2O3 LA2O3!
SPECIES O-2 O1/-2!
SPECIES O1TI1 O1TI1!
SPECIES O2 O2!
SPECIES O2TI1 O2TI1!
SPECIES O3 O3!
SPECIES O3TI2 O3TI2!
SPECIES O5TI3 O5TI3!
SPECIES O7TI4 O7TI4!
SPECIES TI+4 TI1/+4!
SPECIES TI2 TI2!
SPECIES TIO2 O2TI1!
FUNCTION F12306T 2.98150E+02 +418123.955-30.3347885*T-22.06299*T*LN(T)
-.005444405*T**2+4.71447833E-07*T**3+102710.1*T**(-1); 6.00000E+02 Y
+422478.905-85.4786167*T-13.83676*T*LN(T)-.011938995*T**2
+1.33826017E-06*T**3-312130.2*T**(-1); 1.30000E+03 Y
+400310.17+114.016724*T-42.00406*T*LN(T)+.0037094435*T**2
-2.70261E-07*T**3+2891891*T**(-1); 3.20000E+03 Y
+493601.747-246.085237*T+2.791973*T*LN(T)-.006002155*T**2
+1.30043383E-07*T**3-34158815*T**(-1); 8.20000E+03 Y
-96493.044+773.338363*T-111.0188*T*LN(T)+.0037862445*T**2
-2.82257667E-08*T**3+5.418475E+08*T**(-1); 1.00000E+04 N !
FUNCTION F12329T 2.98150E+02 -124719.967-24.5469489*T-31.53764*T*LN(T)
-.0051956*T**2+7.60442333E-07*T**3+103677.85*T**(-1); 9.00000E+02 Y
-126335.849+7.93847572*T-36.65559*T*LN(T)+2.4937065E-04*T**2
-2.05688333E-07*T**3+108868.35*T**(-1); 2.50000E+03 Y
-130958.323-23.9414483*T-31.58251*T*LN(T)-.003177688*T**2
+6.84986667E-08*T**3+5676870*T**(-1); 5.40000E+03 Y
-32341.6729-213.786313*T-10.21743*T*LN(T)-.005021225*T**2
+9.162985E-08*T**3-74562000*T**(-1); 1.00000E+04 N !
FUNCTION F12355T 2.98150E+02 -22020.3276+46.9195451*T-51.12563*T*LN(T)
61
-.005701935*T**2+8.637425E-07*T**3+212452.95*T**(-1); 1.00000E+03 Y
-25871.5823+93.9280348*T-58.13034*T*LN(T)-1.332372E-05*T**2
+4.41584333E-10*T**3+616730*T**(-1); 6.00000E+03 N !
FUNCTION F12359T 2.98150E+02 -611505.065+54.8487779*T-51.72813*T*LN(T)
-.028452875*T**2+4.99643833E-06*T**3+271002.95*T**(-1); 7.00000E+02 Y
-626470.385+256.452172*T-82.32033*T*LN(T)-1.8245965E-04*T**2
+6.891315E-09*T**3+1664162*T**(-1); 5.10000E+03 Y
-641095.137+293.838139*T-86.72291*T*LN(T)+4.319301E-04*T**2
-9.75906E-09*T**3+11187120*T**(-1); 6.00000E+03 N !
FUNCTION F13634T 2.98150E+02 +243206.494-20.8612587*T-21.01555*T*LN(T)
+1.2687055E-04*T**2-1.23131283E-08*T**3-42897.09*T**(-1); 2.95000E+03
Y
+252301.423-52.0847285*T-17.21188*T*LN(T)-5.413565E-04*T**2
+7.64520667E-09*T**3-3973170.5*T**(-1); 6.00000E+03 N !
FUNCTION F13856T 2.98150E+02 +45279.4548-44.8816804*T-27.20855*T*LN(T)
-.01130768*T**2+2.093465E-06*T**3+15817.82*T**(-1); 8.00000E+02 Y
+38441.7464+44.9717327*T-40.8145*T*LN(T)+.001204741*T**2
-1.26287067E-07*T**3+690966.5*T**(-1); 2.60000E+03 Y
+78758.7743-116.513547*T-20.67482*T*LN(T)-.0031585015*T**2
+4.49507333E-08*T**3-14168070*T**(-1); 4.30000E+03 Y
+107274.033-220.711751*T-7.872196*T*LN(T)-.00560405*T**2
+1.29955033E-07*T**3-25273450*T**(-1); 6.00000E+03 N !
FUNCTION F14003T 2.98150E+02 -6960.69252-51.1831473*T-22.25862*T*LN(T)
-.01023867*T**2+1.339947E-06*T**3-76749.55*T**(-1); 9.00000E+02 Y
-13136.0172+24.743296*T-33.55726*T*LN(T)-.0012348985*T**2
+1.66943333E-08*T**3+539886*T**(-1); 3.70000E+03 Y
+14154.6461-51.4854586*T-24.47978*T*LN(T)-.002634759*T**2
+6.01544333E-08*T**3-15120935*T**(-1); 9.60000E+03 Y
-314316.628+515.068037*T-87.56143*T*LN(T)+.0025787245*T**2
-1.878765E-08*T**3+2.9052515E+08*T**(-1); 1.85000E+04 Y
-108797.175+288.483019*T-63.737*T*LN(T)+.0014375*T**2-9E-09*T**3
+.25153895*T**(-1); 2.00000E+04 N !
FUNCTION F14219T 2.98150E+02 -317236.334-34.3402551*T-31.38*T*LN(T)
-.02810811*T**2+5.84100333E-06*T**3+38666.435*T**(-1); 6.00000E+02 Y
-326946.95+118.875262*T-55.31666*T*LN(T)-.0013442355*T**2
+1.16887017E-07*T**3+791905.5*T**(-1); 1.80000E+03 Y
-335731.446+173.77285*T-62.65958*T*LN(T)+.001471994*T**2
-9.15459167E-08*T**3+2826501*T**(-1); 3.90000E+03 Y
-257501.28-63.8977089*T-34.08998*T*LN(T)-.0031802585*T**2
+5.10434E-08*T**3-37446800*T**(-1); 6.00000E+03 N !
FUNCTION F14300T 2.98150E+02 +130696.944-37.9096651*T-27.58118*T*LN(T)
-.02763076*T**2+4.60539333E-06*T**3+99530.45*T**(-1); 7.00000E+02 Y
+114760.623+176.626736*T-60.10286*T*LN(T)+.00206456*T**2
-5.17486667E-07*T**3+1572175*T**(-1); 1.30000E+03 Y
+49468.3958+710.094819*T-134.3696*T*LN(T)+.039707355*T**2
-4.10457667E-06*T**3+12362250*T**(-1); 2.10000E+03 Y
+866367.075-3566.80563*T+421.2001*T*LN(T)-.1284109*T**2
+5.44768833E-06*T**3-2.1304835E+08*T**(-1); 2.80000E+03 Y
+409416.384-1950.70834*T+223.4437*T*LN(T)-.0922361*T**2
62
+4.306855E-06*T**3-21589870*T**(-1); 3.50000E+03 Y
-1866338.6+6101.13383*T-764.8435*T*LN(T)+.09852775*T**2
-2.59784667E-06*T**3+9.610855E+08*T**(-1); 4.90000E+03 Y
+97590.0432+890.79836*T-149.9608*T*LN(T)+.01283575*T**2
-3.555105E-07*T**3-2.1699975E+08*T**(-1); 6.00000E+03 N !
FUNCTION F15809T 2.98150E+02 +467609.96-25.7916835*T-23.45359*T*LN(T)
+.0026178525*T**2-4.83678833E-07*T**3-101456.95*T**(-1); 1.80000E+03 Y
+492971.637-184.379175*T-2.247876*T*LN(T)-.005476885*T**2
+1.10024367E-07*T**3-5945505*T**(-1); 4.50000E+03 Y
+364869.208+112.534909*T-36.55164*T*LN(T)-.0016270125*T**2
+3.69943667E-08*T**3+80422300*T**(-1); 1.00000E+04 N !
