Influence of oxygen partial pressure on the wetting of SiC by a Co–Si alloy

Materials Science and Engineering A 495 (2008) 174–180

Influence of oxygen partial pressure on the wetting of SiC by a Co–Si alloy O. Mailliart a , F. Hodaj b,∗ , V. Chaumat a , N. Eustathopoulos b a

b

CEA – Grenoble, 17 rue des Martyrs, F-38054 Grenoble Cedex, France SIMAP – UMR CNRS 5266, INP Grenoble-UJF, Domaine Universitaire, BP 75-1130, rue de la Piscine, 38402 Saint Martin d’H`eres Cedex, France Received 22 March 2007; received in revised form 7 November 2007; accepted 14 November 2007

Abstract In this investigation the influence of oxygen partial pressure PO2 on the wetting of SiC by a Co–Si alloy was studied. Wetting experiments were carried out in argon with different oxygen contents (from 5 to 1000 ppm). The relationship between wetting and deoxidation of surfaces (SiC and Co–Si alloy) was investigated. Calculations were performed to evaluate the temperature range over which deoxidation is possible. These calculations are in agreement with the experimental results. © 2008 Published by Elsevier B.V. Keywords: Wetting; Silicides; Silicon carbide; Oxidation; Interfaces

1. Introduction Silicon carbide is a covalent ceramic of great technological interest because of its good mechanical properties (high hardness and dimensional stability as well as high resistance to abrasion and erosion), high thermal conductivity, good thermal shock resistance and high oxidation resistance. It is used as a monolithic material as well as a reinforcement in composites, for functional and structural applications. In view of this considerable interest in SiC, many studies have been performed on the wettability of SiC by liquid metals and alloys either under high vacuum or in high-purity neutral gases, see for example Refs. [1–4]. However, in some applications, the ambient gas atmosphere may contain significant amounts of oxygen, an element that can affect the surface chemistry of most metals and SiC. The aim of this work is to study the influence of oxygen partial pressure PO2 on the wetting of SiC by a Co–77.5 at.% Si eutectic alloy. At solidification, this alloy leads to the formation of CoSi2 silicide and pure silicon. This alloy is representative of the family of high melting point silicon alloys that are known not to react with but to wet SiC, forming strong interfaces [5–7]. It is

∗

Corresponding author. Tel.: +33 476826515; fax: +33 476826767. E-mail address: [email protected] (F. Hodaj).

0921-5093/$ – see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.msea.2007.11.090

important to note that both SiC and metal silicides are oxidizable materials. 2. Experimental set-up Experiments were performed by the sessile drop technique in an alumina chamber furnace. The spreading process was filmed by a charge-coupled device (CCD) video camera and recorded on videotape at a film speed of 25 frames per second. The angle θ is not measured using a drop shape analysis software because this method is very sensitive to defects existing on the drop surface, which can appear in oxidizing conditions. Another difficulty appears when significant oxidation of the SiC substrate occurs and this makes it difficult to position the drop/substrate interface. Therefore, R and drop height h are measured directly by the experimentalist using photos with an accuracy of ±5% and θ is calculated assuming a spherical shape of the drop. Selected samples were cut, embedded in a resin and polished for optical and scanning electron microscopy (SEM) analysis of the cross-section. The principal thermal cycle involves heating at a rate of about 400 K h−1 up to 1350 ◦ C and then keeping temperature T constant for about 45 min before cooling. The heating up to the melting point of the alloy (1259 ◦ C) was performed under pure argon (less then 5 ppm O2 ) and afterwards a controlled

