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Thermomigration experiment on board EURECA
0273-l 177(95)00161-l
Adv. Space Res.Vol. 16,No. 7, pp. (7)205-(7)214, 1995 copyrightca 1995CmP~ Rioted in GreatBritain.All . 0273-l 17719 Y@$9.50+ o.od
THERMOMIGRATION EXPERIMENT ON BOARD EURECA J. P. Praizey, S. Van Vaerenbergh and J. P. Garandet Centre d’EtudesNucltfaires,DEWSES, I7 Rue des Martyrs,38054 Grenoble Cedex 9, France
ABSTRACT Results of thermomigration measurements in liquid tin performed on board EURECA (experiment MF067) are presented. The aims of the experimentweretomeasurethethermomigration coefficients of goldand of some Tin isotopes in Sn-Au alloys and more generally, to complete the previous results obtained in Spacelab flights of 1983 (FSLP) and 1985 (Dl). As in those previous flights, the "shear cell" technique, allowing a division of the sample in the liquid state, was used. The completion of those results will allow to determine the systems for which microgravity measurements are mandatory.
INTRODUCTION The diffusion of species is governed in non isothermal conditions by a more general law than the one governing the isothermal diffusion (often refered as Fickian) because the thermal gradient induces a migration of molecules. The resulting diffusive flux J, of species i reads: pi
= -Di
( VXi
+ Si Xi
VT)
(1)
where T is the absolute temperature, Xi the component i mass fraction and Di and Si are respectively the isothermal diffusion coefficient and Soret coefficient of component i.
The steady state obtained in a closed system where no convection is present corresponds to a balance between the two components of diffusive flux, namely the Fickian diffusive flux and the diffusive fluxproportionaltothethermalgradient, calledthermodiffusive flux.
(7)205
J.P.I'm&y
(712~
erd.
This state describes the Soret effect, or the establishment of a solute gradient induced by the thermal gradient as results from equation (1):
Cdln(
'i/'i)
= _
s,
T
1.
d In(T)
=
I. 1
Equation (2) also defines the thermodiffusion factor ri (definition of other main quantities developed for theories of diluted solutions are given in [ll for instance). The attainment of this stationary state is diffusion controlled, and reached after a time of the order of: oi = - L2
F12Di L being the length of the cavity where the samples are processed. Scch kind of diffusion controled processes in melts can be studied in a shear cell technique as described in [1,21. It consists of a s*:perposition of disks in which capillaries are realised in the axial direction and installed in a closed cartridge filled with inert gas. T?.e disks are compressed by a spring in order to resist to vibrations 3x3 accelerations. The processedsamples are dividedbyrotation of the disks that is performed thanks to a rotation spring liberated by a fusible. ground conditions, suchexperiments areperturbedbygravityinduced zznl-ective remixing resulting from the unavoidable lateral thermal gr-adient. Measurements previously performed in FSLP (1983) and Dl _ i-355) Spacelab missions in Tin dilute alloys [3,4] have shown that the Soret coefficients measured w?_.azsverthegroundbasedtechnicused, i___zicrogravity are usually much larger, in the way specified below.
3r.
Y-Y .-_ -he lateral thermal gradient, the tilt with respect to the vertical is subject sr.5-he Soret effect itself, affect the groundmeasurements zz theoretical developments. According to the present theories [9,10], r5.t nain parameters describing those convective perturbations are the rl-azsverse thermal gradient and the axial solute gradient, as detailed ;- ^.#. of Soret confirm that the measurements Both theories bb__ zztificients in microgravity are necessary.
