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Caractérisa)onparDSC:défautsintrinsèqueset
apportsdelamodélisa)on
ErwinFRANQUET([email protected])LaTEP–IPRA/UniversitédePauetdespaysdel’Adour Jeudi16Mars2017
E.Franquet,J.-PBédécarrats,J.-P.Dumas,S.Gibout,D.Haillot
1Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)on 16/03/2017
Généralités§ Analysethermique 3§ DSC 4Interpréta)on§ GrandeursidenSfiables 9§ Erreur(très)courante 13§ Inconnuessurcertainsparamètres 16Modélisa)on§ Analysethéorique 18§ ModélisaSon/SimulaSon 19§ Résultats 21Caractérisa)on§ IdenSficaSon:méthodesinverses 28§ Processusd’inversion 29§ Résultats 35ConclusionAnnexes§ Bibliographie 41§ Discussionssupplémentaires... 44
Sommaire
2
Généralités
16/03/2017
3
Analysethermique
Différentsappareils/mesures§ Calorimètre:mesurechaleur§ DifferenSalthermalanalysis(DTA):mesuretempérature§ AdiabaScscanningcalorimetry(ASC):mesuretempérature§ DifferenSalscanningcalorimetry(DSC):mesurevariaSondeflux
§ méthodeT–history...
§ Thermo-gravimétrie§ Analysethermo-mécanique…
Différentsmodesd’u)lisa)on§ dynamique§ isotherme(step)
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités
16/03/2017
4
DSC§ Deuxtypes:
§ Heatflux(ex:DSC131deSetaram)§ PowercompensaSon(ex:PyrisDiamonddePerkin–Elmer)
§ ImposiSond’unesollicitaSonthermique§ Mesured’unfluxdechaleur
§ ObtenSond’unthermogramme(courbeDSC)§ Modedynamique§ Modeisotherme(step)
16/03/2017
1. Introduction1
The calorimetry is an usual technique which permits to analyze a physical or chemical2
phenomena by the release or the absorption of thermal energy. This paper is restrictive to3
the transformation solid ! liquid and more particularly to the melting. We will present4
different cases as those of pure substances and binary solutions.5
We intend, first, to recall the classical procedure to determine the temperature range of6
transformation of the energy involved. The main principle is to consider the temperature7
inside the sample as homogeneous and at a value practically equal to the programmed tem-8
perature. The difference between these two temperatures being, for a given heating rate, a9
constant and small correction justified by only the thermal resistance between the metallic10
pan and the plate [1].11
For many years [2, 3, 4, 5], we have explained that, at the time of the melting, the tem-12
perature inside the sample is not at all homogeneous. We will recall also our model. It13
will be particularly highlighted that the thermograms, even they are expressed versus the14
programmed temperature, they are curves versus time. n.b. : dire quelque part que l’on va15
comparer avec les droites, pentes. . .16
2. Homogeneous model17
In such a case, schematically depicted in figure 1, it is supposed that the whole sample18
and the reference, and the corresponding metallic cells, may be represented by an unique19
temperature, being respectively TS and TR [1, 6, 8].20
Tplt
RS RR
TS TR
Figure 1: Schematic representation of the calorimeter with the homogeneous model (n.b. : the gap betweenthe cells and the plates is only here to highlight the existence of thermal resistances and is obviously notphysical).
.
