ceramic systems: linear spreading

~)

Pergamon PII S 1359-6454(96)00052-3

Acta mater. Vol. 44. No. 10. pp. 3923-3932. 1996 Copyright ~ 1996 Acta Metallurgica Inc. Published by ElsevierScience Ltd Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00

DYNAMICS OF WETTING IN REACTIVE METAL/CERAMIC SYSTEMS: LINEAR SPREADING

K. LANDRYand N. EUSTATHOPOULOS LTPCM, INP Grenoble, URA 29. BP 75, 38402 Saint Martin d'Heres cedex. France (Received 30 October 1995; in revised form 25 January 1996) Abstract--The kinetics of wetting in the reactive pure aluminium/vitreous carbon (Cv) system was investigated by the sessile drop technique in high vacuum. It was found that the curve showing the radius of the metal drop base R as a function of time t consisted of a central part where the radial spreading of the drop is a linear function of time, and two extremal parts where significant deviations from linearity are observed. By characterising the AI/Cv interface at different stages of the process, both far from and close to the A1/Cv/vapour triple line, it is shown that (i) in the linear spreading regime wetting kinetics is controlled by a nearly 2D reaction between A1 and Cv at the triple line, forming aluminium carbide; and (ii) linearity is closely associated with steady-state growth of the carbide at the triple line. At the beginning of the wetting process, deoxidation of the AI drop and, thereafter, transient-state growth of carbide, cause considerable deviations from linearity in the R(t) curve. Moreover. at the end of spreading. when the contact angle tends towards the steady contact angle of the system, a deviation from linearity is also observed and attributed to the roughness of the reaction product. Finally, examples from the literature are given suggesting that linear spreading may be effective in many reactive metal-on-metal and metal-on-ceramic systems. Copyright ~ 1996 Acta Metallurgica Inc. R6sum6---La cin6tique de mouillage dans le syst~me r6actif aluminium/carbone vitreux (Cv) a dt6 6tudi6e par la methode de goutte posde sous vide secondaire. 11 est montr6 que la courbe d6crivant la variation du rayon de la base de la goutte, R, en fonction du temps, t, est constitute d'une partie centrale o/~ l'6talement radial de la goutte est une fonction lin6aire du temps et de deux parties aux extr6mitds off I'on observe des ddviations significatives par rapport fi la lindaritd. Par une caract6risation de I'interface AI/Cv differents degr6s d'avancement du processus, aussi bien loin que pros de la ligne triple AI/Cv/vapeur, il est montr6 que (i) dans le domaine d'&alement lindaire, la cinetique de mouillage est contr616e par une r6action quasi-bidimensionnelle entre AI et Cv fi la ligne triple avec formation de carbure d'aluminium et (ii) la lindarit6 est 6troitement lice avec un rdgime permanent de croissance du carbure ~ la ligne triple. Au d6but du processus de mouillage, la d6soxydation de la goutte de AI et la croissance du carbure en rdgime transitoire sont ~ l'origine des ddviations importantes par rapport fi la lindarit6. De plus, :i la fin de l'dtalement, quand I'angle de contact tend vers sa valeur stationnaire, une ddviation par rapport ",i la lin6arit6 est 6galement observde et attribu6e ~ la rugosite du produit de la r6action. Enfin des exemples de la littdrature sont donn6s suggerant que l'6talement lin6aire peut intervenir darts plusieurs syst6mes r6actifs du type m&al-m&al et m6tal-cdramique.

1. INTRODUCTION F o r non-reactive solid/liquid systems the dynamics of wetting of small drops on smooth solid surfaces is relatively well understood both for perfect wetting (equilibrium contact angle 0 = 0) [1, 2] and for partial wetting [3, 4]. The above analyses take into account a driving force, due to the surface energy decrease produced when the solid/vapour surface is replaced by solid/liquid and liquid/vapour interfaces, and an opposing force due to the viscosity of the liquid. In the case of metallic drops wetting smooth surfaces of chemically inert solids, the equilibrium contact angle, 0 > 0, is reached rapidly, in times ranging from 10 -4 to 10 -~ s, depending on the values of physical parameters of the metal (viscosity, surface tension) and on the value of the equilibrium contact angle [5, 6]. In reactive metal/ceramic or metal/metal systems,