RESULTS OBTAINED ON BOARD EURECA -'-= --__ MFA067 experiment aimed to take advantage of the specific -_.Z_ ----acteristics of the EURECA 1 mission to comfort such measurements. .1--. increased accuracy has been obtained thanks to the longer duration _= xicrogravity avalaible on EURECA mission (10 days). The systems _-
n~tt~Ggrati~~
Expximeat 00 EURECA
(7)207
studied on board EURECA allow alSO to complete measurements performed only in 1 g up to now in Sn-Au alloys, to refine measurement technique theory, and to measure in pure Sn the isotopic separation induced by thermodiffusion. Thermodiffusionmeasurements inMFA067 experimentareperformedinthe four capillaries of the cartridge. The latter is filled with 100 mbars of Helium, sealed and installed in one of the MFA furnaces. The gradient is obtained by specific design of the cartridge itself. Once the stationnary state is reached, disk rotation is commanded. The chemical composition analysis is performed on solidified samples. The cartridge that has been developed by CEN-G (Grenoble) is sketched on figure 1. Its main characteristics are given in table 1 where they are compared to the one used in previous space and ground experiments reported in this paper. Figure 1 also reports the thermal profile obtained during the experiment. The isotopic and Au contents of the 44 samples has been determined by measuring the y activity of elements activated by neutronic flux (neutronic activation) in the SILOE reactor of CEN-G. This technique allows the detection of compositions inferior to 1 ppb. Figure 2 presents one gamma spectrum so obtained. The accuracy obtained by this method for the determination of relative compositions X/Xm is detailed in table 2 and the nuclear reactions schemes used for the analysis are: Sn 112 (n,y) In 113m y = 0.393 MeV, 1.7 days Sn 116 (n,y) Sn 117m y = 0.32 MeV, 14 days Sn 124 (n,y) Sb 125 y = 0.60 MeV, 60 days Au 197 (n,y) Au 198m y = 0.41 MeV, 2.7 days Thanks to the larger number of samples by capillaryobtainedin EURECA, it has been possible to refine statements on the composition distribution induced by thermodiffusion. For instance, it has been possible to determine the distribution of the isotope 116 of Tin, whose Soret coefficient is very small. Figure 4 shows the isotopic distribution measured in the samples. It is possible also to decrease the uncertainty of the correlations with theory, as explained in next section. The analysis of the results are based on results reported in figure 3 obtained for Au and figure 4 representing the mean isotopic distribution observed in the capillaries 1 to 4.
(7)208
J. P. Pm&y et al.
TABLE
1:
(1983)
shear cells used to measure Soret coefficients
in metals.
: Sn-Co
(1992-93) : Sn,
TXLE
2: summary of composition (in mass %) measurement results of MFA experiment. Thermodiffusion factors are obtained by linear regression of the composition-temperature bilogarithmic plot ("mean r") . The accuracy on the values of the mean composition X, is better than 40 ppm. 067
I t
I
I htil k.
I
I
I
I
I
I *
\
;?
,I I
Figure I: sketch ot the MFA 067 cartridge used in the MFA turnaceJ to measure Soret coefficients in Sn and Sn-Au melts on board EURECA 1 and temperature profile obtained on board EURECA.
c7wJ
J.P.Praiz.ey er al.
r’s,
n
’
1.
-
a
m
I
’
r
*
s
I
’
m
-
1
I
I.
3.
I
Figure 2: ExampleTf y spec;um obtai:ed. The ???levant peaks arc aiT.-enin the text (from D. Beretz, CEN-G).
0.05-.
-0.20-
iqze
3: distribution of Au in capillarie 4.
(7)211
pJ?~(;q-.+f-~ isotopicdistribution:
summary
0.03
.E-0.02 5
.^
I.
ir;
Ilk-T.= O.OJBt-0.005
z L -0.03 . 6.40
. 6.50 mean
6.70 6.80 6.90 6.60 teriperatureof seciion(deg. i:)
81 $112
igure
ISOTOPIC
4:
+
511116
7.00
-T 511124
mean distribution of isotopes in capillaries
1 to 4.
