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Reactive infiltration by Si: Infiltration versus wetting
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Scripta Materialia 62 (2010) 966–971 www.elsevier.com/locate/scriptamat
Viewpoint Paper
Reactive infiltration by Si: Infiltration versus wetting N. Eustathopoulos,a R. Israel,a,b B. Drevetb,* and D. Camelb a
SIMAP, Phelma, Grenoble INP, Domaine Universitaire, BP 75–1130, rue de la Piscine, 38402 Saint Martin d’He`res Cedex, France b CEA, INES/RDI, LITEN/DTS/LMPS, 50 av. du Lac Le´man, 73377 le Bourget du Lac, France Received 13 January 2010; revised 9 February 2010; accepted 13 February 2010 Available online 18 February 2010
Abstract—This paper focuses on spontaneous infiltration by liquid metals in reactive metal/ceramic systems. Two cases of reactive infiltration, where a molten silicon drop is in contact with two different porous bodies, graphite and (oxidized) silicon nitride, are briefly described and discussed. For each solid, the dynamics of wetting on the solid surface is compared to the dynamics of infiltration into the porous medium in order to determine the common points and the main differences between these two processes. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Silicon; Infiltration; Interfaces; Wetting
1. Introduction Metal/ceramic composites are often processed by infiltration of porous ceramics by liquid metals [1]. In the conditions of temperature and atmosphere used in practice, the liquid metals (Cu, Al, etc.) do not wet ceramics such as alumina, silicon carbide or graphite, and for this reason infiltration is obtained by applying a pressure P0 high enough to overcome the capillary pressure PC. In numerous studies published since the 1990s by the teams of Mortensen (see for instance Refs. [2,3]) and Louis [4,5], it has been found that the infiltration distance h increases parabolically with both time t and excess pressure DP = P0 PC in agreement with Darcy’s law (or equivalently, with the Washburn equation) for infiltration limited by viscous friction. In contrast with infiltration, the viscous resistance has little effect on the kinetics of millimetre-sized metallic droplets spreading on solid surfaces [6,7], except for systems with equilibrium contact angles close to zero [6]. Spontaneous (pressureless) infiltration of a liquid in a porous medium occurs when the equilibrium contact angle of the liquid on the pore walls is much lower than 90° [8,9]. For this type of infiltration, studied among others in [10,11–14], the relevant mechanisms, especially the role played by reactions between the liquid metal and the ceramic in the infiltration process, are not yet well understood.
* Corresponding author. Tel.: +33 4 79 44 45 95; fax: +33 4 79 62 37 71; e-mail: [email protected]
The present paper focuses on spontaneous infiltration by liquid metals in reactive metal/ceramic systems. Two cases of reactive infiltration will be considered, concerning both molten silicon and two different porous bodies, graphite and (oxidized) silicon nitride. For each solid, the dynamics of wetting on the solid surface will be compared to the dynamics of infiltration into a porous preform. Although wetting and infiltration both involve the motion of a triple line, the geometry of the region around this line in these two processes is very different. The main question addressed in this paper is: to what extent does this geometry affect the triple line dynamics? 2. Infiltration of porous graphite Liquid silicon is known to wet carbon [15,16] and it can therefore spontaneously infiltrate a carbon preform. Infiltrated Si reacts with carbon to form SiC. Reactive infiltration is used to process the so-called “reactionbonded silicon carbide” [17–19] or SiC composites [20,21]. Infiltration of Si into the graphite crucibles used in Si purification can dramatically affect the lifetime of certain graphites [22]. In Ref. [10], the process of Si infiltration into porous carbon preforms was described as consisting of rapid, non-reactive, infiltration followed by reaction between Si and C to form SiC. The infiltration distance h(t) was assumed to follow Washburn’s equation taking P0 = 0. Experimental results obtained recently in SIMAP for the reactive infiltration of silicon into porous
1359-6462/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2010.02.030
N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
Si infiltrated zone
hf
1 mm
graphite
Figure 1. SEM micrograph of the infiltrated zone produced in 312 s at 1430 °C in a graphite with a volume pore fraction ap = 0.15.
graphite did not confirm the model described in Ref. [10] and led to a different description of infiltration where the reaction between silicon and graphite at the infiltration front provides the driving force for infiltration [22]. The new model was supported by infiltration experiments carried out under a static atmosphere of argon by the sessile drop method that enables the variation in infiltration depth h with time to be monitored in situ [22] (details of h calculation as well as the experimental procedure are given in Ref. [22]). The final infiltration depth hf is also measured a posteriori on metallographic sections (Fig. 1). In addition to the infiltration data, the method provides quantitative information on wetting thus allowing the spreading and infiltration rates to be measured in the same experiment. Figure 2a presents an example of wetting curves (i.e., the time-dependent change in contact angle h and drop
a
base diameter d = 2R) obtained during an infiltration experiment. The time origin corresponds to complete melting of the droplet. Spreading occurs at a nearly constant rate Uspr = dR/dt close to 10 lm s1. This is several orders of magnitude slower than the spreading rates measured previously in non-reactive liquid metal/ solid systems [6,7,23]. These two results, i.e., “linear spreading” and the very small spreading rate, indicate that spreading of Si on graphite (as well as on vitreous carbon substrates [16]) is controlled by the chemical reaction at the solid/liquid/vapour triple line where the wettable reaction product grows parallel to the liquid/ substrate interface (Fig. 2b) [6,24]. Figure 3a gives an example of infiltration kinetics (two different experiments) obtained for a graphite with a volume fraction of pores, ap = 0.15. Infiltration of silicon is linear with time thus strongly suggesting that infiltration is governed by the reaction of SiC formation on the pore walls at the infiltration front (Fig. 3b). The proposed mechanism implies that the infiltration rate Uinf and the wetting rate Uspr at a given temperature are equal or at least of the same order of magnitude. This is confirmed by the experimental values of the ratio Uinf/ Uspr which lie between 0.65 and 0.95 [25]. As argued in Ref. [14], the value of this ratio is less than unity because of the different tortuosities of bulk graphite and of the graphite-free surface. Tortuosity is defined as the ratio between the path followed by a fluid between two points
b
100
13
d
12
967
80
60 10 40
9
θ (deg)
d (mm)
11
L
θ
SiC
θ
8
C
20
7 0
100
200
300
400
500
t (s) Figure 2. (a) Drop base diameter d and contact angle h as a function of time for Si spreading over graphite at 1460 °C. t = 0 corresponds to the complete melting of Si. (b) Schematic presentation of reaction-controlled wetting.
