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Crystallization behavior of a borosilicate nuclear glass in isothermal and thermal gradient conditions Olivier Delattre 1 , Elise Regnier 1 , Sophie Schuller 1 , Guy Matzen 2 (1) CEA DEN/DTCD/SECM/LDMC, Marcoule, France (2) Laboratoire Conditions Extrêmes et Matériaux, Hautes Températures et Irradiations (CEMHTI), CNRS, Orléans, France Glass compositions Glass transition temperature : 518 ± 2 °C Image analysis method An Image analysis method is being developed to study the crystallization kinetics in glass samples treated in both isothermal and thermal gradient conditions. 1. Acquisition of SEM fields or X-Ray maps 2. Segmentation of the image based on contrast thresholding , or separation of the color channel (red, green or blue) of a X-Ray map 3. Determination of : - N s : Number of particles, - A i : Area for each crystal i, - L i : Length of the smallest ellipsoid that can enclose the crystal I (maximum L max ) - L i : Width of the said ellipsoid (maximum l max ) + Calculation of the surface density D and the surface fraction f of the crystalline phase and measurement of the total area A t of the analyzed glass sample. 4. Transposition of surface data to volume (N: number of particles per unit volume) data using stereology methods found in the literature. For example, in the case of ellipsoid (3) (3) D.T. Dehoff, F. N. Rhines, Determination of number of particles per unit volume from measurements made on random plane sections: The general cylinder and ellipsoid, Transactions of the metallurgical society of AIME 221 (1961) 975-982 Study of crystallization under thermal gradient conditions 1- Realization of thermal gradient heat treatments on UOX2 and FN1C114 glass using a vertical thermal gradient furnace. Duration of the experiments : 10, 65 or 100 h Mass of glass : 337 g or 800 g Thermal gradients : 100 to 300°C.cm -1 2- A large number of SEM field are automatically taken by a Zeiss Supra 55 FEG SEM with a constant magnification (Magn:2000). 3- The image analysis method is applied on each line of a SEM field matrix which long axe is parallel to the direction of the thermal gradient, thus allowing to plot the evolution of the crystallization first as a function of the position in the crucible and then as a function of the temperature (which allow us to compare isotherm and thermal gradient crystallization data). Crystalline phases observed in UOX2 and FN1C114 glass, growth kinetics Crystalline phases observed in UOX2 and FN1C114 glass : Crystallization kinetics in glass samples exposed to isothermal heat treatments : 0,66 3,51 1,22 0,62 0,25 0,86 1,36 0,08 0,84 1,3 0,3 0,42 0,03 0,05 0,15 % Weight (theorical) Pr 2 O 3 Nd 2 O 3 Ce 2 O 3 La 2 O 3 Y 2 O 3 BaO Cs 2 O Eu 2 O 3 Pd RuO 2 TeO 2 Sm 2 O 3 SnO 2 CdO Gd 2 O 3 Composé R7T7 type glass “UOX2” Element % Weight (theorical) SiO 2 44,35 B 2 O 3 13,34 Na 2 O 9,22 Al 2 O 3 4,18 CaO 3,81 Li 2 O 1,94 Fe 2 O 3 2,92 NiO 0,08 Cr 2 O 3 0,05 ZnO 2,32 P 2 O 5 0,22 SrO 0,4 ZrO 2 2,77 MoO 3 2,22 MnO 2 0,47 CoO 0,08 Glass frit used to start the industrial process « FN1C114 » glass Element % Weight (theorical) SiO 2 46.63 B 2 O 3 14.68 Al 2 O 3 5.16 Na 2 O 10.05 CaO 4.10 Li 2 O 2.00 Fe 2 O 3 3.99 CoO 0.70 NiO 0.50 ZnO 2.52 ZrO 2 2.52 Nd 2 O 3 7.31 L i l i Area A i ) ( max q K l N N s max max L l q 2 2 1 ) 1 1 ln( 1 2 1 ) ( q q q q q q K Segmentation based on contrast thresholding Segmentatio n based on the separation of color channels Apatites Calcium silicates Aluminosilicat e Powellite CaMoO 4 Apatites Ca 3 Nd 7 (PO 4 )(SiO 4 ) 5 O 2 Aluminosilicate NaAlSi 3 O 8 Calcium silicates CaSiO 3 G row th speed ofpow ellite in the U O X2 glass 0 2E-10 4E-10 6E-10 8E-10 1E-09 1.2E -09 1.4E -09 1.6E -09 550 650 750 850 950 Tem perature (°C ) G row th velocity (m /s) Width_experimental Width_modeled Length_experimentall Lenght_modeled G row th speed ofapatite in the U O X 2 glass 0 2E-10 4E-10 6E-10 8E-10 550 650 750 850 950 Tem pérature (°C ) G rowth velocity (m /s) Length_modeled Length_experimental Width_modeled Width_experimental t s A N D t N i i A A f s 1 ~600°C ~1170°C Crystallize d area 5 cm 764° C 807°C 2.2 mm UOX2 glass treated under a ~300°C.cm -1 thermal gradient BSE SEM field X-Ray Map Segmentation of 3 different crystalline phases 111 µm Cerianites Ce/ZrO 2 SEM Fields Context and aims of the study Context : This work lies in the studies on the vitrification of the high- level nuclear waste with the skull-melting process (described below). We more specifically focus on the crystallization that is likely to appear in the thermal gradient area (“cold-crucible”) near the wall of the crucible (in the R7T7 type glass and glass frit) during the melting process. Aims of the study : In order to study the crystallization kinetics of UOX2 and FN1C114 glass in the experimental conditions of the skull- melting process, a threefold methodology has been followed : Firstly, a method must be developed to quantify the crystallization found in the thin (~5 mm) thermal gradient area of the cold crucible process (method based on image analysis). Secondly, one must replicate the strong thermal gradient (~ 1000°C.cm -1 ) found in the cold crucible process at laboratory scale. Thirdly, the impact of the thermal gradient on the crystallization of high-level waste glass will be determined by comparing data acquired through isothermal heat treatments of glass with data coming from thermal gradient experiments. Stirrin g Glass melt 1200°C Induction coils Water circulation Thermal gradient area (1000°C.cm -1 ) => Solidified glass layer called « self crucible » UOX2 + glass frit « FN1C114 » Crucible Calcined high level waste + glass frit R7T7 type glass « UOX2 » Conclusion and prospects An image analysis method, based on contrast thresholding, is being used to quantify the crystallization kinetics in simulated high-level nuclear waste glass. Kinetics of crystallization of both apatite and powellite are studied in glass which have undergone isothermal and thermal gradient heat treatments. Crystallization content and their morphology in thermal gradients (up to 300°C.cm -1 ) are in good agreement with results obtained by studying glass exposed to isothermal heat treatments. Experiments are on their way to quantify the crystallization kinetics of apatite and powellite in samples which have undergone stronger thermal gradient (~1000°C.cm -1 ). These data, acquired thanks to experimentations realized at laboratory scale, will be compared with data coming from the analysis of samples issued from the thermal gradient area of vitrification tests with the skull-melting process, at an industrial scale. This methodology would allow us to study the relevance of experimentations realized at laboratory scale, thus validating our experimental approach. In the long run, these data will be used to model the behavior of high-level nuclear waste glass in the BSE SEM field X-ray map Cooled wall Heating resistor Observations : => The same type of crystals (nature and morphology) is observed in isothermal and thermal gradient experiments. Pow ellite 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 D istance from the cooled sole (m m) Fraction (% ) 800g_140°C /cm 337g_300°C /cm A patite 0 0.5 1 1.5 2 0 5 10 15 20 25 D istance from the sole (m m) Fraction (% ) 800g_140°C /cm 337g_300°C /cm UO X2,A patite,65h,140 and 300 °C /cm 0 0.5 1 1.5 2 2.5 3 650 700 750 800 850 900 950 1000 1050 Tem perature (°C ) Surface fraction (% ) Theoretical m axim al surface fraction Apatite_300°C /cm Apatite_140°C /cm Isotherm al data_apatite (65h) UO X 2,Pow ellite,65h,140°C /cm 0 0.5 1 1.5 2 2.5 3 3.5 630 680 730 780 830 880 tem perature (°C ) Surface fraction(% ) Theoretical m aximal surface fraction Pow ellite_therm al gradient Isotherm al data_pow ellite (65h) Surface fraction of powellite and apatite as a function of the distance from the sole Comparison between isothermal and thermal gradient data

Crystallization behavior of a borosilicate nuclear glass in isothermal and thermal gradient conditions Olivier Delattre 1, Elise Regnier 1, Sophie Schuller

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  • Crystallization behavior of a borosilicate nuclear glass in isothermal and thermal gradient conditions Olivier Delattre1, Elise Regnier1, Sophie Schuller1, Guy Matzen2 (1) CEA DEN/DTCD/SECM/LDMC, Marcoule, France (2) Laboratoire Conditions Extrmes et Matriaux, Hautes Tempratures et Irradiations (CEMHTI), CNRS, Orlans, FranceGlass compositions

    Glass transition temperature : 518 2 CImage analysis methodAn Image analysis method is being developed to study the crystallization kinetics in glass samples treated in both isothermal and thermal gradient conditions.1. Acquisition of SEM fields or X-Ray maps

    2. Segmentation of the image based on contrast thresholding , or separation of the color channel (red, green or blue) of a X-Ray map

    3. Determination of :Ns: Number of particles, Ai: Area for each crystal i,Li: Length of the smallest ellipsoid that can enclose the crystal I (maximum Lmax)Li: Width of the said ellipsoid (maximum lmax) + Calculation of the surface density D and the surface fraction f of the crystalline phase and measurement of the total area At of the analyzed glass sample.