THERMOMIGRATION
Theories describing the isotopic separation by thermodiffusion are detailed in [6,7] for instance. The results that seems presently more relevant taking into account the resolution of the measurements are deduced from Chapman and Cowling [81 theory that predict that the separation is governed mainly by collisional effects: ri=-C[
mi mi
m2
+ m2
(4)
2
+ 0.2
xi
(2
'i
'i2
-
1) - 0.2 x2 ( - s22
-
111
'i*'
In formula (4), the component 2 can be taken to be the one presenting the mean atomic characteristics of the isotopic mixture. The coefficients s are mean collisional cross sections, and for isotopes representmainlythe effect of atomic dimensions. The contribution due to the dimensional effects are negligible for isotopes. The mean value so obtained for the factor C is -2.57 f 0.21. With this experimentally obtained value of C, the overall isotopic effect on mass variation can be extrapolated with formula (4). The resulting increase of density is of - 1.7 lo-' K-l. It is a of course a very small effect and explain why it does not intervene in interpretations of experimental results.
(7)212
J. P. Pm&y et al.
THERMOMIGRATION
OF Au
The relative accuracies obtained on the slopes of the log-log composition temperature curves of Au in Sn is higher than on Sn isotopes because the Soret coefficient is higher. REPRODUCIBILITY
OF MEASUREMENTS.
The globaluncertaintyof the values of the thermodiffusion factors are given by the standard deviation on the slope of the compositiontemperature bilogarithmic plots. It is possible that this approach masks some unknown temperature or composition dependence, but in counterpart, it allows to account for uncertainties due to processing conditions, irradiation or unknown factors. The standard errors so obtained are given in table 2 for EURECAl s)mstems and may be found in [I] for previous microgravitymeasurements In Tin alloys. It is seen on the basis of the Sn112 results that the accuracy on EURECA is increased by a factor of about 2 with respect to rht SPACELAB Missions. This is partly due to the statistical factor ,V:I 6) on samples numbers. -he only system that allows to determine reproducibility is the Sn112 :n pcre Sn. Evenwiththe differences inexperimentalconditions listed _- table I and the difference of gravity level the reproducibility is ___ kerween the experimental errors. This is remarkable result if one accc,nts for the small amplitude of the isotopic effect. CONCLUSIONS .-: _-: the EURECAlmission, 0 - ___
a series of systematic measurements of Soret zctfficients of Tin diluted alloys and pure Tin have been completed. -__ :_ _= so obtained a spectrum of reference measurements that allows for : ____development orverificationof condensedstatephysics theories and _ ; fluid dynamics theories. __
:r:z the latter it is hoped to infer in a near future an accurate rr.z-:;h description of mechanisms appearing in ground conditions in the .._ _ shear cell technic. This will allow to state more clearly what _:=d _.__emmust be measured in microgravity conditions instead than in the Z-‘=~r~~.z-_d based shear cell. -sotopic effect has been quantified precisely with tree isotopes -; __ -1n. Within the accuracy obtained in the experiments, it can be srartd that the mass effect is largely predominant on this phenomena, z-11 . rhis provides important development in condensed state physics.
-‘^ ____
=
_
'~hermnigrcrtionExperimentonEURIiCA
(7)213
is worthwhile to mention that Soret effect affects morphological stabilityandinduces ingroundconditionrs, specific convective regimes in Bridgman solidification. The latter have been studied in MEPHIsTo program in microgravity conditions [II] in the Sn-Bi system and are presently under study 112,131. It
ACKNOWLEDGMENTS This work was carried out within the context of the GRAMME agreement concluded between the CEA and the CNES. We which to thank F. Gonzalzs (CNES-Toulouse), L. Innocenti (ESA-ESTEC)and H.P. Schmidt (DLR-MUSC) fortheirtechnical support andD. Beret2 andco-workers forperforming the composition measurements in SILOE facility of CEN-G. One of us (S.V.V.) wish to thank the European Communities, Human Capital and Mobility program that supported his work trough a fellowship funding.
