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Functional Coatings: Overview

Wettability, Spreading, and Interfacial Phenomena in High-Temperature Coatings

Rajiv Asthana and Natalia Sobczak

The fundamental phenomena underlying various coating technologies include wetting, spreading, interface evolution, and adhesion. This article reviews the status of wettability and interfacial phenomena in high-temperature solid-liquid couples commonly employed in the coating and joining technologies.

INTRODUCTION

The deposition of a coating on a solid generates new interfaces between dissimilar materials and involves considerations of wettability, spreading, interface evolution, and adhesion. The wettability of a solid by a liquid is characterized in terms of the angle of contact that the liquid makes on the solid.1,2 The contact angle, q, is obtained from a balance of interfacial tensions (Figure 1) and is defined from Young's equation, according to which

slv.cosq + sls = ssv

where slv, sls, and ssv are the interfacial tensions at the boundaries between liquid (l), solid (s), and vapor (v). Here, s represents the force needed to stretch an interface by a unit distance (or, equivalently, energy required to create a unit surface area of a given interface, provided that, in the case of ssv, mechanical distortion and strains are negligible). The condition q < 90 indicates that the solid is wet by the liquid, and q > 90 indicates nonwetting, with the limits q = 0 and q = 180 defining complete wetting and complete nonwetting, respectively. This article reviews the status of high-temperature wettability as manifested in the contact-angle phenomena, with a focus on the behavior of metallic coatings in contact with liquid metals.

USING YOUNG'S EQUATION TO DETERMINE WETTABILITY

A large body of useful scientific information about the wettability of and spreading upon high-temperature metal and ceramic coatings comes from the application of Young's equation to metallurgical systems at elevated temperatures. Young's equation is also used as a foundation for interfacial studies in a variety of other fields. Despite its success in offering practical insight into the wettability and spreading phenomena, however, Young's equation has been the subject of considerable controversy and debate.

Gravitational Effects

Young's equation predicts a unique value of the equilibrium angle, q, in terms of thermodynamic quantities (s's) without regard to the presence of external fields, such as gravitation. This is in contrast to the common observations of shape distortion of droplets on an inclined plane in the earth's gravity. Theories and experiments3-5 have been advanced both to challenge and support Young's equation.

Gravity also influences gas adsorption at nonwetting rough surfaces;6 it opposes adsorption because the gas has to locally lift the liquid to enter into surface troughs. Gas adsorption effectively smoothens the surface because the liquid contacts only a portion of the asperities. However, adsorption creates additional solid-gas and liquid-gas interfaces, and will be energetically favored in a gravitational field if the decrease in ssl due to reduced roughness is greater than the energy increase due to the creation of additional surface.6

Substrate Deformation

Young's equation applies only to one-dimensional spreading and becomes invalid if the substrate is not rigid and the contact-line motion takes place in both horizontal and vertical directions. The force equilibrium of Figure 1 ignores the vertical component of the surface tension, slv sinq, which acts along the line of contact (this force is not countered by the weight that acts at the center of mass). As the capillary forces are not balanced, external forces must be applied to the solid to achieve equilibrium;7-9 these forces can produce deformation in highly deformable solids, such as gels and rubber, destroying the coplanarity of interfacial tensions assumed in Young's equation and causing ridge formation at the interfacial region. A quasi-equilibrium could, however, exist within the window of time when an observation is made, provided the solid's deformation rate is small.

The extent of deformation has been calculated using linear, isotropic, continuum elasticity theory for thin plates, membranes, and plates.9 Ridge formation at the wetting front also occurs in high-temperature systems because of interfacial chemical reactions and diffusion processes.

Precursor Films and Microscopic Angles

In many solid-liquid systems, the liquid front is spearheaded by a thin foot or a precursor film that forms when the liquid develops a finite, non-zero curvature near its periphery due to local intermolecular interactions.1,10 A sharp distinction between solid, liquid, and vapor phases can no longer be assumed as the liquid is gradually thinned, yielding a microscopic angle that does not obey Young's equation.11 This is because the continuum concept of surface energies to represent the local molecular interactions becomes increasingly tenuous for precursor films approaching molecular thicknesses.

Vapor Adsorption

If the liquid vapor is adsorbed on the solid's surface, the surface tension of the solid, ssv, decreases. The concept of a spreading pressure P (defined from P = ss - ssv) is related to the need to maintain a saturated vapor of the liquid around the solid.1,12 Here, ss is the surface tension of the solid in equilibrium with its own vapor or in vacuum, and ssv is the surface tension of the solid in equilibrium with the saturated vapor of the liquid. If the spreading pressure can be neglected (which is true for q > 10), then it is possible to write the Young equation in terms of the true or intrinsic surface tension of the solid. Techniques have been devised to test whether the spreading pressure in a given system is negligible and the measured contact angle is indeed the equilibrium angle.1

Surface Roughness

Young's equation applies to ideal surfaces that are perfectly smooth and devoid of all chemical and structural inhomogeneities. The contact angle measured on a rough surface (called the Wenzel angle, qw) does not obey Young's equation; it is related to the equilibrium (Young) angle qy, from Reference 13

cosqw = rcosqy

where r is the ratio of the true wetted area to the apparent area.

Wenzel's equation applies to equilibrium angles on rough surfaces and not to advancing and receding angles of a droplet on a rough solid surface that give rise to contact-angle hysteresis. Hysteresis, H, is defined as the difference of the advancing and receding angles (i.e., H = qa - qr) and arises because the liquid-vapor interface does not retrace its original path when it recedes on the solid, so that spreading is thermodynamically irreversible.1,14-19 Because roughness hinders the contact line motion by creating energy barriers, the system can reside in any of the potential wells accessible to it that are commensurate with the vibrational (or thermal) energy of the droplet.1 The advancing angle is less sensitive to roughness than is the retreating angle and is usually the one measured and reported.

As surface inhomogeneities exceeding about 10 nm in size can anchor the contact line, contact-angle hysteresis is pervasive in most systems save the most carefully prepared smooth and homogeneous surfaces. Applying acoustic energy (vibrations) diminishes the contact-angle hysteresis. In the case of reactive systems, the additional contact area due to roughness could enhance the chemical attack provided that the high surface tension of the liquid does not restrict the asperity contact with the liquid and gas entrapment at the rough interface does not minimize the solid-liquid contact.