a
b
0.7
L
0.6
hSi (mm)
0.5
SiC 0.4 0.3
C 0.2 0.1 0.0 0
50
100
150
200
250
300
350
400
t(s)
Figure 3. (a) Height of infiltrated Si hSi (where hSi = ap h) in porous graphite as a function of time for two experiments performed at 1430 °C. t = 0 corresponds to the beginning of Si melting. (b) Schematic presentation of reaction-controlled infiltration.
N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
a 100
45
90
40
contact angle (°)
80
35 d
70
30
H
θ
60
25
50
20
40
15
30
10
20
5 0
500
1000
1500 2000 time (s)
2500
b diameter, height (a.u.)
968
L
15 mm
3000
Figure 4. (a) Wetting kinetics of Si on Si3N4-coated SiO2 at 1430 °C. (b) Top view of a sessile drop of Si on Si3N4-coated SiO2 showing the width L of the infiltrated zone parallel to the substrate surface (total time at 1430 °C: 17 min).
lying inside the porous body (or equivalently on the solid surface) and the geometrical distance between these points. In conclusion, for the pure Si/graphite couple, wetting on a solid surface and infiltration into a porous preform are both linear with time and their rate is limited by the same process, namely the reaction between silicon and carbon at the triple line. Some limited difference exists between the spreading and infiltration rates due to the tortuosity of the porous medium. Stronger differences are expected to appear with silicon carbide forming silicon alloys. In this case, alloy depletion in the reactive solute can lead to deviation of the h(t) curve from linearity [14]. In a particular case, the consumption of reactive solute by the reaction at and behind the infiltration front was so high that the Si concentration in the alloy became smaller than the minimum Si concentration needed for SiC formation [26]. Alloy depletion in the reactive solute does not happen in solid surface wetting experiments (except for diluted alloys [27]) in which the ratio between the liquid volume and the wetted (and thus reacted) solid surface is several orders of magnitude higher than in infiltration experiments [14].
a
(1) SiO2 Si
SiO
3. Infiltration of porous silicon nitride When silicon is processed by solidification in direct contact with silica crucibles, sticking of solidified Si on crucible walls leads to thermo-mechanical stress resulting in cracks produced in the Si ingot. In order to avoid sticking, photovoltaic silicon ingots are currently grown in SiO2 crucibles coated with a porous silicon nitride layer which acts as an interface releasing agent between silicon and the crucible. This process, which has its origin in the work of Saito et al. [28], is widely used in industry. However, it is only very recently that the interactions between molten silicon and porous silicon nitride have been studied and understood [29]. In Ref. [29], the silicon nitride coating was prepared by applying (spraying) on a dense SiO2 substrate a slurry composed of Si3N4 submicronic powder and polyvinyl alcohol dissolved in water as binder. The coated substrate is dried to remove the water and then heated in air above 450 °C to burn off the binder. This treatment leads to the formation of a silica layer on the Si3N4 particles, the layer being a few nm or tens of nm thick, depending on temperature and time [30]. The coating, (2)
(3) d H
θ0
θF
Si3N4
b Si
θ
Si3N4
SiO
SiO2
vapour Figure 5. (a) Spreading of a Si drop on oxidized Si3N4. The initial contact angle, h0, corresponds to wetting on the SiO2 passive film (1). Once a direct contact between Si and Si3N4 is established (2), wetting continues by removing the passive oxide film through the reaction SiO2 + Si ? 2SiO until the equilibrium contact angle on Si3N4 is reached (3). (b) Infiltration of Si in the pores of the oxidized Si3N4 coating.
N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
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Table 1. Comparison between the spreading rate Uspr and the infiltration rates Ufilm and Uinf in silicon/graphite (at 1460 °C) and silicon/porous (oxidized) silicon nitride (at 1430 °C) systems. Process
Average rate (lm/s)
Wetting on solid surface Infiltration parallel to the surface ahead of the nominal triple line Infiltration under the drop perpendicular to the interface
Definition and symbol
Si on graphite
Si on porous Si3N4
Uspr = DR/Dt Ufilm = DL/Dt Uinf = Dh/Dt
8.7 5–7 5.7
10 2–3 102
a Si drop
h2
bubble
b
infiltrated coating
non-infiltrated coating
L
infiltrated coating
h1
h
Si
non-infiltrated coating
rupture path
SiO2
Figure 6. Infiltration of Si in Si3N4-coating on SiO2 (total time at 1430 °C: 17 min). SEM image (a) and schematic representation (b) of a crosssection of the sample.
