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Wetting of polycrystalline MgO by molten Mg under evaporation
Materials Chemistry and Physics 122 (2010) 290–294
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Wetting of polycrystalline MgO by molten Mg under evaporation Ping Shen ∗ , Dan Zhang, Qiaoli Lin, Laixin Shi, Qichuan Jiang Key Laboratory of Automobile Materials of Ministry of Education, Department of Materials Science and Engineering, Jilin University, No. 5988 Renmin Street, Changchun 130025, Jilin, PR China
a r t i c l e
i n f o
Article history: Received 4 December 2009 Received in revised form 4 February 2010 Accepted 20 February 2010 Keywords: Wetting Magnesium Ceramics Evaporation
a b s t r a c t The concomitant wetting and evaporation behaviors of molten Mg on polycrystalline MgO surfaces were studied at temperatures 973–1173 K in a controlled Ar atmosphere using an improved sessile drop method. Representative wetting modes were identified by correlating contact angle with contact diameter and drop height. The intrinsic wettability in this nonreactive system can be characterized by the initial contact angles obtained in better precision from solution to a diffusion model. In addition, the excess free energy stored in the system and the potential energy barrier opposing the movement of the triple line were evaluated to account for the distinct “stick-slip” behavior. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The use of magnesium and its alloys as the matrix phase in metal matrix composites is of great interest as an alternative to aluminum-based composites for advanced structural applications such as in automobile and aerospace industries, with the significant advantages of low density, high specific strength and stiffness in combination with reasonable tribological performance and good machinability [1]. The Mg-matrix composites are usually prepared by casting and infiltration routes [1,2], in which the wettability between solid and liquid plays a key role in determining the processability and the quality of the final product. Compared with numerous studies on this issue for molten Al, much less has so far been known for molten Mg basically because of (i) easier oxidation of Mg surface at relative low temperatures (e.g., the critical oxygen partial pressure for the oxidation of the Mg surface is 6.79 × 10−48 Pa at 1073 K based on thermodynamic calculation [3]) and (ii) very high vapor pressure of Mg at elevated temperatures, leading to difficulty in measurement of the wettability and serious pollution of vacuum chamber. Despite the difficulty and pollution of the equipment, knowledge of the wetting of ceramics by molten Mg is highly valuable. It does not only provide helpful guidance for the preparation of Mgmatrix composites, but also concern, from a viewpoint of scientific research, the important issue of the wetting under evaporation at high temperatures. Previous studies on high-temperature capillarity mainly focus on less volatile materials, seldom concerning the
∗ Corresponding author. Tel.: +86 431 85094699; fax: +86 431 85094699. E-mail address: [email protected] (P. Shen). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.02.052
volatile substances such as Mg, Zn, Bi and Pb. However, as long as the atmosphere in the immediate vicinity of the drop is unsaturated with the vapor of the liquid, the occurrence of liquid evaporation is inevitable [4]. On the other hand, determination or assessment of the wettability when evaporation of the drop is involved, as will be shown in this work, is not straightforward but complex and difficult. Therefore, a comprehensive understanding of how evaporation influences the wetting behavior of a sessile drop is virtually not only important but also necessary in the research of fundamental aspects of wetting. In this work, we studied the wetting of polycrystalline magnesia (MgO) by molten Mg. MgO was selected as the substrate because it is readily available and stable with molten Mg at high temperatures, thus simplifying the wetting phenomena. A previous study performed by Fujii et al. [5] has shown a significant evaporation of the Mg drop and an unusual change in contact angle, i.e., a first decrease and then increase, for the molten Mg resting on the MgO surface at temperatures higher than 1173 K. They attributed this behavior to the pinning of the triple line at deep ditch and suggested that the intrinsic contact angles should be decided taking the initial values or the maximum ones just before the disappearance of the drop. Their observations and descriptions are important to us. Nevertheless, a clear picture for the wetting under evaporation was not presented and the nature behind the apparent behaviors not elucidated, making a further study warranted. 2. Experimental procedure The polycrystalline MgO (99.5% purity) substrates used were in dimensions of 20 mm × 20 mm × 5 mm. The surfaces were mechanically polished using diamond pastes down to 0.5 m to an average roughness (Ra ) of 100–150 nm, as measured by using a surface profilometer (DEKTAK 6M, Veeco Metrology Corp., NY) over a distance of 2 mm at a speed of 100 m s−1 . The Mg (99.99% purity) specimen was
P. Shen et al. / Materials Chemistry and Physics 122 (2010) 290–294
Fig. 1. Variations in the contact angle with time for molten Mg on the MgO surfaces during isothermal dwells at 973–1173 K.
in the form of small cubes weighing about 45–50 mg. The metal and the substrate were ultrasonically cleaned in acetone before being placed into a vacuum chamber. The wetting experiments were performed in a controlled flowing Ar (99.999%) atmosphere at a constant pressure of 0.12 MPa (flow rate: 0.5 l min−1 ) using an improved sessile drop method and a non-impingement dropping mode, as described in detail elsewhere [6,7]. The most significant feature of this method lies in the mechanical removal of the oxide film on the Mg surface by squeezing the liquid through a small hole (1 mm diameter) at the bottom of the alumina (99.5 wt.% purity) tube. The Ar gas was purified by passing through a magnesium (99.9%) furnace at 673 K, a dehydrating column filled with molecular sieves and finally an oxygenabsorption column filled with high effective palladium-type agents to reduce water and oxygen levels before being introduced into the chamber. To avoid the reaction between the alumina tube and magnesium, the inner of the bottom tube was preattacked by molten magnesium before it was used for the wetting experiment. On the other hand, to alleviate the pre-deposition of the substrate surface by the Mg vapor, the dwell time for the Mg specimen to melt in the bottom of the alumina tube was controlled to within 30–50 s, decreasing with increasing temperature, and moreover the stainless-steel chamber and the molybdenum shielding reflectors were carefully cleaned after each experiment. The contact angle (), contact diameter (d) and drop height (h) were measured from the captured high-resolution (300 pixels per inch) photographs using drop-analysis software. The volume change of the drop during evaporation was calculated by assuming an ideal spherical cap configuration. The experiment was stopped until the drop completely disappeared.