FUNCTION F15814T 2.98150E+02 +804579.989-13.3244359*T-33.852*T*LN(T)
-.01680915*T**2+4.05913E-06*T**3+159805*T**(-1); 6.00000E+02 Y
+797116.458+109.508534*T-53.131*T*LN(T)+.00501905*T**2-5.1425E-07*T**3
+693380*T**(-1); 1.50000E+03 Y
+796667.915+69.7367642*T-46.792*T*LN(T)-6.3645E-04*T**2
+1.78673333E-07*T**3+2125430*T**(-1); 3.20000E+03 Y
+779355.318+192.57083*T-63.044*T*LN(T)+.00452695*T**2
-9.56883333E-08*T**3+2443585*T**(-1); 6.00000E+03 N !
FUNCTION F14217T 2.98150E+02 -960529.837+452.615001*T-73.60493*T*LN(T)
-5.417235E-04*T**2+2.30475667E-10*T**3+820566*T**(-1); 2.50000E+03 N !
FUNCTION F12364T 2.98150E+02 -1835600.03+674.720454*T-118*T*LN(T)
-.008*T**2+620000*T**(-1); 2.31300E+03 Y
-1835600.03+674.720454*T-118*T*LN(T)-.008*T**2+620000*T**(-1);
2.38300E+03 Y
-1835600.03+674.720454*T-118*T*LN(T)-.008*T**2+620000*T**(-1);
2.58600E+03 Y
-1993673.35+1359.59688*T-200*T*LN(T); 3.50000E+03 N !
FUNCTION F12294T 2.98150E+02 -7968.40253+120.285004*T-26.34*T*LN(T)
-.0012951655*T**2; 5.50000E+02 Y
-6473.78487+90.540705*T-21.79186*T*LN(T)-.004045175*T**2
-5.25864667E-07*T**3; 1.13400E+03 Y
-19863.1881+221.907689*T-39.5388*T*LN(T); 1.19300E+03 Y
-13623.7981+179.627185*T-34.3088*T*LN(T); 4.00000E+03 N !
FUNCTION F13862T 2.98150E+02 -555240.766+255.476941*T-41.99481*T*LN(T)
-.008897925*T**2+1.09704483E-08*T**3+327015.15*T**(-1); 2.50000E+03 N
!
FUNCTION F13864T 2.98150E+02 -553995.486+252.337175*T-42.02033*T*LN(T)
-.00887556*T**2+8.50398E-09*T**3+327636.5*T**(-1); 2.50000E+03 N !
FUNCTION F14385T 2.98150E+02 -1538355.76+186.17228*T-30.39341*T*LN(T)
-.0999589*T**2-5.93279333E-06*T**3-117799.05*T**(-1); 4.70000E+02 Y
-1581243.08+940.165431*T-147.6739*T*LN(T)-.001737113*T**2
-1.5338335E-10*T**3+2395423.5*T**(-1); 2.11500E+03 Y
-1590717.7+1012.14848*T-156.9*T*LN(T); 3.50000E+03 N !
FUNCTION F14558T 2.98150E+02 -2480155.81-145.108389*T+36.566*T*LN(T)
-.45188165*T**2+1.48742467E-04*T**3-55595*T**(-1); 4.50000E+02 Y
-2509088.54+951.683781*T-158.99*T*LN(T)-.0251054*T**2+1.65E-10*T**3
-145*T**(-1); 2.05000E+03 Y
-2626597.38+1787.09774*T-267.776*T*LN(T); 4.00000E+03 N !
63
FUNCTION F14623T 2.98150E+02 -3459640.85+637.993041*T-103.0247*T*LN(T)
-.26368195*T**2+6.825275E-05*T**3+682992*T**(-1); 5.00000E+02 Y
-3510274.22+1643.59334*T-267.0379*T*LN(T)-.02467493*T**2
+2.37708333E-06*T**3+3660393.5*T**(-1); 1.00000E+03 Y
-3523423.82+1791.6491*T-288.7985*T*LN(T)-.008510485*T**2
+1.118704E-07*T**3+5171905*T**(-1); 1.95000E+03 Y
-3642234.52+2439.21992*T-368.192*T*LN(T); 4.00000E+03 N !
FUNCTION F14225T 2.98150E+02 -966837.628+381.983612*T-63.19571*T*LN(T)
-.005910235*T**2+3.25307833E-11*T**3+517357*T**(-1); 2.18500E+03 Y
-1018565.33+675.854121*T-100*T*LN(T); 5.00000E+03 N !
FUNCTION F15795T 2.98150E+02 -8059.92077+133.615208*T-23.9933*T*LN(T)
-.004777975*T**2+1.06715833E-07*T**3+72636*T**(-1); 9.00000E+02 Y
-7811.81451+132.988068*T-23.9887*T*LN(T)-.0042033*T**2
-9.08763333E-08*T**3+42680*T**(-1); 1.15500E+03 Y
+2497.40918+108.976786*T-22.3771*T*LN(T)+.00121707*T**2
-8.4534E-07*T**3-2002750*T**(-1); 1.94100E+03 Y
-38203.0419+309.635108*T-46.29*T*LN(T); 4.00000E+03 N !
FUNCTION F14226T 2.98150E+02 -966837.628+381.983612*T-63.19571*T*LN(T)
-.005910235*T**2+3.25307833E-11*T**3+517357*T**(-1)-966837.628
+381.983612*T-63.19571*T*LN(T)-.005910235*T**2+3.25307833E-11*T**3
+517357*T**(-1); 2.18500E+03 Y
-1018565.33+675.854121*T-100*T*LN(T)-1018565.33+675.854121*T
-100*T*LN(T); 5.00000E+03 N !
FUNCTION UN_ASS 298.15 0; 300 N !
TYPE_DEFINITION % SEQ *!
DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
DEFAULT_COMMAND DEF_SYS_ELEMENT VA /- !
PHASE GAS:G % 1 1.0 !
CONSTITUENT GAS:G :LA,LA1O1,LA2O1,LA2O2,O,O1TI1,O2,O2TI1,O3,TI,TI2 : !
PARAMETER G(GAS,LA;0) 2.98150E+02 +F12306T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF1 !
PARAMETER G(GAS,LA1O1;0) 2.98150E+02 +F12329T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF23 !
PARAMETER G(GAS,LA2O1;0) 2.98150E+02 +F12355T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF45 !
PARAMETER G(GAS,LA2O2;0) 2.98150E+02 +F12359T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF67 !
PARAMETER G(GAS,O;0) 2.98150E+02 +F13634T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF89 !
PARAMETER G(GAS,O1TI1;0) 2.98150E+02 +F13856T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF100 !
PARAMETER G(GAS,O2;0) 2.98150E+02 +F14003T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF115 !
PARAMETER G(GAS,O2TI1;0) 2.98150E+02 +F14219T#+R#*T*LN(1E-05*P);
64
6.00000E+03 N REF123 !
PARAMETER G(GAS,O3;0) 2.98150E+02 +F14300T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF139 !
PARAMETER G(GAS,TI;0) 2.98150E+02 +F15809T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF146 !
PARAMETER G(GAS,TI2;0) 2.98150E+02 +F15814T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF153 !
PHASE LIQUID:Y % 2 2 4 !
CONSTITUENT LIQUID:Y :LA+3,TI+4 : O-2 : !
PARAMETER G(LIQUID,LA+3:O-2;0) 2.98150E+02 +F12364T#+182569.7
-74.6752579*T; 6.00000E+03 N REF0 !