the time needed to reach a steady contact angle is often several orders of magnitude longer than the above durations (see Refs [7, 8]). As noted in the review by Nicholas and Peteves [9], no theoretical description of wetting dynamics exists for this kind o f system, despite the great interest that they present, for instance in brazing of metals and ceramics or in electronic packaging. Only phenomenological treatments have been proposed, that consist in fitting the experimental O(t) or RL(t) curves, where RL is the drop base radius (see Fig. 1) by different functions [10, 11]. Ambrose et al. [7] found that the decay of 0 with time can be described by equations o f the form 0,-0v=(0o-0~)

exp ( - t / z ) ,

(I)

where 0o, 0 , 0v are the contact angles after times O, t and ~ , and z is a characteristic time obtained by fitting the experimental curves by equation (1).

3923

3924

LANDRY and EUSTATHOPOULOS:

Eremenko et al. [10] have successfully fitted experimental O(t) curves for reactive metal/metal couples using the equation cos 0F - cos 0~ = A exp ( - C t ) ,

(2)

where A and C are constants. Fujii and Nakae [12], in their description of the wetting stages in reactive systems, seem to represent 0 as a linear function of the logarithm of time. Note that, in Ref. [13] Ambrose et al. attempted to describe experimental R,(t) curves obtained in reactive liquid alloy/solid alloy systems using the theoretical equation RL ~ t °1

(3)

established by de Gennes [2] for non-reactive, perfectly wetting systems. They found that such a representation is possible for some stages of the spreading process, but even for these stages the experimentally derived values of constants are several orders of magnitude smaller than the calculated values. In the present study, a different approach to the dynamics of reactive wetting is used, which consists of relating the experimental RL(t) curves obtained for the aluminium/vitreous carbon system to the detailed mechanism of growth of interfacial reaction products. From these relations, more general conclusions are drawn. In the A1/Cv system, at temperatures higher than the aluminium melting point, aluminium reacts with carbon to form at the interface A14C3, a carbide which is better wetted by aluminium than the initial carbon surface [14].

2. EXPERIMENTAL PROCEDURE Wetting experiments were performed by the sessile drop method in a high vacuum metallic furnace described in more detail elsewhere [15]. The apparatus consists essentially of a molybdenum heater surrounded by molybdenum radiation shields, located in a water-cooled stainless-steel chamber. The chamber is fitted with two windows enabling the illumination of the sessile drop on the substrate and the projection of its image on a screen with a magnification of about 20 times. Contact angles and linear dimensions of the drop are measured directly from the image of the drop section, with an accuracy of _+2° and 2%, respectively. The pressure can be reduced to 10-6pa at room temperature in the chamber. However, in order to limit evaporation of aluminium, once this vacuum level is reached, the experiments were performed in a dynamic vacuum of 10 -3 Pa obtained by controlled helium micro-leaks. The helium gas was purified before introduction in the furnace by passing through a Zr-A1 getter. The experiments were performed with vitreous carbon substrates. Vitreous carbon is a graphitic although imperfectly crystallised form of carbon. The

DYNAMICS OF WETTING

crystallites, about 1-2 nm in size, exhibit a random orientation. Vitreous carbon has no open porosity and contains less than 50 ppm of impurities. The substrates were mechanically polished to a 0.1 pm diamond paste finish in order to obtain an average height of surface asperities of less than 2 nm. Before the experiments, the substrates were ultrasound cleaned in acetone, dried in a purified air blast and then annealed under about 5 x 10 -~ Pa at 1323 K for 7200 s. The purity of aluminium was 99.998%. A few minutes before introduction into the furnace, the AI specimens were cut on all their faces, since very short exposure to air limits the thickness of the native superficial oxide layer. A limited number of experiments were performed with the AI/AI203 system for comparison purposes. The substrates were platelets of ~t-monocrystalline alumina of 99.993% purity. Their surface had a random crystallographic orientation. The experiments consist of monitoring the time-dependent variation of the contact angle 0 and drop base radius RE (see Fig. l) until steady values are obtained, during isothermal holds. After cooling, interracial reactivity was characterised in selected specimens by scanning electron microscopy and electron probe microanalysis. 3. RESULTS Results on wetting of aluminium on ceramics are very sensitive to oxygen. Indeed, aluminium drops are usually covered by an oxide layer which inhibits wetting. Before the study of the A1/Cv system it was important to check that deoxidation of aluminium drops could be obtained in the employed experimental conditions. For this, sessile drop experiments were performed in the AI/AI:O3 system which was chosen as the reference because it is well known (see for instance Ref. [16]) and non-reactive at low temperature (the solubility of oxygen in aluminium is less than 10-Sat.% at 1200K [17]). Figure 2 shows the variations in contact angle and drop base radius obtained with the A1/Al:O~ system at 1100 K. The origin of time is chosen when liquid aluminium contacts the substrate, as in all kinetics presented in this paper. The contact angle is initially very high, close to 160 °. It decreases in about 250 s to a steady value close to 90 ° . The high value