3. Results and discussion Fig. 1 shows the variations in contact angle () with time during isothermal dwells at temperatures 973–1173 K. As indicated, the initial contact angles are between 95◦ and 76◦ , decreasing with increasing temperature. The wettability of MgO by molten Mg is somewhat similar to that in the Al–Al2 O3 system [7], which also shows a transition from non-wetting to wetting with increasing temperature. In comparison, the initial contact angles measured in this study are approximately 10◦ smaller than those reported
291
by Fujii et al. [5], in whose experiments much larger Mg drops weighing about 0.3 g were used, which may cause gravity-induced flattening of the drop in the presence of wetting hysteresis. Another possibility is due to the larger oxygen partial pressure in their work, leading to the oxidation of the Mg drop surface. The decrease in the contact angle, as will be more clearly explicated later, is due to the evaporation of Mg, and the value of in question may be taken effectively as a receding one. Increasing temperature remarkably speedups the Mg evaporation, thus leading to a more rapid decrease in . It is interesting to note that when decreases to a certain value, it begins to increase. Such a “switch” is observed at all testing temperatures and the critical transition angle seems to be only mildly dependent on the temperature, even though scatter is obvious. The scatter could result from the different roughness of the MgO surfaces due to polishing. As increases to a maximum value, it decreases again at a much larger velocity when the temperature is high but remains almost constant for a period of time and then decreases sharply when the temperature is relatively low. In comparison, the contact angle behavior observed in this study is quite different from that reported by Fujii et al. [5], in which the contact angle did not change noticeably at 973 K but decreased monotonically at 1073 K. The unusual change in the contact angle of the initial decrease and then increase was observed only at temperatures higher than 1073 K. We presume that the different behaviors observed are primarily due to the difference in the oxygen partial pressure in the chamber and the drop mass in two experiments. In fact, the vapor pressure of Mg is strongly dependent on temperature, which increases dramatically at T > 1073 K and thus the drop has a self-cleaning effect on its surface. At T < 1073 K, however, the Mg vapor pressure is much lower, and as a result the drop surface may be re-oxidized after mechanical squeezing provided that the oxygen partial pressure in the chamber was not sufficiently low. In this case, the evaporation would reduce or eventually cease. On the other hand, the large drop mass prolonged drop lifetime, and thus increased opportunity for its oxidation, making the receding of the triple line more difficult. As a consequence, the “switch” of the contact angle from the initial decrease to the subsequent increase was seldom observed by Fujii et al. [5] at low temperatures (T ≤ 1073 K). Fig. 2a shows the variations in normalized drop volume, Vd /V0 (subscripts d and 0 represent the dynamic and initial states, respectively), with time at different temperatures. The drop volume first decreases linearly as a function of time in most of the evaporation stage and then shows a nonlinear behavior. If the behavior of the contact angle (Fig. 1) is correlated to that of the normalized drop volume (Fig. 2a), one can find that the linear variation in the drop volume corresponds to a constant decrease in the contact angle and the deviation from linearity corresponds to the sudden “switch” of the contact angle. Increasing temperature significantly accelerates the evaporation. It is possible to use a linear fitting of ln v
Fig. 2. (a) Variations in the normalized drop volume, Vd /V0 , with time for molten Mg on the MgO surfaces during isothermal dwells at 973–1173 K; (b) Arrhenius plot giving the activation energy for evaporation.
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Fig. 3. (a and c) Variations in , d and h with time and (b and d) schematic representations of the evolution of the Mg sessile drops at (a and b) 973 K and (c and d) 1123 K.
(where v = dV/dt) vs 1/T to calculate evaporation activation energy, as shown in Fig. 2b, giving a value of 127.2 kJ mol−1 . Fig. 3a shows the characteristic variations in contact angle (), contact diameter (d) and drop height (h) with time for the molten Mg drop on the MgO surface at 973 K. Four stages, in a rough sense, can be distinguished: (I) an initial decrease in h and while an increase in d; (II) a continuous decrease in h and while a constant d over most of the evaporation time; (III) a decrease in both h and d while an approximately constant ; and (IV) a rapid decrease in all parameters, , h and d. The decrease in is more marked in stage (I) than in stage (II) because of slight spreading (i.e., simultaneous increase in d and decrease in h) during the first tens of seconds, which is observed only in low-temperature (973–1023 K) experiments and is presumably related to the molten Mg surface deoxidation after dropping. In stage (II), decreases while the contact line holds its original position. When reaches a critical value, the drop de-pins and stage (III) starts. According to the variations in , d and h, this stage, in practice, can be divided again into three different cases: (i) d decreases as h increases simultaneously, and then increases slightly (labeled as III-a); (ii) both d and h decrease approximately in proportion, thus yielding a relatively constant value of (labeled as III-b). It is worth mentioning that this substage is also observed only at relatively low temperatures and the duration varies considerably with the substrates (e.g., in comparison with the behavior of in Fig. 1 at the same temperature), which is presumably influenced by surface roughness of the substrates. A smoother surface obviously favors its appearance and persistence; (iii) the magnitude of the decreasing rate of d is larger than that of h, and as a result, increases again (labeled as III-c). Finally, stage (IV) is found to be similar for all the substrates at all temperatures. This stage corresponds to the final disappearance of the Mg sessile drop, in which h, d and decrease rapidly and finally approach zero. A general scheme of the evolution of the molten Mg sessile drop at 973 K is presented in Fig. 3b. Fig. 3c shows the time variations in , d and h for the wetting at 1123 K. Compared with that at 973 K, the evolution behavior does not vary significantly. Stages (I) and (III), corresponding to stages (II) and (IV) in Fig. 3a, respectively, are essentially the same, but the initial spreading of the drop (i.e., stage (I) in Fig. 3a) is absent because of much higher vapor pressure of Mg at 1123 K, thus precluding its surface oxidation. Moreover, stage (II) presents a new
