- Email: [email protected]
MECHANISMS OF REACTIVE WETTING: THE QUESTION OF TRIPLE LINE CONFIGURATION
Vol.45,No.7,pp. 3079–3085, 1997 ~ 1997ActaMetallurgicInc. PublishedbyElsevierScienceLtd Printedin GreatBritain.Allrightsreserved 1359-6454/97 $17.00+ 0.00
Acta mafer.
Pergamon
@
PII: S1359-6454(96)00372-2
MECHANISMS OF REACTIVE WETTING: THE QUESTION OF TRIPLE LINE CONFIGURATION K. LANDRY, C. RADO, R. VOITOVICH and N. EUSTATHOPOULOS LTPCM, INP Grenoble, UJF, URA 29, BP 75, 38402Saint Martin d’H&rescedex, France (Received 24 May 1996)
Abstract—Thisstudy is focused on the question of surface energy parameters determining the final, or steady-state,contact angle in reactive liquid–solidsystems.Two possibleconfigurationsat the three-phase line are considered:(i) a continuous layer of reaction product extendingonly at the liquid–solidinterface and (ii) a continuous layer also extending on the free surface of the substrate. In order to discriminate between these configurations, wetting experiments are carried out in two reactive copper based alloy/vitreouscarbon systems,as wellas in the correspondingnon-reactivesystems.The generalcharacter of conclusionsdrawn from these experimentsis discussedby calculating the thermodynamicbarriers to the extensionof reaction product layers over the free surface of the substrate. ~ 1997 Acta Metallurgic Inc.
R6sum&Cette etude est focaliseesur la question des parametres d’energiede surface determinant I’angle de contact final ou angle stationnaire clans les systemes reactifs liquide-solide. Deuxconfigurations possiblessent discutees:(i) une couchecontinuedu produit de t+action couvrant seulement l’interface solide–liquideet (ii) une couchecontinuequi s’.+tendegalementsur la surfacelibre du substrat au voisinage de la lignedes trois phrases. Afin de conclure entre ces deux configurations,des exp&iencesde mouillage sent rialis~es pour deux systemes r6actifs du type alliage de cuivre/carbone vitreux ainsi que pour les systemesnon-reactifs correspondents. Le caract?re gt%$raldes conclusionstir&esde ces exp&iencesest discute en calculant les barriires thermodynamiquesa I’extensiondee couchesr&actionnellesinterfaciales sur la surface libre du substrat.
1. INTRODUCTION
In many systems of practical interest the wetting of liquid metals on metallic or ceramic substrates is accompanied by reactions between the liquid and solid phases [1-4]. The mechanisms of reactive wetting, i.e. the origin of the driving force and the factors controlling wetting kinetics are not well understood. Initially, it was proposed that the main contribution to the drivingforce of wettingwas a free energy produced by the reaction at the “immediate vicinity of the interface” [1, 5]. Recently, from discriminating experiments carried out in metal/ceramic systems[6,7] it was concluded that, at least for systems with weak or moderate reactivity, the main effect of interracial reactions on wetting is to change the relevant interracial energies of the system [8,9]. While this conclusion appears now to have gained more general acceptance [10-12] it is not yet clear which interracial energiesdetermine the final contact angle & of the system. When a continuouslayer of a new phase is formed at the interface, two different configurationsat the three-phaseline (hereaftercalled the triple line)have been proposed in order to explain experimental findings. According to Mortimer and Nicholas [13]the final or stationary contact angle & is determined by the asv, apLand aLvsurface energies (where S denotes the initial substrate, P the reaction
product, L liquid and V vapour) and is given by the following equation: Cos& =
(1)
This equation corresponds to the configuration of Fig. l(a) in which the reaction product layer does not extend on the free surface of the substrate (note that although any change in the area of the PL interface implies an equivalent change in the area of the PS interface, equation (1) does not contain a apsenergy term). The configurationof Fig. l(a) was also used by Fujii et al. to explain the results of the wetting of Al on BN and AIN substrates [14].Recently, the same configuration was used by Zhou and de Hosson to discuss the wetting behaviour of several reactive metal/ceramic combinations [12]. Moreover these authors argued that in reactive systemsthe aPL term would be negligible,such that contact angles would depend only on the ratio betweenthe surfaceenergies of the substrate and the liquid: (2) Espie et al. [6], in order to interpret the results of wetting experiments performed with the same alloy on differentoxide substrates, proposed configuration l(b) in which the reaction layer extends over the solid
3079
.—.—.——
asv—aP~ OL”
LANDRY et al,: MECHANISMSOF REACTIVEWETTING
3080
free surface. Neglectingany effectof the roughnessof the reaction Iayer, tl~is simply given by the Young equation applied to the P–L–V system [6]: (3)
The aim of this study is to contribute to the discussion on the triple line configuration by performing sessile drop experiments in reactive CuSi/Cv and CuCr/Cv systems(where C, is vitreous carbon). In these systems, simple, carbide forming reactions occur at the interface. The same wetting experiments are repeated on silicon carbide and chromium carbide substrates which are preciselythe product of the interracial reaction between the copper–silicon(respectivelycopper
orientation. Both types of substrate are polished down to 0.1 ,um diamond paste leading to average and maximum heights of surface asperities of 2 and 15nm, respectively.Just before the experiments the SiC substrates are etched in an HF solution in order to eliminate the superficial oxide film formed by oxidation in air at room temperature. These are then rinsed in ethanol, ultrasound cleaned in acetone and dried in a purified air blast. The vitreous carbon substrates are annealed for 3600s at 1473K under about 5 x 10-4Pa. Copper–silicon alloys containing 40 at.YOSi are used. Indeed, as shown by Rado et al. [15], alloys with XSi> 15at. O/Oare in equilibrium with SiC at 1423K. Consequently,when in contact with vitreous . carbon, siliconcontained in the alloys reacts to form SiC.Alloydrops weighingabout 100mg are prepared in situ during the sessiledrop experimentsby melting on the substrate samplesof 99.999Y0pure copper and 99.9995Y0pure silicon. Just before the experiment, the sample of Cu is cut on all its faces, ultrasound cleaned in acetone and dried in a purified air blast. The sampleof Si is etched in an HF solution and then rinsed in ethanol. ultrasound cleaned in acetone and dried in a purified air blast. The experiment consists of monitoring the time-dependent variations in contact angle, drop base radius and drop height at constant temperature. After cooling, interracial reactivityis characterized in selected specimens by scanning electron microscopy (SEM) and electron probe microanalysis. A slightly different procedure is followed in the case of Cu–1 at.O/O Cr alloys.It is wellestablishedthat at temperatures close to the Cu melting point alloys containing more than 0.1 at.O/O Cr react with carbon forming continuous carbide layers [13]. Drops of about 100mg are prepared by melting of pure metals on monocrystalline alumina under high vacuum. Thesedrops are then used for the wettingexperiments on vitreouscarbon and chromiumcarbide substrates. Sintered chromium carbide can be used for these experiments; however, sintered ceramics usually contain large amounts of oxygen which may significantlymodify the nettability by liquid metals [16]. To avoid these complications a two-stage
Contact angles are measured by the sessile drop method in a high vacuum metallic furnace. The apparatus consists essentially of a molybdenum resistance furnace fitted with two windows,enabling the illumination of the sessiledrop on the substrate and the projection of its image on a screen. Contact angles are measured directly from the image of the drop section with an accuracy of *2 degrees. The pressure in the experimentalchamber can be reduced to 10-6Pa at room temperature by a system of two pumps (a rotary vane pump and an oil-diffusion pump, both connected to a nitrogen-cooledtrap). In order to limit the evaporation of copper, once this vacuum levelis reached, the experimentis performed in a dynamic vacuum of 10-3Pa obtained by controlled helium micro-leaks. The helium gas is purifiedbefore introduction to the furnace by passing through a Zr–Al getter. Vitreous carbon (C”) and siliconcarbide substrates are used. Vitreous carbon is a graphitic although imperfectly crystallized form of carbon in which crystallite, about 1–2nm in size, exhibit a random orientation. These substrates contain less than 50p.p.m of impurities. The siliconcarbide substrates procedure is used. First a wetting experiment with-a consist of high purity singlecrystals of the hexagonal Cu–1 at. % Cr alloy is carried out at 1373 K to form structure type (a-SiC). Their surfaces have a {0001} a continuous layer, a few microns in thickness, of \
L L
\
9F
P\
s
\
\ \v L
P\ + //f/////4//////~//4
s + ‘P
l-z+
Fig. 1.Possibleconfigurationsat solid–liquid–vapourtriple linewhensteady-statecontact angleis reached; (a) Ref. [13],(b) Ref. [6].