Chemical Inhomogeneity

Most solid surfaces (with the exception, perhaps, of single crystals) are seldom consistent and clean, with different surface domains possessing different chemistries and wetting properties. Such chemical inhomogeneity could result from oxidation, corrosion, coatings, multiple phases (e.g., eutectic), adsorbed films, ledges, kinks, dislocations and grain-boundary intersections with the surface, and crystallographic anisotropy (planes having different packing density and exposing different molecular groups). Wettability and spreading are sensitive to such chemical and structural inhomogeneity.1,17,20-28 Carefully prepared single crystals are closest to idealized surfaces, and several studies have focused on the wetting behavior of single crystals by metallic melts.29-33

The wettability on chemically inhomogeneous surfaces is conveniently characterized in terms of an effective contact angle. The effective equilibrium contact angle on a composite surface constituted by chemical phases having different area coverages and contact angles is the area-fraction-weighted angle,20 provided there is no hysteresis. Like Wenzel's equation for roughness, the weighted-average rule applies to the equilibrium state rather than to metastable states. Note also that chemical reactions are often accompanied by reconstruction of the solid's surface, which could promote the chemical inhomogeneity and roughness. For example, in the SiO2-Al system, the reduction of silica by aluminum leads to a 38% volume reduction, which causes cavities to develop ahead of the contact line, thereby enhancing the roughness and hampering the spreading.15

WETTABILITY AND COATING PROCESSES

Wettability is manifested in numerous forms in a variety of coating processes. In many industrial processes, the substrate is immersed in a liquid coating material, then withdrawn to leave a liquid film on the substrate. The film (coating) thickness depends upon the surface tension, withdrawal speed, substrate geometry, roughness, and melt viscosity.34-36

The dispersion of fine, granular solids in a liquid vehicle is a basic step in preparing paints and other coating materials and involves particle transfer across a gas-liquid interface. The transfer of nonwettable solids into liquids requires the solid to overcome a surface energy barrier at the liquid-gas interface,37-44 and energy must be expended to assist the transfer of nonwettable solids. Once the solid enters the liquid, the capillary (attractive) forces and gas bridges between solids control such phenomena as agglomeration, dispersion, and air entrapment.45-51

The interparticle forces between dispersed solids are due to liquid surface tension and pressure difference across the curved liquid-vapor boundary between contacting solids. The maximum interparticle force, F, due to capillary forces between two touching spheres is49

F = 2(2)1/2slv cosq/R

where R is the radius of the sphere. The force increases with increasing liquid surface tension and decreasing contact angle and particle radius. These forces affect the viscosity, density, and sedimentation behavior of the suspension and the properties of the coating deposited using the suspension. Other coating processes, such as thermal spray, which atomize and spray molten or semimolten coating materials, also involve surface energetic considerations. These considerations become important in the shredding of droplets during flight and upon impact on the substrate, as well as in the engulfment of fine particulates into atomized droplets during flight in the case of composite coatings.52,53

WETTING DYNAMICS

The angle of contact as given by Young's equation is a static (equilibrium) angle. However, during its motion toward an equilibrium shape, a liquid droplet scans a range of apparent (dynamic) contact angles. The dynamic angle depends upon the rate of spreading,10,54-65 and several contact angle-velocity relationships have been proposed in the literature (Table I). In reactive systems,66-82 however, the wetting dynamics are interactively coupled with the reaction kinetics, and the spreading behavior becomes complex and less clear. Whereas equilibrium wetting is achieved rapidly (at times on the order of 10-4-0.1 seconds) in inert systems, equilibrium could take from 100 seconds to more than 10,000 seconds in reactive systems.


Table I. Models for Spreading Kinetics of Liquids on Solids

Model/Reference
Assumptions
Kinetic Law
Comments
DeGennes10 Semi-empirical model for inert liquids, applied U ~ q relationship for forced flow of liquids through tubes to droplet spreading a10 ~ t Widely used for polymeric liquids on low energy solids
Van Remoortere and Joos54,64 Empirical model a7 ~ t Applies to inert liquids such as silicone oil and parafin oil on silane- and parafin-coated glass
Yin63 Determines the velocity distribution in the spreading droplet, considers viscous drag as the resisting force, spreading scales with (slv/m) a5 ~ t Applies to molten polymers on smooth surfaces (Al, mica, teflon)
Fritz65 Determines velocity-dependence of dynamic angle from hydrodynamic analysis of flow in a capillary prewetted with a thin film of finite thickness, bulk viscosity is the major resting force a10 ~ t
Dodge-Blake-Haynes55,59 Applies absolute reaction rate theory to spreading, wetting front assumed to propagate over periodic potential wells between adsorption sites a7 ~ t Combines surface physics and fluid mechanics approaches, predicts indefinite spreading
Eustathopoulos66,67 Semi-empirical model, consistent with linear spreading in several high-temperature couples a ~ t Models reactive spreading with interface-control, consistent with Al/vitreous C, CuAgTi/alumina, and other systems
Mortensen et al.70 Diffusion field at the wetting front limits advance, models reactive spreading kinetics under steady-state diffusion a4 ~ t Models reactive spreading with diffusion-control, limited experimental verification,69 ignores convection
Ambrose et al68 Identifies flow regimes consistent with models for inert liquids, applies empirical equations to model flow regimes inconsistent with such models a ~ exp (t/3t) Presentational approach, does not identify flow mechanisms, applies to reactive brazes82 and some ceramic-metal couples81


There is evidence that models for the spreading of inert liquids provide a useful framework to understand the flow behavior in reactive systems.68,81 For example, the spreading kinetics during the initial and final stages of Ni-P braze over Fe-Cr substrates are consistent with the deGennes equation.68 In the intermediate flow regime, an (empirical) exponential relationship appears to be valid. Spreading kinetics consistent with an exponential behavior is also observed in PbSn-Cu, Hg-Ag, AuSi-SiC, CuTi-Al2O3, and several other systems.81

As a first step toward understanding the complex spreading behavior of reactive systems, a presentational approach can be used to identify different flow regimes that are consistent with the classical models for simple liquids. An example of such an approach is shown in Figure 2, where the spreading data in several reactive couples are plotted as ln a versus ln t, where a is the instantaneous radius of the spreading droplet, and t is the time. If the classical models (developed chiefly for viscous polymers and similar inert liquids) were applicable to reactive spreading, then the ln a vs. ln t data in each system would fit a straight line consistent with such relationships as a5 ~ t (Yin63), a7 ~ t (Remoortere and Joos54,64 and Dodge59), or a10 ~ t (deGennes10 and Friz65). Each system of Figure 2, however, displays a complex spreading behavior, exhibiting several different flow patterns. Some of these patterns appear to be broadly consistent with the behavior predicted by the classical models (Table II); whereas, others seem to follow either a linear (a ~ t) or a power law (a4 ~ t) behavior characteristic of reaction- and diffusion-controlled spreading mechanisms,66,69,70 respectively. Still other flow regimes appear to be inconsistent with all previous models.