feature and can be divided into two sub-stages: stage (II-a) is similar to that described before (corresponding to stage (III-a) in Fig. 3a); whereas, stage (II-b) is distinct, where a rapid decrease in d leads to a significant increase in , while h remains almost constant. A general scheme of the evolution of the drop at 1123 K is presented in Fig. 3d. As we have mentioned earlier, because of the Mg evaporation, determination of the intrinsic wettability in the nonreactive Mg–MgO system is somewhat difficult. Fujii et al. [5] suggested that the intrinsic contact angles should be decided using the initial values or the maximum ones just before the disappearance of the drop. However, due to wetting hysteresis, the observed maximum receding angles are usually not accurate enough. The initial contact angles may be more reasonable for characterization of the wettability for an inert evaporating system, as long as the drop and the substrate surfaces are clean (i.e., free of oxidation and other contaminations). On the other hand, if the drop evaporation can be adequately modeled, then it is possible to precisely predict the true initial contact angles. For the sessile drop remaining a constant contact diameter with diminishing contact angles, a diffusion-controlled evaporation model has been established by assuming a spherical cap geometry and neglecting the effect of convection [4]. The time variation in contact angle could be written as [4]: 8D(c∞ − c0 ) sin3 d =− , dt d2 (1 − cos )
(1)
where D is the diffusion coefficient, c0 and c∞ are the concentrations of the vapor at the drop surface and infinite distance, and is the density of the drop. By integrating this equation, one obtains an angular function, F(), on one side and the diffusion parameters on the other side:
F() = ln tan
2
+
(1 − cos ) 16D(c∞ − c0 )(t − t0 ) , =− sin2 d2
(2)
where t0 is the time constant of integration. Fig. 4 shows the plots of F() against time and against at different wetting temperatures using the contact angles before the appearance of the de-pinning (Fig. 1). It can be seen that the contact angles ranging between 95◦ and 30◦ fit well a linear line, regardless of temperature. However, deviation from linearity at smaller
P. Shen et al. / Materials Chemistry and Physics 122 (2010) 290–294
293
Fig. 4. Plots of F() against (a) time (t) and (b) contact angle () for molten Mg on the MgO surfaces in the constant contact diameter stages at 973–1173 K.
contact angles is also observed, which is presumably due to the difficulty in maintaining its spherical shape when the drop decreases to a sufficiently small size. The more accurate initial contact angles can be predicted from the linear regression equations of F() ∼ t providing t = 0 (Fig. 4a) in combination with the linear relationships of F() ∼ (Fig. 4b), giving the values between 90◦ and 76◦ , as shown in Table 1, in generally well consistent with the experimental results. On the other hand, the diffusion coefficients of the magnesium vapor, D, could be calculated from the slopes of Eq. (2) assuming c0 = PM/RT, where P is the saturation vapor pressure, M is the molecular weight of Mg, R is the gas constant, and T is the absolute temperature, respectively. The values of the necessary parameters [8,9] for the calculation together with the calculated results are given in Table 1. The calculated values of D are of the order of 10−6 to 10−5 cm2 s−1 . Nevertheless, they do not show a sound dependence on temperature, invalidating the calculation of diffusion activation energy. A possible error may come from the initial contact diameter (e.g., distortion may occur when the Mg surface oxidation exists) since D strongly depends on it [see Eq. (2)]. In addition, the effect of convection on the Mg evaporation cannot be completely neglected since the experiments were performed in a flowing Ar atmosphere. Moreover, the evaporation led to the decrease in the temperature at the drop surface. Due to presence of the temperature gradient, Marangoni motion would occur at the free surface, which may also exert an influence on the evaporation rate. Additionally, it is of particular interest to concern the de-pinning of the triple line observed in this study. The substrate surfaces, particularly for the polycrystalline ceramics, are usually rough and inhomogeneous due to presence of various defects such as scratches and voids, and thus the pinning can be observed in most cases. From the viewpoint of mechanics, wetting could be described by a competition between capillary and friction forces. As decreases while d remains constant, the horizontal component of liquid surface tension increases. It can overcome the friction force and break the wetting balance when reaches a critical value, and thus the drop de-pins. On the other hand, if one looks from the viewpoint of energy, the drop tends to keep a spherical geometry to minimize its surface excess energy. If the drop is pinned while its volume decreases due to evaporation, the excess free energy, G, defined as the difference between equilibrium and
experimentally observed free energies at any time as a result of the departure of the drop dimensions from capillary equilibrium, will build up. When it exceeds the energy barrier, the drop de-pins. Quantitatively, assuming that the drop maintains the spherical cap geometry during the evaporation and lack of capillary equilibrium is the sole source of energy giving rise to the subsequent de-pinning, the excess free energy could be evaluated based on the ideas of Shanahan [10] and Denison and Boxall [11] as follows. Drop volume, V, and liquid/vapor surface area, Alv , are given by 2
V=
r 3 (1 − cos ) (2 + cos ) , 3 sin3
Alv =
(3)
2r 2 , (1 + cos )
(4)
where r is the contact radius of the drop. When the drop recedes, the solid–liquid interface is changed to a free solid surface. The change in area dAsl = 2rdr leads to a change in surface energy ( sv − sl )dAsl . In addition, the surface area of the liquid–gas interface changes. Thus, we can write the total change in the Gibbs free energy as dG = lv dAlv + (sv − sl )dAsl .
