THERMODYNAMIC MODELLING AND DATABANKING : NUCLEA Bertrand Cheynet, Pierre-Yves Chevalier, Evelyne Fischer

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27 Οκτ 2013 (πριν από 3 χρόνια και 5 μήνες)

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THERMODYNAMIC MODELLING AND DATABANKING

: NUCLEA




Bertrand Cheynet, Pierre
-
Yves Chevalier, Evelyne Fischer

THERMODATA
-
INPG
-
CNRS, 6 rue du Tour de l’Eau, 38400 Saint Martin d’Hères, France.




Abstract


For more than 10 years a special effort to p
roduce a specific thermodynamic database for nuclear
applications was made with the support of several organisations in Europe. Today the database
NUCLEA, containing a consistent set of Gibbs energy parameters for all the phases of a very complex
system is

proposed, including 18 chemical elements from the fuel, clads, control roads, metallic
structures, concrete and fission products.

The Calphad method was used to create such a database. The description of each phase is based
on a phenomenological model in
such a way that the models parameters are adjusted to allow to
reproduce in the best possible way the experimental information available on thermodynamics of the
phases and their thermochemical equilibria.

The thermodynamic modelling of the “key” quaternar
y system Fe
-
O
-
U
-
Zr is taken as example.

Introduction


In the 70’
s

a very poor thermochemistry was introduced in the safety nuclear calculation codes,
often only few equilibrium constants of basic chemical reactions were used. It rapidly became very
clear
that thermochemistry could have an important role in the different accident scenari and the
development of a thermodynamic database for nuclear applications was decided. Today, after ten
years of effort, the NUCLEA thermodynamic database is available, incl
uding all the phases of a very
complex thermochemical system :


O
-
U
-
Zr
-
Ag
-
In
-
B
-
C
-
Fe
-
Cr
-
Ni
-
Ba
-
La
-
Sr
-
Ru
-
Al
-
Ca
-
Mg
-
Si


A consistent set of Gibbs Energy parameters for 46 condensed solution phases, 511
condensed substances, 203 gaseous species, more than 250 bi
nary systems and about 30 ternary
systems are stored in the database. The binary and ternary Gibbs Energy parameters were critically
assessed by means of sophisticated optimisation procedures using the Calphad method and the
compound energy formalism.

Appl
ications of such a database, simultaneously with the use of a high
-
quality
equilibrium calculation code, are numerous :

-

condensed state phase diagrams, transitions, liquidus/solidus, compositions and proportions,

-

coupling thermodynamics and thermo
-
hydr
aulic, viscosity, segregation, residual power distribution,

-

gaseous fission products release in any external conditions …



The CALPHAD method


The generation and application of thermodynamic descriptions constitute the central theme of the
so
-
called ‘Ca
lphad’ method [1, 2, 3], an acronym for CALculation of PHAse Diagrams. In this
method, each phase of the system under consideration is described using a Gibbs energy model. The
model parameters are estimated by the weighted non
-
linear least
-
square optimisa
tion of
thermochemical and constitutional data.


Fig.1 is a flowchart of the Calphad method. The first step of the thermodynamic optimisation of a
phase diagram is collecting and categorising experimental information. All constitutional and
thermochemical

data must be extracted from primary sources. The second step involves the critical
evaluation of the collected data. Critical evaluation requires considerable expertise and some
familiarity with different experimental techniques.

The next step is the choi
ce of the Gibbs energy model and the optimisation process obtain the
values of the model parameters for each phase.. We used, in the case of Nuclea, the sublattice model
[4, 5, 6], using the Compound Energy Formalism (CEF) [7, 8], capable of treating many
types of
phases having arbitrary numbers of constituents and sublattices. The difficulty with Nuclea was the
complexity of the chemical system. We tried to chose the most simple modelling to obtain reasonable
extrapolation characteristics in the higher
-
ord
er systems.

The last step is the merging. After the assessment of the unary, binary and ternary systems the
main purpose is to assemble all these data to obtain a single dataset available to do calculation in the
whole complex system. This objective must b
e considered when performing each assessment because
it imposes some restrictions such as it is essential that a phase which forms or may form a continuous
solution from one system to another is described with the same model in both assessment.





Figure

1. Flowchart of the CALPHAD procedure.



Progress in the Fe
-
O
-
U
-
Zr thermodynamic modelling


The Fe
-
O
-
U
-
Zr quaternary system is one of the most important in the NUCLEA database and it is
being studied for a long time. Today the thermodynamic modelling of t
he major phases is needed for
the understanding of stratification phenomena in reactor applications :

-

(U,Zr)O
2+
-
x

solid solution, fluorite type structure, fcc_C1, with an unknown iron content,

-

metal
-
oxygen quaternary liquid phase, L, presenting for giv
en temperature and composition
ranges a miscibility gap between a metallic (Fe,U,Zr) rich liquid, L
1
, with an unknown oxygen
content, and an oxide (FeO,UO
2
,ZrO
2
) rich liquid, L
2,
with a sub
-
stoichiometry range.