Table II. Model Approximations to Spreading in Reactive Couples (Figure 2)

System
Temperature (K)
Kinetics
Model

Slopes of Linear
Segments in
Figure 2 (mm/s)

Cu-9.5Ti/sapphire
1,35083
a10 ~ t
de Gennes10/Friz65
0.10 (Fig. 2d)
Cu-9.5Ti/sapphire
1,35083
a2.4 ~ t
-
0.42 (Fig. 2d)
Cu-9.5Ti/sapphire
1,35083
a50 ~ t
-
0.02 (Fig. 2d)
Cu-9.5Ti/sapphire
1,35083
a4 ~ t
Mortensen et al.70
0.25 (Fig. 2d)
Cu-12.6Ti/sapphire
1,35083
a50 ~ t
-
0.02 (Fig. 2d)
Cu-12.6Ti/Al2O3
1,35083
a10 ~ t
de Gennes10/Friz65
0.10 (Fig. 2d)
Ag-38Cu-3.7Ti/Al2O3
1,22382
a10 ~ t
de Gennes10/Friz65
0.11 (Fig. 2a)
Pb-40Sn/Cu
52384
a25 ~ t
-
0.04 (Fig. 2c)
Pb-40Sn/Cu
52384
a6.9 ~ t
Remoortere54/Dodge59
0.15 (Fig. 2c)
Pb-40Sn/Cu
52384
a1.6 ~ t
-
0.63 (Fig. 2c)
Pb-30Sn/Cu
53384
a25 ~ t
-
0.04 (Fig. 2c)
Pb-30Sn/Cu
53384
a5 ~ t
Yin63
0.21 (Fig. 2c)
Pb-50Sn/Cu
49384
a10 ~ t
de Gennes10/Friz65
0.10 (Fig. 2c)
Pb-50Sn/Cu
49384
a25 ~ t
-
0.04 (Fig. 2c)
Pb-50Sn/Cu
49384
a4 ~ t
Mortensen et al.70
0.24 (Fig. 2c)
Pb-50Sn/Cu
49384
a50 ~ t
-
0.02 (Fig. 2c)
Cu-12.6Ti/sapphire
1,35084
a6.9 ~ t
Remoortere54/Dodge59
0.14 (Fig. 2d)
Cu-12.6Ti/sapphire
1,35084
a6 ~ t
-
0.17 (Fig. 2d)
Ni-11P/Fe20Cr
1,20368
a10 ~ t
de Gennes10/Friz65
0.11 (Fig. 2a)
Ni-11P/Fe20Cr
1,20368
a4.3 ~ t
Mortensen et al.70
0.23 (Fig. 2a)
Ni-11P/Fe20Cr
1,20368
a10 ~ t
de Gennes10/Friz65
0.11 (Fig. 2a)
Au-Si/SiC
-85
a10 ~ t
de Gennes10/Friz65
0.10 (Fig. 2b)
Au-Si/SiC
-85
a1.2 ~ t
Eustathopoulos66
0.83 (Fig. 2b)
Au-Si/SiC
-85
a3.3 ~ t
-
0.30 (Fig. 2b)

Note, however, that the spreading kinetics in a given system is strongly affected by the experimental conditions, and very different spreading kinetics can be measured for the same system depending upon the experimental technique (oxygen partial pressure, temperature, alloying technique, surface preparation, etc.). Thus, while the presentational scheme of Figure 2 illustrates the complexity of the reactive spreading phenomenon vis--vis inert liquids, it does not shed light upon the underlying mechanisms. On the other hand, characterizing the detailed mechanisms that govern the coupling of chemical reactions and wetting dynamics of spreading droplets in reactive systems affords considerable insight into chemical-reaction-enhanced wettability.

The complex nature of reactive spreading in high-temperature systems is also revealed in the plots of spreading data in the form cosq/cosq0 versus the parameter slv t/m in Figure 3, where q and q0 are the instantaneous and equilibrium values of the contact angle, q; t is time; and slv and m are the surface tension and the viscosity of the liquid, respectively. While the contact-angle data of Figure 3 display trends relative to the ratio slv/m (corrected for the test temperatures using the data from References 96-98), there is a large dispersion in the wettability data. In contrast, the cosq/cosq0 versus slvt/m data for inert liquids can be made to collapse into a master curve57 (after normalizing svt/m by an arbitrary length scale).

REACTIVE SPREADING

Several recent studies66,72,79,99-170 have presented the high-temperature wettability data in numerous systems and attempted to model the complex interfacial phenomena that occur during reactive spreading, offering insights into the coupling of interfacial reactions and spreading kinetics. Several configurations have been conceptualized for the reactive-spreading phenomenon, such as viscous spreading at t ≈ 0, reminiscent of classical liquids (but perhaps outside the observational domain for reactive liquids); ridge formation due to chemical reactions and pinning of the wetting front; evaporation-condensation and/or adsorption of reactive species; nucleation, growth, and coalescence of reaction products at the solid-liquid interface (and lowering of ssl); and, finally, spreading on a reacted layer ahead of the fluid meniscus.