LANDRY ef al.: MECHANISMSOF REACTIVEWETTING
3081
3’ 60 I
%Jj@@-
20~ ;’
–
.
–
–
1‘ ‘ ‘ c ‘ 2000
–
–
–
–
-
‘ 1‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ 4eoo
–
–
‘1
–
–
‘ I 8000
t (s) Fig. 2. Contact angle kineticsobtained for a CU-40at.O/O Si alloy on vitreouscarbon and a-silicon carbide substrates: T = 1423K.
chromium carbide. Then, after dissolution of the CuCr alloy, a small (m = 20 mg) quantity of a Cu–1 at.O/O alloy is placed in the centre of the carbide layer and the wetting experiment is repeated at 1373K. Before working with the alloys, a few sessiledrop experiments were carried out with pure copper on vitreous carbon. 3. RESULTS
Pure copper drops placed on vitreous carbon substrates reach their equilibrium shape “instantaneously” after melting, i.e. for spreading times tF less than 1 s. Three sessiledrop experimentsled to OF values 139t 5, 135~ 5 and 137+ 3 degrees. The relatively high uncertainty given for each value corresponds to the dispersionof Ovaluesmeasured at different positions around the drop base. No measurable change in & was observed when the temperature rose from the copper melting point (1356K) to 1423K. Consequently, we conclude that the contact angle of pure Cu on C“ close to the Cu melting point is OF = 137* 5 degrees. Figure 2 showsthe wettingcurves of a CU-40at. % Si alloy on vitreous carbon and on monocrystalline SiC substrates. The steady-state contact angle on SiC is close to 40 degreesand it is reached in about 200s. On vitreous carbon the spreading time t~ is larger than on SiC by an order of magnitude; however,the steady-state contact angle & hardly differs from the contact angle observed on SiC. Figure 3 shows a SEM micrograph taken from a cross-section perpendicular to the interface in a CU-40at.% Si/Cv specimen cooled after a contact time of 5300s, i.e. once the steady-statecontact angle is reached. It shows the presence of a continuous layer of reaction product at the interface. Analysisby energydispersiveX-ray spectrometryrevealedsilicon inside the layer but, owing to the small thickness of the reaction layer, it was not possible to ascertain the
presence of carbon. It can, however, be concluded unambiguously that the reaction product is silicon carbide. This layer extends up to the triple line as shownin Fig. 4, in whichthe same sampleis observed from above, near the triple line. A layer, about 10pm in width, appears around the drop. This layer is, at least in its inner part, a dewetting area produced by a recedingmovement of the liquid during cooling, as revealed by the presence of numerous metallic droplets of submicronic size in the inner part of the layer. Such droplets do not appear on the outer part of the layer, although the presence of droplets of smaller size cannot be excluded; however, X-ray microanalysis revealed only the presence of carbon and silicon inside the layer. From the above results it can be concludedthat the greylayer is a continuous layer of SiC covering the solid–liquidinterface (and probably the free surface of the substrate near the triple line) before solidificationof the drop. Figure 5 showsthe spreadingkineticsof Cu–1 at.% Cr alloy on a vitreous carbon substrate. A steady-state contact angle is reached in about 100s.
Fig, 3. SEMmicrographof a cross-section perpendicular to interfacein a CW40at.O/O silicon(white)/vitreous carbon (black)systemcooledat steady-statecontactangle.
LANDRYet al.: MECHANISMS OF REACTIVEWETTING
3082
L+z2fif!if ,,,,,\.,.,,,,,,,,:..:,,.:..,,\,l,,,,,,.,,,
,,,,
t Fig. 4, SEM micrograph of a CU40 at.% Si (white)/vitreouscarbon (black) specimen observed from above close to triple line.
Eight independent experimentsled to & values lying between 37 and 46 degrees with an average value OF= 41 ~ 4 degrees. The SEM micrograph of Fig. 6, taken from a cross-section perpendicular to the interface, shows the presenceof a continuous layer, severalmicrons in thickness, extending outside the drop. Electron microprobe analysisrevealed,insidethe layer, carbon and chromium concentrations corresponding to a chromium carbide CrC. with n ~ 0.4. This is closerto the CrTC~carbide (n = 0.428) than to the CrsCj (n= 0.67)identifiedpreviouslyby other workers [17] X-ray diffractionof the carbide layer carried out after dissolution of CuCr alloy confirmedthe formation of CrTC,.The carbide layer appears to consist of small submicronic grains. The average roughness of the layer is 40 * 15nm. Such surfaces were used to carry out two wetting experiments with a Cu–1 at.OZOCr alloy. The steady-state contact angle, equal to 45 and 43 degrees, is reached in less than 1 s (Fig. 5). Figure 7 showsa SEM micrograph taken from above, showing the solidifieddrop on the carbide layer ‘“’substrate” (in grey) situated on the initial vitreous carbon I
I
1
1
1
I
surface (in black). Some cracks, produced on cooling near the solidified dropcarbid+vapour triple line, are also seen. 4. DISCUSSION With non-reactive metallic liquids on solid substrates, the spreading time for drops of millimeter size is less than 1 s [18, 19]. This agrees with the “instantaneous” spreading observedfor pure copper on vitreous carbon. The value & = 137~ 5 degrees is in good agreementwith the contact angle measured by Mortimer and Nicholas on the same type of substrate (145 degrees at 1423K) [13]. As with the Cu/Cv system, the CU40 at.% Si/SiC system is non-reactive [15]; however, the spreading time is as long as 200s (Table 1). In this system, as in the similar AuSi/SiC system [20],spreading is in fact controlled by the deoxidation of the alloy and SiC surfaces, as described in detail elsewhere [15]. In the CuSi/CVsystem, the first spreading stage is attributed by analogy to alloy deoxidation. The second spreading stage, which does not exist in the non-reactive CuSi/SiC system, is attributed to the interracial reaction between vitreous carbon and the Cu–Si alloys. As in the Al/C” couple studied elsewhere [21] when the final contact angle & is
100 -/ —
I
—
Cv
Cr7C3
*SO .; ~ “; jj~
+ -Cu-Cr
:: 40 20
*,
1 o
Crcn
1 20
I 40
1 60
) so
Cv
I 103
t,s Fig. 5. Contact angle vs time curves for a Cu–1at.% Cr alloy on vitreous carbon and CrTCjsubstrates; T = 1373K.