The reliability of calculated phase equilibri
um state (phase compositions and proportions)
strongly depends on the accuracy of the Gibbs energy of these phases (

G

), modelled from the
limiting binary and ternary sub
-
systems.


Our work began with the thermodynamic modelling of the O
-
U
-
Zr ternary syst
em in 1998 [9]
including the binary O
-
U, O
-
Zr, U
-
Zr and quasi
-
binary UO
2
-
ZrO
2

sub
-
systems. At that time, the
inconsistencies found in the various experimental results were not resolved, mainly the solubility of
oxygen in (U,Zr) liquid alloys and the ext
ension of the liquid miscibility gap.

Since then, new experiments such as activity measurements or phase equilibria determinations
(tie lines, solidus, liquidus) have been made available.

O
-
U


The completion of the huge experimental database (phase diagra
m and thermodynamic
properties) allowed us to improve significantly the thermodynamic modelling of the O
-
U binary
system [10] ; very accurate thermodynamic descriptions were obtained for the stoichiometric
compounds UO
3
, U
3
O
8

and U
4
O
9
, and the UO
2+
-
x

solid

solution. In the hypostoichiometric range, the
choice of a low solubility of oxygen in the liquid phase and a wide liquid miscibility gap was retained.
Phase diagram and thermodynamic properties were satisfactorily reproduced. The evolution of the
assesse
d O
-
U phase diagram is shown on Figure 2.


2
a : large O solubility in liquid U (Chevalier and Fischer, 1998 [9]).


2b : small O solubility in liquid U (Chevalier et al., 2002 [10]).

Figure 2 . Calculated O
-
U phase diagram compared to experimental information.

O
-
U
-
Zr


The availability of new experiments and the progress in the O
-
U thermodynamic modelling
justified the very recent re
-
assessment of the O
-
U
-
Zr ternary system [11], consi
sting of the re
-
assessment of the other sub
-
systems and the evaluation of ternary interaction parameters using an
appropriate optimisation procedure. The extrapolation of the excess Gibbs energy of the U
-
Zr and
UO
2
-
ZrO
2

liquid phases was carefully analysed
. The model for the fcc_C1 solid solution was then
simplified to be compatible with the NUCLEA database. The evolution of the assessed O
-
U
-
Zr phase
diagram is shown by two examples (2273 K, 2773 K) on Figures 3 and 4.



3
a : large O solubility in liquid U (Chevalier and Fischer, 1998 [9]).


3b : small O solubility in liquid U (Chevalier et al., 2004 [11]).

Figure 3 . Calculated O
-
U
-
Zr section (2273K) compared to experimental informa
tion.


4a : small liquid miscibility gap (Chevalier and Fischer, 1998 [9]).


4
b : large liquid miscibility gap (Chevalier et al., 2004 [11]).

Figure 4 . Calculated O
-
U
-
Zr section
(2773K) compared to experimental information.

Fe
-
O
-
U
-
Zr


The last stage of this continuous improvement work was the extension of the O
-
U
-
Zr system to
iron [12]. The two binary systems Fe
-
U and Fe
-
Zr were re
-
assessed, including the most recent
experimental

works on the thermodynamics of Fe
-
U stoichiometric compounds, and invariant
reactions and liquidus data in the Fe
-
Zr system. The non stoichiometry range of the Laves phase,
Fe
2
Zr, system was taken into account and extended to the ternary Laves phase , Fe
2

(U,Zr). The
evolution of the assessed Fe
-
Zr phase diagram [13, 14] is shown on Figure 5. Some incoherence
between the liquidus and the enthalpy of liquid alloys remains at high zirconium content.


5a : Servant et al.,

1998 [13].


b : Chevalier and Fischer, 2003 [14].

Figure 5 . Calculated Fe
-
Zr phase diagram compared to experimental information.

The Fe
-
U
-
Zr ternary system was calculated on the basis of the re
-
assessment of the sub
-
s
ystems
and the estimation of the thermodynamic properties of three ternary compounds, Fe
0.333
U
0.25
Zr
0.417

(

),
Fe
0.06
U
0.71
Zr
0.23
(

), Fe
0.5
U
0.18
Zr
0.32

(

) considered as stoichiometric. Two isothermal sections are
presented on Figure 6.


6a : T = 600 K.


6b : T = 1273 K.

Figure 6
-

Calculated Fe
-
U
-
Zr phase diagram (Chevalier et al., 2003 [12] lave modified).