Kinetics

In complex reactive systems, chemical reactions, solute segregation, wetting, and spreading are interactively coupled. Conceptually, spreading can be divided into distinct stages. The first stage is the very rapid spreading under the driving force for the balance of interfacial tensions characteristic of inert liquids. In the second stage, the substrate dissolves in the liquid and forms compounds, initially as discrete crystals that nucleate on preferred sites at the solid-liquid interface, and later grow to form a continuous layer of the reaction product(s). Such reactions yield one or more interfaces in place of a single solid-liquid interface. Subsequently, a reaction band forms around the droplet that grows by the processes of surface, bulk, and short-circuit diffusion paths.

Two limiting behaviors of reactive spreading are identified: systems exhibiting relatively rapid reaction rates (e.g., Al2O3/CuTi), where solute diffusion is rate-limiting and the spreading velocity decreases with time, and systems exhibiting relatively sluggish reaction kinetics (e.g., C/Al), where long-range mass transport (diffusion) is rapid relative to the rate of local chemical reactions, and spreading velocity is roughly constant.

Diffusion-Controlled Spreading


In the diffusion-controlled spreading of liquid droplets,66,69,70,77,168, 171-174 the meniscus advance is limited by the rate of arrival at the reaction front of the reacting species via diffusion. The diffusion field at the reaction front continuously decreases in time as the droplet spreads to a thin hemispherical cap.

The effect of diffusion on spreading has been modeled69,70 by assuming that the curvature effects and convection are negligible, and the spreading droplet is a semi-infinite medium with the thin layer of reaction product at the interface essentially serving as a diffusion barrier. The model shows that the fourth power of droplet radius, a, varies linearly with the product of droplet volume, V, and spreading time, t, according to Reference 70

a4 = KVt

This is in contrast to the linear relationship between R and t that is obtained when the reaction kinetics control the spreading process.

Reaction-Controlled Spreading

In couples such as Al/vitreous C, CuAgTi/Al2O3, and some other systems, linear spreading kinetics is observed, and the droplet-base radius increases linearly with time.66,67,165 In such systems, chemical reactions modify the solid's surface and control the spreading. The initial contact angle is usually large because of the surface oxides that resist spreading. As the deoxidization at high temperatures and under high vacuum erodes the surface oxides, the dynamic angle, q, drops, and high spreading rates, characteristic of inert liquids on untransformed solid, are achieved. However, once solid reaction products form at the interface, the spreading rate adjusts consistent with the wettability of the product phase.

For example, in the Al/vitreous C system, the growth of the (nonwetting) product phase, Al4C3, slows down the spreading. The droplet base radius increases linearly with time, and a constant spreading rate is attained for several hours (e.g., 3.2 h for Al/vitreous C67). Upon prolonged holding, the product layer extends beyond the droplet periphery, and eventually a stable contact angle is attained. As the reaction layer growth overtakes the wetting front, atomic diffusion through the product layer limits further growth. The driving force for spreading is

slv [cosqeq - cosq(t)]

where qeq and q(t) are the equilibrium and instantaneous values of the contact angle of the liquid on reacted layer, respectively. As q(t) tends toward qeq, the driving force for spreading decreases, and eventually flow ceases when qeq is attained.

THE PHYSICOCHEMICAL ASPECTS OF WETTING

High-temperature wettability is influenced by a large number of variables that include temperature; contact time; atmosphere; roughness; crystal structure; composition; surface pretreatments; and interfacial segregation, adsorption, and reactions. Extensive reviews have been published documenting the role of factors that govern wettability.25,66,72,99,116,169,175-177 Basically, three types of interactions can promote wettability in the high-temperature solid-liquid systems: dissociation of surface oxides on liquid metal (oxide scavenging), chemical dissolution of the solid in the melt and interfacial adsorption of reactive solutes (reduction of ssl), and formation of a wettable interfacial compound.

At high temperatures, spreading to an equilibrium shape becomes difficult when a solid reaction product (e.g., an oxide) on the liquid opposes the spreading, resulting in a large value of the contact angle. The stability and protective influence of oxide films is affected by the temperature, atmosphere, and alloying elements. An ultrahigh vacuum erodes the film to form gaseous suboxides at high temperatures, thereby establishing a physical contact and yielding a sudden drop in the contact angle above a critical temperature. Other chemical species present in the atmosphere could affect the wettability. Thus, reaction of water vapor in the test chamber with the graphite susceptor used for induction heating or with the test substrate could form CO and H2. Carbide substrates, such as SiC, could graphitize and form free carbon following silicon sublimation at high temperatures. High temperatures decrease the liquid-surface tension (dslv/dT < 0) and promote wettability. Also, the spreading rate toward equilibrium is enhanced because of diminishing liquid viscosity at high temperatures.

The liquid composition markedly influences its wettability with solids. Thus, chromium and titanium in copper make the Cu/graphite system a wettable one. Likewise, silicon in Al/SiC, magnesium in Al/silica and Al/alumina, and titanium in Al/C all improve wetting although the mechanisms of wetting enhancement are different. Thus, a high silicon content in Al/SiC reduces the propensity for nonwetting Al4C3 formation; whereas, titanium in Al/C promotes wetting by TiC formation. Similarly, magnesium in Al/SiO2 and Al/Al2O3 scavenges the surface oxides and forms wettable reaction products (e.g., spinel MgAl2O4). The dissolution of oxygen in some metals improves wetting and bonding as observed in Cu/AlN, Cu/SiC, and alumina/Cu.

The wettability-enhancing interfacial reactions are limited by interface kinetics, diffusion rate, or a combination thereof. Once a thin product layer forms, growth is usually limited by diffusion through this layer, and the thickness increases parabolically with time,

X = k√t

where k is a parabolic reaction-rate constant, and t is time. Modifications of the simple parabolic law are necessary to account for nonplanar interfaces; diffusion in a finite domain (soft impingement); formation of intermediate nonequilibrium phases; and the existence of short-circuit diffusion paths, such as interfaces, grain boundaries, and dislocations.

The nature of atomic bonding and the thermodynamic stability of solids in contact with liquids are related to their wettability at high temperatures. In the case of carbides, wettability decreases with increasing heat of formation of the carbide. The high heat of formation implies strong interatomic bonds and correspondingly weak interaction with metals. In the case of oxides, wettability decreases with an increase in the free energy of oxide formation. Highly ionic ceramics, such as alumina, are relatively difficult to wet since their electrons are tightly bound. On the other hand, covalently bonded ceramics are more easily wetted by metals than highly ionic ceramics because of a similarity between metallic and covalent bonds. Fundamental atomic bonding and thermodynamic stability considerations have led to the development of several predictive models of wetting (Table III).