O. Mailliart et al. / Materials Science and Engineering A 495 (2008) 174–180

argon–oxygen mixture was introduced in the furnace. Other cycles were also used and their features will be specified later. The standard argon–oxygen mixtures contain 10, 100 and 1000 ppm O2 . An Ar–300 ppm O2 mixture is prepared using gases containing 100 and 1000 ppm O2 and its composition is controlled by oxygen probe analysis. For all experiments, the gas flow rate was 1.3 l min−1 . Due to this high gas flow rate and to the small masses of Co–Si alloys reacting with oxygen (about 50 mg), the oxygen pressure measured by oxygen probe analysis does not vary measurably between the furnace inlet and outlet. SiC samples (d = 15 mm, h = 6 mm) were produced by pressureless sintering at T = 2100 ◦ C by BOOSTEC (France). SiC powder was used with 2 wt.% B4 C as sintering aid. The residual porosity was less than 3% and the average grain size was about 1 ␮m. SiC substrates were mechanically polished using diamond paste up to an average roughness Ra of 7 nm. Note that a fresh SiC surface in contact with air at room temperature is instantaneously covered by an oxide layer of nanometric thickness [8]. The Co–77.5 at.% Si alloy was processed from pure Si (99.999%) and CoSi powder (99%) by melting and alloying in an alumina substrate at 1300 ◦ C in high vacuum (10−6 mbar). All experiments were performed with alloy masses of about 50 mg. One experiment was performed on an amorphous silica substrate produced by VS technologies (France) with a smooth surface (Ra = 12 nm). 3. Results 3.1. Pure argon Fig. 1 presents the time-dependent change in contact angle and drop base radius of a Co–Si drop on SiC. The contact angle at melting is θ 0 = 86 ± 4◦ while the final contact angle is θ F = 40 ± 4◦ . This value is very close to the values θ F = 36–38◦ observed by Gasse [5] for the same system and temperature under high vacuum on sintered or monocrystalline SiC. After cooling, the solidified droplet adheres to the substrate. The alloy microstructure consists of primary Si crystals and Si–CoSi2 eutectic (Fig. 2) and, as expected [5], the alloy/ceramic interface does not show any reactivity at the observation scale (SEM). The presence of cracks in the drop bulk and in the substrate but not at the interface suggests that the alloy/SiC interface is mechanically strong, stronger than SiC itself. A second experiment performed under the same conditions led to θ 0 = 98 ± 4◦ and θ F = 36 ± 4◦ .

175

Fig. 1. Spreading kinetics (contact angle θ and drop radius R normalized to final radius RF ) of two Co–72.5 at.% Si alloys on SiC substrate under pure argon (less then 5 ppm O2 ). t = 0 is taken to be the beginning of melting.

A specific experiment carried out on an amorphous silica substrate shows that, just after melting, the contact angle of Co–Si alloy is 91 ± 4◦ and does not change with holding time. This value, which is in good agreement with the value measured by Sangiorgi et al. [9] for pure Si on silica at T = 1450 ◦ C in neutral gas (θ 0 = 87 ± 1◦ ), supports the fact that in our experiments with pure Ar, the Co–Si alloy is oxide free once it has melted. Moreover, by comparing the value θ 0 = 91 ± 4◦ on SiO2 to the values 86–98◦ on SiC, it appears that the latter are on oxidized SiC. Therefore, the long spreading time tS ≈ 900 s observed on SiC (see Fig. 1) results from SiC deoxidation. In agreement with previous studies performed with Cu–Si alloy on oxidized SiC [2,5], the spreading kinetics in Co–Si/SiC system is attributed to substrate deoxidation occurring at the solid–liquid–vapour triple line by reaction between Si and Si oxide to form the volatile silicon monoxide: (Si) + < SiO2 > → 2[SiO]

(1)

The notations ( ), < > and [ ] designate the liquid, solid and gaseous states, respectively. In other words, despite the fact that the Co–77.5 at.% Si alloy is not reactive with SiC, spreading kinetics is typical of reactive wetting. 3.2. Influence of oxygen content in Ar Fig. 3 shows the wetting curves for different oxygen contents in Ar (100 and 300 ppm O2 ). In the same figure, the wetting curve corresponding to pure argon has been reported for com-

Fig. 2. SEM image of a cross-section of a Co–72.5 at.% Si alloy on SiC (backscattered electron image). Experiment performed under pure Ar.