Fig. 6. SEM micrograph of a cross-sectionperpendicularto interface of a @–Cr alloy on vitreous carbon cooled from T = 1373K at steady-state contact angle.
LANDRY et al,: MECHANISMSOF REACTIVEWETTING
3083
Table2. Wettingparametersandinterracialchemistryof CuPd–Ti (X,,= 15at.%) at 1473K on aluminaand silica substrates (from Ref. 161) Substrate Alumina
Silica
Fig. 7. SEM micrograph of a Cu–1at.% Cr drop (observed from above) on a chromium carbide layer (in grey) formed by prior reaction between a Cu–1at.% Cr alloy and a vitreous carbon substrate (in black); T = 1373K.
reached, a layer of reaction product covers the vitreous carbon substrate at the solid/liquid interface both far from and near the triple line. Table 1 shows that the final contact angles measured in the reactive (CuSi/Cv) system and the non-reactive (CuSi/SiC) system are nearly the same. In terms of work of adhesion, [W, = ~Lv(l+ cos 0)] the differenceis less than 4°/0. Reactivity in Cu–1 at. % Cr/CVis much higher than in CU-40at.YOSi/CVas clearlyshown by the different thicknesses of the reaction layers formed at the interface (Figs 3 and 6) as well as the values of spreading time t~ (Table 1). Despite the large difference in reactivity, the wetting behaviour of CuCr alloysis very similar to that of CuSi alloyswith respect to the following two points: (i) spreading in the reactive CuCr/Cv couple is much slower than in the corresponding non-reactive couple and (ii) the final contact angle OFformed by the CuCr alloy on the initial substrate (vitreous carbon) and on the reaction product (chromium carbide) are nearly the same. It is possible that the O,values of Table 1, all close to 40°, simultaneouslyverifyequations (1) (or 2) and (3). This would imply (i) that the surface energiesof vitreous carbon, silicon carbide and chromium carbide are all equal to one another: this is possible although rather improbable; and (ii) that the surface tension (~LV) of CuSi alloy is equal to the ~LV value of CuCr alloy: this condition is clearly impossible because the value of aLv for the Cu–1 at.% Cr is
Interracial product TizO~
TijO~
Thicknesse, (#m)
(de~;ees)
0.5 10
34* 2 36+ 2
1300mJ/m2 [22] against 900mJ/m2 for the Cu– 40 at. % Si alloy [23]. Consequently, the results of Table 1 are incompatiblewith both equations (1) and (2). Thus, the results of the present study confirm the validity of equation (3), meaning that the final contact angle in a reactive metal/ceramic system is nearlyequal to the Young contact angle of the metal on the reaction product. Indeed, some difference between these two angles (the Young angle and the observed one) can result from the roughness often present on the reaction product surface [21]. For instance, the average roughness of the chromium carbide layer produced by the reaction between Cr and Cv is about 40 nm against 2 nm for the initial CV surface. The findings of the present study are in good agreement with the results of Espie et al. [6].These authors measured the contact angles formed by a CuPd alloy containing 15at.% Ti on two oxide substrates (alumina and silica). Titanium from the alloy reacts with both substrates, formingcontinuous layers of the same Ti oxide, titanium trioxide, at the interface. Knowing that the surface energies of a-alumina and silica differ by 100°/0[24],equations (1) and (2) predict that the contact angles on these oxides would be very different. In fact, the experimentalcontact angleshardly differ(Table 2). In contrast, equation (3) explains these results because it predicts that the same interracial reaction layer leads to the same steady-state contact angle independently of the initial substrate. Equation (3) does not seem to be verified by the results of Fujii et al. [14]for wetting of Al on BN and AIN substrates. These authors found that at 1373K pure Al wets BN substrates perfectly,formingAIN at the interface, but does not wet AIN itself (0 x 130°) [14].This behaviour was explainedon the basis of the configuration of Fig. l(a), by assuming that the solid–vapoursurface energy of BN was much higher than the surface energy of AIN. Rhee [25],however, studied the variation with temperature of the contact
Table 1. Spreading times and steady-statecontact angles measured for CuSi alloys at T = 1423K on vitreous carbon and silicon carbide substrates and for CuCr alloys at T = 1373K on vitreouscarbon and chromiumcarbide [F(seconds) lk (degrees)
—.
l’ (at.%)
SiC
Vitreous carbon
x$ = 40 xc,= 1
200
4000
100
Cr,c,
<1
SiC
Vitreous carbon
36~ 3
42&3
—
41 + 4
Cr7C3 41 * 3
LANDRY et al.: MECHANISMSOF REACTIVEWETTING
3084
angle of Al on AIN under high vacuum in the 960-1160K range. He found that Odecreasessteeply with T and passes below 90 degrees at 1120K. Recently, for the same couple Naidich and Taranets found O~ 45 degrees at 1373K under high vacuum and observed that 6 tends towards zero when the temperature approaches 1473K,,[26]. From these studies it appears that nettability of AIN by Al depends strongly on the experimental conditions (indeed both Al and AIN are oxidizable materials) and that intrinsic nettability in this system is very high. Although the results of Tables 1 and 2 can be well interpreted by equation (3), they do not allow the general validity of this equation to be asserted. Indeed, under certain circumstances, in a particular system or in a certain type of reactive couple, it is possible that the extension of a continuous layer on the free surface of the substrate is blocked by thermodynamic or kinetic barriers. Thermodynamic barriers can be calculated by considering the change per unit length of triple line in the Gibbs energyG produced by a lateral extension of the reaction product layer (of thicknesseP)outside the drop [Fig. l(b)]. It is easily seen that
-() dG . dz
& V.
ep+ (aPV+ aPS— f7sv)
(4)
where AGMand VMare the molar Gibbs energyof the interracial reaction and the molar volume of. the product, respectively. With dG/dz = O a critical layer thickness e$ is obtained: ep * = –(UPV + 6,s –
asv) *.