    4. Transposition of surface data to volume (N: number of particles per unit volume) data using stereology methods found in the literature. For example, in the case of ellipsoid(3)

    (3) D.T. Dehoff, F. N. Rhines, Determination of number of particles per unit volume from measurements made on random plane sections: The general cylinder and ellipsoid, Transactions of the metallurgical society of AIME 221 (1961) 975-982Study of crystallization under thermal gradient conditions 1- Realization of thermal gradient heat treatments on UOX2 and FN1C114 glass using a vertical thermal gradient furnace.

    Duration of the experiments : 10, 65 or 100 hMass of glass : 337 g or 800 g Thermal gradients : 100 to 300C.cm-1

    2- A large number of SEM field are automatically taken by a Zeiss Supra 55 FEG SEM with a constant magnification (Magn:2000).

    3- The image analysis method is applied on each line of a SEM field matrix which long axe is parallel to the direction of the thermal gradient, thus allowing to plot the evolution of the crystallization first as a function of the position in the crucible and then as a function of the temperature (which allow us to compare isotherm and thermal gradient crystallization data).

    Crystalline phases observed in UOX2 and FN1C114 glass, growth kineticsCrystalline phases observed in UOX2 and FN1C114 glass :

    Crystallization kinetics in glass samples exposed to isothermal heat treatments :

    LiliArea AiSegmentation based on contrast thresholdingSegmentation based on the separation of color channelsApatitesCalcium silicatesAluminosilicatePowellite CaMoO4Apatites Ca3Nd7(PO4)(SiO4)5O2Aluminosilicate NaAlSi3O8Calcium silicates CaSiO3~600C~1170CCrystallized area5 cm764C807C2.2 mmUOX2 glass treated under a ~300C.cm-1 thermal gradient BSE SEM fieldX-Ray MapSegmentation of 3 different crystalline phases111 mCerianites Ce/ZrO2SEM FieldsContext and aims of the studyContext : This work lies in the studies on the vitrification of the high-level nuclear waste with the skull-melting process (described below). We more specifically focus on the crystallization that is likely to appear in the thermal gradient area (cold-crucible) near the wall of the crucible (in the R7T7 type glass and glass frit) during the melting process.

    Aims of the study : In order to study the crystallization kinetics of UOX2 and FN1C114 glass in the experimental conditions of the skull-melting process, a threefold methodology has been followed : Firstly, a method must be developed to quantify the crystallization found in the thin (~5 mm) thermal gradient area of the cold crucible process (method based on image analysis). Secondly, one must replicate the strong thermal gradient (~ 1000C.cm-1) found in the cold crucible process at laboratory scale. Thirdly, the impact of the thermal gradient on the crystallization of high-level waste glass will be determined by comparing data acquired through isothermal heat treatments of glass with data coming from thermal gradient experiments.Conclusion and prospectsAn image analysis method, based on contrast thresholding, is being used to quantify the crystallization kinetics in simulated high-level nuclear waste glass. Kinetics of crystallization of both apatite and powellite are studied in glass which have undergone isothermal and thermal gradient heat treatments. Crystallization content and their morphology in thermal gradients (up to 300C.cm-1) are in good agreement with results obtained by studying glass exposed to isothermal heat treatments. Experiments are on their way to quantify the crystallization kinetics of apatite and powellite in samples which have undergone stronger thermal gradient (~1000C.cm-1). These data, acquired thanks to experimentations realized at laboratory scale, will be compared with data coming from the analysis of samples issued from the thermal gradient area of vitrification tests with the skull-melting process, at an industrial scale. This methodology would allow us to study the relevance of experimentations realized at laboratory scale, thus validating our experimental approach. In the long run, these data will be used to model the behavior of high-level nuclear waste glass in the thermal gradient area of the skull-melting process.BSE SEM fieldX-ray mapCooled wallHeating resistor Observations : => The same type of crystals (nature and morphology) is observed in isothermal and thermal gradient experiments.Surface fraction of powellite and apatite as a function of the distance from the soleComparison between isothermal and thermal gradient data

    Glass frit used to start the industrial process FN1C114 glassElement% Weight (theorical)SiO246.63B2O314.68Al2O35.16Na2O10.05CaO4.10Li2O2.00Fe2O33.99CoO0.70NiO0.50ZnO2.52ZrO22.52Nd2O37.31

    Donnes

    TempratureT (kelvin)1E4/TVitesse de croissance (longitudinale)Vitesse de croissance (transversale)Vitesse de cristallisationTaux de nuclation (Nbrepart.m^-2.h-1)I (Nbrepart.m^-2/s^-1Ln(I)

    700973.510.2722136620.34888391970.14916200580.02406178670.00133300244798808540369.8929.1993887823

    725998.510.01502253382.1462590.78692233330.13704607950.00080816152909381559906.0928.6989616522

    7501023.59.7703957011.50942491310.3614863710.11306673860.0001551366558491595447.77227.0485054069

    7751048.59.53743443011.93925756140.53555418460.33977111820.00046268831665677961266.8428.1412533404

    8401113.58.98069151321.34415829930.66984592940.05747389160.0001198907431606394402.99826.7907798858

    8551128.58.86132033671.85688761260.71338526130.09603801780.0001956166704219766702.14427.280356313

    8701143.58.7450808922.48030661291.23229532260.07130167760.0002432704875773610088.74427.4983734585

    9001173.58.521516831.80745957450.89724468090.07136074560.0002161784778242062948.60627.3803034476

    Fit sous origin

    Ln(I)

    10.27221366229.1993887823

    10.015022533828.6989616522

    9.537434430128.1412533404

    8.861320336727.280356313

    8.74508089227.4983734585

    8.5215168327.3803034476

    105.9

    1.38E-23

    1.55E-22

    23201.7647058824

    10.48.7

    TempratureT (kelvin)1E4/TVitesse de croissance max (longitudinale) (m/h)Vitesse de croissance max (transversale) (m/h)Vitesse de croissance max (longitudinale) (m/s)Vitesse de croissance max (transversale) (m/s)Xo longitudinalXO lateralm.hm.hln(u) longitudinalln(u) transversal(1/RT)*1000

    700973.510.2722136621.808750.36278257980.00000000050.00000000015.00E-109.00E-111.80E+003.24E-01-21.4115636834-23.01815126030.1236126794

    725998.510.01502253384.2505651.1447950.00000000120.00000000037.50E-102.00E-102.70E+007.20E-01-20.5571477671-21.86897410070.12051772

    7501023.59.7703957014.627681.281810.00000000130.00000000041.00E-092.00E-103.60E+007.20E-01-20.4721440198-21.75592654080.1175739555

    7751048.59.53743443014.8517421.487030.00000000130.00000000041.24E-093.50E-104.46E+001.26E+00-20.4248618667-21.60741884030.1147705708

    8401113.58.98069151323.902722.506440.00000000110.00000000071.00E-097.00E-103.60E+002.52E+00-20.6425259365-21.08533626270.1080708967

    8551128.58.86132033672.6426781.21140.00000000070.00000000035.40E-107.00E-101.94E+002.52E+00-21.0324068855-21.81242296680.1066344204

    8701143.58.7450808921.245770.7343750.00000000030.00000000022.50E-103.00E-109.00E-011.08E+00-21.7844458698-22.31293516410.1052356305

    9001173.58.521516831.841141.139120.00000000050.0000000003000.00E+000.00E+00-21.3938147374-21.87394364790.1025453289

    Donnes

    0

    0

    0

    0

    0

    0

    Ln(I)

    graphiques

    2.78E-10

    0.0000000019

    graphiques

    0.34888391970.1491620058

    2.1462590.7869223333

    1.50942491310.361486371

    1.93925756140.5355541846

    1.34415829930.6698459294

    1.85688761260.7133852613

    2.48030661291.2322953226

    1.80745957450.8972446809

    Vitesse de croissance (longitudinale)