PARAMETER G(LIQUID,TI+4:O-2;0) 2.98150E+02 +F14226T#+136000-62.242563*T;
6.00000E+03 N REF0 !
PARAMETER G(LIQUID,LA+3,TI+4:O-2;0) 2.98150E+02 -7.34863500E+05
+2.87790675E+02*T;
6.00000E+03 N REF0 !
PARAMETER G(LIQUID,LA+3,TI+4:O-2;1) 2.98150E+02 -8.30032818E+04
+9.19776824E+00*T;
6.00000E+03 N REF0 !
PARAMETER G(LIQUID,LA+3,TI+4:O-2;2) 2.98150E+02 -2.91222006E+05
+1.07217594E+02*T;
6.00000E+03 N REF0 !
PHASE ANATASE % 1 1.0 !
CONSTITUENT ANATASE :O2TI1 : !
PARAMETER G(ANATASE,O2TI1;0) 2.98150E+02 +F14217T#; 6.00000E+03 N
REF164 !
PHASE L2T3 % 2 2 3 !
CONSTITUENT L2T3 :LA2O3 : O2TI1 : !
PARAMETER G(L2T3,LA2O3:O2TI1;0) 2.98150E+02 -6.8647224E+06+
2.7640084E+03*T-4.5257611E+02*T*LN(T)
-2.6907898E-02*T**2+4.2219633E+06*T**(-1); 1.90000E+03 N REF0 !
PHASE L2T9 % 2 2 9 !
CONSTITUENT L2T9 :LA2O3 : O2TI1 : !
PARAMETER G(L2T9,LA2O3:O2TI1;0) 2.98150E+02 +2*F12364T#+9*F14225T#
-3.7075262E+05
+1.0135978E+02*T; 6.00000E+03 N REF0 !
65
PHASE LA2O3_L % 1 1.0 !
CONSTITUENT LA2O3_L :LA2O3 : !
PARAMETER G(LA2O3_L,LA2O3;0) 2.98150E+02 +F12364T#+182569.7
-74.6752579*T; 6.00000E+03 N REF177 !
PHASE LA2O3_S % 1 1.0 !
CONSTITUENT LA2O3_S :LA2O3 : !
PARAMETER G(LA2O3_S,LA2O3;0) 2.98150E+02 +F12364T#; 6.00000E+03 N
REF177 !
PHASE LA2O3_S2 % 1 1.0 !
CONSTITUENT LA2O3_S2 :LA2O3 : !
PARAMETER G(LA2O3_S2,LA2O3;0) 2.98150E+02 +F12364T#+46000-19.8875919*T;
6.00000E+03 N REF177 !
PHASE LA2O3_S3 % 1 1.0 !
CONSTITUENT LA2O3_S3 :LA2O3 : !
PARAMETER G(LA2O3_S3,LA2O3;0) 2.98150E+02 +F12364T#+106000-45.0659385*T;
6.00000E+03 N REF177 !
PHASE LA_L % 1 1.0 !
CONSTITUENT LA_L :LA : !
PARAMETER G(LA_L,LA;0) 2.98150E+02 +F12294T#+9681.8-8.60833593*T;
6.00000E+03 N REF192 !
PHASE LA_S % 1 1.0 !
CONSTITUENT LA_S :LA : !
PARAMETER G(LA_S,LA;0) 2.98150E+02 +F12294T#; 6.00000E+03 N REF192 !
PHASE LA_S2 % 1 1.0 !
CONSTITUENT LA_S2 :LA : !
PARAMETER G(LA_S2,LA;0) 2.98150E+02 +F12294T#+364-.661818182*T;
6.00000E+03 N REF192 !
66
PHASE LA_S3 % 1 1.0 !
CONSTITUENT LA_S3 :LA : !
PARAMETER G(LA_S3,LA;0) 2.98150E+02 +F12294T#+3485.3-3.41428732*T;
6.00000E+03 N REF192 !
PHASE LT % 2 1 1 !
CONSTITUENT LT :LA2O3 : O2TI1 : !
PARAMETER G(LT,LA2O3:O2TI1;0) 2.98150E+02 -2.9123858E+06+1.2461710E+03*T
-2.0568196E+02*T*LN(T)
-1.7808189E-03*T**2+2.1759025E+06*T**(-1); 6.00000E+03 N REF0 !
PHASE LT2CMC21 % 2 1 2 !
CONSTITUENT LT2CMC21 :LA2O3 : O2TI1 : !
PARAMETER G(LT2CMC21,LA2O3:O2TI1;0) 2.98150E+02 -3.9241707E+06
+1.6465507E+03*T-2.7051041E+02*T*LN(T)-6.8867511E-03*T**2
+2.1807586E+06*T**(-1)-1.7292000E+04
+9.7529611E+00*T; 6.00000E+03 N REF0 !
PHASE LT2CMCM % 2 1 2 !
CONSTITUENT LT2CMCM :LA2O3 : O2TI1 : !
PARAMETER G(LT2CMCM,LA2O3:O2TI1;0) 2.98150E+02 -3.9241707E+06
+1.6465507E+03*T-2.7051041E+02*T*LN(T)
-6.8867511E-03*T**2+2.1807586E+06*T**(-1);
6.00000E+03 N REF0 !
PHASE LT2P21 % 2 1 2 !
CONSTITUENT LT2P21 :LA2O3 : O2TI1 : !
PARAMETER G(LT2P21,LA2O3:O2TI1;0) 2.98150E+02 -3.9241707E+06
+1.6465507E+03*T-2.7051041E+02*T*LN(T)
-6.8867511E-03*T**2+2.1807586E+06*T**(-1)
-2.3167279E+04+1.5332523E+01*T; 6.00000E+03 N REF0 !
PHASE O1TI1_ALPHA % 1 1.0 !
CONSTITUENT O1TI1_ALPHA :O1TI1 : !
PARAMETER G(O1TI1_ALPHA,O1TI1;0) 2.98150E+02 +F13862T#; 6.00000E+03
N REF0 !
67
PHASE O1TI1_BETA % 1 1.0 !
CONSTITUENT O1TI1_BETA :O1TI1 : !
PARAMETER G(O1TI1_BETA,O1TI1;0) 2.98150E+02 +F13864T#; 6.00000E+03
N REF0 !
PHASE O3TI2_L % 1 1.0 !
CONSTITUENT O3TI2_L :O3TI2 : !
PARAMETER G(O3TI2_L,O3TI2;0) 2.98150E+02 +F14385T#+105738-51.8775414*T;
6.00000E+03 N REF0 !
PHASE O3TI2_S % 1 1.0 !
CONSTITUENT O3TI2_S :O3TI2 : !
PARAMETER G(O3TI2_S,O3TI2;0) 2.98150E+02 +F14385T#; 6.00000E+03 N
REF0 !
PHASE O3TI2_S2 % 1 1.0 !
CONSTITUENT O3TI2_S2 :O3TI2 : !
PARAMETER G(O3TI2_S2,O3TI2;0) 2.98150E+02 +F14385T#+1138-2.4212766*T;
6.00000E+03 N REF0 !
PHASE O5TI3_L % 1 1.0 !
CONSTITUENT O5TI3_L :O5TI3 : !
PARAMETER G(O5TI3_L,O5TI3;0) 2.98150E+02 +F14558T#+184807-113.153333*T;
6.00000E+03 N REF0 !
PHASE O5TI3_S % 1 1.0 !
CONSTITUENT O5TI3_S :O5TI3 : !
PARAMETER G(O5TI3_S,O5TI3;0) 2.98150E+02 +F14558T#; 6.00000E+03 N
REF0 !
PHASE O5TI3_S2 % 1 1.0 !
CONSTITUENT O5TI3_S2 :O5TI3 : !