(5)
For eP> e~ no thermodynamic barrier to the formation of reaction product outside the drop exists, while for eP< e; the configuration l(a) corresponding to a metastable equilibrium, is possible. For the CuSi/CVsystem the interracial reaction is written as (Si) + Cv- SiC
(6)
where the parenthesis means that silicon is dissolved in molten copper. The quantity AGMfor this reaction is written simply as AG~= RT In ~
(7)
Generally the values of the surface energiesin the quantity ArJ= m.V+ CTPS – GSVare not known. To calculate an order of magnitude of e~ a reasonable value of Acr= 103mJ/m2 is used. Then, taking Vt,i(SiC)~ 15 x 10-6m3/mole we find that e$ ~ 0.5 nm. A similar calculation for the Cu–1 at.% Cr/Cv system, made using the thermodynamic calculations of Ref. [17], leads again to a critical thickness er smaller than 1 nm. Such values of e~ are too low to create a true barrier to the formation of product P outside the drop. Indeed, the slightest growth of P in a direction perpendicularto the interface,i.e. towards the interior of the liquid, would be suilicient to destroy such barriers. Note that in the few cases in which the thickness of the reaction layer at the vicinityof a triple line was measured, it was found to vary from severaltens of nm to a fewmicrons ([6,21], see also Figs 3 and 6). In conclusion, except for very large (but unrealistic) Aa values, or extremely low values of AGM(in this case even the condition of a continuous layer of P becomes questionable), thermodynamicbarriers to the lateral growth of P on the substrate free surface are unlikely. Kinetic barriers to this growth may result from insufficientmobility of reactive species(e.g. very low surface diffusion coefficients or very low partial pressuresof the reactive solute);however,even in the Al/Cv couple, having at T = 1100K a very low reactivity resuking in a very slow spreading rate (tF values higher than 104s were measured) the lateral growth rate of carbide at t> tF was several nanometers per second [21].Taking into account that a value for length z of a few nm is sufficientfor the liquid surface to meet the reaction product rather than the initial substrate surface, it appears that kinetic barriers are equally unlikely. 5, CONCLUSIONS
At temperatures close to its melting point, pure copper does not wet vitreous carbon (& ~ 137 degrees). Cu~O at. % Si and CU–1’YOCr alloys wet this substrate well (& ~ A(Idegrees for both alloys) forming continuous layers of silicon carbide and chromium carbide, respectively, at the interface. Wetting experiments carried out with the same alloys on silicon carbide and chromium carbide substrates led to nearly the same final contact angles as in the corresponding reactive system. These findings show that the reaction product layer extends on the free surface of the substrate and not only, as proposed previously, at the solid–liquid interface. As a result, the steady-state contact angle reached at the end of spreading is close to the Young contact angle of the liquid on the reaction product. From this point of view, reactive wetting is only a way to modify the initial substrate surface in situ. The generality of this
where agiis the thermodynamic activity of silicon in molten copper in equilibrium with vitreous carbon and siliconcarbide and asiis the actual activity in the alloy. At 1423K equilibrium occurs for a molar fraction of Si in Cu of l$i E 0.15 [15]. Introducing into equation (7) values of a~i (X = ~~i) and asi (XSi= 0.40) computed from existing thermodynamic data [27],it is found that AGM~ – 30 kJ/mol, which conclusionis examinedto showthat it is in agreement with prior published data and that pinning of the is rather a low value for a molar reaction energy.
LANDRY et al.: MECHANISMSOF REACTIVEWETTING
reaction product layer at the triple line by thermodynamic or kinetic barriers is very unlikely. Acknowledgements—The authors would like to thank Professor A. Mortensen for critical reading of the manuscript.
REFERENCES 1. Naidich, Yu., Prog. Surf. Membrane Sci., 1981, 14, 353. 2, Nicholas, M., Br. Ceram. Trans. J., 1986, 85, 144. 3. Loehman, R. and Tomsia, A., Am. Ceram. Bull., 1988, 67, 375. 4. Nogi, K., Trams. JWRI, 1993, 22, 183. 5. Aksay, I., Hoge, C. and Pask, J., J. Phys. Chem., 1974, 78, 1178. 6. Espi6, L., Drevet, B. and Eustathopoulos, N., Metall. Trans. A., 1994, 25A, 599. 7. Kritsalis, P., Drevet, B., Valignat,N. and EustathopouIOS,N., Scripta metall. mater., 1994, 30, 1127. 8. Eustathopoulos, N. and Drevet, B., MRS Symp. Proc., 1993, 314, 15. 9. Eustathopoulos, N. and Drevet, B., J. Phys. 111 (Fr), 1994, 4, 1865. 10. Xiao, P. and Derby, B., Acta mater. 1996, 44, 307. 11. Cannon, R., Saiz, E., Tomsia, A. and Carter, W., MRS Symp. Proc., 1995, 357, 279. 12. Zhou, X. and de Hosson, J., Acta mater., 1996,44,421. 13. Mortimer, D. and Nicholas, M., J. Mater. Sci., 1970,
5, 149and 1973,8, 640.
3085
14. Fujii, H., Nakae, H. and Okada, K., Acta meiall. mater., 1993, 41, 2963. 15. Rado, C., Rocabois, P., Kalogeropoulou, S. and Eustathopoulos, N., Proc. 1994 Int. Conf. on High Temperature Capillarity, ed. N. Eustathopo~los.Repr~-
print, Bratislava, 1995,p. 143. 16. Gheta, V., Gayraud, N. and Eustathopoulos, N., Solid St. Phenomena, 1992, 2~26, 105. 17. Devincent, S. and Michal, G., Metall. Trans. A, 1993, 24A, 53. 18. Laurent, V., Contributiona l’6tudedu mouillagereactif:
Etude du systeme alurninium/carbone. Ph.D. thesis, Institut National Polytechniquede Grenoble, France, 1988. 19. Eremenko,V., Kostrova, L. and Lesnik,N., Proc. 1994 Int. Conf. on High Temperature Capillarity, ed. N.
Eustathopoulos. Reproprint, Bratidava, 1995,p. 113. 20. Drevet, B., Kalogeropoulou, S. and Eustathopoulos, N., Acta metall. mater., 1993, 41, 3119. 21. Landry, K. and Eustathopotdos,N., Acta mater., 1996, 44, 3923. 22. Kritsalis, P., Li, J., Coudurier, L. and Eustathopoulos, N., J. Mater. Sci. (L), 1990, 9, 1332. 23. Khilya, G. and Ivashchenko, Y., Dopov Akad Nauk Ukr, RSR Ser B, 1973, 35, 69. 24. Richardson, F. D., Physical Chemistry of Melts in Metallurgy, Vol. 2. Academic Press, London, New
York, 1974,p. 44. 25. Rhee, S., J. Am. Cer. Soc., 1970, 53, 386. 26. Naidich, Y. and Taranets, N., Proc. 1994 Int. Conf. on High Temperature Capillarity. ed. N. Eustathopoulos. Reproprint, Bratislava, 1995, p. 138. 27. Liidecke, D., Calphad, 1987, 11, 135.