    Vitesse de croissance (transversale)

    Temprature (C)

    Vitesse de croissance (m/h)

    Vitesses de croissances longitudinales et laterales

    Rapport des rponses 1

    0.0240617867

    0.1370460795

    0.1130667386

    0.3397711182

    0.0574738916

    0.0960380178

    0.0713016776

    0.0713607456

    Vitesse de cristallisation

    Temprature (C)

    Vitesse de cristallisation (%/h)

    Graph2

    0.0013330024

    0.0008081615

    0.0001551366

    0.0004626883

    0.0001198907

    0.0001956166

    0.0002432704

    0.0002161784

    Taux de nuclation (Nbrepart.m^-2.h-1)

    Temprature (C)

    Nbrepart.m^-2.h^-1

    Taux de nucltation surfacique_powellite

    mthode des moindres carrs

    29.1993887823

    28.6989616522

    27.0485054069

    28.1412533404

    26.7907798858

    27.280356313

    27.4983734585

    27.3803034476

    Ln(I)=f(1/T)

    1/T

    Ln(I)

    y = 0.9515x + 11.962R2 = 0.5321

    1.808750.3627825798

    4.2505651.144795

    4.627681.28181

    4.8517421.48703

    3.902722.50644

    2.6426781.2114

    1.245770.734375

    1.841141.13912

    Vitesse de croissance max (longitudinale) (m/h)

    Vitesse de croissance max (transversale) (m/h)

    Temprature (C)

    Vitesse de croissance (m/h)

    Vitesse de croissance de la powellite

    0.00000000050.00000000010.00000000050.0000000001

    0.00000000120.00000000030.00000000080.0000000002

    0.00000000130.00000000040.0000000010.0000000002

    0.00000000130.00000000040.00000000120.0000000004

    0.00000000110.00000000070.0000000010.0000000007

    0.00000000070.00000000030.00000000050.0000000007

    0.00000000030.00000000020.00000000020.0000000003

    0.00000000050.000000000300

    Vitesse de croissance max (longitudinale) (m/s)

    Vitesse de croissance max (transversale) (m/s)

    Xo longitudinal

    XO lateral

    Temprature (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance de la powellite

    1.808750.36278257981.80.324

    4.2505651.1447952.70.72

    4.627681.281813.60.72

    4.8517421.487034.4641.26

    3.902722.506443.62.52

    2.6426781.21141.9442.52

    1.245770.7343750.91.08

    1.841141.1391200

    Vitesse de croissance max (longitudinale) (m/h)

    Vitesse de croissance max (transversale) (m/h)

    Vitesse de croissance longitudinale max_XO

    Vitesse de croissance latrale max_Xavier Orlhac

    Temprature (C)

    Vitesse de croissance (m.h^1)

    Vitesse de croissance de la powellite

    -21.4115636834-20.6425259365

    -20.5571477671-21.0324068855

    -20.4721440198-21.7844458698

    -20.4248618667-21.3938147374

    ln(uL) BT

    ln(uL) HT

    1000/RT

    ln(U)

    ln(uL)

    Microsoft Excel 11.0 Rapport des rponses

    Feuille: [Vitesses.xls]mthode des moindres carrs

    Date du rapport: 19/04/2012 12:45:14

    Cellule cible (Valeur)

    CelluleNomValeur initialeValeur finale

    $K$10somme des carrs carrs_Ul0.0000000030.000000003

    Cellules variables

    CelluleNomValeur initialeValeur finale

    $B$24A Valeurs2.60E+072.60E+07

    $B$25Gd Valeurs103341.962798267103341.962798267

    $B$26B Valeurs7.00E-077.00E-07

    $B$27Tl Valeurs1215.56239049251215.5623904925

    Contraintes

    Aucune

    0.000000000100.00000000040

    0.000000000300.00000000060

    0.000000000400.00000000070.0000000001

    0.000000000400.00000000130.0000000001

    0.000000000700.00000000110.0000000001

    0.00000000030.00000000010.00000000070.0000000001

    0.00000000020.00000000010.00000000030.0000000001

    0.00000000030.00000000010.00000000050.0000000002

    0.00000000010.0000000002

    0.00000000010.0000000002

    0.00000000010.0000000003

    0.00000000020.0000000003

    0.00000000020.0000000004

    0.00000000020.0000000005

    0.00000000030.0000000005

    0.00000000030.0000000006

    0.00000000040.0000000007

    0.00000000040.0000000008

    0.00000000050.0000000009

    0.00000000050.000000001

    0.00000000060.000000001

    0.00000000060.0000000011

    0.00000000060.0000000011

    0.00000000060.0000000011

    0.00000000060.000000001

    0.00000000060.0000000009

    0.00000000050.0000000007

    0.00000000040.0000000003

    0.0000000002880

    Width_experimental

    Width_modeled

    Length_experimentall

    Lenght_modeled

    Temperature (C)

    Growth velocity (m/s)

    Growth speed of powellite in the UOX2 glass

    TempratureT (kelvin)1E4/TVitesse de croissance max (longitudinale) (m/s)Vitesse de croissance max (transversale) (m/s)Vitesse de croissance max (longitudinale) (m/h)Vitesse de croissance max (transversale) (m/h)Valeur modlise_ULcarrs_UlValeur modlise_ulcarrs_Ul

    700973.510.2722136620.00000000040.00000000011.60.36278257980.000000000300.00000000010

    725998.510.01502253380.00000000060.00000000032.11.1447950.000000000400.00000000020

    7501023.59.7703957010.00000000070.00000000042.41.281810.000000000600.00000000030

    7751048.59.53743443010.00000000130.00000000044.8517421.487030.000000000800.00000000040

    8401113.58.98069151320.00000000110.00000000073.902722.506440.00000000100.00000000060

    8551128.58.86132033670.00000000070.00000000032.6426781.21140.000000000800.00000000060

    8701143.58.7450808920.00000000030.00000000021.245770.7343750.000000000300.00000000040

    9001173.58.521516830.00000000050.00000000031.841141.13912-0.00000000180-0.00000000050

    Paramtres_longitudinaleValeurs

    A4.00E+07

    Gd192000

    B8.00E-07

    Tl1150

    somme des carrs0

    876.5

    Paramtres_transversaleValeurs

    A2.40E+07

    Gd193000

    B7.00E-07

    Tl1161

    887.5

    somme des carrs0

    2.60E+07

    184000

    7.00E-07

    1156

    Modlisation

    600873.500

    610883.500

    620893.50.00000000010

    630903.50.00000000010

    640913.50.00000000010

    650923.50.00000000010.0000000001

    660933.50.00000000010.0000000001

    670943.50.00000000020.0000000001

    680953.50.00000000020.0000000001

    690963.50.00000000020.0000000001

    700973.50.00000000030.0000000001

    710983.50.00000000030.0000000002

    720993.50.00000000040.0000000002

    7301003.50.00000000050.0000000002

    7401013.50.00000000050.0000000003

    7501023.50.00000000060.0000000003

    7601033.50.00000000070.0000000004

    7701043.50.00000000080.0000000004

    7801053.50.00000000090.0000000005

    7901063.50.0000000010.0000000005

    8001073.50.0000000010.0000000006

    8101083.50.00000000110.0000000006

    8201093.50.00000000110.0000000006

    8301103.50.00000000110.0000000006

    8401113.50.0000000010.0000000006

    8501123.50.00000000090.0000000006

    8601133.50.00000000070.0000000005

    8701143.50.00000000030.0000000004

    8801153.50.0000000002

    00

    00

    00

    00

    00

    00

    00

    00

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    vitesse transversale

    Modlisation

    T (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance transversale

    00

    00

    00

    00

    00

    00

    00

    00

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Vitesse de croissance max (longitudinale) (m/s)

    Modlisation

    T (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance longitudinale

    0000

    0000

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    Powellite_transversal

    Modlisation_transversal

    Powellite_longitudinal

    Modlisation_longitudinal

    T (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance longitudinale de la powellite

    00

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    Vitesse de croissance max (longitudinale) (m/s)

    Modlisation

    T (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance longitudinale de la powellite

    0000

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    Growth velocity_width_experimental

    Growth velocity_width_modeled

    Growth velocity_length_experimentall

    Growth velocity_lenght_modeled

    Temperature (C)

    Growth velocity (m/s)

    Growth speed of powellite in the UOX2 glass

    donnes

    TempratureT (kelvin)10000/TI (nbrepart/m/h)I (Nbrepart/m/s)ln(I)