(5)
Regarding dr < 0, to within an additive constant, the associated Gibbs free energy, G, is given by G = lv Alv + r 2 (sl − sv ) = lv r 2
2 − cos 0 . (1 + cos )
(6)
The time variation in G could be calculated using the available data of lv , r, and 0 (using the values of calculated shown in Table 1). On the other hand, provided that the substrate surfaces were extremely smooth and chemically homogeneous, no pinning would occur and the drops move in a constant contact angle mode ( = 0 ) during evaporation. The hypothetical equilibrium drop contact radius, rhyp , as a function of time could then be obtained using Eq. (3) and the known data of V and 0 . Furthermore, using Eq.(4), 0 and rhyp , the time dependence of Ghyp during the evaporation process could be calculated as follows: 2 Ghyp = lv rhyp
2 − cos 0 . (1 + cos 0 )
(7)
Table 1 Parameters for calculation and the calculated results. T (K)
d (cm)
[8] (g cm−3 )
lv [8] (mN m−1 )
Ps [9] (Pa)
meaured (◦ )
calcualted (◦ )
D (cm2 s−1 )
973 1023 1073 1123 1173
0.4708 0.4913 0.4210 0.4970 0.4976
1.577 1.564 1.551 1.538 1.525
564 551 538 525 512
875.3 1953.1 4030.9 7776.8 14148.3
95.4 94.8 88.1 85.8 76.5
90.2 86.1 86.6 85.9 76.5
6.40E−6 8.95E−6 6.76E−6 7.26E−6 9.53E−6
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P. Shen et al. / Materials Chemistry and Physics 122 (2010) 290–294
of 10−4 J m−1 and affected mainly by the surface inhomogeneities of the substrates rather than by the temperature. The influence of temperature on U is largely embodied by lv in Eq. (9), which decreases with increasing temperature; however, this is not the case in U, as indicated in Fig. 5. 4. Summary
Fig. 5. Time dependence of G calculated from Eq. (9) for the molten Mg drops on the MgO surfaces during evaporation at 973–1173 K. The maximum value corresponds to the potential energy barrier, U.
As a consequence, the excess free energy, G, could be derived from Eqs. (6) and (7):
G = G − Ghyp = lv
2 2rhyp 2r 2 − (1 + cos ) (1 + cos 0 )
2 −(r 2 − rhyp ) cos 0
Acknowledgements .
(8)
Then, the excess free energy per unit length of triple line, G, could be written as
G G = = lv 2r r
−
2 rhyp r2 − (1 + cos ) (1 + cos 0 )
2 ) cos (r 2 − rhyp 0
2
.
The wettability of MgO by molten Mg can be characterized by the initial contact angles between 90◦ and 76◦ at temperatures 973–1173 K, decreasing with increasing temperature. The volume loss of the Mg sessile drop is linear with time for most of the lifetime with an evaporation activation energy of 127.2 kJ mol−1 . Representative modes, in particular, a constant contact diameter with diminishing contact angle and a constant contact angle with diminishing contact diameter, were identified for the wetting under evaporation. A simple diffusion model based on the spherical cap geometry could be used to evaluate the initial contact angles in better precision and to estimate the diffusion rate of the Mg vapor. Moreover, the distinct “stick-slip” behavior during evaporation was explained by the competition between the excess free energy stored within the system and the hysteretic energy barrier opposing the movement of the triple line, which is of the order of 10−4 J m−1 , primarily depending on the surface inhomogeneities of the substrates.
(9)
Fig. 5 shows the calculated values of G as a function of time at various temperatures. As indicated, during evaporation, G increases for a pinned triple line until it just exceeds the potential energy barrier, U, associated with surface inhomogeneities, either physical or chemical, of the polycrystalline MgO substrates. At this moment, the triple line de-pins and recedes, leading to a decrease in contact radius and an increase in contact angle; consequently, G decreases. However, it never immediately approaches zero since the original 0 was no longer regained after de-pinning (Fig. 1). Moreover, the maximum G shown in Fig. 5 could be approximated as the potential energy barrier, U, which are of the order
One of the authors (P. Shen) is grateful to Profs. K. Nogi and H. Fujii in Joining and Welding Research Institute (JWRI), Osaka University, Japan for their guidance in leading him to the interesting field of high-temperature wettability. This work is supported by National Natural Science Foundation of China (No. 50871045) and the Key Project of Chinese Ministry of Education (No. 108043). References [1] V. Kevorkijan, Metall. Mater. Trans. A 35A (2007) 707. [2] H.Z. Ye, X.Y. Liu, J. Mater. Sci. 39 (2004) 6153. [3] I. Barin, Thermochemical Data of Pure Substances, 3rd ed., Wiley–VCH Verlag GmbH, Weinheim, 1995. [4] H.Y. Erbil, Surface Chemistry of Solid and Liquid Interfaces, Blackwell Publishing, Oxford, 2006. [5] H. Fujii, S. Izutani, T. Matsumoto, S. Kiguchi, K. Nogi, Mater. Sci. Eng. A 417 (2006) 99. [6] H. Fujii, H. Nakae, K. Okada, Acta Metall. Mater. 41 (1993) 2963. [7] P. Shen, H. Fujii, T. Matsumoto, K. Nogi, J. Am. Ceram. Soc. 87 (2004) 2151. [8] K.C. Mills, Recommended Values of Thermophysical Properties for Selected Commercial Alloys, Woodhead Publishing Ltd., Cambridge, 2002. [9] T. Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, 1993. [10] M.E.R. Shanahan, Langmuir 11 (1995) 1041. [11] K.R. Denison, C. Boxall, Langmuir 23 (2007) 4358.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Wetting of polycrystalline MgO by molten Mg under evaporation Ping Shen ∗ , Dan Zhang, Qiaoli Lin, Laixin Shi, Qichuan Jiang Key Laboratory of Automobile Materials of Ministry of Education, Department of Materials Science and Engineering, Jilin University, No. 5988 Renmin Street, Changchun 130025, Jilin, PR China
a r t i c l e
i n f o
Article history: Received 4 December 2009 Received in revised form 4 February 2010 Accepted 20 February 2010 Keywords: Wetting Magnesium Ceramics Evaporation