Within this assumption, the heat flux measured corresponds to [1]:21
�(t) =Tplt � TS
RS| {z }�S
� Tplt � TR
RR| {z }�R
(1)
4
0pltT t Tβ= + ( )tφ
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités
40
peak
/ ~ t a n g e n t
"(~ l \ ~ l ~ \ l k extrQpatoted finol baseline I-~ samp[e meosuremen! curve , ~ ~ ' ~ . ' ~ _ ~ q , ~ / r
c_C~ ~ , n ; ~ , b a s e l i ~ b ' ~ finolis~ 7"c Tfin ~CI : I extropolofed inifiol J f I t . . . . c_
l isothermol i bosetine I L ,--. ~ J-- - - ~fropoloted isother. Tp oJ .__., I::1_ o linifiol b o s e - J _ _ . - p " - I " - 7 - 'inferpolol'ed isofherlnul hoseline tool fin.l boseline F:::
I~ I isothermol ~ __ ~ ~ jnferpolnfed isofh . . . . I . . . . line isel'hermul Tini ~iso sl. 0 itnitiot zero ~ - - [- - - I - - - " - - ' +
= " + i + ++o,+n+ ine zero line ~:x'fropototed isofher-
�9 ' ~ /st tool fmol zero line
tsf tini te tp tc /'fin fend
t ime t
Figure 14 a.Zerms to describe a measured curve and its characteristic times, illustrated by the example of a DSC curve with peak. Corresponding characteristic temperatures are assigned to the characteristic times. (Subscripts: st start, end end of temperature program).
step
('~ tangent ~ l / - - " l ~ a s u r e m e n t cur ve
extrapotofed finnl
--4---- CJ f-.-
�9 - " f ~ i ~ i n ilia[ bnseline o ...._.,
+ \ D r--
]"sf ~ni re TI/;P ~ ~in Tend
femperofure 7-
Figure 14b. Terms to describe a measured curve and its characteristic temperatures, illustrated by the example of a DSC curve with step. Corre- sponding characteristic times are assigned to the characteristic temperature. (Subscripts" st start, end end of temperature program).
5
DSC
Modedynamique
16/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités
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DSC
Modeisotherme
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-5
-4
-3
-2
-1
0
1
hea
tfl
ow(m
W)
20
30
40
50
60
70
80
90
100
110
120
Tp
(C
)
10000 20000 30000 40000 50000 60000 70000 80000
time (s)
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités
7
DSC
Informa)onsliminaires§ Signaltemporel§ MéthoderelaSve:
§ ForteinfluenceéchanSllon(s)calibraSon§ DéfiniSonlignesdebase/zéro
§ Résultatsdépendants:
§ Masse§ Vitessedechauffe/refroidissement
16/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onGénéralités
816/03/2017
Interpréta)on
916/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
Grandeursiden)fiables§ Températures
§ TransiSonsdepremipremièreèreespèce:Tonset§ TransiSonsdesecondeespèce:Tsolidus
§ GrandeursénergéSques
§ Capacitéscalorifiques(i.e.dansleszonessensibles)§ Chaleurlatente(i.e.variaSonsd’enthalpie)§ Enthalpie(enmodeisotherme)
§ Donnéescourante:latempératuredefusionetlachaleurlatenteImplicitement,onconsidèredoncuncorpspur...
1016/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
E. Franquet et al. / Thermochimica Acta 546 (2012) 61– 80 63
0.0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
[W]
-5 0 5 10 15Tp [ C]
Fig. 1. Experimental thermogram of a pure substance (water).
0
50
100
150
200
250
300
350
400
h(T)
[kJ/kg]
-2 -1 0 1 2 3 4 5 6 7 8T [ C]
0
50
100
150
200
250
300
350
400
-2 -1 0 1 2 3 4 5 6 7 8
Fig. 2. Comparison of the enthalpy profile obtained by a direct integration of thethermogram for a heating rate of 5 K min−1 (dotted red) and 2 K min−1 (dashed blue)with the exact enthalpy (black line) for a pure substance (water). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)
the enthalpy should be discontinuous for a pure substance1 butis instead smeared on several degrees (implicitly implying thanwater melts between 0 ◦C and 7 ◦C for the higher rate and between0 ◦C and 2 ◦C for the lower one). It is worth highlighting herethat this error will always be present, even at low heating rates,since the thermogram has always a non-zero width and there-fore cannot correctly describe a Dirac function. Usually, one seemsto accept such an approximation as long as the error is below0.5 K [10].
1 It also means than the derivative of the enthalpy is here a Dirac function, whichwas not present in the DSC curve.
0
5
10
15
20
25
30
35
40
[mW]
-20 -15 -10 -5 0 5 10Tp [ C]
Fig. 3. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 0.48%).
0
5
10
15
20
25
30
35
[mW]
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Tp [ C]
Fig. 4. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 9.02%).