Table III. Models for Predicting Wetting Behavior

Model/Reference
Main Assumptions
Predictive Relationship
Comments
McDonald-Eberhart178 Wettability of oxides by metals related to oxygen affinity, work of adhesion, Wad, related to free energy of oxide formation
a, b are constants, a related to physical dispersion forces, DGMeO = free energy for oxide formation
Interfacial segregation not considered, predictions of Wad inconsistent with observations in some systems
Naidich72 Relates wettability to DG for S-L reaction near the interface composed of two monolayers (one on liquid side and the other on solid side) Applies to Sn/NiO, Ti/MgO, Zr/MgO and other couples
Laurent-Drevet-Eustathopoulos118 Relates wettability to intensity of reaction and wettability of the resulting interface, identifies wettability of resulting interface as a key factor
q0 = contact angle in the absence of reaction, Dsr = change in the interfacial energy due to reaction, DG = Gibb's free energy change for the reaction
Zisman175 Applies to low-energy solids, identifies critical surface tension for complete wetting ;
s
c = critical surface tension
Neumann179-182 Semi-empirical equation-of-state to predict the surface energies Validated in low-temperature systems, applied to ceramic-metal systems,183-185 disagrees with some grain-boundary grooving data,186 criticized on theoretical grounds187,188
Good-Girifalco1,189 Relates surface energies via an interaction parameter (F), adhesion energy obtained from a geometric combining rule for solid-solid and liquid-liquid pairs, F calculated from polarizabilities, dipole moments, ionization potentials
F
= 0.5 to 1.0
Applies to low-temperature systems
Wu190 Uses Zisman's critical surface tension, calculates sc of any solid using q of any one test liquid Applies to polymers and organic solids
Rhee191,192 Utilizes Zisman's critical surface tension sc for high-energy solid-liquid systems at high temperatures ,
b = constant
Applies to MgO, BeO, UO2, and other solids
Warren193 Applies solution thermodynamics to estimate the s-l surface energy, considers chemical and structural contributions to surface energies
s
's given in terms of bulk and interface compositions, latent heat, melting point, and molar volumes
Miedema194,195 Solution thermodynamics approach, considers surface segregation effects Applies to liquid metals and intermetallic compounds

From a practical standpoint, the coating-substrate adhesion is also of essence. Physical, chemical, and mechanical interactions influence adhesion. For purely mechanical adhesion to develop, the liquid coating material must be able to penetrate the surface porosity in the solid, a phenomenon governed by the interaction of capillary forces driving the penetration (in a wettable system) and the retarding forces due to viscosity and gravity (depending upon the penetration geometry).196-199 In reactive systems, however, additional complexities arise during liquid penetration because of the transient nature of reaction-driven wettability and pore-size reduction and closure due to reaction-product deposition within pores.101,200-203 Such considerations are also important in joining technologies and reactive infiltration of composites.

A large body of data on high-temperature wettability and interfacial bonding is available for materials such as SiC,32,85,113,123-125,138,153,157,170,204-211 Al2O3,72,126-128,130,162,212-220 mullite,221-223 carbon,117,145,146,155, 165,170,224-236 fluoride (CaF2, BaF2, MgF2),33 silica,158,221,237,238 nitrides (AlN, TiN, BN, Si3N4),72,154,159,239-242 CaO,243 TiO2 and ZrO2,134,136,137,147 boron,72 MgO,72 metals (silver, copper in contact with tin, bismuth, SnBi, SnPb),28,31,75,76 and other materials.

The influence of material and test parameters on the high-temperature wettability has been extensively investigated, particularly the effects of alloying;33,111,113,128,134,136-140,155,206-209,231-236,244,245 atmosphere;72,85,141,147,207,246 temperature;90,91,124,125,151,205 time;123-125,151,153,155 ceramic structure/composition (single- vs. polycrystal, crystal orientation, hot pressed, reaction bonded, surface porosity, etc.);29,30-33,72,130,155,166,216,218,234 and surface modification using metallic coatings,160,211,227,228 oxide coatings,247-250 carbon coatings,148 and fluoride coatings.225,230 The effects of some of these factors are discussed in greater detail in Reference 169.

HIGH-TEMPERATURE WETTABILITY OF COATINGS

Figures 4 through 13 show the high-temperature wettability data and interface microstructure for liquid metals, primarily aluminum and copper, on a variety of coated- and monolithic substrates.90,144,169,234,251-257 In the case of aluminum alloys, there is no remarkable difference in the wetting behavior on monolithic substrates and a thin layer of the same material. Small differences noted at the beginning of the wetting process are probably caused by the heterogeneity in the structure and chemistry of multicomponent bulk materials (in contrast, coatings were more homogeneous).

In the Al/alumina system (Figure 4), the lowest contact angles are obtained with the coatings of NiP and NiCoP.169,252 Figure 5a shows the effect of alloying and coating type on the wettability kinetics in the Al/alumina system; Al-Si alloys form contact angles almost twice as large as pure aluminum due to the inhibition of the dissolution of the silicon-containing coating material (Cr-42Si-9W) in the alloy, which also contains silicon.252

In the case of Al-Ti alloys on alumina, a comparison of Figures 4c and 5b indicates that in spite of the semi-solid state of the Al-10Ti alloy at the test temperature, it exhibits a wetting behavior similar to molten pure aluminum, characterized by good wetting of Ni-, CoP-, and NiCoP-coated alumina substrates. The same coatings applied to graphite improve its wettability with aluminum (Figure 6), resulting from the dissolution of the coating in the liquid droplet (Figures 7 and 8). However, in spite of good wetting, the strength of the droplet/coating/substrate joint may be weak if the bonding between the substrate and the coating is poor. Figure 8 illustrates such a situation for the Al/Cu/graphite system; the aluminum drop is detached, along with copper coating from the graphite substrate, because of a lack of chemical interaction between copper and carbon.