I~--RL~ Fig, 1. Definition of contact angle 0, and drop base radius Rt.

LANDRY and EUSTATHOPOULOS: DYNAMICS OF WETTING 1,2

+I-

~:~ 0,6

**

~,

0,2

~

o

o

o oo

0,8

,-1

16oi

0,4

#

¢~ t 1

o

÷ ~

o

3925

o'+.

t2

tF

. . . . . . . . . .8000 ..

. . . . .

]2o0o . . . . . . 6ooo

t (s)

120 +

180

O

÷ 80

i,)..t 0

¢

*

+

o

140 ~

.... ~.... i .... i .... i .... i .... t .... i 1000

20O0

300O

~-,

0

li

.,~..t ~ . . . , , . ~

4OO0

O

Time (s) Fig. 2. Variations with time of the contact angle and drop base radius observed in the AI/AhO3 system at 1100 K.

measured at t = 0 is typical of oxidised drops. The decrease in contact angle is controlled by the deoxidation of the drop [14, 16], which is achieved mainly by reduction of the oxide layer by liquid aluminium with production of gaseous Al20 [16] A1203 (film) + 4 Al(l),~3 Al20 (g).

It

o

(4)

The contact angle measured after deoxidation is in good agreement with results given in the literature obtained with experimental procedures which suppress the influence of the oxide layer on wetting [l 6, 18-20]. Thus, deoxidation of aluminium drops is achieved in a few minutes in the present experimental conditions. Figure 3 shows the variations in contact angle and drop base radius observed in the AI/Cv system at 1100 K. The R,(t) and O(t) curves consist of three kinetic stages, and the wetting kinetics can be characterised by the values of three contact angles. In the first kinetic stage, between time 0 and time tt ~ 400 s, the contact angle decreases rapidly from 00 ~ 160 ° to 0t -~ 139 °, and the velocity of the triple line dRL/dt equals about 1 pm/s. This first stage is very similar to the kinetics obtained in the AI/A1203 system. Consequently, control of wetting kinetics during the first kinetic stage can be attributed to deoxidation of the drop, taking place by reaction (4). At time h, an abrupt change in the slope of the O(t) and RL(t) curves is observed, as the velocity of the triple line decreases significantly [see the enlargement of the O(t) curve in Fig. 3]. The second kinetic stage takes place from t~ to tr. Between times t, and t2 the velocity of the triple line decreases progressively. Thereafter, at times t2 < t < tr, the drop base radius is a nearly linear function of time. Finally, at times t/> tF, 0 and RL remain steady. The second kinetic stage does not exist in the

I

lOO 0

4000

'+

0

8000

800 (s)

12000

16000

t (s) Fig. 3. Variations with time of the contact angle and drop base radius observed in the AI/Cv system at 1100 K.

non-reactive A1/AI203 system, and thus, it is attributed to the interfacial reaction between vitreous carbon and aluminium. Similar spreading behaviour was observed at different temperatures, as illustrated in Fig. 4 by the kinetics obtained at l l 9 0 K. This curve consists of three kinetic steps similar to those of Fig. 3, and a regime of linear spreading is present again. However,

1,5

"• B

0

O0

~ % + ~ o o ~ ~ 000 . . . . .

~

0-0

f

0.5

o

O0~O0000

J

160,

--%Oo

120

80

~ I,,~,

r~ 40

0

.............