PARAMETER G(O5TI3_S2,O5TI3;0) 2.98150E+02 +F14558T#+13263-29.4733333*T;
6.00000E+03 N REF0 !
68
PHASE O7TI4_L % 1 1.0 !
CONSTITUENT O7TI4_L :O7TI4 : !
PARAMETER G(O7TI4_L,O7TI4;0) 2.98150E+02 +F14623T#+225936-115.864615*T;
6.00000E+03 N REF0 !
PHASE O7TI4_S % 1 1.0 !
CONSTITUENT O7TI4_S :O7TI4 : !
PARAMETER G(O7TI4_S,O7TI4;0) 2.98150E+02 +F14623T#; 6.00000E+03 N
REF0 !
PHASE RUTILE % 1 1.0 !
CONSTITUENT RUTILE :O2TI1 : !
PARAMETER G(RUTILE,O2TI1;0) 2.98150E+02 +F14225T#; 6.00000E+03 N
REF0 !
PHASE RUTILE_L % 1 1.0 !
CONSTITUENT RUTILE_L :O2TI1 : !
PARAMETER G(RUTILE_L,O2TI1;0) 2.98150E+02 +F14225T#+68000-31.1212815*T;
6.00000E+03 N REF0 !
PHASE TI_L % 1 1.0 !
CONSTITUENT TI_L :TI : !
PARAMETER G(TI_L,TI;0) 2.98150E+02 +F15795T#+18316-10.8983855*T;
6.00000E+03 N REF0 !
PHASE TI_S % 1 1.0 !
CONSTITUENT TI_S :TI : !
PARAMETER G(TI_S,TI;0) 2.98150E+02 +F15795T#; 6.00000E+03 N REF0 !
PHASE TI_S2 % 1 1.0 !
CONSTITUENT TI_S2 :TI : !
PARAMETER G(TI_S2,TI;0) 2.98150E+02 +F15795T#+4170-3.61038961*T;
6.00000E+03 N REF0 !
LIST_OF_REFERENCES
NUMBER SOURCE
69
REF7114 LA1<G> T.C.R.A.S. Class: 1
H_form changed according to Heyrman et al Calphad 28 (2004)
49-63 (C. Younes, PhD Paris Sud 1986)
REF7125 LA1O1<G> T.C.R.A.S. Class: 2
H_form changed according to Heyrman et al Calphad 28 (2004)
49-63 (C. Younes, PhD Paris Sud 1986)
REF7147 LA2O1<G> T.C.R.A.S. Class: 6
H_form changed according to Heyrman et al Calphad 28 (2004)
49-63 (C. Younes, PhD Paris Sud 1986)
REF7150 LA2O2<G> T.C.R.A.S. Class: 7
H_form changed according to Heyrman et al Calphad 28 (2004)
49-63 (C. Younes, PhD Paris Sud 1986)
REF7934 O1<G> JANAF 1982; ASSESSMENT DATED 3/77 SGTE
OXYGEN <MONATOMIC GAS>
REF8011 O1TI1<G> JANAF THERMOCHEMICAL TABLES((1975 SUPPL.)) SGTE
TITANIUM MONOXIDE <GAS>
PUBLISHED BY JANAF AT 12/73
REF8065 O2<G> T.C.R.A.S. Class: 1
OXYGEN <DIATOMIC GAS>
REF8183 O2TI1<G> JANAF THERMOCHEMICAL TABLES((1975 SUPPL.)) SGTE
TITANIUM DIOXIDE <GAS>
PUBLISHED BY JANAF AT 12/73 .
REF8221 O3<G> T.C.R.A.S. Class: 4
OZONE <GAS>
REF9096 TI1<G> T.C.R.A.S. Class: 1
TITANIUM <GAS>
REF9098 TI2<G> T.C.R.A.S Class: 6
Data provided by T.C.R.A.S. October 1996
REF8180 O2TI1<ANATASE> JANAF SECOND EDIT. SGTE
TITANIUM DIOXIDE <ANATASE>
TF ET LF INCONNUS.
REF7153 LA2O3 GRUNDY ET AL
from Grundy et al J. Phase Equilibria 22 (2001) 105
REF7108 LA1 HULTGREN SELECTED VAL.1973 SGTE **
LANTHANUM
ATOMIC WEIGHT : 138.91
TRANSFORMATIONS : ALPHA-BETA : 550 K , BETA-GAMMA : 1134 K
REF8014 O1TI1<O1TI1_ALPHA> JANAF TABLES SUPPL.75. SGTE
ALPHA-O1TI1
U.D :24/06/86 .
REF8017 O1TI1<O1TI1_BETA> JANAF TABLES SUPPL.75 SGTE
BETA-O1TI1
U.D.:24/06/86 .
REF8271 O3TI2 JANAF THERMOCHEMICAL TABLES SGTE
DITITANIUM TRIOXIDE
PUBLISHED BY JANAF AT 6/73
REF8381 O5TI3 JANAF 4th Edition.
Cp fitted by IA.
REF8416 O7TI4 JANAF THERMOCHEMICAL TABLES((1974 SUPPL.)) SGTE
70
PUBLISHED BY JANAF AT 12/73
Probably melts incongruently.
REF8186 O2TI1<RUTILE> T.C.R.A.S. Class: 6
TITANIUM DIOXIDE <RUTILE>
REF9090 TI1 S.G.T.E. **
TITANIUM
Data from SGTE Unary DB
!
71
Appendix C
Cubic SrCoO3-δ Thermo-Calc database
$ Database file written 2013- 5-28
$ From database: User data 2010. 8.27
ELEMENT /- ELECTRON_GAS 0.0000E+00 0.0000E+00 0.0000E+00!
ELEMENT VA VACUUM 0.0000E+00 0.0000E+00 0.0000E+00!
ELEMENT CO HCP_A3 5.8933E+01 0.0000E+00 0.0000E+00!
ELEMENT O 1/2_MOLE_O2(G) 1.5999E+01 4.3410E+03 1.0252E+02!
ELEMENT SR SR_FCC_A1 8.7620E+01 6.5680E+03 5.5694E+01!
SPECIES CO+2 CO1/+2!
SPECIES CO+3 CO1/+3!
SPECIES CO+4 CO1/+4!
SPECIES CO1O1 CO1O1!
SPECIES CO2 CO2!
SPECIES CO3O4 CO3O4!
SPECIES O-2 O1/-2!
SPECIES O2 O2!
SPECIES O2-2 O2/-2!
SPECIES O2SR1 O2SR1!
SPECIES O3 O3!
SPECIES SR+2 SR1/+2!
SPECIES SR2 SR2!
SPECIES SR2O O1SR2!
SPECIES SRO O1SR1!
SPECIES SRO2 O2SR1!
FUNCTION GSRBCC 2.98150E+02 -6779.234+116.583654*T-25.6708365*T*LN(T)
-.003126762*T**2+2.2965E-07*T**3+27649*T**(-1); 8.20000E+02 Y
-6970.594+122.067301*T-26.57*T*LN(T)-.0019493*T**2-1.7895E-08*T**3
+16495*T**(-1); 1.05000E+03 Y
+8168.357+.423037*T-9.7788593*T*LN(T)-.009539908*T**2+5.20221E-07*T**3
-2414794*T**(-1); 3.00000E+03 N !
FUNCTION GHSERSR 2.98150E+02 -7532.367+107.183879*T-23.905*T*LN(T)
-.00461225*T**2-1.67477E-07*T**3-2055*T**(-1); 8.20000E+02 Y
-13380.102+153.196104*T-30.0905432*T*LN(T)-.003251266*T**2
+1.84189E-07*T**3+850134*T**(-1); 3.00000E+03 N !
FUNCTION GSROSOL 2.98150E+02 -607870+268.9*T-47.56*T*LN(T)-.00307*T**2
+190000*T**(-1); 6.00000E+03 N !