    700973.50.00102722140.000025169190608889979.407525.2298181686

    725998.50.00100150230.000019850871462714638.627824.992441677

    7501023.50.00097703960.0000321063115582786377.32625.4732528753

    7751048.50.00095374340.000022696281706165645.308525.1263953029

    8401113.50.00089806920.0000888547319876762315.79126.4912016408

    8551128.50.00088613200

    8701143.50.000874508100

    9001173.50.000852151700

    graphique

    Ea-99.13kJ/mol

    http://pcml.univ-lyon1.fr/spip.php?article226Ea Deligny-120kJ/mol-20

    0.00075.25

    0.0009252.5

    12222.2222222222

    122.2222222222

    TempratureT (kelvin)1E4/TVitesse de croissance max (longitudinale) (m/h)Vitesse de croissance max (transversale)ln(uL)ln(ul)(1/RT)*1000

    700973.510.2722136620.42539119360.1587945779-0.8547460779-1.84014387510.1236126794

    725998.510.01502253380.81152272730.2030163636-0.2088428859-1.59446869410.12051772

    7501023.59.7703957011.46648181820.29715181820.3828662113-1.21351209850.1175739555

    7751048.59.53743443011.11142928570.27713785710.1056468318-1.28324021740.1147705708

    8401113.58.98069151322.45998142860.55321714290.9001538006-0.59200469110.1080708967

    8551128.58.861320336700000.1066344204

    8701143.58.74508089200000.1052356305

    9001173.58.5215168300000.1025453289

    graphique

    25.2298181686

    24.992441677

    25.4732528753

    25.1263953029

    26.4912016408

    ln(I)

    1/T (1/K)

    Ln(I)

    Ln(I)=f(1/T)

    Graph1

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    Vitesse de croissance max (longitudinale) (m/h)

    Vitesse de croissance max (transversale)

    Temprature (K)

    Vitesse de croissance (m/h)

    Vitesse de croissance des apatites

    mthodes des moindres carrs

    0.0000251691

    0.0000198508

    0.0000321063

    0.0000226962

    0.0000888547

    0

    0

    0

    Nuclation apatites

    Temprature (K)

    Densit surfacique (Nbrepart.m^-2.h^-1)

    Taux de nuclation surfacique_apatites

    00

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    00

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    00

    ln(uL)

    ln(ul)

    1/T

    ln(u)

    ln(u)=f(1/T)

    y = -1.2291x + 12.006R2 = 0.8552

    y = -0.9313x + 7.7432R2 = 0.9523

    00.000000000100

    00.000000000200.0000000001

    00.000000000400.0000000001

    00.000000000300.0000000001

    0.00000000010.000000000700.0000000002

    0.0000000001000

    0.0000000001000

    0.0000000001000

    0.00000000010

    0.00000000010

    0.00000000020

    0.00000000020

    0.00000000020.0000000001

    0.00000000030.0000000001

    0.00000000030.0000000001

    0.00000000040.0000000001

    0.00000000040.0000000001

    0.00000000050.0000000001

    0.00000000050.0000000001

    0.00000000060.0000000001

    0.00000000060.0000000001

    0.00000000070.0000000001

    0.00000000070.0000000002

    0.00000000070.0000000001

    0.00000000060.0000000001

    0.00000000060.0000000001

    0.00000000040.0000000001

    0.00000000020

    -0-0

    Length_modeled

    Length_experimental

    Width_modeled

    Width_experimental

    Temprature (C)

    Growth velocity (m/s)

    Growth speed of apatite in the UOX2 glass

    TempratureT (kelvin)1E4/TVitesse de croissance max (longitudinale) (m/s)Vitesse de croissance max (transversale) (m/s)Vitesse de croissance max (longitudinale) (m/h)Vitesse de croissance max (transversale) (m/h)Valeur modlise_ULcarrs_UlValeur modlise_ulTemprature

    700973.50.000000000100.42539119360.15879457790.000000000200700

    725998.50.00000000020.00000000010.81152272730.20301636360.000000000300.0000000001725

    7501023.50.00000000040.00000000011.46648181820.29715181820.000000000400.0000000001750

    7751048.50.00000000030.00000000011.11142928570.27713785710.000000000500.0000000001775

    8401113.50.00000000070.00000000022.45998142860.55321714290.000000000600.0000000001840

    8551128.500000.000000000500.0000000001855

    8701143.500000.000000000200870

    9001173.50000-0.0000000010-0.0000000002900

    Paramtres_ULValeursParamtres_UL

    A2.80E+07A

    Gd192000Gd

    B6.70E-07B

    Tl1152Tl

    somme des carrs0somme des carrs

    878.5

    Paramtres_UlValeursParamtres_Ul

    A1.10E+07A

    Gd192000Gd

    B4.00E-07B

    Tl1150Tl

    876.5

    somme des carrs6415somme des carrs

    ModlisationModlisation

    600873.500600

    610883.500610

    620893.500620

    630903.500630

    640913.50.00000000010640

    650923.50.00000000010650

    660933.50.00000000010660

    670943.50.00000000010670

    680953.50.00000000010680

    690963.50.00000000010690

    700973.50.00000000020700

    710983.50.00000000020710

    720993.50.00000000020.0000000001720

    7301003.50.00000000030.0000000001730

    7401013.50.00000000030.0000000001740

    7501023.50.00000000040.0000000001750

    7601033.50.00000000040.0000000001760

    7701043.50.00000000050.0000000001770

    7801053.50.00000000050.0000000001780

    7901063.50.00000000060.0000000001790

    8001073.50.00000000060.0000000001800

    8101083.50.00000000070.0000000001810

    8201093.50.00000000070.0000000002820

    8301103.50.00000000070.0000000001830

    8401113.50.00000000060.0000000001840

    8501123.50.00000000060.0000000001850

    8601133.50.00000000040.0000000001860

    8701143.50.00000000020870

    8801153.5-0-0880

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    Vitesse de croissance max (longitudinale) (m/s)

    Vitesse de croissance max (transversale) (m/s)

    00

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    Vitesse de croissance max (longitudinale) (m/s)

    Valeur modlise_UL

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    Vitesse de croissance max (transversale) (m/s)

    Valeur modlise_ul

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    Vitesse de croissance longitudinale

    Donnes exprimentales

    Temprature (K)

    Vitesse de croissance (m/s)

    Vitesses de croissance longitudinale

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    modlisation

    Donnes exprimentales_Ul

    Temprature (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance laterale

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    Vitesse de croissance longitudinale

    Donnes exprimentales

    Temprature (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance longitudinale des apatites

    0000

    0000

    0000

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    modlisation_laterale

    Vitesse de croissance_laterale

    modlisation_longitudinale

    vitesse de croissance_longitudinale

    Temprature (K)

    Vitesse de croissance (m/s)

    Vitesse de croissance des apatites

    Powellite_donnes

    EchantillonsNumro de dossierTemprature estimeAire analyseLongueur moyenneLargeur moyenneNombre de particulesAire moyenne d'une particuleAire totale de phase cristallineFraction surfaciqueDensit surfaciqueFraction avramiT (K)1000/RTnln(-ln(1-x))ln(-ln(1-x))-nln(t)Distance par rapport la soleDistance (mm)TempratureGradient

    SP12/165(bas)1651.444724516428000000000924.94472450.13010176740.73134924380030533.053

    SP12/165(bas)2652.994173516428000000000926.49417350.1298841880.72716573160031643.164

    SP12/165(bas)3654.543622516428000000000928.04362250.12966733520.72298221920032753.275

    SP12/165(bas)4656.093071516428000000000929.59307150.12945120520.7187987070033863.386

    SP12/165(bas)5657.642520516428000000000931.14252050.12923579450.71461519460034973.497

    SP12/165(bas)6659.191969516428000000000932.69196950.12902109950.71043168240036083.608

    SP12/165(bas)7660.741418516428000000000934.24141850.12880711670.706248170037193.719

    SP12/165(bas)8662.290867516428000000000935.79086750.12859384250.70206465780038303.83

    SP12/165(bas)9663.840316516428000000000937.34031650.12838127340.69788114540039413.941

    SP12/165(bas)10665.389765516428000000000938.88976550.12816940590.69369763320040524.052

    SP12/165(bas)11666.939214516428000000000940.43921450.12795823650.68951412080041634.163

    SP12/165(bas)12668.488663516428000000000941.98866350.12774776180.68533060860042744.274

    SP12/165(bas)13*670.038112516428000000000943.53811250.12753797840.68114709620043854.385

    SP12/165(bas)14671.587561516428000000000945.08756150.12732888290.6769635840044964.496

    SP12/165(bas)15673.137010516428000000000946.63701050.12712047180.67278007170046074.607