176

O. Mailliart et al. / Materials Science and Engineering A 495 (2008) 174–180

Fig. 3. Contact angle θ as a function of time for a Co–72.5 at.% Si alloy on SiC for different Ar–O2 mixtures (( ) pure Ar, () 100 ppm and (䊉) 300 ppm O2 ) introduced at melting. t = 0 is taken to be the beginning of melting.

parison purposes. The initial and final contact angles as well as the spreading curves obtained for 100 ppm O2 and pure argon are almost identical. These results clearly show that oxygen partial pressures up to 10−4 bar have practically no influence on the wetting of SiC by Co–Si alloy at 1350 ◦ C. For 300 ppm of O2 in the gas, the contact angle at melting θ 0 ≈ 90◦ is obtained almost instantaneously, indicating that the drop is initially deoxidized. Consequently, like the experiment performed in pure Ar, the spreading kinetics is limited by the substrate deoxidation occurring at the triple line according to reaction (1) and not by the deoxidation of the drop. Nevertheless, in this case the oxygen has a notable effect on spreading kinetics. Indeed, the spreading time is here twice as high as the spreading time for pure argon or Ar–100 ppm O2 . After cooling, the solidified droplet adheres to the substrate and the alloy/SiC interface is mechanically strong as in the previous case (see Fig. 4). A SEM image of the region close to the triple line (see Fig. 5) shows that the SiC surface is covered by a continuous oxide layer, a few microns thick, and reveals the presence of filamentous silica particles. Fig. 4 shows a shift in the alloy composition towards lower silicon content which is revealed by a change in its microstructure: from a slightly hypereutectic (cf. Fig. 2) to a hypoeutectic alloy indicated by the presence of CoSi2 dendrites (cf. Fig. 4). This loss of silicon in the alloy cannot be due to silicon evaporation because this phenomenon was not observed when using pure argon. Consequently, it is due to active oxidation of silicon

Fig. 5. SEM image of the region close to the triple line for a Co–72.5 at.% Si alloy on SiC (backscattered electron image). Ar–300 ppm O2 mixture is introduced at melting.

leading to the formation of the volatile silicon monoxide: 2(Si) + [O2 ] → 2[SiO]

(2)

followed by its transfer to the gas and to SiC surface in the vicinity of the triple line. As will be shown in the next section, at a certain distance from the drop surface, the SiO gas species leaving the drop (reaction (2)) reacts with oxygen from the gas atmosphere leading to the formation of silica particles observed in Fig. 5. The effect of oxygen is very marked for 1000 ppm O2 : the drop is visibly oxidized (passive oxidation) making the measured values of θ and R meaningless. These results indicate that a transition from active to passive oxidation of the Co–Si alloy occurs for an oxygen content in the gas between 300 and 1000 ppm. 3.3. Influence of oxidation during heating In order to study the influence of oxidation of Co–Si alloy on spreading kinetics during heating, the argon–oxygen mixtures are introduced right from the start of the heating cycle. Afterwards, the partial pressure of oxygen is kept constant until the end of the experiment. The thermal cycle is identical to that described in Section 2. Fig. 6 shows the wetting curves for different oxygen contents in the Ar–O2 mixture (10, 100 and 300 ppm O2 ) including the wetting curve for pure Ar. For all oxygen contents in Ar, the

Fig. 4. SEM image of a cross-section of a Co–72.5 at.% Si alloy on SiC (backscattered electron image). Ar–300 ppm O2 mixture is introduced at melting.