about 150 lm thick, exhibits a microscopic porosity between individual Si3N4 grains and a macroscopic porosity formed by bubbles of some tens of microns produced by the spraying process. Figure 4a presents the wetting curves (contact angle h, drop base diameter d and drop height H) obtained for molten Si on Si3N4-coated SiO2 under argon flow. The initial contact angle, equal to 88°, corresponds to the angle on oxidized Si3N4. The contact angle decreases strongly with time and within a few 100s of seconds reaches 43°, a value close to the contact angle of Si on non-oxidized sintered Si3N4 [31]. During this period, the average spreading rate Uspr is about 10 lm s1. The spreading kinetics is controlled by the deoxidation of Si3N4 grains occurring by reaction between molten Si and the SiO2 passive film with formation of volatile Si monoxide: SiO2 þ Si ! 2SiO
ð1Þ
Reaction (1) occurs at any point on the solid/liquid interface but it is more intense at the triple line where the evacuation of SiO species far from the interface is
easier (Fig. 5a). Under these conditions, the spreading rate dR/dt is expected to be constant with time, in agreement with the experimental R(t) curve obtained with dense oxidized Si3N4 [31]. As far as infiltration is concerned, the infiltrated silicon volume cannot be determined in situ because, due to the rough surface of coating, the sessile drop is far from axisymmetric (Fig. 4b). However, some information on infiltration can be obtained by carefully observing the wetting curves (Fig. 4a). Thus, at t > 400 s the contact angle and drop height continue to decrease very slightly while the drop base diameter remains constant. These results indicate that the visible volume of the drop decreases with time but only very slightly, meaning that Si infiltration in the coating at t > 400 s is very limited, as confirmed by a post-experiment examination: – The top view of the sample clearly shows a “secondary wetting” film ahead of the nominal substrate/Si/vapour triple line (Fig. 4b). This film, of width L, results from Si infiltration from the triple line into the channels of the porous coating. This phenomenon takes place at times
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N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
higher than the spreading time of 400 s, i.e., after the macroscopic triple line has attained its final position. The average rate of extension of the “secondary wetting” film parallel to the surface Ufilm is 2–3 lm s1, which is lower than but of the same order as the spreading rate of the primary wetting process (Table 1). – The cross-section of the infiltrated zone (Fig. 6) shows that the infiltration depth h1 under the bulk of the drop is very small, about 10 lm, corresponding to an average infiltration rate Uinf close to 102 lm s1 (while h increases in the vicinity of the triple line to a value h2 equal to several 10s of lm). The value Uinf 102 lm s1 is 2–3 orders of magnitude lower than both Uspr and Ufilm (Table 1). These results show that infiltration in this system is strongly “anisotropic”, the infiltration parallel to the coating surface being much faster than infiltration under the droplet. The equilibrium contact angle of Si on silica is close to 90°. As a consequence, molten Si does not infiltrate the porous coating, as long as pore walls are oxidized (Fig. 5b). However, molten Si wets deoxidized Si3N4 well. Thus, infiltration is possible with a rate controlled by deoxidation of the pore walls, i.e., by Reaction (1), in a similar way to wetting on the surface of oxidized Si3N4 (Fig. 5a). The critical factor for the rate of Reaction (1) is the SiO evacuation rate from the infiltration or the wetting front. In the spreading process, the SiO is evacuated easily and quickly and for this reason the rate-limiting stage is the atomic process at the silica/Si interface close to the triple line [32]. During infiltration, the evacuation rate is obviously considerably reduced in the region under the drop, where the SiO travel path is very long. This explanation is also consistent with the very high values of the Ufilm/Uinf ratio observed in the experiment on Si3N4-coated SiO2. Indeed, infiltration parallel to the surface is promoted by the easy evacuation of SiO into the gas. For this reason, Ufilm values are much closer to Uspr than to Uinf (Table 1). In contrast, for the Si/graphite couple where no gaseous species participate in the reaction at the triple line, the values of Uspr, Ufilm and Uinf are very close (Table 1). The above results obtained with pure Si show that wetting on the surface of oxidized Si3N4 and infiltration into porous (oxidized) Si3N4-coating are processes controlled both by the rate of removal of the passive silica layer (acting as a barrier to wetting and to infiltration) from the nitride surface. However, due to the very different geometries of these two configurations, the rate-limiting steps are different: long-range gaseous diffusion of SiO molecules into the pore network ahead of the infiltration front for infiltration perpendicular to the interface, compared with a local chemical process at the triple line for wetting on the flat surface. This results in an infiltration rate perpendicular to the interface Uinf 2–3 orders of magnitude lower than Uspr and Ufilm. 4. Conclusions and prospects Wetting on a solid surface and infiltration in a porous preform in the Si/graphite and Si/(oxidized) Si3N4 systems are governed by the reactions occurring at the solid/liquid/vapour triple lines of these systems.
In the Si/graphite couple at temperatures close to the Si melting point, wetting and infiltration kinetics in neutral gas are controlled by the local chemical process at the triple line moving on the solid surface or on the pore walls. In this system, the geometry has a limited influence on the triple line velocity, the infiltration rate being lower than the spreading rate by a few 10s of percent. Non-local contributions are however expected in the following two cases: (i) in high vacuum, the transport of Si atoms through the vapour phase can modify the surface chemistry of graphite in front of the triple line and thus enhance wetting and infiltration rates even at temperatures close to the Si melting point. A similar effect is expected to occur under inert gas but at much higher temperatures. Although some experimental evidence for this type of surface modification exists [22], a general description of reactive wetting and infiltration taking into account both the localized and delocalized reactions is still missing. (ii) When Si (and any other reactive element) is present in the liquid as alloying element, longrange diffusion of the reactive solute from the preform entrance to the infiltration front can also affect and even control the reactive infiltration. The calculated rate of diffusion-controlled reactive infiltration depends on the same thermochemical and physicochemical quantities as the diffusion-controlled reactive spreading modelled in Ref. [33]. However, due to the different geometries, the time-dependent variations in infiltration distance and drop base radius are predicted to follow different laws: h t1/2 [14,34] and R t1/4 [33], respectively. Note that while the diffusion-controlled reactive wetting is a phenomenon well verified experimentally [27,35], to date, no experiments have been undertaken to demonstrate the occurrence of diffusion-controlled reactive infiltration. However, a transition from reaction to diffusion control is expected to occur with increasing temperature for any alloy/ceramic system, since the activation energy of diffusion in metallic liquids (10s of kJ mol1) is one order of magnitude smaller than the activation energy for reaction-controlled reactive infiltration (100s of kJ mol1 [14,22]). In the Si/(oxidized) silicon nitride couple, the progress of the interfacial reaction at the triple line needs the removal ahead of the infiltration (or the wetting) front of a gaseous species (SiO) produced by the deoxidation reaction. As a consequence, in this case, the geometry strongly influences the triple line velocity leading to infiltration rates several orders of magnitude lower than the spreading rate. Such pronounced effects are expected to appear every time a gaseous species is involved in the reaction at the triple line. The sessile drop technique is the standard method used at high temperatures in wettability studies [6,36]. As it has been shown in Ref. [14,22], this technique is also interesting for simultaneous in situ monitoring of infiltration and wetting kinetics. A first limitation of this technique in infiltration studies comes from the roughness of the porous solid surface. A high roughness can result in non-axisymmetric droplets so that a quantitative or even semi-quantitative measurement of the infiltrated volume becomes impossible. Another limitation comes from the small quantity of liquid compared to the porous solids involved in sessile drop experiments.