a b s t r a c t The concomitant wetting and evaporation behaviors of molten Mg on polycrystalline MgO surfaces were studied at temperatures 973–1173 K in a controlled Ar atmosphere using an improved sessile drop method. Representative wetting modes were identified by correlating contact angle with contact diameter and drop height. The intrinsic wettability in this nonreactive system can be characterized by the initial contact angles obtained in better precision from solution to a diffusion model. In addition, the excess free energy stored in the system and the potential energy barrier opposing the movement of the triple line were evaluated to account for the distinct “stick-slip” behavior. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The use of magnesium and its alloys as the matrix phase in metal matrix composites is of great interest as an alternative to aluminum-based composites for advanced structural applications such as in automobile and aerospace industries, with the significant advantages of low density, high specific strength and stiffness in combination with reasonable tribological performance and good machinability [1]. The Mg-matrix composites are usually prepared by casting and infiltration routes [1,2], in which the wettability between solid and liquid plays a key role in determining the processability and the quality of the final product. Compared with numerous studies on this issue for molten Al, much less has so far been known for molten Mg basically because of (i) easier oxidation of Mg surface at relative low temperatures (e.g., the critical oxygen partial pressure for the oxidation of the Mg surface is 6.79 × 10−48 Pa at 1073 K based on thermodynamic calculation [3]) and (ii) very high vapor pressure of Mg at elevated temperatures, leading to difficulty in measurement of the wettability and serious pollution of vacuum chamber. Despite the difficulty and pollution of the equipment, knowledge of the wetting of ceramics by molten Mg is highly valuable. It does not only provide helpful guidance for the preparation of Mgmatrix composites, but also concern, from a viewpoint of scientific research, the important issue of the wetting under evaporation at high temperatures. Previous studies on high-temperature capillarity mainly focus on less volatile materials, seldom concerning the
∗ Corresponding author. Tel.: +86 431 85094699; fax: +86 431 85094699. E-mail address: [email protected] (P. Shen). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.02.052
volatile substances such as Mg, Zn, Bi and Pb. However, as long as the atmosphere in the immediate vicinity of the drop is unsaturated with the vapor of the liquid, the occurrence of liquid evaporation is inevitable [4]. On the other hand, determination or assessment of the wettability when evaporation of the drop is involved, as will be shown in this work, is not straightforward but complex and difficult. Therefore, a comprehensive understanding of how evaporation influences the wetting behavior of a sessile drop is virtually not only important but also necessary in the research of fundamental aspects of wetting. In this work, we studied the wetting of polycrystalline magnesia (MgO) by molten Mg. MgO was selected as the substrate because it is readily available and stable with molten Mg at high temperatures, thus simplifying the wetting phenomena. A previous study performed by Fujii et al. [5] has shown a significant evaporation of the Mg drop and an unusual change in contact angle, i.e., a first decrease and then increase, for the molten Mg resting on the MgO surface at temperatures higher than 1173 K. They attributed this behavior to the pinning of the triple line at deep ditch and suggested that the intrinsic contact angles should be decided taking the initial values or the maximum ones just before the disappearance of the drop. Their observations and descriptions are important to us. Nevertheless, a clear picture for the wetting under evaporation was not presented and the nature behind the apparent behaviors not elucidated, making a further study warranted. 2. Experimental procedure The polycrystalline MgO (99.5% purity) substrates used were in dimensions of 20 mm × 20 mm × 5 mm. The surfaces were mechanically polished using diamond pastes down to 0.5 m to an average roughness (Ra ) of 100–150 nm, as measured by using a surface profilometer (DEKTAK 6M, Veeco Metrology Corp., NY) over a distance of 2 mm at a speed of 100 m s−1 . The Mg (99.99% purity) specimen was
P. Shen et al. / Materials Chemistry and Physics 122 (2010) 290–294
Fig. 1. Variations in the contact angle with time for molten Mg on the MgO surfaces during isothermal dwells at 973–1173 K.
in the form of small cubes weighing about 45–50 mg. The metal and the substrate were ultrasonically cleaned in acetone before being placed into a vacuum chamber. The wetting experiments were performed in a controlled flowing Ar (99.999%) atmosphere at a constant pressure of 0.12 MPa (flow rate: 0.5 l min−1 ) using an improved sessile drop method and a non-impingement dropping mode, as described in detail elsewhere [6,7]. The most significant feature of this method lies in the mechanical removal of the oxide film on the Mg surface by squeezing the liquid through a small hole (1 mm diameter) at the bottom of the alumina (99.5 wt.% purity) tube. The Ar gas was purified by passing through a magnesium (99.9%) furnace at 673 K, a dehydrating column filled with molecular sieves and finally an oxygenabsorption column filled with high effective palladium-type agents to reduce water and oxygen levels before being introduced into the chamber. To avoid the reaction between the alumina tube and magnesium, the inner of the bottom tube was preattacked by molten magnesium before it was used for the wetting experiment. On the other hand, to alleviate the pre-deposition of the substrate surface by the Mg vapor, the dwell time for the Mg specimen to melt in the bottom of the alumina tube was controlled to within 30–50 s, decreasing with increasing temperature, and moreover the stainless-steel chamber and the molybdenum shielding reflectors were carefully cleaned after each experiment. The contact angle (), contact diameter (d) and drop height (h) were measured from the captured high-resolution (300 pixels per inch) photographs using drop-analysis software. The volume change of the drop during evaporation was calculated by assuming an ideal spherical cap configuration. The experiment was stopped until the drop completely disappeared.