Acta mafer.
Pergamon
@
PII: S1359-6454(96)00372-2
MECHANISMS OF REACTIVE WETTING: THE QUESTION OF TRIPLE LINE CONFIGURATION K. LANDRY, C. RADO, R. VOITOVICH and N. EUSTATHOPOULOS LTPCM, INP Grenoble, UJF, URA 29, BP 75, 38402Saint Martin d’H&rescedex, France (Received 24 May 1996)
Abstract—Thisstudy is focused on the question of surface energy parameters determining the final, or steady-state,contact angle in reactive liquid–solidsystems.Two possibleconfigurationsat the three-phase line are considered:(i) a continuous layer of reaction product extendingonly at the liquid–solidinterface and (ii) a continuous layer also extending on the free surface of the substrate. In order to discriminate between these configurations, wetting experiments are carried out in two reactive copper based alloy/vitreouscarbon systems,as wellas in the correspondingnon-reactivesystems.The generalcharacter of conclusionsdrawn from these experimentsis discussedby calculating the thermodynamicbarriers to the extensionof reaction product layers over the free surface of the substrate. ~ 1997 Acta Metallurgic Inc.
R6sum&Cette etude est focaliseesur la question des parametres d’energiede surface determinant I’angle de contact final ou angle stationnaire clans les systemes reactifs liquide-solide. Deuxconfigurations possiblessent discutees:(i) une couchecontinuedu produit de t+action couvrant seulement l’interface solide–liquideet (ii) une couchecontinuequi s’.+tendegalementsur la surfacelibre du substrat au voisinage de la lignedes trois phrases. Afin de conclure entre ces deux configurations,des exp&iencesde mouillage sent rialis~es pour deux systemes r6actifs du type alliage de cuivre/carbone vitreux ainsi que pour les systemesnon-reactifs correspondents. Le caract?re gt%$raldes conclusionstir&esde ces exp&iencesest discute en calculant les barriires thermodynamiquesa I’extensiondee couchesr&actionnellesinterfaciales sur la surface libre du substrat.
1. INTRODUCTION
In many systems of practical interest the wetting of liquid metals on metallic or ceramic substrates is accompanied by reactions between the liquid and solid phases [1-4]. The mechanisms of reactive wetting, i.e. the origin of the driving force and the factors controlling wetting kinetics are not well understood. Initially, it was proposed that the main contribution to the drivingforce of wettingwas a free energy produced by the reaction at the “immediate vicinity of the interface” [1, 5]. Recently, from discriminating experiments carried out in metal/ceramic systems[6,7] it was concluded that, at least for systems with weak or moderate reactivity, the main effect of interracial reactions on wetting is to change the relevant interracial energies of the system [8,9]. While this conclusion appears now to have gained more general acceptance [10-12] it is not yet clear which interracial energiesdetermine the final contact angle & of the system. When a continuouslayer of a new phase is formed at the interface, two different configurationsat the three-phaseline (hereaftercalled the triple line)have been proposed in order to explain experimental findings. According to Mortimer and Nicholas [13]the final or stationary contact angle & is determined by the asv, apLand aLvsurface energies (where S denotes the initial substrate, P the reaction
product, L liquid and V vapour) and is given by the following equation: Cos& =
(1)
This equation corresponds to the configuration of Fig. l(a) in which the reaction product layer does not extend on the free surface of the substrate (note that although any change in the area of the PL interface implies an equivalent change in the area of the PS interface, equation (1) does not contain a apsenergy term). The configurationof Fig. l(a) was also used by Fujii et al. to explain the results of the wetting of Al on BN and AIN substrates [14].Recently, the same configuration was used by Zhou and de Hosson to discuss the wetting behaviour of several reactive metal/ceramic combinations [12]. Moreover these authors argued that in reactive systemsthe aPL term would be negligible,such that contact angles would depend only on the ratio betweenthe surfaceenergies of the substrate and the liquid: (2) Espie et al. [6], in order to interpret the results of wetting experiments performed with the same alloy on differentoxide substrates, proposed configuration l(b) in which the reaction layer extends over the solid
3079
.—.—.——
asv—aP~ OL”
LANDRY et al,: MECHANISMSOF REACTIVEWETTING
3080
free surface. Neglectingany effectof the roughnessof the reaction Iayer, tl~is simply given by the Young equation applied to the P–L–V system [6]: (3)
The aim of this study is to contribute to the discussion on the triple line configuration by performing sessile drop experiments in reactive CuSi/Cv and CuCr/Cv systems(where C, is vitreous carbon). In these systems, simple, carbide forming reactions occur at the interface. The same wetting experiments are repeated on silicon carbide and chromium carbide substrates which are preciselythe product of the interracial reaction between the copper–silicon(respectivelycopper
orientation. Both types of substrate are polished down to 0.1 ,um diamond paste leading to average and maximum heights of surface asperities of 2 and 15nm, respectively.Just before the experiments the SiC substrates are etched in an HF solution in order to eliminate the superficial oxide film formed by oxidation in air at room temperature. These are then rinsed in ethanol, ultrasound cleaned in acetone and dried in a purified air blast. The vitreous carbon substrates are annealed for 3600s at 1473K under about 5 x 10-4Pa. Copper–silicon alloys containing 40 at.YOSi are used. Indeed, as shown by Rado et al. [15], alloys with XSi> 15at. O/Oare in equilibrium with SiC at 1423K. Consequently,when in contact with vitreous . carbon, siliconcontained in the alloys reacts to form SiC.Alloydrops weighingabout 100mg are prepared in situ during the sessiledrop experimentsby melting on the substrate samplesof 99.999Y0pure copper and 99.9995Y0pure silicon. Just before the experiment, the sample of Cu is cut on all its faces, ultrasound cleaned in acetone and dried in a purified air blast. The sampleof Si is etched in an HF solution and then rinsed in ethanol. ultrasound cleaned in acetone and dried in a purified air blast. The experiment consists of monitoring the time-dependent variations in contact angle, drop base radius and drop height at constant temperature. After cooling, interracial reactivityis characterized in selected specimens by scanning electron microscopy (SEM) and electron probe microanalysis. A slightly different procedure is followed in the case of Cu–1 at.O/O Cr alloys.It is wellestablishedthat at temperatures close to the Cu melting point alloys containing more than 0.1 at.O/O Cr react with carbon forming continuous carbide layers [13]. Drops of about 100mg are prepared by melting of pure metals on monocrystalline alumina under high vacuum. Thesedrops are then used for the wettingexperiments on vitreouscarbon and chromiumcarbide substrates. Sintered chromium carbide can be used for these experiments; however, sintered ceramics usually contain large amounts of oxygen which may significantlymodify the nettability by liquid metals [16]. To avoid these complications a two-stage
Contact angles are measured by the sessile drop method in a high vacuum metallic furnace. The apparatus consists essentially of a molybdenum resistance furnace fitted with two windows,enabling the illumination of the sessiledrop on the substrate and the projection of its image on a screen. Contact angles are measured directly from the image of the drop section with an accuracy of *2 degrees. The pressure in the experimentalchamber can be reduced to 10-6Pa at room temperature by a system of two pumps (a rotary vane pump and an oil-diffusion pump, both connected to a nitrogen-cooledtrap). In order to limit the evaporation of copper, once this vacuum levelis reached, the experimentis performed in a dynamic vacuum of 10-3Pa obtained by controlled helium micro-leaks. The helium gas is purifiedbefore introduction to the furnace by passing through a Zr–Al getter. Vitreous carbon (C”) and siliconcarbide substrates are used. Vitreous carbon is a graphitic although imperfectly crystallized form of carbon in which crystallite, about 1–2nm in size, exhibit a random orientation. These substrates contain less than 50p.p.m of impurities. The siliconcarbide substrates procedure is used. First a wetting experiment with-a consist of high purity singlecrystals of the hexagonal Cu–1 at. % Cr alloy is carried out at 1373 K to form structure type (a-SiC). Their surfaces have a {0001} a continuous layer, a few microns in thickness, of \
L L
\
9F
P\
s
\
\ \v L
P\ + //f/////4//////~//4
s + ‘P
l-z+
Fig. 1.Possibleconfigurationsat solid–liquid–vapourtriple linewhensteady-statecontact angleis reached; (a) Ref. [13],(b) Ref. [6].
