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Scripta Materialia 62 (2010) 966–971

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Reactive infiltration by Si: Infiltration versus wetting

N. Eustathopoulos,a R. Israel,a,b B. Drevetb,* and D. Camelb

aSIMAP, Phelma, Grenoble INP, Domaine Universitaire, BP 75–1130, rue de la Piscine, 38402 Saint Martin d’Heres Cedex, FrancebCEA, INES/RDI, LITEN/DTS/LMPS, 50 av. du Lac Leman, 73377 le Bourget du Lac, France

Received 13 January 2010; revised 9 February 2010; accepted 13 February 2010Available online 18 February 2010

Abstract—This paper focuses on spontaneous infiltration by liquid metals in reactive metal/ceramic systems. Two cases of reactiveinfiltration, where a molten silicon drop is in contact with two different porous bodies, graphite and (oxidized) silicon nitride, arebriefly described and discussed. For each solid, the dynamics of wetting on the solid surface is compared to the dynamics of infil-tration into the porous medium in order to determine the common points and the main differences between these two processes.� 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 infil-tration of porous ceramics by liquid metals [1]. In the con-ditions of temperature and atmosphere used in practice,the liquid metals (Cu, Al, etc.) do not wet ceramics suchas alumina, silicon carbide or graphite, and for this reasoninfiltration is obtained by applying a pressure P0 high en-ough to overcome the capillary pressure PC. In numerousstudies published since the 1990s by the teams of Morten-sen (see for instance Refs. [2,3]) and Louis [4,5], it has beenfound that the infiltration distance h increases paraboli-cally with both time t and excess pressure DP = P0 � PC

in agreement with Darcy’s law (or equivalently, with theWashburn equation) for infiltration limited by viscous fric-tion. In contrast with infiltration, the viscous resistance haslittle effect on the kinetics of millimetre-sized metallic drop-lets spreading on solid surfaces [6,7], except for systemswith equilibrium contact angles close to zero [6].

Spontaneous (pressureless) infiltration of a liquid in aporous medium occurs when the equilibrium contact an-gle of the liquid on the pore walls is much lower than 90�[8,9]. For this type of infiltration, studied among othersin [10,11–14], the relevant mechanisms, especially therole played by reactions between the liquid metal andthe ceramic in the infiltration process, are not yet wellunderstood.

1359-6462/$ - see front matter � 2010 Acta Materialia Inc. Published by Eldoi:10.1016/j.scriptamat.2010.02.030

* Corresponding author. Tel.: +33 4 79 44 45 95; fax: +33 4 79 62 3771; e-mail: beatrice.drevet@cea.fr

The present paper focuses on spontaneous infiltrationby liquid metals in reactive metal/ceramic systems. Twocases of reactive infiltration will be considered, concern-ing 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 com-pared to the dynamics of infiltration into a porous pre-form. Although wetting and infiltration both involve themotion of a triple line, the geometry of the regionaround this line in these two processes is very different.The main question addressed in this paper is: to what ex-tent does this geometry affect the triple line dynamics?

2. Infiltration of porous graphite

Liquid silicon is known to wet carbon [15,16] and itcan therefore spontaneously infiltrate a carbon preform.Infiltrated Si reacts with carbon to form SiC. Reactiveinfiltration is used to process the so-called “reaction-bonded silicon carbide” [17–19] or SiC composites[20,21]. Infiltration of Si into the graphite crucibles usedin Si purification can dramatically affect the lifetime ofcertain graphites [22].

In Ref. [10], the process of Si infiltration into porouscarbon preforms was described as consisting of rapid,non-reactive, infiltration followed by reaction betweenSi and C to form SiC. The infiltration distance h(t)was assumed to follow Washburn’s equation takingP0 = 0. Experimental results obtained recently in SI-MAP for the reactive infiltration of silicon into porous

sevier Ltd. All rights reserved.

1 mmgraphite

Si

infiltrated zonehf

Figure 1. SEM micrograph of the infiltrated zone produced in 312 s at1430 �C in a graphite with a volume pore fraction ap = 0.15.

N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971 967

graphite did not confirm the model described in Ref. [10]and led to a different description of infiltration where thereaction between silicon and graphite at the infiltrationfront provides the driving force for infiltration [22].

The new model was supported by infiltration experi-ments carried out under a static atmosphere of argon bythe sessile drop method that enables the variation ininfiltration depth h with time to be monitored in situ[22] (details of h calculation as well as the experimentalprocedure are given in Ref. [22]). The final infiltrationdepth hf is also measured a posteriori on metallographicsections (Fig. 1). In addition to the infiltration data, themethod provides quantitative information on wettingthus allowing the spreading and infiltration rates to bemeasured in the same experiment.