3. Results and discussion Fig. 1 shows the variations in contact angle () with time during isothermal dwells at temperatures 973–1173 K. As indicated, the initial contact angles are between 95◦ and 76◦ , decreasing with increasing temperature. The wettability of MgO by molten Mg is somewhat similar to that in the Al–Al2 O3 system [7], which also shows a transition from non-wetting to wetting with increasing temperature. In comparison, the initial contact angles measured in this study are approximately 10◦ smaller than those reported
291
by Fujii et al. [5], in whose experiments much larger Mg drops weighing about 0.3 g were used, which may cause gravity-induced flattening of the drop in the presence of wetting hysteresis. Another possibility is due to the larger oxygen partial pressure in their work, leading to the oxidation of the Mg drop surface. The decrease in the contact angle, as will be more clearly explicated later, is due to the evaporation of Mg, and the value of in question may be taken effectively as a receding one. Increasing temperature remarkably speedups the Mg evaporation, thus leading to a more rapid decrease in . It is interesting to note that when decreases to a certain value, it begins to increase. Such a “switch” is observed at all testing temperatures and the critical transition angle seems to be only mildly dependent on the temperature, even though scatter is obvious. The scatter could result from the different roughness of the MgO surfaces due to polishing. As increases to a maximum value, it decreases again at a much larger velocity when the temperature is high but remains almost constant for a period of time and then decreases sharply when the temperature is relatively low. In comparison, the contact angle behavior observed in this study is quite different from that reported by Fujii et al. [5], in which the contact angle did not change noticeably at 973 K but decreased monotonically at 1073 K. The unusual change in the contact angle of the initial decrease and then increase was observed only at temperatures higher than 1073 K. We presume that the different behaviors observed are primarily due to the difference in the oxygen partial pressure in the chamber and the drop mass in two experiments. In fact, the vapor pressure of Mg is strongly dependent on temperature, which increases dramatically at T > 1073 K and thus the drop has a self-cleaning effect on its surface. At T < 1073 K, however, the Mg vapor pressure is much lower, and as a result the drop surface may be re-oxidized after mechanical squeezing provided that the oxygen partial pressure in the chamber was not sufficiently low. In this case, the evaporation would reduce or eventually cease. On the other hand, the large drop mass prolonged drop lifetime, and thus increased opportunity for its oxidation, making the receding of the triple line more difficult. As a consequence, the “switch” of the contact angle from the initial decrease to the subsequent increase was seldom observed by Fujii et al. [5] at low temperatures (T ≤ 1073 K). Fig. 2a shows the variations in normalized drop volume, Vd /V0 (subscripts d and 0 represent the dynamic and initial states, respectively), with time at different temperatures. The drop volume first decreases linearly as a function of time in most of the evaporation stage and then shows a nonlinear behavior. If the behavior of the contact angle (Fig. 1) is correlated to that of the normalized drop volume (Fig. 2a), one can find that the linear variation in the drop volume corresponds to a constant decrease in the contact angle and the deviation from linearity corresponds to the sudden “switch” of the contact angle. Increasing temperature significantly accelerates the evaporation. It is possible to use a linear fitting of ln v
Fig. 2. (a) Variations in the normalized drop volume, Vd /V0 , with time for molten Mg on the MgO surfaces during isothermal dwells at 973–1173 K; (b) Arrhenius plot giving the activation energy for evaporation.
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Fig. 3. (a and c) Variations in , d and h with time and (b and d) schematic representations of the evolution of the Mg sessile drops at (a and b) 973 K and (c and d) 1123 K.
(where v = dV/dt) vs 1/T to calculate evaporation activation energy, as shown in Fig. 2b, giving a value of 127.2 kJ mol−1 . Fig. 3a shows the characteristic variations in contact angle (), contact diameter (d) and drop height (h) with time for the molten Mg drop on the MgO surface at 973 K. Four stages, in a rough sense, can be distinguished: (I) an initial decrease in h and while an increase in d; (II) a continuous decrease in h and while a constant d over most of the evaporation time; (III) a decrease in both h and d while an approximately constant ; and (IV) a rapid decrease in all parameters, , h and d. The decrease in is more marked in stage (I) than in stage (II) because of slight spreading (i.e., simultaneous increase in d and decrease in h) during the first tens of seconds, which is observed only in low-temperature (973–1023 K) experiments and is presumably related to the molten Mg surface deoxidation after dropping. In stage (II), decreases while the contact line holds its original position. When reaches a critical value, the drop de-pins and stage (III) starts. According to the variations in , d and h, this stage, in practice, can be divided again into three different cases: (i) d decreases as h increases simultaneously, and then increases slightly (labeled as III-a); (ii) both d and h decrease approximately in proportion, thus yielding a relatively constant value of (labeled as III-b). It is worth mentioning that this substage is also observed only at relatively low temperatures and the duration varies considerably with the substrates (e.g., in comparison with the behavior of in Fig. 1 at the same temperature), which is presumably influenced by surface roughness of the substrates. A smoother surface obviously favors its appearance and persistence; (iii) the magnitude of the decreasing rate of d is larger than that of h, and as a result, increases again (labeled as III-c). Finally, stage (IV) is found to be similar for all the substrates at all temperatures. This stage corresponds to the final disappearance of the Mg sessile drop, in which h, d and decrease rapidly and finally approach zero. A general scheme of the evolution of the molten Mg sessile drop at 973 K is presented in Fig. 3b. Fig. 3c shows the time variations in , d and h for the wetting at 1123 K. Compared with that at 973 K, the evolution behavior does not vary significantly. Stages (I) and (III), corresponding to stages (II) and (IV) in Fig. 3a, respectively, are essentially the same, but the initial spreading of the drop (i.e., stage (I) in Fig. 3a) is absent because of much higher vapor pressure of Mg at 1123 K, thus precluding its surface oxidation. Moreover, stage (II) presents a new