2000

' ....

Or

.O---

' .....

4000

t (s) Fig. 4. Variations with time of the contact angle and drop base radius observed in the AI/Cv system at !190 K.

3926

LANDRY and EUSTATHOPOULOS:

DYNAMICS OF WETTING

Fig, 5. Micrograph of a cross-section perpendicular to the interface in an AI/Cv specimen cooled at the steady state after 3 h 40 at 1100 K x 2000 (Cv is black, AI is grey).

relatively large deviations from linearity are observed at the end of the spreading process. For instance, at t ~ 2500 s, the contact angle tends to stabilise but thereafter decreases further. In order to establish the relationship between wetting and interfacial reactivity during the second spreading stage, selected samples were characterised by scanning electron microscopy and electron probe microanalysis. Figure 5 shows a micrograph of a cross-section in a sample cooled at the steady state, after 13,200 s at 1100 K. The observed area is situated near the drop centre. The micrograph shows that the substrate is covered by a continuous layer of reaction product, A14C3, approximately 4 p m wide. The morphology of the reaction layer shows that it results from the coalescence of discrete and faceted AhC3 particles. The AI,C~/Cv interface is much rougher than the substrate surface before the experiment, and holes, 2 or 3 pm deep, are present around some particles. This shows that the reaction proceeds by dissolution of carbon into aluminium followed by growth of isolated particles, which locally protect the substrate surface from dissolution (Fig. 6). Figure 7 shows a micrograph taken from above in a sample cooled from 1100 K at the beginning of the steady state, i.e. at t ~ IF. The observation is made near the triple line. A A14C3 border is observed around the entire periphery of the drop on the free surface of the substrate. This carbide layer appears to be relatively rough, and no metallic retentions, which form typically on dewetted areas, could be observed on it. Consequently, the presence of the layer outside the drop cannot be explained by a receding

movement of the liquid during cooling. Figure 8 shows a sample cooled from 1100 K 2 h after the beginning of the steady state. The carbide layer outside the drop is 10-20#m wide. Aluminium carbide is found to grow in the form of platelets as already observed in several studies [21-25]. Figure 9 shows a micrograph taken from above in a specimen cooled from 1100 K at the beginning of the linear spreading regime, i.e. at t ~ t2. AI4C~ particles are already present in some places on the free surface of the substrate, at the triple line. The same sample was observed after partial dissolution of the drop in an NaOH solution. In the region closest to the centre of the drop [Fig, 10(a)], the surface of the substrate is completely covered by AI4C3 platelets. Near the triple line [Fig. 10(b)], substrate attack by liquid aluminium is visible on the interface, although the substrate surface is only partially covered by A14C3. The incomplete covering can be attributed to partial hydrolysis of A14C3 during dissolution

AI4C3

Carbon

Fig. 6. Schematic representation of the interracial reaction mechanism at the interface between liquid aluminium and vitreous carbon.

LANDRY and EUSTATHOPOULOS: DYNAMICS OF WETTING

3927

/

t.~.-..? _. .......

..........

0

<--_Z_ t Fig. 7. Micrograph taken from above in an AI/Cv sample cooled from 1100 K at t ,~ tv (AI is grey, Cv is black).

of the drop, since aluminium carbide is soluble in water. 4. DISCUSSION 4.1. Characteristic contact angles

The contact angle 0o measured at melting of aluminium is not characteristic of the AI/Cv system because its value is determined by the presence of an oxide layer at the surface of the drop. Further evidence of this is given by the comparison of the kinetics obtained in the present study with that obtained with the same materials and at the same

temperatures with the capillary purification method [14]. This method consists of heating the metal separately from the substrate, and then dropping it on the substrate once the experimental temperature is reached. At dropping, atuminium is extruded under pressure through a capillary, which breaks the superficial oxide layer. With this procedure, initial contact angles as high as 160° are no longer measured. Instead, the contact angle measured at dropping is close to the angle 0~ [14]. The first characteristic contact angle is the angle 0t measured at the abrupt decrease in the slope of the curves, taking place at the end of the deoxidation

¢ t Fig. 8. Micrograph taken from above in an Al/Cv sample cooled from 1100 K at t ~ tr + 2 h x 2000 (A1 is grey, Cv is black).