Complete dissolution of a coating might lead to dewetting; therefore, the time, temperature, atmosphere, and other process parameters must be judiciously selected. It is interesting to note that in the case of metallic coatings made by chemical reduction from salt solutions, the effect of wettability improvement is very stable, even when complete dissolution of the coating, confirmed by optical microscopy, takes place (Figure 7c). Studies169,256 on the effect of aluminum alloying additions on wettability improvement in the Al/graphite system clearly indicate that nickel and copper additions do not ensure good wetting (Figure 9), and in copper- or nickel-rich aluminum droplets, the dissolution of the coating is not responsible for the stable effects of wettability enhancement.

Unlike the situation in a sessile-drop test, however, nickel- and copper-coatings on ceramic reinforcements reduce the threshold pressure for infiltration and yield larger penetration lengths, indicating improvements in the wettability.210,211 In such pressurized infiltrations tests, however, the contact times are on the order of a few tens of seconds, and spreading is completed prior to the attainment of equilibrium wettability.

Another interesting aspect of the wetting behavior of coatings is the effect of the substrate on equilibrium wetting in a sessile-drop test. The coatings of a similar chemical composition deposited using similar procedures show different wetting properties with a given metal depending upon the type of substrate material on which the coating is applied. For example, metallized graphite substrates show lower contact angles with aluminum compared to alumina substrates (Figure 10).

Contrary to technological coatings developed to promote wettability, certain types of barrier coatings are employed to protect the substrate materials from the aggressive attack of different environments. For example, in metallurgical and foundry practices, barrier coatings are used to increase the lifetime of crucibles, dies, and other appliances that routinely come in contact with molten metals. In such cases, the engineered coatings must impair the wettability and minimize the spreading and contact area. Figure 11 illustrates the effect of boron nitride (lubricant) coating (BNlub; dry composition is 87% BN and 13% Al2O3) on the wetting behavior of an aluminum droplet containing 10 wt.% titanium on a graphite substrate. Although the Al-10Ti alloy droplet is semi-solid at the test temperature, a strong chemical interaction between titanium and carbon yields significant wettability improvements, that, depending upon graphite type, results either in infiltration or erosion of the substrate material.234

The application of a BNlub coating provides effective protection against such attack in the case of aluminum alloys, but the same coating might play a negative role in contact with other materials containing active alloying elements. For example, as shown in Figure 12, Cu-Ti alloys wet graphite at high titanium contents (~ 17 wt.%), but BNlub coatings on graphite provoke a sudden decrease in the contact angle of Cu-10.5Ti alloy (Figure 12a), consistent with the data for Cu-Ti/BN system (Figure 12b). Additionally, the BNlub coating cracks due to stresses generated during the formation of titanium-rich reaction products, such as TiN and TiB2 (Figure 13). Finally, because of a very strong interfacial bond at the BNlub/graphite joint, a dramatic situation is encountered wherein the graphite substrate completely cracks through its thickness of about 5 mm (Figure 13). Such a situation is inadmissible in practice because it may cause breaking of crucibles, dies, and other appliances in contact with reactive melts.

WETTING AND ADHESION

The performance of a coating during service depends not only on the inherent characteristics of the coating (and substrate) materials but also on the coating-substrate adhesion. Wettability promotes adhesion through physical, chemical, and/or mechanical bonds acting across the coating-substrate interface. As the interface represents a region of compositional and structural discontinuities, it is inherently unstable and evolves during service, serving as a site for morphological, chemical, and structural transformations. Additionally, the interface topography is important because it affects the stress concentration and crack-deflection paths.

Adhesion develops from physical (e.g., weak van der Waals) bonds, chemical interactions, and friction from irregular surface topography. Residual stresses arising from the mismatch of coefficients of thermal expansion (CTE) between the coating and substrate during temperature excursions influence the adhesion; CTE mismatch gives rise to stresses that could cause interfacial cracking and debonding if these stresses are not accommodated by plastic flow. Stress-absorbing compliant layers are used to promote the thermoelastic compatibility between dissimilar materials. Similarly, reaction-barrier coatings are used to protect the underlying solid from chemical degradation; however, all such layers introduce additional interfaces that must meet appropriate criteria for material compatibility.

The effect of wettability on interface adhesion can be quantified by the work of adhesion, WAd, which is defined as1

Wad = slv (1 + cosq)

A high work of adhesion indicates good wetting; whereas, a low work of adhesion indicates poor wetting. The work of adhesion, Wad, between metals and oxide ceramics (primarily alumina) correlates with both the tensile strength and bend strength of the metals,258,259 suggesting that good wetting generally yields good interface bonding. This has been confirmed (Figure 14) experimentally using shear tests directly on (solidified) sessile drop test specimens.255

The inherent plasticity of the material is also important; metals with a low yield strength could cause plastic flow and provide for blunting of the interfacial cracks, resulting in higher interfacial toughness and low stress concentration even when the interface chemistry is not such as to ensure good wetting. In other words, good wetting resulting from chemical reactions may not be a necessary precondition for achieving a high adhesion strength.258 More complete discussions of the relationship between wettability, adhesion, and interface processes have been presented in References 72, 132, 154, 169, 258-273.