N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
This is an inconvenience especially for studies with alloys diluted in the reactive element where the consumption during infiltration of reactive solute can rapidly lead to solute depletion. References [1] A. Evans, C. SanMarchi, A. Mortensen, Metal Matrix Composites in Industry: An Introduction and a Survey, Kluwer Academic publishers, Dordrecht, NL, 2003. [2] A. Mortensen, Comprehensive composite materials, in: A. Kelly, C. Zweben (Eds.), Melt Infiltration of Metal Matrix Composites, vol. 3, Pergamon, Oxford, 2000, pp. 521–554. [3] M. Bahrami, J.M. Molina, M. Kida, L. Weber, J. Narciso, A. Mortensen, Curr. Opin. Solid State Mater. Sci. 9 (2005) 196. [4] J.M. Molina, E. Piero, J. Narciso, C. Garcia Cordovilla, E. Louis, Curr. Opin. Solid State Mater. Sci. 9 (2005) 202. [5] A. Rodriguez-Guerrero, S.A. Sanchez, J. Narciso, E. Louis, A. Rodriguez-Reinoso, Acta Mater. 54 (2006) 1281. [6] N. Eustathopoulos, M. Nicholas, B. Drevet, Wettability at high temperature, Pergamon Materials Series, vol. 3., Pergamon, Oxford, 1999. [7] E. Saiz, A.P. Tomsia, Nat. Mater. 3 (2004) 903. [8] G. Kaptay, T. Barczy, J. Mater. Sci. 40 (2005) 2531. [9] K.P. Trumble, Acta Mater. 46 (1998) 2363. [10] E.O. Einset, J. Am. Ceram. Soc. 79 (1996) 333. [11] B.S. Rao, V. Jayaram, Acta Mater. 49 (2001) 2373. [12] D. Muscat, R.A.L. Drew, Metall. Trans. A 25 (1994) 2357. [13] P. Yi, S.Y. Xiao, J.L. Baptista, J. Am. Ceram. Soc. 82 (1999) 3459. [14] R. Voytovych, V. Bougiouri, N.R. Calderon, J. Narciso, N. Eustathopoulos, Acta Mater. 56 (2008) 2237. [15] T.J. Whalen, A.T. Anderson, J. Am. Ceram. Soc. 58 (1975) 396.
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[16] O. Dezellus, S. Jaques, F. Hodaj, N. Eustathopoulos, J. Mater. Sci. 40 (2005) 2307. [17] C.W. Forrest, P. Kennedy, J.V. Shennan, in: P. Popper (Ed.), Special Ceramics, vol. 5, Stroke-on-Trent, British Ceramic Research Association, 1972, pp. 99–112. [18] J.N. Ness, T.F. Page, J. Mater. Sci. 21 (1986) 1377. [19] Y. Wang, S. Tan, D. Jiang, Carbon 42 (2004) 1833. [20] R. Messner, Y.M. Chiang, J. Am. Ceram. Soc. 73 (1990) 1193. [21] L. Hozer, J.R. Lee, Y.M. Chiang, Mater. Sci. Eng. A 195 (1995) 131. [22] R. Israel, R. Voytovych, P. Protsenko, B. Drevet, D. Camel, N. Eustathopoulos, J. Mater. Sci. (2009), doi:10.1007/ s10853-009-3889-6. [23] P. Protsenko, O. Kozlova, R. Voytovych, N. Eustathopoulos, J. Mater. Sci. 43 (2008) 5669. [24] N. Eustathopoulos, Curr. Opin. Solid State Mater. Sci. 9 (2005) 152. [25] R. Israel, Ph.D. Thesis, Grenoble-INP, France, 2009. [26] N. Rojo-Calderon, Ph.D. Thesis, University of Alicante, Spain, 2009. [27] R. Voytovych, A. Mortensen, F. Hodaj, N. Eustathopoulos, Acta Mater. 47 (1999) 1117. [28] T. Saito, A. Shimura, S. Ichikawa, in: XV IEEE Photovoltaic Specialists Conference, 1981, pp. 576–580. [29] B. Drevet, O. Pajani, N. Eustathopoulos, Sol. Energy Mater. Sol. Cells 94 (2010) 425. [30] S.I. Raider, R. Flitsch, J.A. Aboaf, W.A. Pliskin, J. Electrochem. Soc. 123 (1976) 560. [31] B. Drevet, R. Voytovych, R. Israel, N. Eustathopoulos, J. Eur. Ceram. Soc. 29 (2009) 2363. [32] O. Dezellus, F. Hodaj, C. Rado, J.N. Barbier, N. Eustathopoulos, Acta Mater. 50 (2002) 979. [33] A. Mortensen, B. Drevet, N. Eustathopoulos, Scripta Mater. 36 (1997) 645. [34] M. Bahrami, Ph.D. Thesis, EFP Lausanne, Switzerland, 2007. [35] F. Hodaj, O. Dezellus, J.N. Barbier, A. Mortensen, N. Eustathopoulos, J. Mater. Sci. 42 (2007) 8071. [36] N. Eustathopoulos, N. Sobczak, A. Passerone, K. Nogi, J. Mater. Sci. 40 (2005) 2271.