Let us now deal with a binary solution, e.g. a H2O/NH4Cl samplewith a solute mass fraction x = 2.98%. This test is performed witha 11.9 mg sample still heated at a heating rate = 5 K min−1. Theexperimental thermogram is shown in Fig. 3. Usually, the eutec-tic temperature is obtained thanks to the onset temperature ofthe first peak, as for a pure substance. Then, an analog method,based on graphical projections on the baseline, is applied to thesecond peak in order to obtain the so-called liquidus temperature.Yet, this method leads to wrong estimations when the two peaksare closed together, as in the case of Fig. 4 where a greater massfraction was considered. Moreover, the raw determination of theenthalpy from the experimental thermogram still lead to spuriousresults [8], as shown in Figs. 5 and 6. In the first case, of a lowconcentration, the integrated profile is much more spread than theexact enthalpy and an offset of the liquidus temperature (i.e. endof the melting) of 2–5 ◦C is observed. Generally, the corresponding
1116/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
-5
0
5
10
15
20
25
30
35
'[m
W]
0 2 4 6 8 10
Tp [�C]
T ?/ TM
Limit ?
Area / LM
E. Franquet et al. / Thermochimica Acta 546 (2012) 61– 80 63
0.0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
[W]
-5 0 5 10 15Tp [ C]
Fig. 1. Experimental thermogram of a pure substance (water).
0
50
100
150
200
250
300
350
400
h(T)
[kJ/kg]
-2 -1 0 1 2 3 4 5 6 7 8T [ C]
0
50
100
150
200
250
300
350
400
-2 -1 0 1 2 3 4 5 6 7 8
Fig. 2. Comparison of the enthalpy profile obtained by a direct integration of thethermogram for a heating rate of 5 K min−1 (dotted red) and 2 K min−1 (dashed blue)with the exact enthalpy (black line) for a pure substance (water). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)
the enthalpy should be discontinuous for a pure substance1 butis instead smeared on several degrees (implicitly implying thanwater melts between 0 ◦C and 7 ◦C for the higher rate and between0 ◦C and 2 ◦C for the lower one). It is worth highlighting herethat this error will always be present, even at low heating rates,since the thermogram has always a non-zero width and there-fore cannot correctly describe a Dirac function. Usually, one seemsto accept such an approximation as long as the error is below0.5 K [10].
1 It also means than the derivative of the enthalpy is here a Dirac function, whichwas not present in the DSC curve.
0
5
10
15
20
25
30
35
40
[mW]
-20 -15 -10 -5 0 5 10Tp [ C]
Fig. 3. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 0.48%).
0
5
10
15
20
25
30
35
[mW]
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Tp [ C]
Fig. 4. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 9.02%).
Let us now deal with a binary solution, e.g. a H2O/NH4Cl samplewith a solute mass fraction x = 2.98%. This test is performed witha 11.9 mg sample still heated at a heating rate = 5 K min−1. Theexperimental thermogram is shown in Fig. 3. Usually, the eutec-tic temperature is obtained thanks to the onset temperature ofthe first peak, as for a pure substance. Then, an analog method,based on graphical projections on the baseline, is applied to thesecond peak in order to obtain the so-called liquidus temperature.Yet, this method leads to wrong estimations when the two peaksare closed together, as in the case of Fig. 4 where a greater massfraction was considered. Moreover, the raw determination of theenthalpy from the experimental thermogram still lead to spuriousresults [8], as shown in Figs. 5 and 6. In the first case, of a lowconcentration, the integrated profile is much more spread than theexact enthalpy and an offset of the liquidus temperature (i.e. endof the melting) of 2–5 ◦C is observed. Generally, the corresponding
E. Franquet et al. / Thermochimica Acta 546 (2012) 61– 80 63
0.0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
[W]
-5 0 5 10 15Tp [ C]
Fig. 1. Experimental thermogram of a pure substance (water).