Figure 2a presents an example of wetting curves (i.e.,the time-dependent change in contact angle h and drop

0 100 200 300 4007

8

9

10

11

12

13

d (m

m)

t (s)

θ

d

a

Figure 2. (a) Drop base diameter d and contact angle h as a function of timcomplete melting of Si. (b) Schematic presentation of reaction-controlled we

0 50 100 150 200 250 300 350.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

hS

i (m

m)

t(s)

a

Figure 3. (a) Height of infiltrated Si hSi (where hSi = ap h) in porous graphitecorresponds to the beginning of Si melting. (b) Schematic presentation of re

base diameter d = 2R) obtained during an infiltrationexperiment. The time origin corresponds to completemelting of the droplet. Spreading occurs at a nearly con-stant rate Uspr = dR/dt close to 10 lm s�1. This is sev-eral orders of magnitude slower than the spreadingrates measured previously in non-reactive liquid metal/solid systems [6,7,23]. These two results, i.e., “linearspreading” and the very small spreading rate, indicatethat spreading of Si on graphite (as well as on vitreouscarbon substrates [16]) is controlled by the chemicalreaction at the solid/liquid/vapour triple line where thewettable 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 witha volume fraction of pores, ap = 0.15. Infiltration of sil-icon is linear with time thus strongly suggesting thatinfiltration is governed by the reaction of SiC formationon the pore walls at the infiltration front (Fig. 3b).

The proposed mechanism implies that the infiltrationrate Uinf and the wetting rate Uspr at a given temperatureare equal or at least of the same order of magnitude. Thisis confirmed by the experimental values of the ratio Uinf/Uspr which lie between 0.65 and 0.95 [25]. As argued inRef. [14], the value of this ratio is less than unity becauseof the different tortuosities of bulk graphite and of thegraphite-free surface. Tortuosity is defined as the ratiobetween the path followed by a fluid between two points

500

20

40

60

80

100

θ (d

eg) L

SiC

C

θ

b

e for Si spreading over graphite at 1460 �C. t = 0 corresponds to thetting.

C

L

SiC

0 400

b

as a function of time for two experiments performed at 1430 �C. t = 0action-controlled infiltration.

15 mm

L

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500 3000

time (s)

cont

act

ang

le (

°)

5

10

15

20

25

30

35

40

45

dia

met

er, h

eig

ht (

a.u

.)

d

H

θ

a b

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 ofthe infiltrated zone parallel to the substrate surface (total time at 1430 �C: 17 min).

968 N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971

lying inside the porous body (or equivalently on the solidsurface) and the geometrical distance between thesepoints.

In conclusion, for the pure Si/graphite couple, wet-ting on a solid surface and infiltration into a porous pre-form are both linear with time and their rate is limitedby the same process, namely the reaction between siliconand carbon at the triple line. Some limited difference ex-ists between the spreading and infiltration rates due tothe tortuosity of the porous medium. Stronger differ-ences are expected to appear with silicon carbide form-ing silicon alloys. In this case, alloy depletion in thereactive solute can lead to deviation of the h(t) curvefrom linearity [14]. In a particular case, the consumptionof reactive solute by the reaction at and behind the infil-tration front was so high that the Si concentration in thealloy became smaller than the minimum Si concentra-tion needed for SiC formation [26]. Alloy depletion inthe reactive solute does not happen in solid surface wet-ting experiments (except for diluted alloys [27]) in whichthe ratio between the liquid volume and the wetted (andthus reacted) solid surface is several orders of magnitudehigher than in infiltration experiments [14].

Si3N4

θ0

SiO2

)1(SiO

Si

Si3N4

θ

SiO

Si

SiO2

vapour

a

b

Figure 5. (a) Spreading of a Si drop on oxidized Si3N4. The initial contact angcontact between Si and Si3N4 is established (2), wetting continues by removingequilibrium contact angle on Si3N4 is reached (3). (b) Infiltration of Si in th

3. Infiltration of porous silicon nitride

When silicon is processed by solidification in directcontact with silica crucibles, sticking of solidified Si oncrucible walls leads to thermo-mechanical stress result-ing in cracks produced in the Si ingot. In order to avoidsticking, photovoltaic silicon ingots are currently grownin SiO2 crucibles coated with a porous silicon nitridelayer which acts as an interface releasing agent betweensilicon and the crucible. This process, which has its ori-gin in the work of Saito et al. [28], is widely used inindustry. However, it is only very recently that the inter-actions between molten silicon and porous silicon ni-tride have been studied and understood [29].