    SP12/165(bas)16674.686459516428000000000948.18645950.12691274190.66859655940047184.718

    SP12/165(bas)17676.235908516428000000000949.73590850.12670568980.6644130470048294.829

    SP12/165(bas)18677.785357516428000000000951.28535750.12649931220.66022953480049404.94

    SP12/165(bas)19679.33480651642801.80657684210.7079021053950.997843157994.79510.05770337230.0005782810.0005770337952.83480650.12629360580.6560460224-7.4573212617-15.568068355450515.051

    SP12/165(bas)20680.88425551642802.01633809520.6484333333211.034338095221.72110.0132219990.00012783050.00013222954.38425550.12608856730.6518625102-8.9309773161-16.990003327751625.162

    SP12/165(bas)21682.43370451642801.98293609470.73401183431691.1607224852196.16210.11940717070.00102873140.0011940717955.93370450.12588419350.6476789979-6.7297888767-14.737093806252735.273

    SP12/165(bas)22683.98315351642801.74115517240.69825448285800.9375241379543.7640.33099829560.00353055760.003309983957.48315350.12568048120.6434954856-5.7091549604-13.664738807653845.384

    SP12/165(bas)23685.53260251642801.73382644380.74109270523291.0313887538339.32690.20655399320.00200267840.0020655399959.03260250.12547742710.6393119733-6.1813299586-14.085192723754955.495

    SP12/165(bas)24687.08205151642801.94286032790.84087213116101.3336852459813.5480.49522035550.00371317260.0049522036960.58205150.1252750280.635128461-5.3054414126-13.157583095556065.606

    SP12/165(bas)25688.63150051642801.8704982490.8178165375141.2518077821643.42920.39166617970.00312880450.0039166618962.13150050.12507328090.6309449487-5.5405540361-13.340974636957175.717

    SP12/165(bas)26690.18094951642802.07746088990.78825152224271.3865936768592.07550.36040631850.00259922080.0036040632963.68094950.12487218250.6267614364-5.623888664-13.372588182658285.828

    SP12/165(bas)27691.73039851642801.90610431770.880767232112971.42658103321850.27561.12629388850.00789505720.0112629389965.23039850.12467172980.6225779241-4.4805796108-12.177558047359395.939

    SP12/165(bas)28693.27984751642802.02983905010.74522744063791.202598153455.78470.27744381540.00230703680.0027744382966.77984750.12447191960.6183944118-5.8859181938-13.531175548160506.05

    SP12/165(bas)29694.82929651642801.81987225610.79101692076561.1946242378783.67350.47703524470.00399318240.0047703524968.32929650.12427274880.6142108995-5.3429451578-12.9364814361616.161

    SP12/165(bas)30696.37874551642801.8421205630.80961762558171.2116722154989.93620.60259082060.00497321650.0060259082969.87874550.12407421440.6100273872-5.108666525-12.65048171562726.272

    SP12/165(bas)31697.92819451642801.80759456020.81209780098641.20280057871039.21970.63259051620.00525931340.0063259052971.42819450.12387631340.6058438749-5.0599308247-12.550024932663836.383

    SP12/165(bas)32699.47764351642802.04433845640.905668187914901.55010154362309.65131.4059236060.00906988070.0140592361972.97764350.12367904260.6016603626-4.2574045799-11.695777605564946.494

    SP12/165(bas)33701.02709251642801.78971144140.802964594611101.17314216221302.18780.79266362310.00675675680.0079266362974.52709250.12348239920.5974768503-4.8335500454-12.220201988966056.605

    SP12/165(bas)34702.57654151642801.83457661690.837937893912061.2695582091531.08720.93199853910.00734112490.0093199854976.07654150.123286380.593293338-4.670916027-12.005846888367166.716

    SP12/165(bas)35704.12599051642801.99865028470.924200398617561.57193849662760.3241.68025566110.01068906740.0168025566977.62599050.12309098220.5891098257-4.0777635287-11.360973307968276.827

    SP12/165(bas)36705.67543951642802.24664372740.999464113416581.91751501813179.23991.93525681760.0100925250.0193525682979.17543950.12289620290.5849263134-3.9351749181-11.166663615169386.938

    SP12/165(bas)37707.22488851642801.96423427720.892599925513421.44693375561941.78511.18199726080.00816897980.0118199726980.72488850.12270203890.5807428011-4.4320252834-11.611792898270497.049

    SP12/165(bas)38708.77433751642802.16232608210.968125693718021.78886470593223.53421.96221950330.01096907720.019622195982.27433750.12250848750.5765592888-3.9212016841-11.049248216871607.16

    SP12/165(bas)39710.32378651642802.21528635120.973086625514581.85671289442707.08741.64784964690.00887509130.0164784965983.82378650.12231554580.5723757765-4.0974026072-11.173728057872717.271

    SP12/165(bas)40711.87323551642802.38519364011.048647631914782.20962354533265.82361.98796177260.00899683470.0198796177985.37323550.12212321090.5681922642-3.9080371691-10.932641537573827.382

    SP12/165(bas)41713.42268451642802.0110894090.864809420717091.51701421882592.57731.57814542240.01040297050.0157814542986.92268450.12193147990.5640087519-4.1409767014-11.113859987674937.493

    SP12/165(bas)42714.97213351642802.22775453320.991580040614781.87991792962778.51871.69133108110.00899683470.0169133108988.47213350.12174034990.5598252396-4.0711374819-10.992299685976047.604

    SP12/165(bas)43716.52158251642802.40357961431.071112121218152.24353168044072.012.47870099830.01104821040.02478701990.02158250.12154981830.5556417273-3.6849121128-10.554353234677157.715

    SP12/165(bas)44718.07103151642802.57213849951.258561226718262.90950120485312.74923.23395982470.01111516920.0323395982991.57103150.12135988210.551458215-3.4150708377-10.232790877478267.826

    SP12/165(bas)45719.62048051642802.2230354231.023372550216431.9809412663254.68651.98118243240.01000121740.0198118243993.12048050.12117053850.5472747027-3.911487661-10.677486618679377.937

    SP12/165(bas)46721.16992951642802.05976938780.977888775511761.71047032312011.51311.22444186750.00715850990.0122444187994.66992950.12098178490.5430911904-4.3965313888-11.110809264280488.048

    SP12/165(bas)47722.71937851642802.21769923660.94480887410481.78858005731874.43191.14099823470.00637935230.0114099823996.21937850.12079361840.5389076781-4.4675343615-11.130091154781598.159

    SP12/165(bas)48724.26882751642802.32382741151.090578144116382.26687985353713.14922.26025639150.00997078160.0226025639997.76882750.12060603630.5347241658-3.7782827506-10.389118461782708.27

    SP12/165(bas)49725.81827651642802.30392180131.121024303113992.25698298783157.51921.92203506210.00851594840.0192203506999.31827650.12041903590.5305406535-3.9420975953-10.501212224283818.381

    SP12/165(bas)50727.367725573230.60852.33646473151.06193120466892.19119027581509.73012.06161075390.00940863410.02061610751000.86772550.12023261450.5263571412-3.8712848776-10.378678424484928.492

    SP12/166(milieu)51728.9171745145067.33211.95839125820.869917810512241.40811903591723.53771.18809498670.00843746130.01188094991002.41717450.12004676950.5221736289-4.4268489191-10.882521383786038.603

    SP12/166(milieu)52730.46662351642802.39861706511.091032470115062.27471699873425.72382.08529571460.00916727540.02085295711003.96662350.1198614980.5179901166-3.8597412896-10.26369267287148.714

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    SP12/166(milieu)136860.62033951642802.6470681.5157162254.47138755561006.06220.61240698810.00136961290.00612406991134.12033950.10610597420.1665750834-5.0924585131-7.1518389941803818.038

    SP12/166(milieu)137862.16978851642801.80203245610.9485668864561.8050458333823.10090.50103536640.00277574870.00501035371135.66978850.10596120870.1623915711-5.2937383521-7.30139775081814918.149

    SP12/166(milieu)138863.71923751642802.58473191491.5501457447944.1859606383393.48030.23951807890.00057219380.00239518081137.21923750.10581683770.1582080588-6.0330977777-7.98903609421826018.26

    SP12/166(milieu)139865.26868651642802.23185323741.43764100721393.7596503597522.59140.31811017770.00084611640.00318110181138.76868650.10567285950.1540245465-5.7489350082-7.65315224251837118.371

    SP12/166(milieu)140866.81813551642803.3868739132.2507304348237.737826087177.970.10833333330.00014000490.00108333331140.31813550.10552927270.1498410342-6.82717066-8.67966681221848218.482