Scripta Materialia 62 (2010) 966–971 www.elsevier.com/locate/scriptamat
Viewpoint Paper
Reactive infiltration by Si: Infiltration versus wetting N. Eustathopoulos,a R. Israel,a,b B. Drevetb,* and D. Camelb a
SIMAP, Phelma, Grenoble INP, Domaine Universitaire, BP 75–1130, rue de la Piscine, 38402 Saint Martin d’He`res Cedex, France b CEA, INES/RDI, LITEN/DTS/LMPS, 50 av. du Lac Le´man, 73377 le Bourget du Lac, France Received 13 January 2010; revised 9 February 2010; accepted 13 February 2010 Available online 18 February 2010
Abstract—This paper focuses on spontaneous infiltration by liquid metals in reactive metal/ceramic systems. Two cases of reactive infiltration, where a molten silicon drop is in contact with two different porous bodies, graphite and (oxidized) silicon nitride, are briefly described and discussed. For each solid, the dynamics of wetting on the solid surface is compared to the dynamics of infiltration into the porous medium in order to determine the common points and the main differences between these two processes. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Silicon; Infiltration; Interfaces; Wetting
1. Introduction Metal/ceramic composites are often processed by infiltration of porous ceramics by liquid metals [1]. In the conditions of temperature and atmosphere used in practice, the liquid metals (Cu, Al, etc.) do not wet ceramics such as alumina, silicon carbide or graphite, and for this reason infiltration is obtained by applying a pressure P0 high enough to overcome the capillary pressure PC. In numerous studies published since the 1990s by the teams of Mortensen (see for instance Refs. [2,3]) and Louis [4,5], it has been found that the infiltration distance h increases parabolically with both time t and excess pressure DP = P0 PC in agreement with Darcy’s law (or equivalently, with the Washburn equation) for infiltration limited by viscous friction. In contrast with infiltration, the viscous resistance has little effect on the kinetics of millimetre-sized metallic droplets spreading on solid surfaces [6,7], except for systems with equilibrium contact angles close to zero [6]. Spontaneous (pressureless) infiltration of a liquid in a porous medium occurs when the equilibrium contact angle of the liquid on the pore walls is much lower than 90° [8,9]. For this type of infiltration, studied among others in [10,11–14], the relevant mechanisms, especially the role played by reactions between the liquid metal and the ceramic in the infiltration process, are not yet well understood.
* Corresponding author. Tel.: +33 4 79 44 45 95; fax: +33 4 79 62 37 71; e-mail: [email protected]
The present paper focuses on spontaneous infiltration by liquid metals in reactive metal/ceramic systems. Two cases of reactive infiltration will be considered, concerning both molten silicon and two different porous bodies, graphite and (oxidized) silicon nitride. For each solid, the dynamics of wetting on the solid surface will be compared to the dynamics of infiltration into a porous preform. Although wetting and infiltration both involve the motion of a triple line, the geometry of the region around this line in these two processes is very different. The main question addressed in this paper is: to what extent does this geometry affect the triple line dynamics? 2. Infiltration of porous graphite Liquid silicon is known to wet carbon [15,16] and it can therefore spontaneously infiltrate a carbon preform. Infiltrated Si reacts with carbon to form SiC. Reactive infiltration is used to process the so-called “reactionbonded silicon carbide” [17–19] or SiC composites [20,21]. Infiltration of Si into the graphite crucibles used in Si purification can dramatically affect the lifetime of certain graphites [22]. In Ref. [10], the process of Si infiltration into porous carbon preforms was described as consisting of rapid, non-reactive, infiltration followed by reaction between Si and C to form SiC. The infiltration distance h(t) was assumed to follow Washburn’s equation taking P0 = 0. Experimental results obtained recently in SIMAP for the reactive infiltration of silicon into porous
1359-6462/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2010.02.030
N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
Si infiltrated zone
hf
1 mm
graphite
Figure 1. SEM micrograph of the infiltrated zone produced in 312 s at 1430 °C in a graphite with a volume pore fraction ap = 0.15.
graphite did not confirm the model described in Ref. [10] and led to a different description of infiltration where the reaction between silicon and graphite at the infiltration front provides the driving force for infiltration [22]. The new model was supported by infiltration experiments carried out under a static atmosphere of argon by the sessile drop method that enables the variation in infiltration depth h with time to be monitored in situ [22] (details of h calculation as well as the experimental procedure are given in Ref. [22]). The final infiltration depth hf is also measured a posteriori on metallographic sections (Fig. 1). In addition to the infiltration data, the method provides quantitative information on wetting thus allowing the spreading and infiltration rates to be measured in the same experiment. Figure 2a presents an example of wetting curves (i.e., the time-dependent change in contact angle h and drop
a
base diameter d = 2R) obtained during an infiltration experiment. The time origin corresponds to complete melting of the droplet. Spreading occurs at a nearly constant rate Uspr = dR/dt close to 10 lm s1. This is several orders of magnitude slower than the spreading rates measured previously in non-reactive liquid metal/ solid systems [6,7,23]. These two results, i.e., “linear spreading” and the very small spreading rate, indicate that spreading of Si on graphite (as well as on vitreous carbon substrates [16]) is controlled by the chemical reaction at the solid/liquid/vapour triple line where the wettable reaction product grows parallel to the liquid/ substrate interface (Fig. 2b) [6,24]. Figure 3a gives an example of infiltration kinetics (two different experiments) obtained for a graphite with a volume fraction of pores, ap = 0.15. Infiltration of silicon is linear with time thus strongly suggesting that infiltration is governed by the reaction of SiC formation on the pore walls at the infiltration front (Fig. 3b). The proposed mechanism implies that the infiltration rate Uinf and the wetting rate Uspr at a given temperature are equal or at least of the same order of magnitude. This is confirmed by the experimental values of the ratio Uinf/ Uspr which lie between 0.65 and 0.95 [25]. As argued in Ref. [14], the value of this ratio is less than unity because of the different tortuosities of bulk graphite and of the graphite-free surface. Tortuosity is defined as the ratio between the path followed by a fluid between two points
b
100
13
d
12
967
80
60 10 40
9
θ (deg)
d (mm)
11
L
θ
SiC
θ
8
C
20
7 0
100
200
300
400
500
t (s) Figure 2. (a) Drop base diameter d and contact angle h as a function of time for Si spreading over graphite at 1460 °C. t = 0 corresponds to the complete melting of Si. (b) Schematic presentation of reaction-controlled wetting.