REFERENCES
[l] J.P. Praizey, "Benefits of microgravity for measuring thermotransport coefficients in liquidmetallic alloys", I&. J. Heat Mass Transfer vol. 32, no 12, (1989), pp. 2385-2401. [2] c. Potard, Contribution a la diffusion dans les alliages ternaires, Thesis, Grenoble (1972). [3] Y. Malmejac and J.P. Praizey, "Thermomigrationof Cobalt in liquid Tin (1 ES 320)) Proc. Third European Symp. on Material Sciences in Space, Grenoble France, ESA SP-191, (1984), pp. 127-132. [4] J.P. Praizey, "Thermomigration in liquid metallic alloys", Advace in Space Research, vol. 6, n"5, (1986), pp. (51-60). 151 A. Bruson and M. Gerl, "Diffusion coefficients of Sn113, Sb124, AgllOm and Au195 in liquid Sn", Phys. Rev. B, vol. 21, no 12, (1980), pp. 5447-5454. [61 M. Gerl, "Contribution au calcul des forces agissant sur une impuretd d'un metal soumis 2 un gradient de tempCrature". J. Phys. Chem. Solids vol. 28, (1967), pp. 725-736 171 M. Balourdet, PhD thesis, "Contribution a l'btude des mdcanismes
de thermmodiffusion dans les metaux et alliages liquides", (1976). [81 S. Chapman andT.G. Cowling, Themathematical theory of non-uniform gases, Cambridge University Press, London, (1952). [91 J.E. Hart, "On sideway diffusive instabilities", J. Fluid Mach., vol 49, n"2, (1971), pp. 279-288. [lo] D. Henry and B. Roux, "Three dimensional numerical study of convection in a cylindrical thermal diffusion cell: its influence on the separation of constituents", Phyrice of fluids vol 29, no 11, (1986), pp. 3562-3572. [II] J.-J. Favier and A. Rouzaud, Adv. Space Res., vol 6, no 5, (1986),
(7)214
J. P.Pmizeyetal. 11-122. [12] S. Van Vaerenbergh, S. Coriell, G. McFadden and B. Murray, "The Role of Soret effect on Morphological stability", submited to Journal of Crystal Growth, 1994. [13] J.J. Favier, J.P. Garandet, A. Rouzaud and D. Camel, “Mass transportphenomenaduring solidificationinmicrogravity. Preliminary results of the first MEPHISTO fight experiment", submited to the Journal of Crystal Growth, 1994. pp.
Adv. Space Res.Vol. 16,No. 7, pp. (7)205-(7)214, 1995 copyrightca 1995CmP~ Rioted in GreatBritain.All . 0273-l 17719 Y@$9.50+ o.od
THERMOMIGRATION EXPERIMENT ON BOARD EURECA J. P. Praizey, S. Van Vaerenbergh and J. P. Garandet Centre d’EtudesNucltfaires,DEWSES, I7 Rue des Martyrs,38054 Grenoble Cedex 9, France
ABSTRACT Results of thermomigration measurements in liquid tin performed on board EURECA (experiment MF067) are presented. The aims of the experimentweretomeasurethethermomigration coefficients of goldand of some Tin isotopes in Sn-Au alloys and more generally, to complete the previous results obtained in Spacelab flights of 1983 (FSLP) and 1985 (Dl). As in those previous flights, the "shear cell" technique, allowing a division of the sample in the liquid state, was used. The completion of those results will allow to determine the systems for which microgravity measurements are mandatory.
INTRODUCTION The diffusion of species is governed in non isothermal conditions by a more general law than the one governing the isothermal diffusion (often refered as Fickian) because the thermal gradient induces a migration of molecules. The resulting diffusive flux J, of species i reads: pi
= -Di
( VXi
+ Si Xi
VT)
(1)
where T is the absolute temperature, Xi the component i mass fraction and Di and Si are respectively the isothermal diffusion coefficient and Soret coefficient of component i.
The steady state obtained in a closed system where no convection is present corresponds to a balance between the two components of diffusive flux, namely the Fickian diffusive flux and the diffusive fluxproportionaltothethermalgradient, calledthermodiffusive flux.
(7)205
J.P.I'm&y
(712~
erd.