    SP12/166(milieu)141868.36758451642802.91823636361.7011090909334.9505181818163.36710.09944430240.00020087660.0009944431141.86758450.10538607550.1456575219-6.9128303246-8.71360539471859318.593

    SP12/166(milieu)142869.91703351642802.29047751.1935825403.0254825121.01930.07366648410.00024348670.00073666481143.41703350.10524326640.1414740096-7.2130090855-8.96206307341870418.704

    SP12/166(milieu)143871.46648251642802.48259655171.7106517241294.208762069122.05410.07429638420.00017652790.00074296381144.96648250.10510084380.1372904973-7.204491582-8.90182448781881518.815

    SP12/166(milieu)144873.01593151642802.89267704921.46689180331224.8146893443587.39210.35755545410.00074263450.00357555451146.51593150.10495880620.133106985-5.631844552-7.27745637561892618.926

    SP12/166(milieu)145874.56538051642804.260343751.9309625167.22526875115.60430.07037028240.00009739470.00070370281148.06538050.1048171520.1289234727-7.2588024607-8.85269320211903719.037

    SP12/166(milieu)146876.11482951642803.49241.6974388889185.499666666798.9940.06025931340.0001095690.00060259311149.61482950.10467587960.1247399604-7.4139669536-8.95613661281914819.148

    SP12/166(milieu)147877.6642785164280000000001151.16427850.10453498750.1205564481001925919.259

    SP12/166(milieu)148879.213727516428000001152.71372750.10439447420.1163729358001937019.37

    SP12/166(milieu)149880.763176516428000001154.26317650.10425433810.1121894235001948119.481

    SP12/166(milieu)150882.312625516428000001155.81262550.10411457770.1080059112001959219.592

    SP12/166(milieu)151883.86207451642800001157.36207450.10397519160.1038223989001970319.703

    SP12/166(milieu)152885.41152351642800001158.91152350.10383617820.0996388866001981419.814

    SP12/166(milieu)153886.96097251642800001160.46097250.1036975360.0954553743001992519.925

    SP12/166(milieu)154888.51042151642800001162.01042150.10355926350.091271862002003620.036

    SP12/166(milieu)155890.05987051642800001163.55987050.10342135930.0870883497002014720.147

    SP12/166(milieu)156891.60931951642800001165.10931950.10328382190.0829048374002025820.258

    SP12/166(milieu)157893.15876851642800001166.65876850.10314664980.0787213251002036920.369

    SP12/166(milieu)158894.70821751642800001168.20821750.10300984160.0745378128002048020.48

    SP12/166(milieu)159896.25766651642800001169.75766650.10287339580.0703543005002059120.591

    SP12/166(milieu)160897.80711551642800001171.30711550.1027373110.0661707882002070220.702

    SP12/166(milieu)161899.35656451642800001172.85656450.10260158580.0619872759002081320.813

    SP12/166(milieu)162900.90601351642800001174.40601350.10246621870.0578037636002092420.924

    SP12/166(milieu)163902.45546251642800001175.95546250.10233120830.0536202513002103521.035

    SP12/166(milieu)164904.00491151642800001177.50491150.10219655330.049436739002114621.146

    SP12/166(milieu)165905.55436051642800001179.05436050.10206225220.0452532267002125721.257

    SP12/166(milieu)166907.10380951642800001180.60380950.10192830350.0410697144002136821.368

    SP12/166(milieu)167908.65325851642800001182.15325850.1017947060.0368862021002147921.479

    SP12/166(milieu)168910.20270751642800001183.70270750.10166145830.0327026898002159021.59

    SP12/166(milieu)169911.75215651642800001185.25215650.10152855890.0285191775002170121.701

    SP12/166(milieu)170913.30160551642800001186.80160550.10139600660.0243356652002181221.812

    Apatites_donnes

    EchantillonsNumro de dossierTemprature estimeAire analyseLongueur moyenneLargeur moyenneNombre de particulesAire moyenne d'une particuleAire totale de phase cristallineFraction surfaciqueDensit surfaciqueT (K)1000/RTnln(-ln(1-x))ln(-ln(1-x))-nln(t)Distance par rapport la soleDistance (mm)

    SP12/165(bas)1651.444724516428000924.94472450.13010176741.98112059790030533.053

    SP12/165(bas)2652.994173516428000926.49417350.1298841881.97213379370031643.164

    SP12/165(bas)3654.543622516428000928.04362250.12966733521.96314698950032753.275

    SP12/165(bas)4656.093071516428000929.59307150.12945120521.95416018530033863.386

    SP12/165(bas)5657.642520516428000931.14252050.12923579451.94517338110034973.497

    SP12/165(bas)6659.191969516428000932.69196950.12902109951.93618657690036083.608

    SP12/165(bas)7660.741418516428000934.24141850.12880711671.92719977270037193.719

    SP12/165(bas)8662.290867516428000935.79086750.12859384251.91821296850038303.83

    SP12/165(bas)9663.840316516428000937.34031650.12838127341.90922616430039413.941

    SP12/165(bas)10665.389765516428000938.88976550.12816940591.90023936010040524.052

    SP12/165(bas)11666.939214516428000940.43921450.12795823651.89125255590041634.163

    SP12/165(bas)12668.488663516428000941.98866350.12774776181.88226575170042744.274

    SP12/165(bas)13670.038112516428000943.53811250.12753797841.87327894750043854.385

    SP12/165(bas)14671.587561516428000945.08756150.12732888291.86429214330044964.496

    SP12/165(bas)15673.137010516428000946.63701050.12712047181.85530533910046074.607

    SP12/165(bas)16674.686459516428000948.18645950.12691274191.84631853490047184.718

    SP12/165(bas)17676.235908516428000949.73590850.12670568981.83733173070048294.829

    SP12/165(bas)18677.785357516428000951.28535750.12649931221.82834492650049404.94

    SP12/165(bas)19679.334806516428000952.83480650.12629360581.81935812230050515.051

    SP12/165(bas)20680.884255516428000954.38425550.12608856731.81037131810051625.162

    SP12/165(bas)21682.433704516428000955.93370450.12588419351.80138451390052735.273

    SP12/165(bas)22683.983153516428000957.48315350.12568048121.79239770970053845.384

    SP12/165(bas)23685.532602516428000959.03260250.12547742711.78341090550054955.495

    SP12/165(bas)24687.082051516428000960.58205150.1252750281.77442410130056065.606

    SP12/165(bas)25688.631500516428000962.13150050.12507328091.76543729710057175.717

    SP12/165(bas)26690.180949516428000963.68094950.12487218251.75645049290058285.828

    SP12/165(bas)27691.730398516428000965.23039850.12467172981.74746368870059395.939

    SP12/165(bas)28693.279847516428000966.77984750.12447191961.73847688450060506.05

    SP12/165(bas)29694.829296516428000968.32929650.12427274881.72949008030061616.161

    SP12/165(bas)30696.378745516428000969.87874550.12407421441.72050327610062726.272

    SP12/165(bas)31697.928194516428000971.42819450.12387631341.71151647190063836.383

    SP12/165(bas)32699.477643516428000972.97764350.12367904261.70252966770064946.494

    SP12/165(bas)33701.027092516428000974.52709250.12348239921.69354286350066056.605

    SP12/165(bas)34702.576541516428000976.07654150.123286381.68455605930067166.716

    SP12/165(bas)35704.125990516428000977.62599050.12309098221.67556925510068276.827

    SP12/165(bas)36705.675439516428000979.17543950.12289620291.66658245090069386.938

    SP12/165(bas)37707.224888516428000980.72488850.12270203891.65759564670070497.049

    SP12/165(bas)38708.774337516428000982.27433750.12250848751.64860884250071607.16

    SP12/165(bas)39710.323786516428000983.82378650.12231554581.63962203830072717.271

    SP12/165(bas)40711.873235516428000985.37323550.12212321091.63063523410073827.382

    SP12/165(bas)41713.422684516428000986.92268450.12193147991.62164842990074937.493

    SP12/165(bas)42714.972133516428000988.47213350.12174034991.61266162570076047.604

    SP12/165(bas)43716.521582516428000990.02158250.12154981831.60367482150077157.715

    SP12/165(bas)44718.071031516428000991.57103150.12135988211.59468801730078267.826

    SP12/165(bas)45719.620480516428000993.12048050.12117053851.58570121310079377.937

    SP12/165(bas)46721.169929516428000994.66992950.12098178491.57671440890080488.048

    SP12/165(bas)47722.719378516428000996.21937850.12079361841.56772760470081598.159

    SP12/165(bas)48724.268827516428000997.76882750.12060603631.55874080050082708.27

    SP12/165(bas)49725.818276516428000999.31827650.12041903591.54975399630083818.381

    SP12/165(bas)50727.3677255145067.3321001000.86772550.12023261451.54076719210084928.492