O. Mailliart et al. / Materials Science and Engineering A 495 (2008) 174–180

Fig. 6. Contact angle θ as a function of time for a Co–72.5 at.% Si alloy on SiC for different Ar–O2 mixtures (( ) pure Ar, () 10 ppm, () 100 ppm and (䊉) 300 ppm O2 ) introduced since the beginning of heating. t = 0 is taken to be the beginning of melting.

contact angle at melting θ 0 ≈ 140◦ is much higher than for pure Ar. For Ar–100 ppm O2 the spreading time is about five times longer than for pure argon while for 300 ppm O2 , the final contact angle is not attained even after 60 min of spreading. This slowdown in spreading kinetics is due to the presence of an oxide layer on the alloy surface that forms during heating. This explains the high non-wetting apparent contact angle close to 140◦ formed at melting (Figs. 6 and 7a). Afterwards, the liquid alloy becomes completely deoxidized after a certain time (Fig. 7c) and spreading continues until the final contact angle is attained (Fig. 7d). Note that, as before, this deoxidation process is accompanied by reformation of silicon oxide on the SiC surface in the region close to the drop. 4. Discussion 4.1. Summary of main experimental results - Wetting of SiC by Co–Si alloy needs above all a clean, oxidefree Si alloy. Once a clean alloy surface is obtained, the alloy can react at the solid–liquid–vapour triple line with the oxide layer covering SiC thus removing this wetting barrier. - A transition from active oxidation of Si alloy (SiO formation implying wetting) to passive oxidation (SiO2 formation implying non-wetting) occurs for an oxygen content in the gas between 300 and 1000 ppm. - Active oxidation of the drop leads to reformation of silicon oxide on the SiC surface around the drop. - The sample history (i.e., conditions used during heating) was found to have a strong influence on the surface condition of

177

Fig. 8. Formation of a clean alloy surface: active oxidation (b) and oxidized alloy surface: passive oxidation (c) starting from a broken oxide layer configuration (a)—schematic.

liquid alloy even for an oxygen content in the gas as low as 10 ppm. 4.2. Surface condition of Co–Si alloy The surface condition of Co–Si alloy will be discussed considering the configuration of a broken oxide layer (cf. Fig. 8a). In practice, this configuration can be obtained for a thick oxide layer broken under the effect of thermomechanical stress. Another case is a continuous but very thin layer (typically a few nanometers or tens of nanometers), such that diffusion through this layer is extremely rapid at high temperature. In both cases the alloy–silica–gas three-phase equilibrium is assumed to occur. For this configuration, the transition from active to passive oxidation will be calculated by assuming that diffusion in the gas is infinitely rapid in comparison with the processes at the liquid–vapour surface. With this assumption, the above transition can be defined by two quantities: - The partial pressure of SiO defined by the bivariant equis . Indeed, the librium (1): (Si) + → 2[SiO] noted PSiO number of independent constituents is three (Co, Si and oxygen) and the number of phases is also three (liquid alloy, solid SiO2 and gas). Thus if the temperature and alloy composition are fixed, the system is completely determined. g - The partial pressure of O2 in the Ar–O2 mixture noted PO2 . Note that reaction (1) results from the combination of the two following elementary reactions: < SiO2 > → (Si) + [O2 ]

(1a)

2(Si) + [O2 ] → 2[SiO]

(1b)

Fig. 7. Successive images of a Co–72.5 at.% Si drop on SiC showing its deoxidation and spreading as well as reformation of silicon oxide on the SiC surface in the region close to the drop. Experiment performed under Ar–100 ppm O2 mixture introduced from the very beginning of heating.

178

O. Mailliart et al. / Materials Science and Engineering A 495 (2008) 174–180

Fig. 9. Variation in partial pressures of oxygen and SiO for reaction (1) at equilibrium as a function of temperature. When the temperature is fixed, there is a g∗ threshold oxygen pressure in the gas PO2 above which oxidation is passive and below which oxidation is active.