The oxide pseudo
-
binary systems FeO
-
UO
2
, FeO
-
ZrO
2
, Fe
2
O
3
-
UO
2

and Fe
2
O
3
-
ZrO
2
w
ere
checked, but the most recent experimental results obtained in the CORPHAD [15, 16] and ECOSTAR
[17] projects should be included in a future update of the database. They assume a non negligible solid
solubility of FeO in UO
2

(fcc_C1) and ZrO
2

(fcc_C1),

and of Fe
2
O
3

in ZrO
2

(tet). A liquid miscibility
gap appears in the Fe
2
O
3
-
ZrO
2

system.


The Fe
-
O
-
U and Fe
-
O
-
Zr ternary systems have been calculated from the binary and quasi
-
binary
re
-
assessed sub
-
systems. The thermodynamic properties of UFeO
4

were asses
sed. The calculated limit
of solubility of oxygen in Fe
-
Zr liquid alloys was optimised from experimental information in the iron
rich domain (1800
-
2100K). As examples, the isothermal sections at 2773 K (Figure 7) and 2673 K
(Figure 8) are presented.


Figure 7 . Calculated Fe
-
O
-
U section (Chevalier et al., 2003 [12]).



Figure 8
-

Calculated Fe
-
O
-
Zr isothermal section (Chevalier et al., 2003 [12]).

References


[1]

L. Kaufman, H. Bern
stein, Computer Calculation of Phase Diagrams, Acadamis Press, New
York, 1970.

[2]

N. Saunders, A.P. Miodownik, Calphad (Calculation of Pase Diagrams) : A comprehensive
Guide, Pergamon, 1998.

[3]

K.C. Hari Kumar, P. Wollants, Some guidelines for thermodyna
mic optimisation of phase
diagrams, Journal of Alloys and Compounds 320 (2001) 189
-
198.

[4]

H.Schmalzried, Progress in Solis State Chemistry, II, Pergamon Press, Oxford, 1965.

[5]

M. Hillert, L.I. Staffansson, Acta Chem. Scand. 24 (10) (1970) 3618.

[6]

B.
Sundman, J. Agren, J. Phys. Chem. Solids 42 (1981) 297.

[7]

M. Hillert, The compound energy formalism, Journal of Alloys and Compounds 320 (2001) 161
-
176.

[8]

K. Frisk, M. Selleby, The compound energy formalism : applications, Journal of Alloys and
Compoun
ds 320 (2001) 177
-
188.

[9]

P.Y. Chevalier, E. Fischer, “Thermodynamic modelling of the O
-
U
-
Zr system”, Journal of
Nuclear Materials, 257 (1998) 213
-
255.

[10]

P.Y. Chevalier, E. Fischer, B. Cheynet, “Progress in the thermodynamic modelling of the O
-
U
binary

system”, Journal of Nuclear Materials, 303 (2002) 1
-
28.

[11]

P.Y. Chevalier, E. Fischer, B. Cheynet, “Progress in the thermodynamic modelling of the O
-
U
-
Zr
ternary system”, Calphad, under press (2004).

[12]

P.Y. Chevalier, E. Fischer, B. Cheynet, “Improv
ement of the thermodynamic modelling of the
Fe
-
O
-
U
-
Zr quaternary system”, IRSN Contract N°31000971, Report 2003
-
136, October 2003.

[13]

C. Servant, C. Gueneau, I. Ansara, “Experimental and thermodynamic assessment of the Fe
-
Zr
system”, Journal of Alloys a
nd Compounds, 220 (1995) 19
-
26.

[14]

P.Y. Chevalier, E. Fischer, “Fe
-
Zr presentation”, communication to SGTE, Report 2003
-
65, June
2003.

[15]

Y. Petrov, A.P. Alexandrov Research Institute, “Study of UO2
-
FeO system at induction melting
in inert atmosphere”,

second CORPHAD Meeting, St Petersburg, September 17, 2003.

[16]

V. Gusarov, A.P. Alexandrov Research Institute, “Phase diagram of the ZrO2
-
FeO system”,
second CORPHAD Meeting, St Petersburg, September 17, 2003.

[17]

P. Piluso, “Validation of the European
thermodynamic database with the experiments performed
at NRI
-
REZ on the (U,Zr)O2
-
Fe2O3 system”, Note Technique DTP/STH/LMA
-
03/001,
ENTHALPY : SAM
-
ENTHA(03)D020, from Y.B. Petrov, Y.P. Udalov, J. Slovak, Y.G.
Motosov, Phus. Chem. Glass, N°2, 2001.



Links


http://thermodata.online.fr

http://thermodata.online.fr/nuclea/Nuclea03
-
1.htm

http:
//thermodata.online.fr/mox/Mox03
-
1.html