LANDRY ef al.: MECHANISMSOF REACTIVEWETTING
3081
3’ 60 I
%Jj@@-
20~ ;’
–
.
–
–
1‘ ‘ ‘ c ‘ 2000
–
–
–
–
-
‘ 1‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ 4eoo
–
–
‘1
–
–
‘ I 8000
t (s) Fig. 2. Contact angle kineticsobtained for a CU-40at.O/O Si alloy on vitreouscarbon and a-silicon carbide substrates: T = 1423K.
chromium carbide. Then, after dissolution of the CuCr alloy, a small (m = 20 mg) quantity of a Cu–1 at.O/O alloy is placed in the centre of the carbide layer and the wetting experiment is repeated at 1373K. Before working with the alloys, a few sessiledrop experiments were carried out with pure copper on vitreous carbon. 3. RESULTS
Pure copper drops placed on vitreous carbon substrates reach their equilibrium shape “instantaneously” after melting, i.e. for spreading times tF less than 1 s. Three sessiledrop experimentsled to OF values 139t 5, 135~ 5 and 137+ 3 degrees. The relatively high uncertainty given for each value corresponds to the dispersionof Ovaluesmeasured at different positions around the drop base. No measurable change in & was observed when the temperature rose from the copper melting point (1356K) to 1423K. Consequently, we conclude that the contact angle of pure Cu on C“ close to the Cu melting point is OF = 137* 5 degrees. Figure 2 showsthe wettingcurves of a CU-40at. % Si alloy on vitreous carbon and on monocrystalline SiC substrates. The steady-state contact angle on SiC is close to 40 degreesand it is reached in about 200s. On vitreous carbon the spreading time t~ is larger than on SiC by an order of magnitude; however,the steady-state contact angle & hardly differs from the contact angle observed on SiC. Figure 3 shows a SEM micrograph taken from a cross-section perpendicular to the interface in a CU-40at.% Si/Cv specimen cooled after a contact time of 5300s, i.e. once the steady-statecontact angle is reached. It shows the presence of a continuous layer of reaction product at the interface. Analysisby energydispersiveX-ray spectrometryrevealedsilicon inside the layer but, owing to the small thickness of the reaction layer, it was not possible to ascertain the
presence of carbon. It can, however, be concluded unambiguously that the reaction product is silicon carbide. This layer extends up to the triple line as shownin Fig. 4, in whichthe same sampleis observed from above, near the triple line. A layer, about 10pm in width, appears around the drop. This layer is, at least in its inner part, a dewetting area produced by a recedingmovement of the liquid during cooling, as revealed by the presence of numerous metallic droplets of submicronic size in the inner part of the layer. Such droplets do not appear on the outer part of the layer, although the presence of droplets of smaller size cannot be excluded; however, X-ray microanalysis revealed only the presence of carbon and silicon inside the layer. From the above results it can be concludedthat the greylayer is a continuous layer of SiC covering the solid–liquidinterface (and probably the free surface of the substrate near the triple line) before solidificationof the drop. Figure 5 showsthe spreadingkineticsof Cu–1 at.% Cr alloy on a vitreous carbon substrate. A steady-state contact angle is reached in about 100s.
Fig, 3. SEMmicrographof a cross-section perpendicular to interfacein a CW40at.O/O silicon(white)/vitreous carbon (black)systemcooledat steady-statecontactangle.
LANDRYet al.: MECHANISMS OF REACTIVEWETTING
3082
L+z2fif!if ,,,,,\.,.,,,,,,,,:..:,,.:..,,\,l,,,,,,.,,,
,,,,
t Fig. 4, SEM micrograph of a CU40 at.% Si (white)/vitreouscarbon (black) specimen observed from above close to triple line.
Eight independent experimentsled to & values lying between 37 and 46 degrees with an average value OF= 41 ~ 4 degrees. The SEM micrograph of Fig. 6, taken from a cross-section perpendicular to the interface, shows the presenceof a continuous layer, severalmicrons in thickness, extending outside the drop. Electron microprobe analysisrevealed,insidethe layer, carbon and chromium concentrations corresponding to a chromium carbide CrC. with n ~ 0.4. This is closerto the CrTC~carbide (n = 0.428) than to the CrsCj (n= 0.67)identifiedpreviouslyby other workers [17] X-ray diffractionof the carbide layer carried out after dissolution of CuCr alloy confirmedthe formation of CrTC,.The carbide layer appears to consist of small submicronic grains. The average roughness of the layer is 40 * 15nm. Such surfaces were used to carry out two wetting experiments with a Cu–1 at.OZOCr alloy. The steady-state contact angle, equal to 45 and 43 degrees, is reached in less than 1 s (Fig. 5). Figure 7 showsa SEM micrograph taken from above, showing the solidifieddrop on the carbide layer ‘“’substrate” (in grey) situated on the initial vitreous carbon I
I
1
1
1
I
surface (in black). Some cracks, produced on cooling near the solidified dropcarbid+vapour triple line, are also seen. 4. DISCUSSION With non-reactive metallic liquids on solid substrates, the spreading time for drops of millimeter size is less than 1 s [18, 19]. This agrees with the “instantaneous” spreading observedfor pure copper on vitreous carbon. The value & = 137~ 5 degrees is in good agreementwith the contact angle measured by Mortimer and Nicholas on the same type of substrate (145 degrees at 1423K) [13]. As with the Cu/Cv system, the CU40 at.% Si/SiC system is non-reactive [15]; however, the spreading time is as long as 200s (Table 1). In this system, as in the similar AuSi/SiC system [20],spreading is in fact controlled by the deoxidation of the alloy and SiC surfaces, as described in detail elsewhere [15]. In the CuSi/CVsystem, the first spreading stage is attributed by analogy to alloy deoxidation. The second spreading stage, which does not exist in the non-reactive CuSi/SiC system, is attributed to the interracial reaction between vitreous carbon and the Cu–Si alloys. As in the Al/C” couple studied elsewhere [21] when the final contact angle & is
100 -/ —
I
—
Cv
Cr7C3
*SO .; ~ “; jj~
+ -Cu-Cr
:: 40 20
*,
1 o
Crcn
1 20
I 40
1 60
) so
Cv
I 103
t,s Fig. 5. Contact angle vs time curves for a Cu–1at.% Cr alloy on vitreous carbon and CrTCjsubstrates; T = 1373K.