feature and can be divided into two sub-stages: stage (II-a) is similar to that described before (corresponding to stage (III-a) in Fig. 3a); whereas, stage (II-b) is distinct, where a rapid decrease in d leads to a significant increase in , while h remains almost constant. A general scheme of the evolution of the drop at 1123 K is presented in Fig. 3d. As we have mentioned earlier, because of the Mg evaporation, determination of the intrinsic wettability in the nonreactive Mg–MgO system is somewhat difficult. Fujii et al. [5] suggested that the intrinsic contact angles should be decided using the initial values or the maximum ones just before the disappearance of the drop. However, due to wetting hysteresis, the observed maximum receding angles are usually not accurate enough. The initial contact angles may be more reasonable for characterization of the wettability for an inert evaporating system, as long as the drop and the substrate surfaces are clean (i.e., free of oxidation and other contaminations). On the other hand, if the drop evaporation can be adequately modeled, then it is possible to precisely predict the true initial contact angles. For the sessile drop remaining a constant contact diameter with diminishing contact angles, a diffusion-controlled evaporation model has been established by assuming a spherical cap geometry and neglecting the effect of convection [4]. The time variation in contact angle could be written as [4]: 8D(c∞ − c0 ) sin3 d =− , dt d2 (1 − cos )
(1)
where D is the diffusion coefficient, c0 and c∞ are the concentrations of the vapor at the drop surface and infinite distance, and is the density of the drop. By integrating this equation, one obtains an angular function, F(), on one side and the diffusion parameters on the other side:
F() = ln tan
2
+
(1 − cos ) 16D(c∞ − c0 )(t − t0 ) , =− sin2 d2
(2)
where t0 is the time constant of integration. Fig. 4 shows the plots of F() against time and against at different wetting temperatures using the contact angles before the appearance of the de-pinning (Fig. 1). It can be seen that the contact angles ranging between 95◦ and 30◦ fit well a linear line, regardless of temperature. However, deviation from linearity at smaller
P. Shen et al. / Materials Chemistry and Physics 122 (2010) 290–294
293
Fig. 4. Plots of F() against (a) time (t) and (b) contact angle () for molten Mg on the MgO surfaces in the constant contact diameter stages at 973–1173 K.
contact angles is also observed, which is presumably due to the difficulty in maintaining its spherical shape when the drop decreases to a sufficiently small size. The more accurate initial contact angles can be predicted from the linear regression equations of F() ∼ t providing t = 0 (Fig. 4a) in combination with the linear relationships of F() ∼ (Fig. 4b), giving the values between 90◦ and 76◦ , as shown in Table 1, in generally well consistent with the experimental results. On the other hand, the diffusion coefficients of the magnesium vapor, D, could be calculated from the slopes of Eq. (2) assuming c0 = PM/RT, where P is the saturation vapor pressure, M is the molecular weight of Mg, R is the gas constant, and T is the absolute temperature, respectively. The values of the necessary parameters [8,9] for the calculation together with the calculated results are given in Table 1. The calculated values of D are of the order of 10−6 to 10−5 cm2 s−1 . Nevertheless, they do not show a sound dependence on temperature, invalidating the calculation of diffusion activation energy. A possible error may come from the initial contact diameter (e.g., distortion may occur when the Mg surface oxidation exists) since D strongly depends on it [see Eq. (2)]. In addition, the effect of convection on the Mg evaporation cannot be completely neglected since the experiments were performed in a flowing Ar atmosphere. Moreover, the evaporation led to the decrease in the temperature at the drop surface. Due to presence of the temperature gradient, Marangoni motion would occur at the free surface, which may also exert an influence on the evaporation rate. Additionally, it is of particular interest to concern the de-pinning of the triple line observed in this study. The substrate surfaces, particularly for the polycrystalline ceramics, are usually rough and inhomogeneous due to presence of various defects such as scratches and voids, and thus the pinning can be observed in most cases. From the viewpoint of mechanics, wetting could be described by a competition between capillary and friction forces. As decreases while d remains constant, the horizontal component of liquid surface tension increases. It can overcome the friction force and break the wetting balance when reaches a critical value, and thus the drop de-pins. On the other hand, if one looks from the viewpoint of energy, the drop tends to keep a spherical geometry to minimize its surface excess energy. If the drop is pinned while its volume decreases due to evaporation, the excess free energy, G, defined as the difference between equilibrium and
experimentally observed free energies at any time as a result of the departure of the drop dimensions from capillary equilibrium, will build up. When it exceeds the energy barrier, the drop de-pins. Quantitatively, assuming that the drop maintains the spherical cap geometry during the evaporation and lack of capillary equilibrium is the sole source of energy giving rise to the subsequent de-pinning, the excess free energy could be evaluated based on the ideas of Shanahan [10] and Denison and Boxall [11] as follows. Drop volume, V, and liquid/vapor surface area, Alv , are given by 2
V=
r 3 (1 − cos ) (2 + cos ) , 3 sin3
Alv =
(3)
2r 2 , (1 + cos )
(4)
where r is the contact radius of the drop. When the drop recedes, the solid–liquid interface is changed to a free solid surface. The change in area dAsl = 2rdr leads to a change in surface energy ( sv − sl )dAsl . In addition, the surface area of the liquid–gas interface changes. Thus, we can write the total change in the Gibbs free energy as dG = lv dAlv + (sv − sl )dAsl .