    SP12/166(milieu)51728.9171745164280001002.41717450.12004676951.53178038790086038.603

    SP12/166(milieu)52730.4666235164280001003.96662350.1198614981.52279358370087148.714

    SP12/166(milieu)53732.0160725164280001005.51607250.11967679751.51380677950088258.825

    SP12/166(milieu)54733.5655215164280001007.06552150.11949266541.50481997530089368.936

    SP12/166(milieu)55735.1149705164280001008.61497050.11930909911.49583317110090479.047

    SP12/166(milieu)56736.6644195164280001010.16441950.11912609581.48684636690091589.158

    SP12/166(milieu)57738.2138685164280001011.71386850.11894365311.47785956270092699.269

    SP12/166(milieu)58739.76331751642801.98343846150.91523461541301.6750884615217.76150.13255508890.00079133191013.26331750.11876176841.4688727585-7.1413973212-25.301183448193809.38700

    SP12/166(milieu)59741.31276651642801.86642748091.02605267182621.7935141221469.90070.28603646210.00159483811014.81276650.11858043911.4598859543-6.4401851149-24.488866694994919.491702.0394736842

    SP12/166(milieu)60742.86221551642801.64263629630.96313481481351.385442963187.03480.11385122960.00082176771016.36221550.11839966261.4508991501-7.103641765-25.041218798296029.602704.0789473684

    SP12/166(milieu)61744.41166451642801.82122857140.97976306622871.7381954704498.86210.30366575360.00174701731017.91166450.11821943661.4419123459-6.3489712072-24.175443693597139.713706.1184210526

    SP12/166(milieu)62745.96111351642801.92891.07523195492661.8934947368503.66960.30659215970.00161918681019.46111350.11803975831.4329255417-6.4250211192-24.140389058698249.824708.1578947368

    SP12/166(milieu)63747.51056251642802.52821354171.1928333333962.9021583333278.60720.16959289020.00058436821021.01056250.11786062541.4239387375-7.4446871214-25.048950513999359.935710.1973684211

    SP12/166(milieu)64749.06001151642802.78266666671.27812549021023.2533872549331.84550.20199993910.00062089121022.56001150.11768203541.4149519333-7.3840442289-24.87720307461004610.046712.2368421053

    SP12/166(milieu)65750.60946051642802.7624011.2466311003.336706333.67060.20311090820.00060871681024.10946050.11750398571.4059651291-7.4038529464-24.78590724531015710.157714.2763157895

    SP12/166(milieu)66752.15890951642802.11581590911.18135795451762.6138903409460.04470.28003694910.00107134161025.65890950.11732647411.3969783249-6.838307663-24.10925741491026810.268716.3157894737

    SP12/166(milieu)67753.70835851642802.21987626261.1587898991982.5222737374499.41020.30399939130.00120525931027.20835850.11714949791.3879915207-6.7204576049-23.880302811037910.379718.3552631579

    SP12/166(milieu)68755.25780751642802.11647630521.14577028112492.4528325301610.75530.3717770270.00151570491028.75780750.11697305481.3790047165-6.4911163401-23.53985699841049010.49720.3947368421

    SP12/166(milieu)69756.80725651642802.25138861791.18189715452462.7879581301685.83770.41748094720.00149744341030.30725650.11679714251.3700179123-6.5032468429-23.44088295421060110.601722.4342105263

    SP12/166(milieu)70758.35670551642802.51272083331.22218214291683.3754154762567.06980.34518492820.00102264431031.85670550.11662175841.3610311081-6.8848520485-23.7113836131071210.712724.4736842105

    SP12/166(milieu)71759.90615451642803.16899103771.55824952832125.92171367921255.40330.76418511080.00129047971033.40615450.11644690031.3520443039-6.6520957063-23.3675227241082310.823726.5131578947

    SP12/166(milieu)72761.45560351642802.44454396141.26712246384143.19065652171320.93180.80407341120.00252008771034.95560350.11627256571.3430574997-5.9822002253-22.58652269611093410.934728.5526315789

    SP12/166(milieu)73763.00505251642802.62904296581.3173384032633.6985520913972.71920.5921105430.00160092521036.50505250.11609875241.3340706955-6.4363725388-22.92959046271104511.045730.5921052632

    SP12/166(milieu)74764.55450151642803.43484918031.63524098361835.88761311481077.43320.65585171660.00111395181038.05450150.11592545791.3250838913-6.7992841806-23.18139755771115611.156732.6315789474

    SP12/166(milieu)75766.10395051642803.52912922081.71208181821546.0228077922927.51240.56459240320.00093742391039.60395050.115752681.3160970871-6.9719060705-23.24291490071126711.267734.6710526316

    SP12/166(milieu)76767.65339951642803.24822186231.59321538462475.26390688261300.1850.7914444850.00150353061041.15339950.11558041641.3071102829-6.4991869948-22.65909127811137811.378736.7105263158

    SP12/166(milieu)77769.20284851642802.85312413791.33507624522613.97423601531037.27560.63140710980.00158875091042.70284850.11540866471.2981234787-6.4440122589-22.49281199541148911.489738.75

    SP12/166(milieu)78770.75229751642803.17301542061.47045093462145.26247056071126.16870.68551783540.0013026541044.25229750.11523742271.2891366745-6.6426998722-22.58039506181160011.6740.7894736842

    SP12/166(milieu)79772.30174651642803.48520964471.58763604061975.75736497461134.20090.69040717070.00119917211045.80174650.11506668821.2801498703-6.7255239535-22.55211459621171111.711742.8289473684

    SP12/166(milieu)80773.85119551642803.54402687751.72065098812537.30974861661849.36641.12574044310.00154005361047.35119550.11489645881.2711630661-6.475167558-22.19065365381182211.822744.8684210526

    SP12/166(milieu)81775.40064451642803.19138204331.48182043343235.09661083591646.20531.00207286340.00196615531048.90064450.11472673231.2621762619-6.2306913609-21.83507290981193311.933746.9078947368

    SP12/166(milieu)82776.95009351642803.24994829061.53408846152345.40163205131263.98190.76940704890.00142439741050.45009350.11455750651.2531894577-6.553293831-22.04657083311204412.044748.9473684211

    SP12/166(milieu)83778.49954251642802.85775545451.45928727273304.87566515151608.96950.97940680550.00200876551051.99954250.11438877931.2442026535-6.2092296892-21.59140214441215512.155750.9868421053

    SP12/166(milieu)84780.04899151642803.47323839661.85560506332376.84692320681622.72080.98777745310.00144265891053.54899150.11422054831.2352158493-6.5405456635-21.81161357191226612.266753.0263157895

    SP12/166(milieu)85781.59844051642803.34971716741.83480171672337.33267038631708.51221.04000012170.00141831021055.09844050.11405281141.2262290451-6.55757954-21.71754290151237712.377755.0657894737

    SP12/166(milieu)86783.14788951642804.02367339451.88775596332189.42641880732054.95931.25088830050.00132700271056.64788950.11388556651.2172422409-6.6241686368-21.67302745151248812.488757.1052631579

    SP12/166(milieu)87784.69733851642803.62491858411.87485796462267.76116681421754.02371.06770373750.00137571058.19733850.11371881131.2082554367-6.5881043242-21.5258585921259912.599759.1447368421

    SP12/166(milieu)88786.24678751642803.97128272251.97159476441918.84537905761689.46741.02840723160.00116264911059.74678750.11355254371.1992686325-6.7564725336-21.58312225461271012.71761.1842105263

    SP12/166(milieu)89787.79623651642803.56142018351.81456743122187.1924839451567.96150.95444454590.00132700271061.29623650.11338676171.1902818283-6.6241686368-21.33971381091282112.821763.2236842105

    SP12/166(milieu)90789.34568551642803.29822664671.6042044913346.10593922162039.38371.24140717070.00203311421062.84568550.1132214631.1812950241-6.1971691558-20.8016097831293212.932765.2631578947

    SP12/166(milieu)91790.89513451642804.20115593221.79707076272368.61644745762033.48161.23781446310.00143657171064.39513450.11305664551.1723082199-6.5447770469-21.03811312721304313.043767.3026315789

    SP12/166(milieu)92792.44458351642804.02773315221.93439945651849.11145760871676.50821.02051874850.0011200391065.94458350.11289230731.1633214157-6.7938315295-21.17606306291315413.154769.3421052632

    SP12/166(milieu)93793.99403251642804.31443914891.74442808512358.98452255322111.36281.28522205990.00143048451067.49403250.1127284461.1543346115-6.549026385-20.82015337161326513.265771.3815789474