FUNCTION GSRO2SOL 2.98150E+02 +GSROSOL#+GHSEROO#-43740+70*T;
6.00000E+03 N !
FUNCTION GSRLIQ 2.98150E+02 +2194.997-10.118994*T-5.0668978*T*LN(T)
-.031840595*T**2+4.981237E-06*T**3-265559*T**(-1); 1.05000E+03 Y
-10855.29+213.406219*T-39.463*T*LN(T); 3.00000E+03 N !
FUNCTION GSROLIQ 2.98150E+02 -566346+449*T-73.1*T*LN(T); 6.00000E+03
72
N !
FUNCTION F7397T 2.98150E+02 +243206.529-42897.0876*T**(-1)
-20.7513421*T-21.0155542*T*LN(T)+1.26870532E-04*T**2
-1.23131285E-08*T**3; 2.95000E+03 Y
+252301.473-3973170.33*T**(-1)-51.974853*T-17.2118798*T*LN(T)
-5.41356254E-04*T**2+7.64520703E-09*T**3; 6.00000E+03 N !
FUNCTION GHSEROO 2.98150E+02 -3480.87-25.503038*T-11.136*T*LN(T)
-.005098888*T**2+6.61846E-07*T**3-38365*T**(-1); 1.00000E+03 Y
-6568.763+12.65988*T-16.8138*T*LN(T)-5.95798E-04*T**2+6.781E-09*T**3
+262905*T**(-1); 3.30000E+03 Y
-13986.728+31.259625*T-18.9536*T*LN(T)-4.25243E-04*T**2
+1.0721E-08*T**3+4383200*T**(-1); 6.00000E+03 N !
FUNCTION F7683T 2.98150E+02 +133772.042-11328.9959*T**(-1)
-84.8602165*T-19.8314069*T*LN(T)-.0392015696*T**2+7.90727187E-06*T**3;
6.00000E+02 Y
+120765.524+997137.156*T**(-1)+120.113376*T-51.8410152*T*LN(T)
-.00353983136*T**2+3.20640143E-07*T**3; 1.50000E+03 Y
+115412.196+1878139.02*T**(-1)+164.679664*T-58.069736*T*LN(T)
-2.84399032E-04*T**2+5.95650279E-10*T**3; 6.00000E+03 N !
FUNCTION F14450T 2.98150E+02 +154227.522-24.1431703*T-20.98549*T*LN(T)
+1.951298E-04*T**2-3.09095833E-08*T**3+4675.2365*T**(-1); 1.80000E+03
Y
+111247.483+242.365806*T-56.52776*T*LN(T)+.0133862*T**2
-9.57800833E-07*T**3+9843260*T**(-1); 3.30000E+03 Y
+770872.513-2114.76782*T+233.253*T*LN(T)-.04337796*T**2
+1.134592E-06*T**3-2.7250735E+08*T**(-1); 4.90000E+03 Y
-196742.694+263.327068*T-44.45892*T*LN(T)-.008078665*T**2
+2.96671167E-07*T**3+3.57637E+08*T**(-1); 6.20000E+03 Y
-949056.902+1952.13337*T-239.3059*T*LN(T)+.01421437*T**2
-1.79062E-07*T**3+8.9842E+08*T**(-1); 9.60000E+03 Y
+34305.7758+474.957384*T-77.25547*T*LN(T)+.00232914*T**2
-1.54504333E-08*T**3-2.2245325E+08*T**(-1); 1.00000E+04 N !
FUNCTION F14465T 2.98150E+02 +295010.66+61.845039*T-54.13634*T*LN(T)
+.040485225*T**2-9.264165E-06*T**3-70453.75*T**(-1); 5.00000E+02 Y
+307156.188-147.411671*T-20.95926*T*LN(T)+1.012636E-04*T**2
-8.03856667E-09*T**3-905190.5*T**(-1); 3.00000E+03 N !
FUNCTION F12810T 2.98150E+02 -25476.9742+3.04351985*T-34.37623*T*LN(T)
-.0026980695*T**2+3.78874167E-07*T**3+120146.05*T**(-1); 9.00000E+02 Y
-44602.142+205.651627*T-63.83687*T*LN(T)+.017645965*T**2
-2.284235E-06*T**3+2463047*T**(-1); 1.80000E+03 Y
+243278.077-1500.21201*T+161.9497*T*LN(T)-.0612273*T**2
+2.896125E-06*T**3-66468000*T**(-1); 2.90000E+03 Y
-571113.316+1685.71589*T-234.6556*T*LN(T)+.024571595*T**2
-5.82819833E-07*T**3+2.468897E+08*T**(-1); 4.50000E+03 Y
-14433.8514+256.066959*T-66.76292*T*LN(T)+.002226246*T**2
-2.98498E-08*T**3-97083400*T**(-1); 8.80000E+03 Y
+52967.3441+134.904343*T-53.17021*T*LN(T)+.001008387*T**2
-9.46948833E-09*T**3-1.6008755E+08*T**(-1); 1.00000E+04 N !
73
FUNCTION GCOOLIQ 2.98150E+02 +GCOOS#+42060-20*T; 6.00000E+03 N !
FUNCTION GCOOS 2.98150E+02 -252530+270.075*T-47.825*T*LN(T)
-.005112*T**2+225008*T**(-1); 6.00000E+03 N !
FUNCTION GCOLIQ 2.98140E+02 +15085.037-8.931932*T+GHSERCO#
-2.19801E-21*T**7; 1.76800E+03 Y
-846.61+243.599944*T-40.5*T*LN(T); 6.00000E+03 N !
FUNCTION NCO3O4 2.98150E+02 -969727+915.076*T-150.26*T*LN(T)
-.004773*T**2+1358967*T**(-1); 6.00000E+03 N !
FUNCTION ICO3O4 2.98150E+02 +NCO3O4#+95345-85.852*T; 6.00000E+03 N
!
FUNCTION GFCCCO 2.98150E+02 +427.591-.615248*T+GHSERCO#; 6.00000E+03
N !
FUNCTION GHSERCO 2.98140E+02 +310.241+133.36601*T-25.0861*T*LN(T)
-.002654739*T**2-1.7348E-07*T**3+72527*T**(-1); 1.76800E+03 Y
-17197.666+253.28374*T-40.5*T*LN(T)+9.3488E+30*T**(-9); 6.00000E+03
N !
FUNCTION F7439T 2.98150E+02 +416729.448-35.265807*T-20.78*T*LN(T)
-.0080941*T**2+1.95473333E-06*T**3+68440*T**(-1); 6.00000E+02 Y
+415600.439-4.47823809*T-25.919*T*LN(T)-3.217E-04*T**2+1.228E-08*T**3
+69800*T**(-1); 1.60000E+03 Y
+404059.608+60.9456563*T-34.475*T*LN(T)+.00226985*T**2
-1.11743333E-07*T**3+2845480*T**(-1); 5.30000E+03 Y
+619409.166-455.183402*T+25.674*T*LN(T)-.00531515*T**2
+7.04183333E-08*T**3-1.4391985E+08*T**(-1); 1.00000E+04 N !
FUNCTION F7532T 2.98150E+02 +275841.927+24.0962563*T-38.62*T*LN(T)
+.0010486*T**2-5.3089E-07*T**3+44960*T**(-1); 1.00000E+03 Y
+271341.103+44.7689137*T-41.009*T*LN(T)-1.055E-05*T**2
-9.90866667E-08*T**3+1003100*T**(-1); 2.90000E+03 Y
+390604.342-373.916021*T+10.233*T*LN(T)-.0095202*T**2
+2.18581667E-07*T**3-49953335*T**(-1); 5.60000E+03 Y
+339256.902-297.790942*T+2.109*T*LN(T)-.00931405*T**2
+2.32998333E-07*T**3-1285140*T**(-1); 6.00000E+03 N !