References
1. A.W. Neumann and R.J. Good, Surface and Colloid Science, vol. II, ed. R.J. Good and R.R. Stromberg (New York: Plenum Press, 1979).
2. L.E. Murr, Interfacial Phenomena in Metals and Alloys (New York: Addison Wesley Publ. Company, 1974).
3. B.A. Pethica, J. Colloid Interface Sci., 62 (3) (1977), p. 567.
4. J.P. Garandet, B. Drevet, and N. Eustathopoulos, Scripta Mater., 38 (9) (1998), p. 1391.
5. Y. Liu and R.M. German, Acta Mater., 44 (4) (1996), p. 1657.
6. H. Sakai and T. Fujii, J. Colloid Interface Sci., 210 (1999), p. 152.
7. G.R. Wickham and S.D.R. Wilson, J. Colloid Interface Sci., 51 (1) (1975), p. 189.
8. G.R. Lester, J. Colloid Sci., 16 (1961), p. 315.
9. M.A. Fortes, J. Colloid Interface Sci., 100 (1) (1984), p. 17.
10. P.G. de Gennes, Rev. Modern Phys., Part I, 57 (3) (July 1985), p. 827.
11. G.J. Jameson and M.G. Delcerro, J. Chem. Soc. Faraday Trans., 72 (1) (1976), p. 883.
12. M. Morra, E. Occhielo, and F. Garbassi, Prog. in Surf. Sci., p. 79.
13. R.N. Wenzel, Ind. Eng. Chem., 28 (1936), p. 988.
14. X.B. Zhou and J.Th.M. De Hosson, J. Mater. Res., 10 (8) (1995), p. 1984.
15. X.B. Zhou and J.Th.M. De Hosson, Acta Mater., 44 (2) (1996), p. 421.
16. V. de Jonghe and D. Chatain, Acta Metall. Mater., 43 (4) (1995), p. 1505.
17. J. Drelich and J.D. Miller, J. Colloid Interface Sci., 164 (1994), p. 252
18. H. Nakae et al., Acta Mater., 46 (7) (1998), p. 2313.
19. F.G. Yost, J.R. Michael, and E.T. Eisenmann, Acta Metall. Mater., 43 (1) (1995), p. 299.
20. A.B.D. Cassie, Disc. Faraday Society, 3 (1) (1948), p. 11.
21. A.W. Neumann et al., J. Colloid Interface Sci., 71 (2) (1979), p. 293.
22. R. Asthana, Metall. Trans., 24A (1993), p. 1673.
23. R. Asthana, Scripta Metall. Mater., 29 (1993), p. 1261.
24. J.G. Li and H. Hausner, Scripta Metall. Mater., 32 (3) (1995), p. 377.
25. A.W. Neumann and R.J. Good, J. Colloid Interface Sci., 38 (1972), p. 341.
26. X.B. Zhou and J.Th.M. Hosson, Acta Mater., 44 (2) (1996), p. 421.
27. R.P. Voitovich, Yu.V. Naidich, and G.A. Kolesnichenko, Poroshk. Metall., English translation, 6 (354) (1992), p. 40 (New York: Plenum Publ. Co., 1992, p. 494).
28. H.K. Kim, H.K. Liou, and K.N. Tu, J. Mater. Res., 10 (3) (1995), p. 497.
29. N. Grigorenko et al., Proc. Int. Conf. High-Temperature Capillarity - 97 (HTC-97), ed. N. Eustathopoulos and N. Sobczak (Krakow, Poland: Foundry Research Institute, 1998), p. 133.
30. C. Rado, C. Senillou, and N. Eustathopoulos, in Ref. 29, p. 53.
31. F.G. Yost and E.J. O'Toole, Acta Mater., 46 (14) (1998), p. 5143.
32. Y.V. Naidich, V. Zhuravlev, and N. Krasovskaya, in Ref. 29, p. 118.
33. Y.V. Naidich and V.P. Krasovsky, in Ref. 29, p. 87.
34. B.V. Derjagun and S.N. Levi, Film Coating Theory (London: Focal Press, 1964).
35. D.A. White and J.A. Talimadge, AIChE J., 13 (1967), p. 747.
36. A.R. Swenson and S.K. Nicol, J. Colloid Interface Sci., 60 (3) (1977), p.568.
37. S. Hartland and J.D. Robinson, J. Colloid Interface Sci., 35 (3) (1971), p.372.
38. A.V. Rapacchietta, A.W. Neumann, and S.N. Omenyi, J. Colloid Interface Sci., 59 (3) (1977), p. 541.
39. A.V. Rapacchietta and A.W. Neumann, J. Colloid Interface Sci., 59 (3) (1977), p. 555.
40. P.K. Rohatgi and R. Asthana, Cast Reinforced Metal Composites, ed. S.G. Fishman and A.K. Dhingra (Materials Park, OH: ASM, 1988), p. 61.
41. P.K. Rohatgi et al., Metall. Trans., 21A (1990), p. 2073.
42. J.M. DiMeglio and E. Raphael, J. Colloid Interface Sci., 136 (2) (1990), p. 581.
43. H.M. Princen, J. Colloid Sci., 18 (1963), p. 178.
44. O.J. Ilegbusi and J. Szekely, J. Colloid Interface Sci., 125 (2) (1988), p. 567.
45. V.S. Yushchenko, V.V. Yaminsky, and E.D. Shchukin, J. Colloid Interface Sci., 96 (2) (1983), p. 307.
46. V.V. Yaminsky et al., J. Colloid Interface Sci., 96 (2) (1983), p. 301.
47. Ya.I. Rabinovich, Kolloidn. Zh., 39 (1977), p. 1094.
48. G. Ramani, T.R. Ramamohan, and B.C. Pai, Scripta Metall., 24 (1990), p. 1419.
49. R.B. Heady and J.W. Cahn, Metall. Trans., 1 (1970), p. 185.
50. J.W. Cahn and R.B. Heady, J. Amer. Ceram. Soc., 53 (7) (1970), p. 406.
51. W.C. Carter, Acta Metall., 36 (8) (1988), p. 2283.
52. L. Pawlowski, The Science and Engineering of Thermal Spray Coatings (New York: John Wiley and Sons, 1995).
53. E.J. Lavernia, J.A. Ayers, and T.S. Srivatsan, Int. Mater. Revs., 37 (1992), p. 1.
54. P. Joos, P. van Remoortere, and M. Bracke, J. Colloid Interface Sci., 136 (1) (1990), p. 189.
55. T.D. Blake and J.M. Haynes, J. Colloid Interface Sci., 30 (3) (1969), p. 421.
56. W. Rose and R.W. Heins, J. Colloid Sci., 17 (1962), p. 39.
57. H. Schonhorn, H.L. Frisch, and T.K. Kwei, J. Appl. Phys., 37 (1966), p. 4967.