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    SP12/166(milieu)128848.22474751642803.21040447761.5643343284676.1198597015410.03060.2495925250.00040784031121.72474750.10727849560.8397964645-7.8044309939-18.18689884021715017.15842.7631578947

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    SP12/166(milieu)130851.32364551642803.23493926381.37585766871635.7895521472943.6970.57444424150.00099220841124.82364550.10698294250.8218228561-6.9150810578-17.07533981041737217.372846.8421052632

    SP12/166(milieu)131852.87309451642802.39836251.16461544122722.8187496324766.69990.46670312880.00165570981126.37309450.10683577580.8128360519-6.4026970752-16.45185128091748317.483848.8815789474

    SP12/166(milieu)132854.42254351642802.20914776121.2191014925672.6508238806177.60520.10811127340.00040784031127.92254350.10668901350.8038492477-7.8044309939-17.74248065271759417.594850.9210526316

    SP12/166(milieu)133855.97199251642802.07528518521.343162963272.611870.51860.04292585830.00016435351129.47199250.10654265380.7948624435-8.7134085197-18.54035363161770517.705852.9605263158

    SP12/166(milieu)134857.52144151642801.71024897961.0280857143491.670116326581.83570.04981476750.00029827121131.02144150.10639669510.7858756393-8.1173581158-17.83319868091781617.8168552.0394736842

    SP12/166(milieu)135859.070890516428000000001132.57089050.10625113580.7768888351001792717.9270.0183736368

    SP12/166(milieu)136860.620339516428000000001134.12033950.10610597420.7679020309001803818.038183.7363679469

    SP12/166(milieu)137862.169788516428000000001135.66978850.10596120870.7589152267001814918.149

    SP12/166(milieu)138863.719237516428000000001137.21923750.10581683770.7499284225001826018.26

    SP12/166(milieu)139865.268686516428000000001138.76868650.10567285950.7409416183001837118.371

    SP12/166(milieu)140866.818135516428000000001140.31813550.10552927270.7319548141001848218.482

    SP12/166(milieu)141868.367584516428000000001141.86758450.10538607550.7229680099001859318.593

    SP12/166(milieu)142869.917033516428000000001143.41703350.10524326640.7139812057001870418.704

    SP12/166(milieu)143871.466482516428000000001144.96648250.10510084380.7049944015001881518.815

    SP12/166(milieu)144873.015931516428000000001146.51593150.10495880620.6960075973001892618.926

    SP12/166(milieu)145874.565380516428000000001148.06538050.1048171520.6870207931001903719.037

    SP12/166(milieu)146876.114829516428000000001149.61482950.10467587960.6780339889001914819.148

    SP12/166(milieu)147877.664278516428000000001151.16427850.10453498750.6690471847001925919.259

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    SP12/166(milieu)153886.960972516428000000001160.46097250.1036975360.6151263595001992519.925

    SP12/166(milieu)154888.510421516428000000001162.01042150.10355926350.6061395553002003620.036

    SP12/166(milieu)155890.059870516428000000001163.55987050.10342135930.5971527511002014720.147

    SP12/166(milieu)156891.609319516428000000001165.10931950.10328382190.5881659469002025820.258

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    SP12/166(milieu)167908.653258516428000000001182.15325850.1017947060.4893111007002147921.479

    SP12/166(milieu)168910.202707516428000000001183.70270750.10166145830.4803242965002159021.59

    SP12/166(milieu)169911.752156516428000000001185.25215650.10152855890.4713374923002170121.701

    SP12/166(milieu)170913.301605516428000000001186.80160550.10139600660.4623506881002181221.812

    Graph2

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    800g_140C/cm

    337g_300C/cm

    Distance from the cooled sole (mm)

    Fraction (%)

    Powellite

    Powellite_graphique

    Domaine arhnien

    T727862C

    600687

    07826

    0.0111167902C/m

    1.2339637107C/photo

    111.1679018656

    600700

    05217

    0.0191681043

    2.1276595745C/photo

    19.1681042745

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    Powellite_graphique

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    1.8065924641

    1.4709257365

    1.797960616

    1.4636642318

    2.1204074142

    1.6095553932

    1.7257413562

    2.1171102386

    2.1590714634

    1.6356648405

    1.490961103

    1.4757387387

    1.5082966886

    1.4631850499

    1.0589986608

    2.2396665449

    1.2377772096

    1.7212208425

    1.6712587047

    1.8775163136

    1.3168875091

    1.3737387387

    1.5026276479

    1.0109614682

    0.894073046

    1.8371477964

    1.2162582785

    1.2032592525

    1.3677021549

    1.4890361578

    1.4094439981

    1.5223708912

    1.3001104212

    1.1991107865

    1.6569239713

    1.1271102995

    1.3343696129

    1.3403319333

    1.4487033114

    1.4424813124

    0.9168875091

    1.2706653884

    1.5304438154

    1.4591841977

    1.4159609813

    1.8450726199

    0.9163694911

    0.7471107865

    1.0000364621

    1.046851534

    1.0133698563

    1.8068853786

    0.8172218164

    0.7331106038

    0.8846298393

    1.1719251278

    1.0606291088

    1.1911473703

    1.3493696129

    0.9155550889

    0.7470738982

    0.8087778792

    0.7630742635

    0.8715177137

    0.831147553

    0.81392598

    0.9652957755

    0.6227401388

    0.8064443633

    0.4780739591

    0.6786664841

    0.7565178963

    0.6992593742

    0.707926467

    0.719777514

    0.599703981

    0.5483335159

    0.5803336377

    0.6124069881

    0.5010353664

    0.2395180789

    0.3181101777

    0.1083333333

    0.0994443024

    0.0736664841

    0.0742963842

    0.3575554541

    0.0703702824

    0.0602593134

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Temprature (C)

    Fraction (%)

    Fraction surfacique_powellite

    Apatites_graphique

    1.80657684210.7079021053

    2.01633809520.6484333333

    1.98293609470.7340118343

    1.74115517240.6982544828

    1.73382644380.7410927052

    1.94286032790.8408721311

    1.8704982490.817816537

    2.07746088990.7882515222

    1.90610431770.8807672321

    2.02983905010.7452274406

    1.81987225610.7910169207

    1.8421205630.8096176255

    1.80759456020.8120978009

    2.04433845640.9056681879

    1.78971144140.8029645946

    1.83457661690.8379378939

    1.99865028470.9242003986

    2.24664372740.9994641134

    1.96423427720.8925999255

    2.16232608210.9681256937

    2.21528635120.9730866255

    2.38519364011.0486476319

    2.0110894090.8648094207

    2.22775453320.9915800406

    2.40357961431.0711121212

    2.57213849951.2585612267

    2.2230354231.0233725502

    2.05976938780.9778887755

    2.21769923660.944808874

    2.32382741151.0905781441

    2.30392180131.1210243031

    2.33646473151.0619312046

    1.95839125820.8699178105

    2.39861706511.0910324701

    2.39982175371.126568407

    2.03148712960.8776082981

    2.26534072481.0618740172

    2.36689587181.112059581

    2.46185543341.1210646831

    2.50512875771.0895798313

    2.24846378920.9938142093

    2.1238180240.9782725749

    2.12835351510.950133429

    2.36976624611.1172685804

    2.43451791811.1056000853

    2.55645092351.1730600704

    2.67842813261.2333628941

    2.30911871921.0873648399

    2.26795724241.0620696359

    2.21625742811.0380925719

    2.17301546790.9925864656

    2.50256420231.1319608949

    2.69904399571.1174213603

    2.30137887030.9682799163

    2.53181291871.1459626111

    2.42928675351.0893542888

    2.61756019141.2138319617

    2.40765146551.131189569

    2.49963413421.1734406794

    2.37523284521.1163246862

    2.54413340861.1780768623

    2.31466965391.0905679681

    2.43358907461.0676417738

    2.26532178221.1014973126

    2.59455046381.2116272727

    2.43754539561.2486156939

    2.59104867131.2609552448

    2.53295330191.1956353774

    2.92502716051.4330334877

    2.53392864721.3648965517

    2.48038917051.3216634793

    2.16315279831.1423591341

    2.42326364851.1952886818

    2.86911743341.2759979419

    2.51873969471.2506763359

    2.70354023321.3207163265

    2.54245012791.2073512788

    2.59611851371.2487026076

    2.62147301811.3774116829

    2.4902901281.2334592322

    2.52645777131.2909278592

    3.02904522691.3575558685

    2.7831468751.3735225852

    2.18519109851.0815587121

    2.12828348871.0499460719

    2.33093052631.2085024561

    2.66696277171.4300315217

    2.81579348841.5025132558

    3.19665751.6228266667

    2.85943215081.3916771619

    2.13250219941.037714956

    2.74830404311.4165374663

    2.8


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