0
50
100
150
200
250
300
350
400
h(T)
[kJ/kg]
-2 -1 0 1 2 3 4 5 6 7 8T [ C]
0
50
100
150
200
250
300
350
400
-2 -1 0 1 2 3 4 5 6 7 8
Fig. 2. Comparison of the enthalpy profile obtained by a direct integration of thethermogram for a heating rate of 5 K min−1 (dotted red) and 2 K min−1 (dashed blue)with the exact enthalpy (black line) for a pure substance (water). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)
the enthalpy should be discontinuous for a pure substance1 butis instead smeared on several degrees (implicitly implying thanwater melts between 0 ◦C and 7 ◦C for the higher rate and between0 ◦C and 2 ◦C for the lower one). It is worth highlighting herethat this error will always be present, even at low heating rates,since the thermogram has always a non-zero width and there-fore cannot correctly describe a Dirac function. Usually, one seemsto accept such an approximation as long as the error is below0.5 K [10].
1 It also means than the derivative of the enthalpy is here a Dirac function, whichwas not present in the DSC curve.
0
5
10
15
20
25
30
35
40
[mW]
-20 -15 -10 -5 0 5 10Tp [ C]
Fig. 3. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 0.48%).
0
5
10
15
20
25
30
35
[mW]
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Tp [ C]
Fig. 4. Experimental thermogram of a binary solution (H2O/NH4Cl, x = 9.02%).
Let us now deal with a binary solution, e.g. a H2O/NH4Cl samplewith a solute mass fraction x = 2.98%. This test is performed witha 11.9 mg sample still heated at a heating rate = 5 K min−1. Theexperimental thermogram is shown in Fig. 3. Usually, the eutec-tic temperature is obtained thanks to the onset temperature ofthe first peak, as for a pure substance. Then, an analog method,based on graphical projections on the baseline, is applied to thesecond peak in order to obtain the so-called liquidus temperature.Yet, this method leads to wrong estimations when the two peaksare closed together, as in the case of Fig. 4 where a greater massfraction was considered. Moreover, the raw determination of theenthalpy from the experimental thermogram still lead to spuriousresults [8], as shown in Figs. 5 and 6. In the first case, of a lowconcentration, the integrated profile is much more spread than theexact enthalpy and an offset of the liquidus temperature (i.e. endof the melting) of 2–5 ◦C is observed. Generally, the corresponding
1216/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
0
50
100
150
200
250
300
enth
alpy
(Jk
g-1
)
40 50 60 70 80 90 100 110 120
temperature ( C)
0
50
100
150
200
250
300
enth
alpy
(Jk
g-1
)
40 50 60 70 80 90 100 110 120
temperature ( C)
1316/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
Erreur(très)courante
Enthalpies:h=h(β)§ Incohérencethermodynamique…§ Variabled’étatindépendanteducheminsuivi§ spécialistesobSennentdesvaleurséloignéesdecellesavancéesparlesfournisseurs(#10–47%)[Lazaro2006,Barreneche2013,Lazaro2016]
1416/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
0
50
100
150
200
250
300
350
400
h(T
)[k
J/k
g]
-2 -1 0 1 2 3 4 5 6 7 8
T [ C]
0
50
100
150
200
250
300
350
400
-2 -1 0 1 2 3 4 5 6 7 8
-50
0
50
100
150
200
250
300
350
400
h(T
)[k
J/k
g]
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
T [ C]
1516/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
1616/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onInterpréta5on
Inconnuessurcertainsparamètres
Modestep§ Paramétrageetinfluencedesdifférentssteps:
§ Intervalledetempérature§ Vitessedechauffe
§ Influencedubruitsurlesignal§ StabilitédescondiSonsopératoires(cyclecomplet#jour)
17
Modélisa)on
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Analysethéorique
Comportementdelacellule§ Présencedetransfertsthermiquespendantlechangementdephase
Erreurcommise§ Hypothèsedesuited’étatàl’équilibrefausselorsdelatransiSon
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
16/03/2017
FT
plt FT T>
φ(t) ≅ φ(TP ) ≠dhdT
19