In Ref. [29], the silicon nitride coating was preparedby applying (spraying) on a dense SiO2 substrate a slurrycomposed of Si3N4 submicronic powder and polyvinylalcohol dissolved in water as binder. The coated sub-strate is dried to remove the water and then heated inair above 450 �C to burn off the binder. This treatmentleads to the formation of a silica layer on the Si3N4 par-ticles, the layer being a few nm or tens of nm thick,depending on temperature and time [30]. The coating,

θF

)3()2(d

H

le, h0, corresponds to wetting on the SiO2 passive film (1). Once a directthe passive oxide film through the reaction SiO2 + Si ? 2SiO until the

e pores of the oxidized Si3N4 coating.

Si drop

bubbleinfiltratedcoating non-infiltrated

coatingh1

h2

Lh

Si

SiO2rupturepath

non-infiltratedcoating

infiltratedcoating

a

b

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 cross-section of the sample.

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)

Definition and symbol Si on graphite Si on porous Si3N4

Wetting on solid surface Uspr = DR/Dt 8.7 �10Infiltration parallel to the surface ahead of the nominal triple line Ufilm = DL/Dt �5–7 �2–3Infiltration under the drop perpendicular to the interface Uinf = Dh/Dt 5.7 �10�2

N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971 969

about 150 lm thick, exhibits a microscopic porosity be-tween individual Si3N4 grains and a macroscopic poros-ity formed by bubbles of some tens of microns producedby the spraying process.

Figure 4a presents the wetting curves (contact angle h,drop base diameter d and drop height H) obtained formolten Si on Si3N4-coated SiO2 under argon flow. The ini-tial contact angle, equal to 88�, corresponds to the angleon oxidized Si3N4. The contact angle decreases stronglywith time and within a few 100s of seconds reaches 43�,a value close to the contact angle of Si on non-oxidizedsintered Si3N4 [31]. During this period, the averagespreading rate Uspr is about 10 lm s�1. The spreadingkinetics is controlled by the deoxidation of Si3N4 grainsoccurring by reaction between molten Si and the SiO2 pas-sive film with formation of volatile Si monoxide:

SiO2 þ Si! 2SiO ð1ÞReaction (1) occurs at any point on the solid/liquid

interface but it is more intense at the triple line wherethe evacuation of SiO species far from the interface is

easier (Fig. 5a). Under these conditions, the spreadingrate dR/dt is expected to be constant with time, in agree-ment with the experimental R(t) curve obtained withdense oxidized Si3N4 [31].

As far as infiltration is concerned, the infiltrated sili-con volume cannot be determined in situ because, due tothe rough surface of coating, the sessile drop is far fromaxisymmetric (Fig. 4b). However, some information oninfiltration can be obtained by carefully observing thewetting curves (Fig. 4a). Thus, at t > 400 s the contactangle and drop height continue to decrease very slightlywhile the drop base diameter remains constant. Theseresults indicate that the visible volume of the drop de-creases with time but only very slightly, meaning thatSi 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/vapourtriple line (Fig. 4b). This film, of width L, results from Siinfiltration from the triple line into the channels of theporous coating. This phenomenon takes place at times

970 N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971

higher than the spreading time of 400 s, i.e., after themacroscopic triple line has attained its final position.The average rate of extension of the “secondary wet-ting” film parallel to the surface Ufilm is 2–3 lm s�1,which is lower than but of the same order as the spread-ing rate of the primary wetting process (Table 1).

– The cross-section of the infiltrated zone (Fig. 6) showsthat the infiltration depth h1 under the bulk of the dropis very small, about 10 lm, corresponding to an aver-age infiltration rate Uinf close to 10�2 lm s�1 (while hincreases in the vicinity of the triple line to a value h2

equal to several 10s of lm). The valueUinf � 10�2 lm s�1 is 2–3 orders of magnitude lowerthan both Uspr and Ufilm (Table 1).These results show that infiltration in this system is