3928

L A N D R Y and E U S T A T H O P O U L O S :

D Y N A M I C S OF W E T T I N G

/

0/

r

t Fig. 9. Micrograph taken from above in an AI/Cv sample cooled from 1100 K at t ~ t: × 10,000 (A1 is grey, Cv is black).

stage. In the first area the velocity of the triple line is high, so that liquid aluminium remains in contact, near the triple line, with a virtually unreacted surface of vitreous carbon [Fig. 1 l(a)]. Thus, 0~ is the contact

angle of aluminium on nearly non-reacted vitreous carbon. The value of 0~, about 135-140 °, is typical of non-reactive metal/graphite systems, like Cu/C~ph,0 or Ag/Cgraph,e, in which adhesion has been attributed to van der Waals interactions [5]. During the steady state, the vitreous carbon substrate is covered by a continuous layer of aluminium carbide, which extends both at the solid/liquid interface and on the substrate free surface. Consequently, the final contact angle is the contact angle of aluminium on aluminium carbide. Indeed, the value of 0r, about 70 °, is higher but comparable to the value of 5Y measured on sintered AI, C3 by Ferro and Derby [26] at a higher temperature (1373 K against ll00K). The work of adhesion (Wa = aLV [1 + COS0]) of the final interface is high and equal to 68% of the work of cohesion of liquid aluminium (W, = 2 aLv). This shows that adhesion at the AI/AlaC3 interface is due to strong covalent bonds [14]. Note that the uncontrolled roughness of the reaction product layer may be rather high, due to the platelet morphology of the layer. Consequently, the value of 0r may differ from the , RL

t= t1 Fig. 10. (a) Micrograph taken from above in an AI/Cv sample cooled from I I 0 0 K at t ~ t 2 , after partial dissolution of the aluminium drop ( x 200); (b) region near the centre of the drop ( x 2000) (AI is grey, Cv is black).

tI
t2
t>t F

(a) (b) (c) (d) Fig. 11. Schematic representation of changes in interfaces and in spreading process.

LANDRY and EUSTATHOPOULOS: DYNAMICS OF WETTING

3929

Table 1. Mechanism controlling spreading, triple line velocity and contact angles measured at I I 0 0 K Interval of time

Controlling mechanism

0 to t~

D r o p deoxidation

t~ to t: tz to tF

Transient state reaction Steady state reaction (roughness) Interfacial equilibrium

t > tv

dRLJdt tnm.s) ~ 1000 230 to 40 40 ~0"

Value (degrees) and significance of the contact angles 0,, ~ 165: oxidised AI 0~ ~ 139: AI on non-reacted Cv Non-significant Non-significant 0F = 69: AI on A h C h

*At t > t~, d R L / d t "~ 0 but d R p / d t ~ O.

Young contact angle of aluminium on aluminium carbide. The values of the contact angle and triple line velocity measured on the wetting curves are summarised in Table 1 for each time interval.

4.2. Kinetic regime controlled by the interracial reaction The main feature of the Re(t) curves in the reactive (tj~tv) area is the presence of a nearly linear spreading regime, in which the solid/liquid interface is completely covered by a continuous layer of A14C3. During this regime, the advance of the liquid is hindered by the presence, in front of the triple line, of a non-wettable vitreous carbon surface. Thus, the only way to move ahead is by lateral growth of the wettable carbide layer on the substrate free surface [Fig. 12(a)]. Taking into account that the lateral carbide growth rate during this regime (dRp/dt ~ dRe/dt) is higher by two orders of magnitude than the rate of thickening of the layer at the solid/liquid interface (Table 2), it can be concluded that the controlling mechanisms of growth at the interface are different far from the triple line and at the triple line. Indeed, the former needs diffusion of carbon (or aluminium) atoms through a continuous carbide layer, while the latter takes place at the solid/liquid/vapour line. where direct contact between aluminium and carbon is possible.