Fig. 6. SEM micrograph of a cross-sectionperpendicularto interface of a @–Cr alloy on vitreous carbon cooled from T = 1373K at steady-state contact angle.
LANDRY et al,: MECHANISMSOF REACTIVEWETTING
3083
Table2. Wettingparametersandinterracialchemistryof CuPd–Ti (X,,= 15at.%) at 1473K on aluminaand silica substrates (from Ref. 161) Substrate Alumina
Silica
Fig. 7. SEM micrograph of a Cu–1at.% Cr drop (observed from above) on a chromium carbide layer (in grey) formed by prior reaction between a Cu–1at.% Cr alloy and a vitreous carbon substrate (in black); T = 1373K.
reached, a layer of reaction product covers the vitreous carbon substrate at the solid/liquid interface both far from and near the triple line. Table 1 shows that the final contact angles measured in the reactive (CuSi/Cv) system and the non-reactive (CuSi/SiC) system are nearly the same. In terms of work of adhesion, [W, = ~Lv(l+ cos 0)] the differenceis less than 4°/0. Reactivity in Cu–1 at. % Cr/CVis much higher than in CU-40at.YOSi/CVas clearlyshown by the different thicknesses of the reaction layers formed at the interface (Figs 3 and 6) as well as the values of spreading time t~ (Table 1). Despite the large difference in reactivity, the wetting behaviour of CuCr alloysis very similar to that of CuSi alloyswith respect to the following two points: (i) spreading in the reactive CuCr/Cv couple is much slower than in the corresponding non-reactive couple and (ii) the final contact angle OFformed by the CuCr alloy on the initial substrate (vitreous carbon) and on the reaction product (chromium carbide) are nearly the same. It is possible that the O,values of Table 1, all close to 40°, simultaneouslyverifyequations (1) (or 2) and (3). This would imply (i) that the surface energiesof vitreous carbon, silicon carbide and chromium carbide are all equal to one another: this is possible although rather improbable; and (ii) that the surface tension (~LV) of CuSi alloy is equal to the ~LV value of CuCr alloy: this condition is clearly impossible because the value of aLv for the Cu–1 at.% Cr is
Interracial product TizO~
TijO~
Thicknesse, (#m)
(de~;ees)
0.5 10
34* 2 36+ 2
1300mJ/m2 [22] against 900mJ/m2 for the Cu– 40 at. % Si alloy [23]. Consequently, the results of Table 1 are incompatiblewith both equations (1) and (2). Thus, the results of the present study confirm the validity of equation (3), meaning that the final contact angle in a reactive metal/ceramic system is nearlyequal to the Young contact angle of the metal on the reaction product. Indeed, some difference between these two angles (the Young angle and the observed one) can result from the roughness often present on the reaction product surface [21]. For instance, the average roughness of the chromium carbide layer produced by the reaction between Cr and Cv is about 40 nm against 2 nm for the initial CV surface. The findings of the present study are in good agreement with the results of Espie et al. [6].These authors measured the contact angles formed by a CuPd alloy containing 15at.% Ti on two oxide substrates (alumina and silica). Titanium from the alloy reacts with both substrates, formingcontinuous layers of the same Ti oxide, titanium trioxide, at the interface. Knowing that the surface energies of a-alumina and silica differ by 100°/0[24],equations (1) and (2) predict that the contact angles on these oxides would be very different. In fact, the experimentalcontact angleshardly differ(Table 2). In contrast, equation (3) explains these results because it predicts that the same interracial reaction layer leads to the same steady-state contact angle independently of the initial substrate. Equation (3) does not seem to be verified by the results of Fujii et al. [14]for wetting of Al on BN and AIN substrates. These authors found that at 1373K pure Al wets BN substrates perfectly,formingAIN at the interface, but does not wet AIN itself (0 x 130°) [14].This behaviour was explainedon the basis of the configuration of Fig. l(a), by assuming that the solid–vapoursurface energy of BN was much higher than the surface energy of AIN. Rhee [25],however, studied the variation with temperature of the contact
Table 1. Spreading times and steady-statecontact angles measured for CuSi alloys at T = 1423K on vitreous carbon and silicon carbide substrates and for CuCr alloys at T = 1373K on vitreouscarbon and chromiumcarbide [F(seconds) lk (degrees)
—.
l’ (at.%)
SiC
Vitreous carbon
x$ = 40 xc,= 1
200
4000
100
Cr,c,
<1
SiC
Vitreous carbon
36~ 3
42&3
—
41 + 4
Cr7C3 41 * 3
LANDRY et al.: MECHANISMSOF REACTIVEWETTING
3084
angle of Al on AIN under high vacuum in the 960-1160K range. He found that Odecreasessteeply with T and passes below 90 degrees at 1120K. Recently, for the same couple Naidich and Taranets found O~ 45 degrees at 1373K under high vacuum and observed that 6 tends towards zero when the temperature approaches 1473K,,[26]. From these studies it appears that nettability of AIN by Al depends strongly on the experimental conditions (indeed both Al and AIN are oxidizable materials) and that intrinsic nettability in this system is very high. Although the results of Tables 1 and 2 can be well interpreted by equation (3), they do not allow the general validity of this equation to be asserted. Indeed, under certain circumstances, in a particular system or in a certain type of reactive couple, it is possible that the extension of a continuous layer on the free surface of the substrate is blocked by thermodynamic or kinetic barriers. Thermodynamic barriers can be calculated by considering the change per unit length of triple line in the Gibbs energyG produced by a lateral extension of the reaction product layer (of thicknesseP)outside the drop [Fig. l(b)]. It is easily seen that
-() dG . dz
& V.
ep+ (aPV+ aPS— f7sv)
(4)
where AGMand VMare the molar Gibbs energyof the interracial reaction and the molar volume of. the product, respectively. With dG/dz = O a critical layer thickness e$ is obtained: ep * = –(UPV + 6,s –
asv) *.