a
b
0.7
L
0.6
hSi (mm)
0.5
SiC 0.4 0.3
C 0.2 0.1 0.0 0
50
100
150
200
250
300
350
400
t(s)
Figure 3. (a) Height of infiltrated Si hSi (where hSi = ap h) in porous graphite as a function of time for two experiments performed at 1430 °C. t = 0 corresponds to the beginning of Si melting. (b) Schematic presentation of reaction-controlled infiltration.
N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971
a 100
45
90
40
contact angle (°)
80
35 d
70
30
H
θ
60
25
50
20
40
15
30
10
20
5 0
500
1000
1500 2000 time (s)
2500
b diameter, height (a.u.)
968
L
15 mm
3000
Figure 4. (a) Wetting kinetics of Si on Si3N4-coated SiO2 at 1430 °C. (b) Top view of a sessile drop of Si on Si3N4-coated SiO2 showing the width L of the infiltrated zone parallel to the substrate surface (total time at 1430 °C: 17 min).
lying inside the porous body (or equivalently on the solid surface) and the geometrical distance between these points. In conclusion, for the pure Si/graphite couple, wetting on a solid surface and infiltration into a porous preform are both linear with time and their rate is limited by the same process, namely the reaction between silicon and carbon at the triple line. Some limited difference exists between the spreading and infiltration rates due to the tortuosity of the porous medium. Stronger differences are expected to appear with silicon carbide forming silicon alloys. In this case, alloy depletion in the reactive solute can lead to deviation of the h(t) curve from linearity [14]. In a particular case, the consumption of reactive solute by the reaction at and behind the infiltration front was so high that the Si concentration in the alloy became smaller than the minimum Si concentration needed for SiC formation [26]. Alloy depletion in the reactive solute does not happen in solid surface wetting experiments (except for diluted alloys [27]) in which the ratio between the liquid volume and the wetted (and thus reacted) solid surface is several orders of magnitude higher than in infiltration experiments [14].
a
(1) SiO2 Si
SiO
3. Infiltration of porous silicon nitride When silicon is processed by solidification in direct contact with silica crucibles, sticking of solidified Si on crucible walls leads to thermo-mechanical stress resulting in cracks produced in the Si ingot. In order to avoid sticking, photovoltaic silicon ingots are currently grown in SiO2 crucibles coated with a porous silicon nitride layer which acts as an interface releasing agent between silicon and the crucible. This process, which has its origin in the work of Saito et al. [28], is widely used in industry. However, it is only very recently that the interactions between molten silicon and porous silicon nitride have been studied and understood [29]. In Ref. [29], the silicon nitride coating was prepared by applying (spraying) on a dense SiO2 substrate a slurry composed of Si3N4 submicronic powder and polyvinyl alcohol dissolved in water as binder. The coated substrate is dried to remove the water and then heated in air above 450 °C to burn off the binder. This treatment leads to the formation of a silica layer on the Si3N4 particles, the layer being a few nm or tens of nm thick, depending on temperature and time [30]. The coating, (2)
(3) d H
θ0
θF
Si3N4
b Si
θ
Si3N4
SiO
SiO2
vapour Figure 5. (a) Spreading of a Si drop on oxidized Si3N4. The initial contact angle, h0, corresponds to wetting on the SiO2 passive film (1). Once a direct contact between Si and Si3N4 is established (2), wetting continues by removing the passive oxide film through the reaction SiO2 + Si ? 2SiO until the equilibrium contact angle on Si3N4 is reached (3). (b) Infiltration of Si in the pores of the oxidized Si3N4 coating.
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969
Table 1. Comparison between the spreading rate Uspr and the infiltration rates Ufilm and Uinf in silicon/graphite (at 1460 °C) and silicon/porous (oxidized) silicon nitride (at 1430 °C) systems. Process
Average rate (lm/s)
Wetting on solid surface Infiltration parallel to the surface ahead of the nominal triple line Infiltration under the drop perpendicular to the interface
Definition and symbol
Si on graphite
Si on porous Si3N4
Uspr = DR/Dt Ufilm = DL/Dt Uinf = Dh/Dt
8.7 5–7 5.7
10 2–3 102
a Si drop
h2
bubble
b
infiltrated coating
non-infiltrated coating
L
infiltrated coating
h1
h
Si
non-infiltrated coating
rupture path
SiO2
Figure 6. Infiltration of Si in Si3N4-coating on SiO2 (total time at 1430 °C: 17 min). SEM image (a) and schematic representation (b) of a crosssection of the sample.