The equilibrium conditions of reactions (1) and (1a) lead to:   −G◦1 1/2 s PSiO = aSi exp and 2RT   −G◦1a −1 s PO2 = aSi exp (3) RT G◦1 and G◦1a , the standard Gibbs energy of reactions (1) and (1a), are calculated using data from Ref. [10]. For T > 1259 ◦ C the Co–77.5 at.% Si alloy is liquid and silicon activity, aSi = 0.74, is calculated from data given in Ref. [11]. For T < 1259 ◦ C, silicon is solid and aSi = 1. s and P s with T are presented in Fig. 9. The variations of PSiO O2 Note that, regardless of the value of T, POs 2 is several orders g of magnitude lower than PO2 in the argon–oxygen mixtures g used. This clearly demonstrates that in the T and PO2 conditions described, obtaining an oxide-free Si alloy surface by decomposition of silica (reaction (1a)) is thermodynamically impossible. 4.2.1. Active oxidation s  P g (in practice this As it will be shown below, if PSiO O2 g s condition is indicative of a value of PSiO exceeding PO2 by a factor of ten and more), reaction (1) will be shifted towards the right leading to a clean metallic surface (see Fig. 8b). Active oxidation will occur by reaction (1b) on this surface. Knowing the partial pressures of SiO and O2 at the liquid surface, the SiO (ΦSiO ) and O2 (ΦO2 ) fluxes near the drop are evaluated. For this purpose, the oxygen concentration profile around the drop is described on the basis of the model developed in Ref. [12] in the case of laminar flow. This condition is satisfied in these experimental conditions as the Reynolds number Re = vDρ/η ≈ 1, calculated from data given in Table 1, is much lower

Fig. 10. Schematic presentation of the variation in partial pressures of oxygen and SiO close to the Co–Si alloy/gas interface (diffusion layer approximation).

than the critical value of 103 . The oxygen concentration around s value up to C δ at a distance the drop will increase from the CO O2 2 δ from this surface. The thickness of the diffusion layer, δ, can be determined from the mass transfer coefficient for the system gasdrop: δ = dd /Sh where Sh is the Sherwood number, Sh = kdd /D, relating the mass transfer coefficient k to the size of the system (in this case, the drop diameter dd ) and to the diffusion coefficient in the gas D. For a sphere, Sh is related to the Peclet number Ped = vdd /D and Schmidt number Sc = η/ρD by Sh = 2 + 0.6Re1/2 Sc1/3 [13]. Using data from Table 1, the Sherwood number value is close to 3 leading to δ ≈ dd /3 ≈ 1 mm. Under these conditions δ is given by: CO 2 g

δ = CO2 CO 2

f Peδ 1 + f Peδ

(4)

g

In this expression, CO2 is the oxygen concentration in the Ar–O2 mixture, Peδ = vδ/D is the Peclet number associated with the diffusion layer and f = dt2 /dd2 is a “shape factor” depending on the furnace tube diameter (dt ) and the drop diameter (dd ). δ ≈ 0.99 C g . This Using data from Table 1, Eq. (4) leads to CO O2 2 result shows that the oxygen (and SiO) concentration varies only within a diffusion layer of thickness δ ≈ 1 mm close to the drop. This situation is schematised in Fig. 10 according to which the condition of active oxidation expressed, from a general point of s  Pg . view, by ΦSiO  ΦO2 becomes PSiO O2 As Fig. 9 shows, at a fixed temperature T there is a threshold g∗ oxygen pressure in the gas PO2 above which oxidation is passive and below which oxidation is active. The predictions given by Fig. 9 are in quantitative agreement with experimental results showing that the transition from active to passive oxidation at 1260 ◦ C occurs for an oxygen content in the gas between 300 and 1000 ppm (i.e., g 3 × 10−4 < PO2 < 10−3 bar)—see Section 3.2. Note that when the active oxidation of Co–Si alloy occurs, SiO and O2 cannot

Table 1 Summary of parameters used in calculations dd (mm)

dt (mm)

Lt (mm)

D (m2 s−1 )

v (m s−1 )

ρ (kg m−3 )

η (Pa s)

Vm (m−3 mol−1 )

1

75

70

1.6 × 10−4 [17]

4.5 × 10−3

0.4

6.1 × 10−5 [17]

2.6 × 10−5 [18]

dd : drop diameter, dt : tube diameter, 2Lt : tube length, D: gas diffusivity, v: mean gas velocity, ρ: gas density, η: gas dynamic viscosity, Vm : silica molar volume.