(a) t 2 < t < t F

The fact that the lateral growth of AhC~ on vitreous carbon occurs strictly at the solid/liquid;vapour line is evidenced by the strong decrease in dRp/dt at t > tv, i.e. when the distance between the source of aluminium atoms and the growth front increases: increasingly long-range diffusion is then needed for growth to continue [Fig. 12(b)]. In the (t,.--*tr) step the linearity of the RL(t) curve is due to the constancy of the lateral growth rate of the carbide layer, which in turn results from a nearly unchanged configuration of the system at the triple line. Constant growth rate and linear spreading may not be possible in some other cases, for instance if the growth of the layer is controlled by the diffusion of a reactive solute (B) from the bulk liquid (AB) to the triple line (Fig. 13). In this case, the reduction in the diffusion field during the spreading process will decrease the growth rate and consequently the velocity of the triple line itself. The first non-linear part of the reactive kinetic regime, situated between t, and t:, corresponds to a progressive transformation of the solid/liquid interface near the triple line from non-reacted [Fig. I l(b)] to fully reacted. For any intermediate configuration between t~ and t.~ direct contact between liquid aluminium and a fresh, non-reacted vitreous carbon surface occurs not only along the drop periphery but also at several places in the solid/liquid interface. Consequently, the reaction rate, as reflected by the dRL/dt values, is maximum at t = t, and decreases towards a constant value when t approaches t2. From the point of view of wetting, the instantaneous contact angle O(t) between t~ and t, satisfies

Rp = RL

Oc~ < O(t) < 0v,

¢ (b) t > tF Rp > RL

(5)

where 0w is the equilibrium contact angle of aluminium on vitreous carbon, and 0c,s is the equilibrium contact angle on a non-homogeneous surface as defined by Cassie [27] by the expression cos 0cas = ~bA,,c,COS Ovz + [1 -- ~bA,,C,]COS 0v,, (6)

r///////////////A~

~RL

=====~

-

Rp

-

~-

Fig. 12. Schematic representation of the configuration of the system near the triple line. Re and ep represent, respectively, the radius and the thickness of the carbide layer.

where ~bA~,c,is the surface fraction of AI4C3 near the triple line, and 0v2 is the equilibrium contact angle of aluminium on aluminium carbide. At any time between 12 and IF, RL ~ Rp and the contact angle takes a value between 0~ and 0F, which depends only on the lateral extent of the carbide layer

LANDRY and EUSTATHOPOULOS:

3930

DYNAMICS OF WETTING

Table 2. Average thickening rate and radial growth rate at t > tF o f the carbide layer compared with

the velocityof the triple line in the linear regime (see also Fig. 12l T(K)

Aep/At (holding time at T)

ARp,'At (holding time at t > tv)

dRL/dt (tz-.-,tv)

1100 1190

0 2 nm/s (20,400 s) 0.6 nm/s (16.200 s)

2 nm. s (7200 s) 1.8 n m ' s (9000 s)

40 n m s 340 n m s

[Fig. 1 l(c)]. At t = t~, 0 ~ 0v2 and, as a consequence, the triple line stops (but not the reaction layer) [Fig. l l(d)]. How can the deviation from linearity observed when t tends towards IF b e explained? At any time t > t2, the driving force of wetting is Fd(t) = aLV [COS O F - COS 0(t)],

temperature is reached (at t ~ 2 0 m i n , Fig. 15), spreading of the drop occurs linearly. For this system and for other similar systems (CuSi/SiC [29], AISi/SiC [30]), isothermal spreading is controlled by the SiC surface deoxidation reaction occurring at or close to the S - L - V triple line. This deoxidation takes

(7)

where 0r ~ 0^,/A,,c~ and O(t) is the instantaneous contact angle. Fd(t) decreases when t tends towards tr. This, associated with the roughness of the carbide layer due to its growth mechanism (in platelets) and with the very small velocity of the triple line, is responsible for pinning of the triple line on surface asperities. Pinning is evidenced by the oscillating shape of the triple line in Fig. 7 and by the jumps on the O(t) curves, which take place at the end of the spreading process (see Fig. 4). As a consequence of local pinning, the distance between the layer growth front and the aluminium source increases, leading to a decrease in growth rate and consequently in spreading rate (Fig. 14). The "linear" wetting in the AI/Cv system is not a unique case. For instance, Nicholas and Peteves [9] presented results for the reactive CuAgTi/AI20~ system, showing the radial spreading of alloy drops to be a linear function of time. These authors proposed that spreading, in this system, may be controlled by the lateral growth of titanium oxide layers formed at the interface by reaction between Ti and alumina. Moreover, on the R(t) curves given by Ambrose et al. [7] for an Ni-P braze alloy on Fe-Cr substrates, a linear spreading regime clearly appears, situated between two non-linear regimes. Another example is the spreading of AuSi drops on SiC studied by Drevet et al. [28]. When the experimental