FUNCTION F7591T 2.98150E+02 +739344.57+228.270513*T-75.86201*T*LN(T)
+.02653785*T**2-3.82613167E-06*T**3+589055*T**(-1); 9.00000E+02 Y
+766271.806-69.2721015*T-32.277*T*LN(T)-.0051345*T**2+5.3545E-07*T**3
-2559210*T**(-1); 2.50000E+03 Y
+742734.911+122.487527*T-58.296*T*LN(T)+.0049326*T**2
-1.22191667E-07*T**3-1487375*T**(-1); 5.80000E+03 Y
+1148759.49-821.285064*T+51.18*T*LN(T)-.0082646*T**2
+1.77621667E-07*T**3-2.8575475E+08*T**(-1); 6.00000E+03 N !
FUNCTION F13634T 2.98150E+02 +243206.494-20.8612587*T-21.01555*T*LN(T)
+1.2687055E-04*T**2-1.23131283E-08*T**3-42897.09*T**(-1); 2.95000E+03
Y
+252301.423-52.0847285*T-17.21188*T*LN(T)-5.413565E-04*T**2
+7.64520667E-09*T**3-3973170.5*T**(-1); 6.00000E+03 N !
FUNCTION F14003T 2.98150E+02 -6960.69252-51.1831473*T-22.25862*T*LN(T)
-.01023867*T**2+1.339947E-06*T**3-76749.55*T**(-1); 9.00000E+02 Y
-13136.0172+24.743296*T-33.55726*T*LN(T)-.0012348985*T**2
+1.66943333E-08*T**3+539886*T**(-1); 3.70000E+03 Y
74
+14154.6461-51.4854586*T-24.47978*T*LN(T)-.002634759*T**2
+6.01544333E-08*T**3-15120935*T**(-1); 9.60000E+03 Y
-314316.628+515.068037*T-87.56143*T*LN(T)+.0025787245*T**2
-1.878765E-08*T**3+2.9052515E+08*T**(-1); 1.85000E+04 Y
-108797.175+288.483019*T-63.737*T*LN(T)+.0014375*T**2-9E-09*T**3
+.25153895*T**(-1); 2.00000E+04 N !
FUNCTION F14300T 2.98150E+02 +130696.944-37.9096651*T-27.58118*T*LN(T)
-.02763076*T**2+4.60539333E-06*T**3+99530.45*T**(-1); 7.00000E+02 Y
+114760.623+176.626736*T-60.10286*T*LN(T)+.00206456*T**2
-5.17486667E-07*T**3+1572175*T**(-1); 1.30000E+03 Y
+49468.3958+710.094819*T-134.3696*T*LN(T)+.039707355*T**2
-4.10457667E-06*T**3+12362250*T**(-1); 2.10000E+03 Y
+866367.075-3566.80563*T+421.2001*T*LN(T)-.1284109*T**2
+5.44768833E-06*T**3-2.1304835E+08*T**(-1); 2.80000E+03 Y
+409416.384-1950.70834*T+223.4437*T*LN(T)-.0922361*T**2
+4.306855E-06*T**3-21589870*T**(-1); 3.50000E+03 Y
-1866338.6+6101.13383*T-764.8435*T*LN(T)+.09852775*T**2
-2.59784667E-06*T**3+9.610855E+08*T**(-1); 4.90000E+03 Y
+97590.0432+890.79836*T-149.9608*T*LN(T)+.01283575*T**2
-3.555105E-07*T**3-2.1699975E+08*T**(-1); 6.00000E+03 N !
FUNCTION F15641T 2.98150E+02 +153602.922-22.5981707*T-20.98549*T*LN(T)
+1.951298E-04*T**2-3.09095833E-08*T**3+4675.2365*T**(-1); 1.80000E+03
Y
+110622.883+243.910805*T-56.52776*T*LN(T)+.0133862*T**2
-9.57800833E-07*T**3+9843260*T**(-1); 3.30000E+03 Y
+770247.913-2113.22282*T+233.253*T*LN(T)-.04337796*T**2
+1.134592E-06*T**3-2.7250735E+08*T**(-1); 4.90000E+03 Y
-197367.294+264.872067*T-44.45892*T*LN(T)-.008078665*T**2
+2.96671167E-07*T**3+3.57637E+08*T**(-1); 6.20000E+03 Y
-949681.502+1953.67837*T-239.3059*T*LN(T)+.01421437*T**2
-1.79062E-07*T**3+8.9842E+08*T**(-1); 9.60000E+03 Y
+33681.1759+476.502383*T-77.25547*T*LN(T)+.00232914*T**2
-1.54504333E-08*T**3-2.2245325E+08*T**(-1); 1.00000E+04 N !
FUNCTION F15650T 2.98150E+02 +296202.76+61.7700383*T-54.13634*T*LN(T)
+.040485225*T**2-9.264165E-06*T**3-70453.75*T**(-1); 5.00000E+02 Y
+308348.288-147.486672*T-20.95926*T*LN(T)+1.012636E-04*T**2
-8.03856667E-09*T**3-905190.5*T**(-1); 3.00000E+03 N !
FUNCTION GCO2O3 2.98150E+02 -678388.128+739.277235*T
-117.191055*T*LN(T)-.00807331588*T**2+1258302.79*T**(-1); 6.00000E+03
N !
FUNCTION GMN1O1 2.98150E+02 -402477.557+259.355626*T
-46.8352649*T*LN(T)-.00385001409*T**2+212922.234*T**(-1); 6.00000E+03
N !
FUNCTION GMN1O2 2.98150E+02 -545091.278+395.379396*T
-65.2766201*T*LN(T)-.00780284521*T**2+664955.386*T**(-1); 6.00000E+03
N !
FUNCTION GMN2O3 2.98150E+02 -998618.105+588.618611*T
-101.955918*T*LN(T)-.018843507*T**2+589054.519*T**(-1); 6.00000E+03
75
N !
FUNCTION GLA2O3 2.98150E+02 -1835600+674.72*T-118*T*LN(T)-.008*T**2
+620000*T**(-1); 6.00000E+03 N !
FUNCTION GLM2O 2.98150E+02 +.5*GLA2O3#+GMN1O1#+27672; 6.00000E+03
N !
FUNCTION GLM3O 2.98150E+02 +.5*GLA2O3#+.5*GMN2O3#-63367+51.77*T
-7.19*T*LN(T)+232934*T**(-1); 6.00000E+03 N !
FUNCTION GLM4O 2.98150E+02 +.5*GLA2O3#+.75*GMN1O2#-91857+20.31*T;
6.00000E+03 N !
FUNCTION GVM4O 2.98150E+02 +.333333*GLA2O3#+GMN1O2#-53760;
6.00000E+03 N !
FUNCTION GSM3O 2.98150E+02 +GSROSOL#+.5*GMN2O3#-7730-14455-17*T;
6.00000E+03 N !
FUNCTION GS4O 2.98150E+02 +GHSERSR#+GHSERCO#+3*GHSEROO#-
7.8903236E+05+1.9868203E+02*T;
6.00000E+03 N !
FUNCTION GS3OV 2.98150E+02 +GHSERSR#+GHSERCO#+2.5*GHSEROO#-
8.0348280E+05+1.2050666E+02*T;
6.00000E+03 N !
FUNCTION GS2OV 2.98150E+02 +GHSERSR#+GHSERCO#+2*GHSEROO#-
7.3818232E+05+4.0237529E+01*T;
6.00000E+03 N !
FUNCTION GSVOV 2.98150E+02 +GHSERSR#+GHSEROO#;
6.00000E+03 N !
FUNCTION GVVV 2.98150E+02 +6*GLM2O#+4*GLM4O#+3*GVM4O#-12*GLM3O#
-254212; 6.00000E+03 N !