This state describes the Soret effect, or the establishment of a solute gradient induced by the thermal gradient as results from equation (1):
Cdln(
'i/'i)
= _
s,
T
1.
d In(T)
=
I. 1
Equation (2) also defines the thermodiffusion factor ri (definition of other main quantities developed for theories of diluted solutions are given in [ll for instance). The attainment of this stationary state is diffusion controlled, and reached after a time of the order of: oi = - L2
F12Di L being the length of the cavity where the samples are processed. Scch kind of diffusion controled processes in melts can be studied in a shear cell technique as described in [1,21. It consists of a s*:perposition of disks in which capillaries are realised in the axial direction and installed in a closed cartridge filled with inert gas. T?.e disks are compressed by a spring in order to resist to vibrations 3x3 accelerations. The processedsamples are dividedbyrotation of the disks that is performed thanks to a rotation spring liberated by a fusible. ground conditions, suchexperiments areperturbedbygravityinduced zznl-ective remixing resulting from the unavoidable lateral thermal gr-adient. Measurements previously performed in FSLP (1983) and Dl _ i-355) Spacelab missions in Tin dilute alloys [3,4] have shown that the Soret coefficients measured w?_.azsverthegroundbasedtechnicused, i___zicrogravity are usually much larger, in the way specified below.
3r.
Y-Y .-_ -he lateral thermal gradient, the tilt with respect to the vertical is subject sr.5-he Soret effect itself, affect the groundmeasurements zz theoretical developments. According to the present theories [9,10], r5.t nain parameters describing those convective perturbations are the rl-azsverse thermal gradient and the axial solute gradient, as detailed ;- ^.#. of Soret confirm that the measurements Both theories bb__ zztificients in microgravity are necessary.
RESULTS OBTAINED ON BOARD EURECA -'-= --__ MFA067 experiment aimed to take advantage of the specific -_.Z_ ----acteristics of the EURECA 1 mission to comfort such measurements. .1--. increased accuracy has been obtained thanks to the longer duration _= xicrogravity avalaible on EURECA mission (10 days). The systems _-
n~tt~Ggrati~~
Expximeat 00 EURECA
(7)207
studied on board EURECA allow alSO to complete measurements performed only in 1 g up to now in Sn-Au alloys, to refine measurement technique theory, and to measure in pure Sn the isotopic separation induced by thermodiffusion. Thermodiffusionmeasurements inMFA067 experimentareperformedinthe four capillaries of the cartridge. The latter is filled with 100 mbars of Helium, sealed and installed in one of the MFA furnaces. The gradient is obtained by specific design of the cartridge itself. Once the stationnary state is reached, disk rotation is commanded. The chemical composition analysis is performed on solidified samples. The cartridge that has been developed by CEN-G (Grenoble) is sketched on figure 1. Its main characteristics are given in table 1 where they are compared to the one used in previous space and ground experiments reported in this paper. Figure 1 also reports the thermal profile obtained during the experiment. The isotopic and Au contents of the 44 samples has been determined by measuring the y activity of elements activated by neutronic flux (neutronic activation) in the SILOE reactor of CEN-G. This technique allows the detection of compositions inferior to 1 ppb. Figure 2 presents one gamma spectrum so obtained. The accuracy obtained by this method for the determination of relative compositions X/Xm is detailed in table 2 and the nuclear reactions schemes used for the analysis are: Sn 112 (n,y) In 113m y = 0.393 MeV, 1.7 days Sn 116 (n,y) Sn 117m y = 0.32 MeV, 14 days Sn 124 (n,y) Sb 125 y = 0.60 MeV, 60 days Au 197 (n,y) Au 198m y = 0.41 MeV, 2.7 days Thanks to the larger number of samples by capillaryobtainedin EURECA, it has been possible to refine statements on the composition distribution induced by thermodiffusion. For instance, it has been possible to determine the distribution of the isotope 116 of Tin, whose Soret coefficient is very small. Figure 4 shows the isotopic distribution measured in the samples. It is possible also to decrease the uncertainty of the correlations with theory, as explained in next section. The analysis of the results are based on results reported in figure 3 obtained for Au and figure 4 representing the mean isotopic distribution observed in the capillaries 1 to 4.