about 150 lm thick, exhibits a microscopic porosity between individual Si3N4 grains and a macroscopic porosity formed by bubbles of some tens of microns produced by the spraying process. Figure 4a presents the wetting curves (contact angle h, drop base diameter d and drop height H) obtained for molten Si on Si3N4-coated SiO2 under argon flow. The initial contact angle, equal to 88°, corresponds to the angle on oxidized Si3N4. The contact angle decreases strongly with time and within a few 100s of seconds reaches 43°, a value close to the contact angle of Si on non-oxidized sintered Si3N4 [31]. During this period, the average spreading rate Uspr is about 10 lm s1. The spreading kinetics is controlled by the deoxidation of Si3N4 grains occurring by reaction between molten Si and the SiO2 passive film with formation of volatile Si monoxide: SiO2 þ Si ! 2SiO
ð1Þ
Reaction (1) occurs at any point on the solid/liquid interface but it is more intense at the triple line where the evacuation of SiO species far from the interface is
easier (Fig. 5a). Under these conditions, the spreading rate dR/dt is expected to be constant with time, in agreement with the experimental R(t) curve obtained with dense oxidized Si3N4 [31]. As far as infiltration is concerned, the infiltrated silicon volume cannot be determined in situ because, due to the rough surface of coating, the sessile drop is far from axisymmetric (Fig. 4b). However, some information on infiltration can be obtained by carefully observing the wetting curves (Fig. 4a). Thus, at t > 400 s the contact angle and drop height continue to decrease very slightly while the drop base diameter remains constant. These results indicate that the visible volume of the drop decreases with time but only very slightly, meaning that Si infiltration in the coating at t > 400 s is very limited, as confirmed by a post-experiment examination: – The top view of the sample clearly shows a “secondary wetting” film ahead of the nominal substrate/Si/vapour triple line (Fig. 4b). This film, of width L, results from Si infiltration from the triple line into the channels of the porous coating. This phenomenon takes place at times
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higher than the spreading time of 400 s, i.e., after the macroscopic triple line has attained its final position. The average rate of extension of the “secondary wetting” film parallel to the surface Ufilm is 2–3 lm s1, which is lower than but of the same order as the spreading rate of the primary wetting process (Table 1). – The cross-section of the infiltrated zone (Fig. 6) shows that the infiltration depth h1 under the bulk of the drop is very small, about 10 lm, corresponding to an average infiltration rate Uinf close to 102 lm s1 (while h increases in the vicinity of the triple line to a value h2 equal to several 10s of lm). The value Uinf 102 lm s1 is 2–3 orders of magnitude lower than both Uspr and Ufilm (Table 1). These results show that infiltration in this system is strongly “anisotropic”, the infiltration parallel to the coating surface being much faster than infiltration under the droplet. The equilibrium contact angle of Si on silica is close to 90°. As a consequence, molten Si does not infiltrate the porous coating, as long as pore walls are oxidized (Fig. 5b). However, molten Si wets deoxidized Si3N4 well. Thus, infiltration is possible with a rate controlled by deoxidation of the pore walls, i.e., by Reaction (1), in a similar way to wetting on the surface of oxidized Si3N4 (Fig. 5a). The critical factor for the rate of Reaction (1) is the SiO evacuation rate from the infiltration or the wetting front. In the spreading process, the SiO is evacuated easily and quickly and for this reason the rate-limiting stage is the atomic process at the silica/Si interface close to the triple line [32]. During infiltration, the evacuation rate is obviously considerably reduced in the region under the drop, where the SiO travel path is very long. This explanation is also consistent with the very high values of the Ufilm/Uinf ratio observed in the experiment on Si3N4-coated SiO2. Indeed, infiltration parallel to the surface is promoted by the easy evacuation of SiO into the gas. For this reason, Ufilm values are much closer to Uspr than to Uinf (Table 1). In contrast, for the Si/graphite couple where no gaseous species participate in the reaction at the triple line, the values of Uspr, Ufilm and Uinf are very close (Table 1). The above results obtained with pure Si show that wetting on the surface of oxidized Si3N4 and infiltration into porous (oxidized) Si3N4-coating are processes controlled both by the rate of removal of the passive silica layer (acting as a barrier to wetting and to infiltration) from the nitride surface. However, due to the very different geometries of these two configurations, the rate-limiting steps are different: long-range gaseous diffusion of SiO molecules into the pore network ahead of the infiltration front for infiltration perpendicular to the interface, compared with a local chemical process at the triple line for wetting on the flat surface. This results in an infiltration rate perpendicular to the interface Uinf 2–3 orders of magnitude lower than Uspr and Ufilm. 4. Conclusions and prospects Wetting on a solid surface and infiltration in a porous preform in the Si/graphite and Si/(oxidized) Si3N4 systems are governed by the reactions occurring at the solid/liquid/vapour triple lines of these systems.
In the Si/graphite couple at temperatures close to the Si melting point, wetting and infiltration kinetics in neutral gas are controlled by the local chemical process at the triple line moving on the solid surface or on the pore walls. In this system, the geometry has a limited influence on the triple line velocity, the infiltration rate being lower than the spreading rate by a few 10s of percent. Non-local contributions are however expected in the following two cases: (i) in high vacuum, the transport of Si atoms through the vapour phase can modify the surface chemistry of graphite in front of the triple line and thus enhance wetting and infiltration rates even at temperatures close to the Si melting point. A similar effect is expected to occur under inert gas but at much higher temperatures. Although some experimental evidence for this type of surface modification exists [22], a general description of reactive wetting and infiltration taking into account both the localized and delocalized reactions is still missing. (ii) When Si (and any other reactive element) is present in the liquid as alloying element, longrange diffusion of the reactive solute from the preform entrance to the infiltration front can also affect and even control the reactive infiltration. The calculated rate of diffusion-controlled reactive infiltration depends on the same thermochemical and physicochemical quantities as the diffusion-controlled reactive spreading modelled in Ref. [33]. However, due to the different geometries, the time-dependent variations in infiltration distance and drop base radius are predicted to follow different laws: h t1/2 [14,34] and R t1/4 [33], respectively. Note that while the diffusion-controlled reactive wetting is a phenomenon well verified experimentally [27,35], to date, no experiments have been undertaken to demonstrate the occurrence of diffusion-controlled reactive infiltration. However, a transition from reaction to diffusion control is expected to occur with increasing temperature for any alloy/ceramic system, since the activation energy of diffusion in metallic liquids (10s of kJ mol1) is one order of magnitude smaller than the activation energy for reaction-controlled reactive infiltration (100s of kJ mol1 [14,22]). In the Si/(oxidized) silicon nitride couple, the progress of the interfacial reaction at the triple line needs the removal ahead of the infiltration (or the wetting) front of a gaseous species (SiO) produced by the deoxidation reaction. As a consequence, in this case, the geometry strongly influences the triple line velocity leading to infiltration rates several orders of magnitude lower than the spreading rate. Such pronounced effects are expected to appear every time a gaseous species is involved in the reaction at the triple line. The sessile drop technique is the standard method used at high temperatures in wettability studies [6,36]. As it has been shown in Ref. [14,22], this technique is also interesting for simultaneous in situ monitoring of infiltration and wetting kinetics. A first limitation of this technique in infiltration studies comes from the roughness of the porous solid surface. A high roughness can result in non-axisymmetric droplets so that a quantitative or even semi-quantitative measurement of the infiltrated volume becomes impossible. Another limitation comes from the small quantity of liquid compared to the porous solids involved in sessile drop experiments.