Modélisa)on/Simula)on
Solu)on§ Prendreencomptelesphénomènesdetransfertsthermiques§ Biland’énergiecompletdusystèmeenrégimeinstaSonnaire
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
16/03/2017
Z zR
r
1α
2α2α2α
pltT
TP
r
z@⌦3
@⌦1
@⌦2
↵3
↵2
↵1
( ).h Ttρ
λ∂
= ∇ ∇∂
( )i i plt ii
S T Tφ α= −∑
20
Modélisa)on/Simula)on
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
16/03/2017
21
Résultats
Influencedesparamètresdebase§ masse§ vitesse
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
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-50000
0
50000
100000
150000
200000
250000
-5 0 5 10 15 20
0.5K/min 1K/min 2K/min 5K/min
10K/min 15K/min 20K/min
J/kg.K
Tplt
22
Résultats
Challengedesméthodesusuelles
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
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-20
0
20
40
60
80
-20 -15 -10 -5 0 5 10
mW
TpltTonset
TMTE
-20
0
20
40
60
80
-20 -15 -10 -5 0 5 10
mW
Tplt
TE TM
(a)(b)
(c)
23
Résultats
Challengedesméthodesusuelles
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
16/03/2017
�2 0 2 4 6 80
0.5
1
1.5
2·10�2
A
B
C
D
E
F
Tplt(�C)
�(W
)
Figure 8: Thermogram (red) and baseline (blue) for the water–L case.
23
24
Résultats
Challengedesméthodesusuelles
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
16/03/2017
100
150
200
250
300
350
400
h(T
)[kJ/k
g]
260 270 280 290 300 310 320
T [�C]href (T ){Ti, hi}
106
107
"[�
]
1
2
5
10
2
⌧[hrs]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
�T [K]
"⌧
5
106
"[�
]
2
5
10
⌧[hrs]
0 1 2 3 4 5 6 7 8 9 10� [K/min]
"⌧
25
Résultats
Analysedelafermeturethermodynamique
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
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-100
0
100
200
300
400
500
h[kJ/kg]
255 260 265 270 275 280 285 290 295 300
T [K]
TMSolid
Melting
Liquid
LM
-50
0
50
100
150
200
250
300
350
h[k
J/kg]
-20 -15 -10 -5 0
T [ C]
TE
TM
26
Résultats
Analysedelafermeturethermodynamique
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onModélisa5on
16/03/2017
2716/03/2017
Caractérisa)on
2816/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Iden)fica)on:méthodesinverses
Combinaisonexp./num.§ MesuredufluxdechaleurenfoncSondutemps§ ModélisaSonetsimulaSondelacellulesollicitée
Couplage§ DéfiniSond’uncritèredecomparaison(foncSonobjecSf)§ ModificaSondesparamètresd’entrée,dontlesparamètresthermodynamiques,pourminimiserlafoncSonobjecSf
§ Simplex...§ AlgorithmesgénéSques
Mesure
ModèleDirect
Thermo
Réponse
Systèmeréel
Algorithmed’inversion
2916/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Processusd’inversion
3016/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Processusd’inversion
3116/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Processusd’inversion
3216/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Processusd’inversion
3316/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Processusd’inversion
3416/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Processusd’inversion
3516/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Résultats
Corpspurs
3616/03/2017Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onCaractérisa5on
Résultats
Mélanges
-50
0
50
100
150
200
250
300
350
h(T
)[k
J/k
g]
-20 -15 -10 -5 0
T [ C]
x=10.0%
x=9.02%
x=5.0%
x=0.48%
37
Conclusion
16/03/2017
38
Conclusion
Méthodepra)que§ InformaSonsparcellaires§ Biaisdemesurecourant§ InterprétaSonerronée(très)répandue
Numériqueindispensable§ Meilleurecompréhensiondesphénomènesimpliqués,etdeleursconséquences§ ChallengeetamélioraSondesméthodesusuelles§ Aideàlamiseenplacedenouvellesméthodeset/ouprotocoles§ CaractérisaSonpluspoussée
§ Thermodynamiqueconsistante§ Touttypedeloid’état
Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onConclusion
16/03/2017
40
Annexes
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41Caractérisa)onparDSC:défautsintrinsèquesetapportsdelamodélisa)onBibliographie
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