(7)208
J. P. Pm&y et al.
TABLE
1:
(1983)
shear cells used to measure Soret coefficients
in metals.
: Sn-Co
(1992-93) : Sn,
TXLE
2: summary of composition (in mass %) measurement results of MFA experiment. Thermodiffusion factors are obtained by linear regression of the composition-temperature bilogarithmic plot ("mean r") . The accuracy on the values of the mean composition X, is better than 40 ppm. 067
I t
I
I htil k.
I
I
I
I
I
I *
\
;?
,I I
Figure I: sketch ot the MFA 067 cartridge used in the MFA turnaceJ to measure Soret coefficients in Sn and Sn-Au melts on board EURECA 1 and temperature profile obtained on board EURECA.
c7wJ
J.P.Praiz.ey er al.
r’s,
n
’
1.
-
a
m
I
’
r
*
s
I
’
m
-
1
I
I.
3.
I
Figure 2: ExampleTf y spec;um obtai:ed. The ???levant peaks arc aiT.-enin the text (from D. Beretz, CEN-G).
0.05-.
-0.20-
iqze
3: distribution of Au in capillarie 4.
(7)211
pJ?~(;q-.+f-~ isotopicdistribution:
summary
0.03
.E-0.02 5
.^
I.
ir;
Ilk-T.= O.OJBt-0.005
z L -0.03 . 6.40
. 6.50 mean
6.70 6.80 6.90 6.60 teriperatureof seciion(deg. i:)
81 $112
igure
ISOTOPIC
4:
+
511116
7.00
-T 511124
mean distribution of isotopes in capillaries
1 to 4.
THERMOMIGRATION
Theories describing the isotopic separation by thermodiffusion are detailed in [6,7] for instance. The results that seems presently more relevant taking into account the resolution of the measurements are deduced from Chapman and Cowling [81 theory that predict that the separation is governed mainly by collisional effects: ri=-C[
mi mi
m2
+ m2
(4)
2
+ 0.2
xi
(2
'i
'i2
-
1) - 0.2 x2 ( - s22
-
111
'i*'
In formula (4), the component 2 can be taken to be the one presenting the mean atomic characteristics of the isotopic mixture. The coefficients s are mean collisional cross sections, and for isotopes representmainlythe effect of atomic dimensions. The contribution due to the dimensional effects are negligible for isotopes. The mean value so obtained for the factor C is -2.57 f 0.21. With this experimentally obtained value of C, the overall isotopic effect on mass variation can be extrapolated with formula (4). The resulting increase of density is of - 1.7 lo-' K-l. It is a of course a very small effect and explain why it does not intervene in interpretations of experimental results.
(7)212
J. P. Pm&y et al.
THERMOMIGRATION
OF Au
The relative accuracies obtained on the slopes of the log-log composition temperature curves of Au in Sn is higher than on Sn isotopes because the Soret coefficient is higher. REPRODUCIBILITY
OF MEASUREMENTS.
The globaluncertaintyof the values of the thermodiffusion factors are given by the standard deviation on the slope of the compositiontemperature bilogarithmic plots. It is possible that this approach masks some unknown temperature or composition dependence, but in counterpart, it allows to account for uncertainties due to processing conditions, irradiation or unknown factors. The standard errors so obtained are given in table 2 for EURECAl s)mstems and may be found in [I] for previous microgravitymeasurements In Tin alloys. It is seen on the basis of the Sn112 results that the accuracy on EURECA is increased by a factor of about 2 with respect to rht SPACELAB Missions. This is partly due to the statistical factor ,V:I 6) on samples numbers. -he only system that allows to determine reproducibility is the Sn112 :n pcre Sn. Evenwiththe differences inexperimentalconditions listed _- table I and the difference of gravity level the reproducibility is ___ kerween the experimental errors. This is remarkable result if one accc,nts for the small amplitude of the isotopic effect. CONCLUSIONS .-: _-: the EURECAlmission, 0 - ___
a series of systematic measurements of Soret zctfficients of Tin diluted alloys and pure Tin have been completed. -__ :_ _= so obtained a spectrum of reference measurements that allows for : ____development orverificationof condensedstatephysics theories and _ ; fluid dynamics theories. __
:r:z the latter it is hoped to infer in a near future an accurate rr.z-:;h description of mechanisms appearing in ground conditions in the .._ _ shear cell technic. This will allow to state more clearly what _:=d _.__emmust be measured in microgravity conditions instead than in the Z-‘=~r~~.z-_d based shear cell. -sotopic effect has been quantified precisely with tree isotopes -; __ -1n. Within the accuracy obtained in the experiments, it can be srartd that the mass effect is largely predominant on this phenomena, z-11 . rhis provides important development in condensed state physics.