(5)
For eP> e~ no thermodynamic barrier to the formation of reaction product outside the drop exists, while for eP< e; the configuration l(a) corresponding to a metastable equilibrium, is possible. For the CuSi/CVsystem the interracial reaction is written as (Si) + Cv- SiC
(6)
where the parenthesis means that silicon is dissolved in molten copper. The quantity AGMfor this reaction is written simply as AG~= RT In ~
(7)
Generally the values of the surface energiesin the quantity ArJ= m.V+ CTPS – GSVare not known. To calculate an order of magnitude of e~ a reasonable value of Acr= 103mJ/m2 is used. Then, taking Vt,i(SiC)~ 15 x 10-6m3/mole we find that e$ ~ 0.5 nm. A similar calculation for the Cu–1 at.% Cr/Cv system, made using the thermodynamic calculations of Ref. [17], leads again to a critical thickness er smaller than 1 nm. Such values of e~ are too low to create a true barrier to the formation of product P outside the drop. Indeed, the slightest growth of P in a direction perpendicularto the interface,i.e. towards the interior of the liquid, would be suilicient to destroy such barriers. Note that in the few cases in which the thickness of the reaction layer at the vicinityof a triple line was measured, it was found to vary from severaltens of nm to a fewmicrons ([6,21], see also Figs 3 and 6). In conclusion, except for very large (but unrealistic) Aa values, or extremely low values of AGM(in this case even the condition of a continuous layer of P becomes questionable), thermodynamicbarriers to the lateral growth of P on the substrate free surface are unlikely. Kinetic barriers to this growth may result from insufficientmobility of reactive species(e.g. very low surface diffusion coefficients or very low partial pressuresof the reactive solute);however,even in the Al/Cv couple, having at T = 1100K a very low reactivity resuking in a very slow spreading rate (tF values higher than 104s were measured) the lateral growth rate of carbide at t> tF was several nanometers per second [21].Taking into account that a value for length z of a few nm is sufficientfor the liquid surface to meet the reaction product rather than the initial substrate surface, it appears that kinetic barriers are equally unlikely. 5, CONCLUSIONS
At temperatures close to its melting point, pure copper does not wet vitreous carbon (& ~ 137 degrees). Cu~O at. % Si and CU–1’YOCr alloys wet this substrate well (& ~ A(Idegrees for both alloys) forming continuous layers of silicon carbide and chromium carbide, respectively, at the interface. Wetting experiments carried out with the same alloys on silicon carbide and chromium carbide substrates led to nearly the same final contact angles as in the corresponding reactive system. These findings show that the reaction product layer extends on the free surface of the substrate and not only, as proposed previously, at the solid–liquid interface. As a result, the steady-state contact angle reached at the end of spreading is close to the Young contact angle of the liquid on the reaction product. From this point of view, reactive wetting is only a way to modify the initial substrate surface in situ. The generality of this
where agiis the thermodynamic activity of silicon in molten copper in equilibrium with vitreous carbon and siliconcarbide and asiis the actual activity in the alloy. At 1423K equilibrium occurs for a molar fraction of Si in Cu of l$i E 0.15 [15]. Introducing into equation (7) values of a~i (X = ~~i) and asi (XSi= 0.40) computed from existing thermodynamic data [27],it is found that AGM~ – 30 kJ/mol, which conclusionis examinedto showthat it is in agreement with prior published data and that pinning of the is rather a low value for a molar reaction energy.
LANDRY et al.: MECHANISMSOF REACTIVEWETTING
reaction product layer at the triple line by thermodynamic or kinetic barriers is very unlikely. Acknowledgements—The authors would like to thank Professor A. Mortensen for critical reading of the manuscript.
REFERENCES 1. Naidich, Yu., Prog. Surf. Membrane Sci., 1981, 14, 353. 2, Nicholas, M., Br. Ceram. Trans. J., 1986, 85, 144. 3. Loehman, R. and Tomsia, A., Am. Ceram. Bull., 1988, 67, 375. 4. Nogi, K., Trams. JWRI, 1993, 22, 183. 5. Aksay, I., Hoge, C. and Pask, J., J. Phys. Chem., 1974, 78, 1178. 6. Espi6, L., Drevet, B. and Eustathopoulos, N., Metall. Trans. A., 1994, 25A, 599. 7. Kritsalis, P., Drevet, B., Valignat,N. and EustathopouIOS,N., Scripta metall. mater., 1994, 30, 1127. 8. Eustathopoulos, N. and Drevet, B., MRS Symp. Proc., 1993, 314, 15. 9. Eustathopoulos, N. and Drevet, B., J. Phys. 111 (Fr), 1994, 4, 1865. 10. Xiao, P. and Derby, B., Acta mater. 1996, 44, 307. 11. Cannon, R., Saiz, E., Tomsia, A. and Carter, W., MRS Symp. Proc., 1995, 357, 279. 12. Zhou, X. and de Hosson, J., Acta mater., 1996,44,421. 13. Mortimer, D. and Nicholas, M., J. Mater. Sci., 1970,
5, 149and 1973,8, 640.
3085
14. Fujii, H., Nakae, H. and Okada, K., Acta meiall. mater., 1993, 41, 2963. 15. Rado, C., Rocabois, P., Kalogeropoulou, S. and Eustathopoulos, N., Proc. 1994 Int. Conf. on High Temperature Capillarity, ed. N. Eustathopo~los.Repr~-
print, Bratislava, 1995,p. 143. 16. Gheta, V., Gayraud, N. and Eustathopoulos, N., Solid St. Phenomena, 1992, 2~26, 105. 17. Devincent, S. and Michal, G., Metall. Trans. A, 1993, 24A, 53. 18. Laurent, V., Contributiona l’6tudedu mouillagereactif:
Etude du systeme alurninium/carbone. Ph.D. thesis, Institut National Polytechniquede Grenoble, France, 1988. 19. Eremenko,V., Kostrova, L. and Lesnik,N., Proc. 1994 Int. Conf. on High Temperature Capillarity, ed. N.
Eustathopoulos. Reproprint, Bratidava, 1995,p. 113. 20. Drevet, B., Kalogeropoulou, S. and Eustathopoulos, N., Acta metall. mater., 1993, 41, 3119. 21. Landry, K. and Eustathopotdos,N., Acta mater., 1996, 44, 3923. 22. Kritsalis, P., Li, J., Coudurier, L. and Eustathopoulos, N., J. Mater. Sci. (L), 1990, 9, 1332. 23. Khilya, G. and Ivashchenko, Y., Dopov Akad Nauk Ukr, RSR Ser B, 1973, 35, 69. 24. Richardson, F. D., Physical Chemistry of Melts in Metallurgy, Vol. 2. Academic Press, London, New
York, 1974,p. 44. 25. Rhee, S., J. Am. Cer. Soc., 1970, 53, 386. 26. Naidich, Y. and Taranets, N., Proc. 1994 Int. Conf. on High Temperature Capillarity. ed. N. Eustathopoulos. Reproprint, Bratislava, 1995, p. 138. 27. Liidecke, D., Calphad, 1987, 11, 135.