FUNCTION GL3OSSUB 2.98150E+02 -1261010.71-70.3237561*T+6.17*T*LN(T)
-.14132*T**2-1179500*T**(-1); 5.50000E+02 Y
-1301031.07+751.034485*T-125.1*T*LN(T)-.009245*T**2+958500*T**(-1);
1.22000E+03 Y
-1288831.07+669.968423*T-115.1*T*LN(T)-.009245*T**2+958500*T**(-1);
2.50000E+03 N !
FUNCTION GHSERLA 2.98150E+02 -7968.403+120.284604*T-26.34*T*LN(T)
-.001295165*T**2; 5.50000E+02 Y
-3381.413+59.06113*T-17.1659411*T*LN(T)-.008371705*T**2
+6.8932E-07*T**3-399448*T**(-1); 2.00000E+03 Y
-15608.882+181.390071*T-34.3088*T*LN(T); 4.00000E+03 N !
FUNCTION LV1 2.98150E+02 -4468; 6.00000E+03 N !
FUNCTION LV2 2.98150E+02 7.786; 6.00000E+03 N !
FUNCTION GL3O 2.98150E+02 +GL3OSSUB#+LV1#+LV2#*T; 6.00000E+03 N !
FUNCTION LV3 2.98150E+02 -1172133; 6.00000E+03 N !
FUNCTION LV4 2.98150E+02 218.918515; 6.00000E+03 N !
FUNCTION GL2OV 2.98150E+02 +GHSERLA#+GHSERCO#+2.5*GHSEROO#+LV3#
+LV4#*T; 6.00000E+03 N !
FUNCTION LV5 2.98150E+02 -1089320; 6.00000E+03 N !
FUNCTION LV6 2.98150E+02 310.899; 6.00000E+03 N !
FUNCTION GL4VO 2.98150E+02 +GHSERLA#+.75*GHSERCO#+3*GHSEROO#+LV5#
+LV6#*T; 6.00000E+03 N !
FUNCTION LV7 2.98150E+02 -1089320; 6.00000E+03 N !
76
FUNCTION LV8 2.98150E+02 310.899; 6.00000E+03 N !
FUNCTION GLV4O 2.98150E+02
+.666666*GHSERLA#+GHSERCO#+3*GHSEROO#+LV7#
+LV8#*T; 6.00000E+03 N !
FUNCTION UN_ASS 298.15 0; 300 N !
TYPE_DEFINITION % SEQ *!
DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
DEFAULT_COMMAND DEF_SYS_ELEMENT VA /- !
PHASE GAS:G % 1 1.0 !
CONSTITUENT GAS:G :CO,CO1O1,CO2,O,O2,O3,SR,SR2,SRO : !
PARAMETER G(GAS,CO;0) 2.98150E+02 +F7439T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF1 !
PARAMETER G(GAS,CO1O1;0) 2.98150E+02 +F7532T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF20 !
PARAMETER G(GAS,CO2;0) 2.98150E+02 +F7591T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF39 !
PARAMETER G(GAS,O;0) 2.98150E+02 +F13634T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF50 !
PARAMETER G(GAS,O2;0) 2.98150E+02 +F14003T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF69 !
PARAMETER G(GAS,O3;0) 2.98150E+02 +F14300T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF77 !
PARAMETER G(GAS,SR;0) 2.98150E+02 +F15641T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF84 !
PARAMETER G(GAS,SR2;0) 2.98150E+02 +F15650T#+R#*T*LN(1E-05*P);
6.00000E+03 N REF93 !
PARAMETER G(GAS,SRO;0) 2.98150E+02 +F12810T#+RTLNP#; 6.00000E+03 N
REF0 !
PHASE IONIC_LIQUID:Y % 2 2 2.06091 !
CONSTITUENT IONIC_LIQUID:Y :CO+2,CO+3,SR+2 : O-2,VA : !
PARAMETER G(IONIC_LIQUID,CO+2:O-2;0) 2.98150E+02 +2*GCOOLIQ#;
6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,CO+3:O-2;0) 2.98150E+02 +2*GCOOS#+GHSEROO#
-76314+103.63*T; 6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,SR+2:O-2;0) 2.98150E+02 +2*GSROLIQ#;
6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,CO+2:VA;0) 2.98150E+02 +GCOLIQ#; 6.00000E+03
N REF0 !
PARAMETER G(IONIC_LIQUID,CO+3:VA;0) 2.98150E+02 +2*GCOLIQ#+2*GCOOS#
+GHSEROO#-76314+103.63*T-3*GCOOLIQ#; 6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,SR+2:VA;0) 2.98150E+02 +GSRLIQ#; 6.00000E+03
N REF0 !
77
PARAMETER G(IONIC_LIQUID,CO+2,SR+2:O-2;0) 2.98150E+02 +V98#+V99#*T;
6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,CO+2:O-2,VA;0) 2.98150E+02 +182675-30.556*T;
6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,CO+2:O-2,VA;2) 2.98150E+02 +54226-20*T;
6.00000E+03 N REF0 !
PARAMETER G(IONIC_LIQUID,CO+3,SR+2:O-2;0) 2.98150E+02 +V98#+V99#*T;
6.00000E+03 N REF0 !
TYPE_DEFINITION & GES A_P_D BCC_A2 MAGNETIC -1.0 4.00000E-01 !
PHASE BCC_A2 %& 2 1 1.5 !
CONSTITUENT BCC_A2 :SR : O,VA : !
PARAMETER G(BCC_A2,SR:O;0) 2.98150E+02 0.0 ; 3.00000E+03 N REF0 !
PARAMETER G(BCC_A2,SR:VA;0) 2.98150E+02 +GSRBCC#; 3.00000E+03 N REF0 !
PHASE CO2O3 % 2 2 3 !
CONSTITUENT CO2O3 :CO+3 : O-2 : !
PARAMETER G(CO2O3,CO+3:O-2;0) 2.98150E+02 +GCO2O3#; 6.00000E+03 N
REF0 !
PHASE CO3O4:I % 3 1 2 4 !
CONSTITUENT CO3O4:I :CO+2,CO+3 : CO+2,CO+3 : O-2 : !
PARAMETER G(CO3O4,CO+2:CO+2:O-2;0) 2.98150E+02 +NCO3O4#+2*ICO3O4#
+23.05272*T; 6.00000E+03 N REF0 !
PARAMETER G(CO3O4,CO+3:CO+2:O-2;0) 2.98150E+02 +2*ICO3O4#+23.05272*T;
6.00000E+03 N REF0 !
PARAMETER G(CO3O4,CO+2:CO+3:O-2;0) 2.98150E+02 +NCO3O4#; 6.00000E+03
N REF0 !
PARA G(CO3O4,CO+3:CO+3:O-2;0) 298.15 0; 6000 N!
PARAMETER G(CO3O4,CO+2,CO+3:CO+2:O-2;0) 2.98150E+02 -30847+44.249*T;
6.00000E+03 N REF0 !
PARAMETER G(CO3O4,CO+2,CO+3:CO+3:O-2;0) 2.98150E+02 -30847+44.249*T;
6.00000E+03 N REF0 !
TYPE_DEFINITION ' GES A_P_D COO MAGNETIC -3.0 2.80000E-01 !
PHASE COO %' 2 1 1 !
CONSTITUENT COO :CO+2 : O-2 : !
PARAMETER G(COO,CO+2:O-2;0) 2.98150E+02 +GCOOS#; 6.00000E+03 N REF0 !
PARAMETER TC(COO,CO+2:O-2;0) 2.98150E+02 -870; 6.00000E+03 N REF0 !
PARAMETER BMAGN(COO,CO+2:O-2;0) 2.98150E+02 2; 6.00000E+03 N REF0 !