RL j

(a) F

t2

tF

t

Fig. 14. Schematic variation of the drop base radius at t > t2. Region (a) corresponds to the linear spreading regime. In region (b), a decrease in spreading rate is observed at high temperature.

1473

Temperature(K)

1273]/ 873 O 10 20 3 0 Diameter (mm) 160 T

40

50

60

70

80

9 0 100 110 120 130 140

,,°1

t

60

O ;

AB

s•

160

.

.

.

.

.

10 20 30 4 0 Contact angle (o)

. 50

.

.

.

60

70

80

.

.

.

.

90 100 110 120 130 140

140 120 AJ203 fumsce

100 80

Au*30 at,% Si

60 40 20 O 10

Fig. 13. If the growth of the layer is controlled by diffusion of a reactive solute (B) from the bulk liquid (AB) to the triple line, the reduction in the diffusion field during the spreading process will decrease the growth rate and consequently the velocity of the triple line.

20

30

40

50

60

70

80

90 100110120

130140

Time (rain)

Fig. 15. Variation of drop base diameter 2R (magnified 20 times) and contact angle as a function of time during

temperature rise for an Au-30at% Si alloy on SiC. From Drevet et al. [28].

LANDRY and EUSTATHOPOULOS:

sio2

,

SiO

DYNAMICS OF WETTING

3931

aluminium carbide surface, delays the movement of the triple line by pinning. A linear spreading regime can be observed each time the conditions of steady-state growth of a wettable reaction product at the triple line are met. In real reactive systems, a single function can hardly describe the full range of wetting curves.

s i c

Fig. 16. Schematic representation of wetting of a AuSi alloy on Si. At constant temperature spreading rate is controlled by the SiC surface deoxidation occurring at the triple line by reaction between the silica film and silicon of the molten alloy [reaction (8)].

Acknowledgements--The authors thank the French Ministry of Research and Technology for financial support (grant decision No. 90T0778).

REFERENCES place by a reaction between the few-nanometres thick silica film covering the SiC and the silicon of the molten alloy, forming the volatile silicon monoxide according to the following three-phase reaction (Fig. 16) SiO., (film) + Si (l)--*2SiO (g).

(8)

F r o m the above examples, it appears that linear spreading may occur for different types of interfacial reactions and different liquid/solid combinations (metal/metal, metal/ceramic, etc.). Finally, it must be emphasised that in real reactive systems, a single function can hardly describe the full range of R(t) and O(t) curves which actually result from the action of several different phenomena: deoxidation of the drop and/or the solid substrate surface, transient and steady-state interfacial reactions, roughness of the initial surface or roughness induced by interfacial reactions,

5. CONCLUSIONS In the nonooxidised A1/Cv system the contact angle changes from about 135 ° characterising the non-reacted AI/Cv couple, to about 70 ~, a value close to the contact angle of aluminium on aluminium carbide. The wetting kinetics is controlled by the kinetics of lateral growth of AI,C~ at the solid/liquid/vapour line. A wetting regime corresponding to R, ~ t ° with n ~ 1 was observed and was shown to correspond to a fully covered solid/liquid interface. Under these conditions, the growth of the layer occurs mainly at the solid/liquid/vapour line at a nearly constant rate. Two deviations from linearity were observed. The first occurs at the beginning of the kinetic regime controlled by interfacial reactivity, when steady-state conditions of growth have still not been established, due to incomplete covering of the solid/liquid interface near the triple line by the reaction product. Then, the reaction rate, as well as the triple line velocity are higher than in the linear wetting regime. The second deviation takes place after longer times, when 0 tends towards the final contact angle, and was explained by the decrease in the wetting driving force, which, associated with the roughness of the

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