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This is an inconvenience especially for studies with alloys diluted in the reactive element where the consumption during infiltration of reactive solute can rapidly lead to solute depletion. References [1] A. Evans, C. SanMarchi, A. Mortensen, Metal Matrix Composites in Industry: An Introduction and a Survey, Kluwer Academic publishers, Dordrecht, NL, 2003. [2] A. Mortensen, Comprehensive composite materials, in: A. Kelly, C. Zweben (Eds.), Melt Infiltration of Metal Matrix Composites, vol. 3, Pergamon, Oxford, 2000, pp. 521–554. [3] M. Bahrami, J.M. Molina, M. Kida, L. Weber, J. Narciso, A. Mortensen, Curr. Opin. Solid State Mater. Sci. 9 (2005) 196. [4] J.M. Molina, E. Piero, J. Narciso, C. Garcia Cordovilla, E. Louis, Curr. Opin. Solid State Mater. Sci. 9 (2005) 202. [5] A. Rodriguez-Guerrero, S.A. Sanchez, J. Narciso, E. Louis, A. Rodriguez-Reinoso, Acta Mater. 54 (2006) 1281. [6] N. Eustathopoulos, M. Nicholas, B. Drevet, Wettability at high temperature, Pergamon Materials Series, vol. 3., Pergamon, Oxford, 1999. [7] E. Saiz, A.P. Tomsia, Nat. Mater. 3 (2004) 903. [8] G. Kaptay, T. Barczy, J. Mater. Sci. 40 (2005) 2531. [9] K.P. Trumble, Acta Mater. 46 (1998) 2363. [10] E.O. Einset, J. Am. Ceram. Soc. 79 (1996) 333. [11] B.S. Rao, V. Jayaram, Acta Mater. 49 (2001) 2373. [12] D. Muscat, R.A.L. Drew, Metall. Trans. A 25 (1994) 2357. [13] P. Yi, S.Y. Xiao, J.L. Baptista, J. Am. Ceram. Soc. 82 (1999) 3459. [14] R. Voytovych, V. Bougiouri, N.R. Calderon, J. Narciso, N. Eustathopoulos, Acta Mater. 56 (2008) 2237. [15] T.J. Whalen, A.T. Anderson, J. Am. Ceram. Soc. 58 (1975) 396.
971
[16] O. Dezellus, S. Jaques, F. Hodaj, N. Eustathopoulos, J. Mater. Sci. 40 (2005) 2307. [17] C.W. Forrest, P. Kennedy, J.V. Shennan, in: P. Popper (Ed.), Special Ceramics, vol. 5, Stroke-on-Trent, British Ceramic Research Association, 1972, pp. 99–112. [18] J.N. Ness, T.F. Page, J. Mater. Sci. 21 (1986) 1377. [19] Y. Wang, S. Tan, D. Jiang, Carbon 42 (2004) 1833. [20] R. Messner, Y.M. Chiang, J. Am. Ceram. Soc. 73 (1990) 1193. [21] L. Hozer, J.R. Lee, Y.M. Chiang, Mater. Sci. Eng. A 195 (1995) 131. [22] R. Israel, R. Voytovych, P. Protsenko, B. Drevet, D. Camel, N. Eustathopoulos, J. Mater. Sci. (2009), doi:10.1007/ s10853-009-3889-6. [23] P. Protsenko, O. Kozlova, R. Voytovych, N. Eustathopoulos, J. Mater. Sci. 43 (2008) 5669. [24] N. Eustathopoulos, Curr. Opin. Solid State Mater. Sci. 9 (2005) 152. [25] R. Israel, Ph.D. Thesis, Grenoble-INP, France, 2009. [26] N. Rojo-Calderon, Ph.D. Thesis, University of Alicante, Spain, 2009. [27] R. Voytovych, A. Mortensen, F. Hodaj, N. Eustathopoulos, Acta Mater. 47 (1999) 1117. [28] T. Saito, A. Shimura, S. Ichikawa, in: XV IEEE Photovoltaic Specialists Conference, 1981, pp. 576–580. [29] B. Drevet, O. Pajani, N. Eustathopoulos, Sol. Energy Mater. Sol. Cells 94 (2010) 425. [30] S.I. Raider, R. Flitsch, J.A. Aboaf, W.A. Pliskin, J. Electrochem. Soc. 123 (1976) 560. [31] B. Drevet, R. Voytovych, R. Israel, N. Eustathopoulos, J. Eur. Ceram. Soc. 29 (2009) 2363. [32] O. Dezellus, F. Hodaj, C. Rado, J.N. Barbier, N. Eustathopoulos, Acta Mater. 50 (2002) 979. [33] A. Mortensen, B. Drevet, N. Eustathopoulos, Scripta Mater. 36 (1997) 645. [34] M. Bahrami, Ph.D. Thesis, EFP Lausanne, Switzerland, 2007. [35] F. Hodaj, O. Dezellus, J.N. Barbier, A. Mortensen, N. Eustathopoulos, J. Mater. Sci. 42 (2007) 8071. [36] N. Eustathopoulos, N. Sobczak, A. Passerone, K. Nogi, J. Mater. Sci. 40 (2005) 2271.