O. Mailliart et al. / Materials Science and Engineering A 495 (2008) 174–180

179

Table 2 g s∗ SiO partial pressure PSiO (in bar) corresponding to reaction (5) at equilibrium at different T for two fixed values of PO2 (10−6 and 10−4 bar) and erosion rate of silica −1 de/dt (in nm s ) according to Eq. (6) PO2 →

10−6

10−4

(◦ C)

s∗ PSiO

de/dt

s∗ PSiO

de/dt

4 × 10−10

5 × 10−5

4 × 10−11

5 × 10−6 0.01

g

T

↓

1350 1600

9.4 × 10−7

9.4 × 10−8

0.1

s PSiO

de/dt

3.5 × 10−3 8.3 × 10−2

440 104

s For comparison purposes, the last columns give the SiO partial pressures for the three-phase equilibrium (1) PSiO and corresponding erosion rates.

react at the liquid surface to form SiO2 according to reaction 2[SiO] + [O2 ] → 2 because, as explained previously, under active oxidation conditions, silica is not stable in contact with the molten alloy. However, moving from the liquid surface to the gas (see Fig. 10), PSiO decreases while PO2 increases in such way that, at a certain distance from the liquid surface, 2 P the product PSiO O2 may become higher than the inverse of the equilibrium constant of reaction 2[SiO] + [O2 ] → 2, thus leading to silica precipitation inside the diffusion layer of thickness δ. This is in agreement with the experimental observations of silica formation at the SiC surface around the drop (Figs. 5 and 7). 4.2.2. Passive oxidation g s P g , a continuous If, for a fixed value of PO2 and T, PSiO O2 and dense oxide layer will build up and grow at the interface (see Fig. 8c) with the growth rate depending on the diffusion of oxygen through the silica layer towards the layer/alloy interface where silicon reacts with diffusing oxygen according to the inverse of reaction (1a) [14]. Indeed, during heating with oxygen containing Ar, oxidation of Si alloy is passive over g a wide temperature range. For instance, for PO2 = 10−4 bar, passive oxidation is predicted at T ≤ 1130 ◦ C (cf. Fig. 9). Consequently, thick oxide layers are expected to form during heating in oxygen-rich argon (cf. Fig. 7a). How can such an oxide layer be removed from the drop surface when, at higher temperatures, active oxidation becomes possible? A first possibility is by silica evaporation at the oxide/gas interface [15] according to the reaction: 2 < SiO2 > → 2[SiO] + [O2 ]

(5)

An upper limit of the erosion rate de/dt can be obtained by neglecting the growth rate at the oxide/alloy interface, which yields: Vm Dg s∗ de =− P dt RTδ SiO

(6)

s∗ , is the partial pressure of SiO at the oxide/gas interface, PSiO s∗ related to PO2 by the equilibrium condition of reaction (5). It g can easily be shown that POs∗2 is practically equal to PO2 . Some ∗ values of PSiO , obtained using data from Ref. [10], are listed in ∗ are several orders of magnitude Table 2. Note that values of PSiO g s lower than values of PSiO regardless of the value of T and PO2 . ◦ The application of relation (6) at 1350 C, with data given in Tables 1 and 2 leads to a negligible erosion rate even for an oxy-