(5)
Regarding dr < 0, to within an additive constant, the associated Gibbs free energy, G, is given by G = lv Alv + r 2 (sl − sv ) = lv r 2
2 − cos 0 . (1 + cos )
(6)
The time variation in G could be calculated using the available data of lv , r, and 0 (using the values of calculated shown in Table 1). On the other hand, provided that the substrate surfaces were extremely smooth and chemically homogeneous, no pinning would occur and the drops move in a constant contact angle mode ( = 0 ) during evaporation. The hypothetical equilibrium drop contact radius, rhyp , as a function of time could then be obtained using Eq. (3) and the known data of V and 0 . Furthermore, using Eq.(4), 0 and rhyp , the time dependence of Ghyp during the evaporation process could be calculated as follows: 2 Ghyp = lv rhyp
2 − cos 0 . (1 + cos 0 )
(7)
Table 1 Parameters for calculation and the calculated results. T (K)
d (cm)
[8] (g cm−3 )
lv [8] (mN m−1 )
Ps [9] (Pa)
meaured (◦ )
calcualted (◦ )
D (cm2 s−1 )
973 1023 1073 1123 1173
0.4708 0.4913 0.4210 0.4970 0.4976
1.577 1.564 1.551 1.538 1.525
564 551 538 525 512
875.3 1953.1 4030.9 7776.8 14148.3
95.4 94.8 88.1 85.8 76.5
90.2 86.1 86.6 85.9 76.5
6.40E−6 8.95E−6 6.76E−6 7.26E−6 9.53E−6
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of 10−4 J m−1 and affected mainly by the surface inhomogeneities of the substrates rather than by the temperature. The influence of temperature on U is largely embodied by lv in Eq. (9), which decreases with increasing temperature; however, this is not the case in U, as indicated in Fig. 5. 4. Summary
Fig. 5. Time dependence of G calculated from Eq. (9) for the molten Mg drops on the MgO surfaces during evaporation at 973–1173 K. The maximum value corresponds to the potential energy barrier, U.
As a consequence, the excess free energy, G, could be derived from Eqs. (6) and (7):
G = G − Ghyp = lv
2 2rhyp 2r 2 − (1 + cos ) (1 + cos 0 )
2 −(r 2 − rhyp ) cos 0
Acknowledgements .
(8)
Then, the excess free energy per unit length of triple line, G, could be written as
G G = = lv 2r r
−
2 rhyp r2 − (1 + cos ) (1 + cos 0 )
2 ) cos (r 2 − rhyp 0
2
.
The wettability of MgO by molten Mg can be characterized by the initial contact angles between 90◦ and 76◦ at temperatures 973–1173 K, decreasing with increasing temperature. The volume loss of the Mg sessile drop is linear with time for most of the lifetime with an evaporation activation energy of 127.2 kJ mol−1 . Representative modes, in particular, a constant contact diameter with diminishing contact angle and a constant contact angle with diminishing contact diameter, were identified for the wetting under evaporation. A simple diffusion model based on the spherical cap geometry could be used to evaluate the initial contact angles in better precision and to estimate the diffusion rate of the Mg vapor. Moreover, the distinct “stick-slip” behavior during evaporation was explained by the competition between the excess free energy stored within the system and the hysteretic energy barrier opposing the movement of the triple line, which is of the order of 10−4 J m−1 , primarily depending on the surface inhomogeneities of the substrates.
(9)
Fig. 5 shows the calculated values of G as a function of time at various temperatures. As indicated, during evaporation, G increases for a pinned triple line until it just exceeds the potential energy barrier, U, associated with surface inhomogeneities, either physical or chemical, of the polycrystalline MgO substrates. At this moment, the triple line de-pins and recedes, leading to a decrease in contact radius and an increase in contact angle; consequently, G decreases. However, it never immediately approaches zero since the original 0 was no longer regained after de-pinning (Fig. 1). Moreover, the maximum G shown in Fig. 5 could be approximated as the potential energy barrier, U, which are of the order
One of the authors (P. Shen) is grateful to Profs. K. Nogi and H. Fujii in Joining and Welding Research Institute (JWRI), Osaka University, Japan for their guidance in leading him to the interesting field of high-temperature wettability. This work is supported by National Natural Science Foundation of China (No. 50871045) and the Key Project of Chinese Ministry of Education (No. 108043). References [1] V. Kevorkijan, Metall. Mater. Trans. A 35A (2007) 707. [2] H.Z. Ye, X.Y. Liu, J. Mater. Sci. 39 (2004) 6153. [3] I. Barin, Thermochemical Data of Pure Substances, 3rd ed., Wiley–VCH Verlag GmbH, Weinheim, 1995. [4] H.Y. Erbil, Surface Chemistry of Solid and Liquid Interfaces, Blackwell Publishing, Oxford, 2006. [5] H. Fujii, S. Izutani, T. Matsumoto, S. Kiguchi, K. Nogi, Mater. Sci. Eng. A 417 (2006) 99. [6] H. Fujii, H. Nakae, K. Okada, Acta Metall. Mater. 41 (1993) 2963. [7] P. Shen, H. Fujii, T. Matsumoto, K. Nogi, J. Am. Ceram. Soc. 87 (2004) 2151. [8] K.C. Mills, Recommended Values of Thermophysical Properties for Selected Commercial Alloys, Woodhead Publishing Ltd., Cambridge, 2002. [9] T. Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, 1993. [10] M.E.R. Shanahan, Langmuir 11 (1995) 1041. [11] K.R. Denison, C. Boxall, Langmuir 23 (2007) 4358.