-‘^ ____
=
_
'~hermnigrcrtionExperimentonEURIiCA
(7)213
is worthwhile to mention that Soret effect affects morphological stabilityandinduces ingroundconditionrs, specific convective regimes in Bridgman solidification. The latter have been studied in MEPHIsTo program in microgravity conditions [II] in the Sn-Bi system and are presently under study 112,131. It
ACKNOWLEDGMENTS This work was carried out within the context of the GRAMME agreement concluded between the CEA and the CNES. We which to thank F. Gonzalzs (CNES-Toulouse), L. Innocenti (ESA-ESTEC)and H.P. Schmidt (DLR-MUSC) fortheirtechnical support andD. Beret2 andco-workers forperforming the composition measurements in SILOE facility of CEN-G. One of us (S.V.V.) wish to thank the European Communities, Human Capital and Mobility program that supported his work trough a fellowship funding.
REFERENCES
[l] J.P. Praizey, "Benefits of microgravity for measuring thermotransport coefficients in liquidmetallic alloys", I&. J. Heat Mass Transfer vol. 32, no 12, (1989), pp. 2385-2401. [2] c. Potard, Contribution a la diffusion dans les alliages ternaires, Thesis, Grenoble (1972). [3] Y. Malmejac and J.P. Praizey, "Thermomigrationof Cobalt in liquid Tin (1 ES 320)) Proc. Third European Symp. on Material Sciences in Space, Grenoble France, ESA SP-191, (1984), pp. 127-132. [4] J.P. Praizey, "Thermomigration in liquid metallic alloys", Advace in Space Research, vol. 6, n"5, (1986), pp. (51-60). 151 A. Bruson and M. Gerl, "Diffusion coefficients of Sn113, Sb124, AgllOm and Au195 in liquid Sn", Phys. Rev. B, vol. 21, no 12, (1980), pp. 5447-5454. [61 M. Gerl, "Contribution au calcul des forces agissant sur une impuretd d'un metal soumis 2 un gradient de tempCrature". J. Phys. Chem. Solids vol. 28, (1967), pp. 725-736 171 M. Balourdet, PhD thesis, "Contribution a l'btude des mdcanismes
de thermmodiffusion dans les metaux et alliages liquides", (1976). [81 S. Chapman andT.G. Cowling, Themathematical theory of non-uniform gases, Cambridge University Press, London, (1952). [91 J.E. Hart, "On sideway diffusive instabilities", J. Fluid Mach., vol 49, n"2, (1971), pp. 279-288. [lo] D. Henry and B. Roux, "Three dimensional numerical study of convection in a cylindrical thermal diffusion cell: its influence on the separation of constituents", Phyrice of fluids vol 29, no 11, (1986), pp. 3562-3572. [II] J.-J. Favier and A. Rouzaud, Adv. Space Res., vol 6, no 5, (1986),
(7)214
J. P.Pmizeyetal. 11-122. [12] S. Van Vaerenbergh, S. Coriell, G. McFadden and B. Murray, "The Role of Soret effect on Morphological stability", submited to Journal of Crystal Growth, 1994. [13] J.J. Favier, J.P. Garandet, A. Rouzaud and D. Camel, “Mass transportphenomenaduring solidificationinmicrogravity. Preliminary results of the first MEPHISTO fight experiment", submited to the Journal of Crystal Growth, 1994. pp.