78
TYPE_DEFINITION ( GES A_P_D FCC_A1 MAGNETIC -3.0 2.80000E-01 !
PHASE FCC_A1 %( 2 1 1 !
CONSTITUENT FCC_A1 :CO,SR : O,VA : !
PARAMETER G(FCC_A1,CO:O;0) 2.98150E+02 +GFCCCO#+GHSEROO#-213318
+107.071*T; 6.00000E+03 N REF0 !
PARAMETER G(FCC_A1,SR:O;0) 2.98150E+02 0.0 ; 3.00000E+03 N REF0 !
PARAMETER G(FCC_A1,CO:VA;0) 2.98150E+02 +GFCCCO#; 6.00000E+03 N
REF0 !
PARAMETER TC(FCC_A1,CO:VA;0) 2.98150E+02 1396; 6.00000E+03 N REF0 !
PARAMETER BMAGN(FCC_A1,CO:VA;0) 2.98150E+02 1.35; 6.00000E+03 N
REF0 !
PARAMETER G(FCC_A1,SR:VA;0) 2.98150E+02 +GHSERSR#; 3.00000E+03 N REF0 !
TYPE_DEFINITION ) GES A_P_D HCP_A3 MAGNETIC -3.0 2.80000E-01 !
PHASE HCP_A3 %) 2 1 .5 !
CONSTITUENT HCP_A3 :CO : O,VA : !
PARAMETER G(HCP_A3,CO:O;0) 2.98150E+02 +GFCCCO#+.5*GHSEROO#-122309
+66.269*T; 6.00000E+03 N REF0 !
PARAMETER G(HCP_A3,CO:VA;0) 2.98150E+02 +GHSERCO#; 6.00000E+03 N
REF0 !
PARAMETER TC(HCP_A3,CO:VA;0) 2.98150E+02 1396; 6.00000E+03 N REF0 !
PARAMETER BMAGN(HCP_A3,CO:VA;0) 2.98150E+02 1.35; 6.00000E+03 N
REF0 !
PHASE SR2CO2O5 % 4 2 1 1 5 !
CONSTITUENT SR2CO2O5 :SR+2 : CO+2 : CO+4 : O-2 : !
PARAMETER G(SR2CO2O5,SR+2:CO+2:CO+4:O-2;0) 2.98150E+02 -
1.7445327E+06+1.1128024E+03*T
-2.1373449E+02*T*LN(T)-2.3798830E-02*T**2+1.6354101E+06*T**(-1); 6.00000E+03 N
REF0 !
PHASE SR2COO4 % 3 2 1 4 !
CONSTITUENT SR2COO4 :SR+2 : CO+4 : O-2 : !
PARAMETER G(SR2COO4,SR+2:CO+4:O-2;0) 2.98150E+02 -
1.5915017E+06+8.7617033E+02*T
-1.4951359E+02*T*LN(T)-3.1876258E-02*T**2+3.8665981E+05*T**(-1); 6.00000E+03 N
REF0 !
PHASE SR6CO5O15 % 4 6 4 1 15 !
CONSTITUENT SR6CO5O15 :SR+2 : CO+4 : CO+2 : O-2 : !
79
PARAMETER G(SR6CO5O15,SR+2:CO+4:CO+2:O-2;0) 2.98150E+02 -
5.8879969E+06+3.8040193E+03*T
-6.0223129E+02*T*LN(T)-8.9528710E-02*T**2+4.8635240E+06*T**(-1); 6.00000E+03 N
REF0 !
PHASE SRCOO3:I % 3 1 1 3 !
CONSTITUENT SRCOO3:I :SR+2,VA : CO+2,CO+3,CO+4,VA : O-2,VA : !
PARAMETER G(SRCOO3,SR+2:CO+2:O-2;0) 2.98150E+02 +GHSEROO#+GS2OV#
+15.8759*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+2:O-2;0) 2.98150E+02 +.5*GVVV#+GL2OV#-
2*GL4VO#
+1.5*GLV4O#+2*GHSEROO#+9.82536*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+3:O-2;0) 2.98150E+02 +.5*GHSEROO#+GS3OV#
+11.2379*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+3:O-2;0) 2.98150E+02 +GL3O#+.5*GVVV#-
2*GL4VO#
+1.5*GLV4O#+1.5*GHSEROO#-1.41254*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+4:O-2;0) 2.98150E+02 +GS4O#; 6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+4:O-2;0) 2.98150E+02 +.33333*GVVV#
-1.33333*GL4VO#+2*GLV4O#+GHSEROO#+4.35029*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:VA:O-2;0) 2.98150E+02 +GSM3O#-
GLM3O#+2*GLM4O#
-1.5*GVM4O#+.5*GVVV#+2*GHSEROO#+12.62121*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:VA:O-2;0) 2.98150E+02 +GVVV#+3*GHSEROO#;
6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+2:VA;0) 2.98150E+02 -2*GHSEROO#+GS2OV#
+15.8759*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+2:VA;0) 2.98150E+02 +.5*GVVV#+GL2OV#-
2*GL4VO#
+1.5*GLV4O#-GHSEROO#+9.82536*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+3:VA;0) 2.98150E+02 -2.5*GHSEROO#+GS3OV#
+11.2379*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+3:VA;0) 2.98150E+02 +GL3O#+.5*GVVV#-
2*GL4VO#
+1.5*GLV4O#-1.5*GHSEROO#-1.41254*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+4:VA;0) 2.98150E+02 -3*GHSEROO#+GS4O#;
6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+4:VA;0) 2.98150E+02 +.33333*GVVV#
-1.33333*GL4VO#+2*GLV4O#-2*GHSEROO#+4.35029*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,SR+2:VA:VA;0) 2.98150E+02 +GSM3O#+2*GLM4O#
-1.5*GVM4O#+.5*GVVV#-GLM3O#-GHSEROO#+12.62121*T; 6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:VA:VA;0) 2.98150E+02 +GVVV#; 6.00000E+03 N
REF0 !
PARAMETER G(SRCOO3,SR+2,VA:CO+2:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
80
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+2,VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+2:O-2,VA;0) 2.98150E+02 +3.5878637E+05;
6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+2,VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+2:O-2,VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2,VA:CO+3:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+3,VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+3:O-2,VA;0) 2.98150E+02 +2.0604770E+05;
6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+3,VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+3:O-2,VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2,VA:CO+4:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+4,VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+4:O-2,VA;0) 2.98150E+02 -4.5330455E+05;
6.00000E+03 N REF0 !
PARAMETER G(SRCOO3,VA:CO+4,VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+4:O-2,VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2,VA:VA:O-2;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:VA:O-2,VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:VA:O-2,VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03 N
REF0 !
81
PARAMETER G(SRCOO3,SR+2,VA:CO+2:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+2,VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+2,VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2,VA:CO+3:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+3,VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+3,VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2,VA:CO+4:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2:CO+4,VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,VA:CO+4,VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PARAMETER G(SRCOO3,SR+2,VA:VA:VA;0) 2.98150E+02 +1.0000000E+07;
6.00000E+03
N REF0 !
PHASE SRO % 2 1 1 !
CONSTITUENT SRO :SR+2,VA : O-2 : !
PARAMETER G(SRO,SR+2:O-2;0) 2.98150E+02 +GSROSOL#; 6.00000E+03 N
REF0 !
PARA G(SRO,VA:O-2;0) 298.15 0; 6000 N!
PHASE SRO2 % 1 1.0 !
CONSTITUENT SRO2 :SRO2 : !
PARAMETER G(SRO2,SRO2;0) 2.98150E+02 +GSRO2SOL#; 6.00000E+03 N REF0 !
LIST_OF_REFERENCES
NUMBER SOURCE
REF1 9
REF20 6
82
REF39 1
REF50 4
REF69 5
REF77 1
REF84 8
REF93 0
!
83
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