gen content in the gas atmosphere as low as 1 ppm (see Table 2). This result clearly shows that, if a continuous and dense layer is formed at the surface of an Si alloy, this layer cannot be removed by evaporation even under high-purity neutral gas atmosphere, and even at temperatures as high as 1600 ◦ C. Another possible mechanism for oxide skin removal is the dissolution of silica in the molten alloy due to the increase in oxygen solubility in the alloy occurring at melting. However, for pure Si and Si-rich alloys this solubility remains extremely low [16], and this cannot explain the removal of oxide skins as thick as shown by Fig. 7. The only way to explain the observed removal of the oxide skin is to assume that this skin is broken under the effect of thermomechanical stress during heating and/or melting. Then, oxide removal takes place by the monovariant reaction (1). The only difference – but an important difference – is that diffusion of gas species will be slowed down, as diffusion occurs through defects (cracks) developed in the fragmented oxide. 5. Conclusions In the present investigation, the influence of oxygen content in argon (from a few ppm to 1000 ppm) on the wetting behaviour (contact angles, spreading kinetics) is studied in a model system consisting of SiC and Co–77.5 at.% Si alloy. In this system, in which both SiC and Si alloy are oxidizable materials, it is shown that wetting depends critically on the surface condition of the Si alloy. For example, once a clean, oxide-free Si alloy surface is obtained, the alloy promotes SiC deoxidation and wetting by reacting with the oxide layer covering this substrate (“reactive wetting”). In turn, the surface condition of an Si alloy at given temperature and PO2 depends critically on the type of oxidation, active or passive, occurring at its surface. At low temperatures, passive oxidation predominates leading to thickening of the oxide skin, a fact that hinders wetting and adhesion. Above a certain temperature, which is a function of PO2 , active oxidation takes over, leading to clean, oxide-free alloy surfaces, thereby promoting wetting and adhesion. The passive to active oxidation transition and the phenomena occurring in the vicinity of the sessile drop are successfully interpreted by a model taking into account the reactions at the liquid–vapour surface coupled with diffusion of reactive species in the gas. References [1] C. Rado, S. Kalogeropoulou, N. Eustathopoulos, Acta Mater. 47 (1999) 461–473.

180

O. Mailliart et al. / Materials Science and Engineering A 495 (2008) 174–180

[2] O. Dezellus, F. Hodaj, C. Rado, J.N. Barbier, N. Eustathopoulos, Acta Mater. 50 (2002) 979–991. [3] A. Ferrero, B. Derby, Acta Metall. Mater. 43 (1995) 3061–3073. [4] C. Iwamoto, S. Tanaka, Acta Mater. 50 (2002) 749–755. [5] A. Gasse, PhD Thesis, Institut National Polytechnique de Grenoble, France, 1996. [6] C. Rado, PhD Thesis, Institut National Polytechnique de Grenoble, France, 1997. [7] N. Eustathopoulos, M. Nicholas, B. Drevet, Wettability at High Temperatures, Pergamon Materials Series, 3, Pergamon, Oxford, 1999, pp. 265–278. [8] C. Rado, N. Eustathopoulos, Interface Sci. 12 (2004) 85–92. [9] R. Sangiorgi, M.L. Muolo, D. Chatain, N. Eustathopoulos, J. Am. Ceram. Soc. 71 (1988) 742–748. [10] Nist-Janaf Thermochemical Tables, J. Phys. Chem. Ref. Data, Monograph №9, Fourth Edition, American Chemical Society - American Institute of Physics, New York, 1998.

[11] O. Kubaschewski, C.B. Alcock, Metallurgical Thermochemistry, Pergamon Press, Oxford, 1979, pp. 394. [12] E. Ricci, A. Passerone, P. Castello, P. Costa, J. Mater. Sci. 29 (1994) 833–1846. [13] F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, fourth ed., John Wiley & Sons, 1996, pp. 374. [14] B.E. Deal, A.S. Grove, J. Appl. Phys. 36 (1965) 3770–3778. [15] C. Chatillon, L. Coudurier, N. Eustathopoulos, Mater. Sci. Forum 251–254 (1997) 701–708. [16] B. Hallstedt, Calphad 16 (1992) 53–61. [17] J.O. Hirchfilder, C.F. Curtis, R.B. Bird, Molecular Theory of Gases and Liquids, second ed., John Wiley, New York, 1965. [18] E.A. Brandes, G.B. Brook, Smithells Metals Reference Book, seventh ed., Butterworth-Heinemann, 1998, pp. 27–25.