strongly “anisotropic”, the infiltration parallel to thecoating surface being much faster than infiltration underthe droplet. The equilibrium contact angle of Si on silicais close to 90�. As a consequence, molten Si does notinfiltrate the porous coating, as long as pore walls areoxidized (Fig. 5b). However, molten Si wets deoxidizedSi3N4 well. Thus, infiltration is possible with a rate con-trolled by deoxidation of the pore walls, i.e., by Reac-tion (1), in a similar way to wetting on the surface ofoxidized Si3N4 (Fig. 5a). The critical factor for the rateof Reaction (1) is the SiO evacuation rate from the infil-tration or the wetting front. In the spreading process,the SiO is evacuated easily and quickly and for this rea-son the rate-limiting stage is the atomic process at thesilica/Si interface close to the triple line [32]. Duringinfiltration, the evacuation rate is obviously consider-ably reduced in the region under the drop, where theSiO travel path is very long. This explanation is alsoconsistent with the very high values of the Ufilm/Uinf ra-tio observed in the experiment on Si3N4-coated SiO2. In-deed, infiltration parallel to the surface is promoted bythe easy evacuation of SiO into the gas. For this reason,Ufilm values are much closer to Uspr than to Uinf (Table1). In contrast, for the Si/graphite couple where no gas-eous 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 thatwetting on the surface of oxidized Si3N4 and infiltrationinto porous (oxidized) Si3N4-coating are processes con-trolled both by the rate of removal of the passive silicalayer (acting as a barrier to wetting and to infiltration)from the nitride surface. However, due to the very differ-ent geometries of these two configurations, the rate-lim-iting steps are different: long-range gaseous diffusion ofSiO molecules into the pore network ahead of the infil-tration front for infiltration perpendicular to the inter-face, compared with a local chemical process at thetriple line for wetting on the flat surface. This resultsin 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 porouspreform in the Si/graphite and Si/(oxidized) Si3N4 sys-tems are governed by the reactions occurring at the so-lid/liquid/vapour triple lines of these systems.

In the Si/graphite couple at temperatures close to theSi melting point, wetting and infiltration kinetics in neu-tral gas are controlled by the local chemical process atthe triple line moving on the solid surface or on the porewalls. In this system, the geometry has a limited influ-ence on the triple line velocity, the infiltration rate beinglower than the spreading rate by a few 10s of percent.Non-local contributions are however expected in the fol-lowing two cases: (i) in high vacuum, the transport of Siatoms through the vapour phase can modify the surfacechemistry of graphite in front of the triple line and thusenhance wetting and infiltration rates even at tempera-tures close to the Si melting point. A similar effect is ex-pected to occur under inert gas but at much highertemperatures. Although some experimental evidencefor this type of surface modification exists [22], a generaldescription of reactive wetting and infiltration takinginto account both the localized and delocalized reactionsis still missing. (ii) When Si (and any other reactive ele-ment) is present in the liquid as alloying element, long-range diffusion of the reactive solute from the preformentrance to the infiltration front can also affect and evencontrol the reactive infiltration. The calculated rate ofdiffusion-controlled reactive infiltration depends on thesame thermochemical and physicochemical quantitiesas the diffusion-controlled reactive spreading modelledin Ref. [33]. However, due to the different geometries,the time-dependent variations in infiltration distanceand drop base radius are predicted to follow differentlaws: h � t1/2 [14,34] and R � t1/4 [33], respectively. Notethat while the diffusion-controlled reactive wetting is aphenomenon well verified experimentally [27,35], todate, no experiments have been undertaken to demon-strate the occurrence of diffusion-controlled reactiveinfiltration. However, a transition from reaction to diffu-sion control is expected to occur with increasing temper-ature for any alloy/ceramic system, since the activationenergy of diffusion in metallic liquids (10s of kJ mol�1)is one order of magnitude smaller than the activation en-ergy for reaction-controlled reactive infiltration (100s ofkJ mol�1 [14,22]).

In the Si/(oxidized) silicon nitride couple, the pro-gress of the interfacial reaction at the triple line needsthe removal ahead of the infiltration (or the wetting)front of a gaseous species (SiO) produced by the deoxi-dation reaction. As a consequence, in this case, thegeometry strongly influences the triple line velocity lead-ing to infiltration rates several orders of magnitude low-er than the spreading rate. Such pronounced effects areexpected to appear every time a gaseous species is in-volved in the reaction at the triple line.

The sessile drop technique is the standard methodused at high temperatures in wettability studies [6,36].As it has been shown in Ref. [14,22], this technique isalso interesting for simultaneous in situ monitoring ofinfiltration and wetting kinetics. A first limitation of thistechnique in infiltration studies comes from the rough-ness of the porous solid surface. A high roughness canresult in non-axisymmetric droplets so that a quantita-tive or even semi-quantitative measurement of the infil-trated volume becomes impossible. Another limitationcomes from the small quantity of liquid compared tothe porous solids involved in sessile drop experiments.

N. Eustathopoulos et al. / Scripta Materialia 62 (2010) 966–971 971

This is an inconvenience especially for studies with al-loys diluted in the reactive element where the consump-tion during infiltration of reactive solute can rapidlylead to solute depletion.

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