58. M.C. Phillips and A.C. Riddiford, J. Colloid Interface Sci., 41 (1) (1972), p. 77.
59. F.T. Dodge, J. Colloid Interface Sci. (1988), p. 154.
60. V.E.B. Dussan, J. Fluid Mech., 77 (1976), p. 665.
61. I. Rivollet, D. Chatain, and N. Eustathopoulos, J. Mater. Sci., 25 (1990), p. 3179.
62. S.J. Hitchcock, N.T. Carrol, and M.G. Nicholas, J. Mater. Sci., 16 (1981), p. 714.
63. T.P. Yin, J. Phys. Chem., 73 (1969), p. 2413.
64. P. Van Remoortere and P. Joos, J. Colloid Interface Sci., 160 (1993), p. 387.
65. G. Friz, Z. Angew. Phys., 19 (4) (1965), p. 374.
66. N. Eustathopoulos, Acta Mater., 46 (7) (1998), p. 2319.
67. K. Landry and N. Eustathopoulos, Acta Mater., 44 (10) (1996), p. 3923.
68. J.C. Ambrose, M.G. Nicholas, and A.M. Stoneham, Acta Metall. Mater., 40 (10) (1992), p. 2483.
69. R. Voitovich et al., Acta Mater., 47 (4) (1999), p. 1117.
70. Mortensen, B. Drevet, and N. Eustathopoulos, Scripta Mater., 36 (1997), p. 645.
71. J.G. Li and H. Hausner, J. Mater. Sci. Lett., 10 (1991), p. 1275.
72. Y. Ju. Naidich, Progress in Surface and Membrane Science, ed. D.A. Cadenhead and J.F. Danielli (New York: Academic Press, 1981).
73. P.R. Sharps, A.P. Tomsia, and J.A. Pask, Acta Metall., 29 (1981), p. 855
74. F.G. Yost, Scripta Mater., 38 (8) (1998), p. 1225.
75. X. H. Wang and H. Conrad, Metall. Mater. Trans., 26A (1995), p. 459.
76. X. H. Wang and H. Conrad, Scripta Metall. Mater., 31 (4) (1994), p. 375.
77. W.J. Boettinger, C.A. Handwerker, and U.R. Kattner, The Mechanics of Solder Alloy Wetting and Spreading, ed. F.G. Yost et al. (New York: Van Nostrand Reinhold, 1997), p. 103.
78. H. Nakae and A. Goto, in Ref. 29, p. 12.
79. A. Meier, D.A. Javernic, and G.R. Edwards, JOM, 51 (2) (1999), p. 44.
80. R. Asthana, Metall. Mater. Trans., 26A (1995), p. 1307.
81. R. Asthana, Scripta Mater., 38 (8) (1998), p 1203.
82. M.G. Nicholas and S.D. Peteves, Scripta Metall. Mater., 31 (1994), p. 1091.
83. J.G. Li, J. Mater. Sci. Lett., 11 (1992), p. 1551.
84. G.L.J. Bailey and H.C. Watkins, J. Inst. Metals, 80 (1951-52), p. 57.
85. B. Drevet, S. Kalogeropoulos, and N. Eustathopoulos, Acta Metall. Mater., 41 (1993), p. 3119.
86. J.J. Brennan and J.A. Pask, J. Amer. Ceram. Soc., 51 (10) (1972), p. 569.
87. H. Fuji, H. Nakae, and K. Okada, Acta Metall. Mater., 41 (10) (1993), p. 2963.
88. F.P. Chiaramonte and B.N. Rosenthal, J. Amer. Ceram. Soc., 74 (3) (1991), p. 658.
89. T.J. Whelan and A.T. Anderson, J. Amer. Ceram. Soc., 58 (9) (1975), p. 396.
90. N. Sobczak, J. Sobczak, and W. Radziwill, Proc. Int. Conf. Composite Engineering (ICCE-3), ed. D. Hui, p. 777.
91. N. Sobczak et al., Proc. II Conf. Surf. Phenomena in Foundry Processes, p. 115.
92. H. Fuji and H. Nakae, Acta Metall. Mater., 44 (9) (1996), p. 3567.
93. P. Sebo, S. Kavecky, and P. Stefanik, J. Mater. Sci. Lett., 13 (1994), p. 592.
94. V. Laurent, D. Chatain, and N. Eustathopoulos, Mater. Sci. Eng., A135 (1991), p. 89.
95. C. Marumo and J.A. Pask, J. Mater. Sci., 12 (1977), p. 223.
96. L. Battezatti and A.L. Greer, Acta Metall. Mater., 37 (1989), p. 1791.
97. B.J. Keene, Int. Mater. Revs., 38 (1993), p. 157.
98. Smithels, Metals Reference Book (1983), pp. 14-17.
99. In Ref. 29
100. E. Saiz and A.P. Tomsia, J. Amer. Ceram. Soc., 81 (9) (1998), p. 2381.
101. D. Muscat and R.A.L. Drew, Metall. Mater. Trans., 25A (1994), p. 2357.
102. Y. Gao et al., J. Mater. Res., 10 (5) (1995), p. 1216.
103. S.M. DeVincent and G.M. Michael, Metall. Trans., 24A (1993), p. 53.
104. C. Toy and W.D. Scott, J. Amer. Ceram. Soc., 73 (1990), p. 97.
105. A. Meir, P.R. Chidambaram, and G.R. Edwards, Acta Mater., 46 (12) (1998), p. 4453.
106. J. Narcisco et al., Metall. Mater. Trans., 26A (1995), p. 983.
107. A. Alonso et al., Metall. Trans., 24A, 1993, p. 1423.
108. S.Y. Oh, K.C. Russel, and J.A. Cornie, Metall. Trans., 20A (1989), p. 533.
109. P.B. Maxwell et al., Metall. Trans., 21B (1990), p. 475.
110. J.H. Ahn, N. Terao, and A. Berghezen, Scripta Metall., 22 (1988), p. 793.
111. S.M. DeVincent, D.L. Ellis, and G.M. Michal, NASA CR # 187087 (Washington, D.C.: NASA, 1991).
112. A. Mortensen and T. Wong, Metall. Trans., 21A (1990), p. 2257.
113. T. Choh and T. Oki, Mater. Sci. Tech., 3 (1987), p. 378.
114. T. Choh, R. Kammel, and T. Oki, Z. Metallk., 78 (1987), p. 286.
115. H.K. Kim, H.K. Liou, and K.N. Tu, J. Mater. Res., 10 (3) (1995), p. 497.
116. N. Eustathopoulos, Int. Metals Revs., 28 (4) (1983), p. 189.
117. N. Eustathopoulos et al., J. Mater. Sci., 9 (1974), p. 1233.
118. N. Eustathopoulos and L. Coudurier, J. Adhes. Sci. Tech., 6 (3) (1992), p. 1011.
119. N. Eustathopoulos, D. Chatain, and L. Coudurier, Mater. Sci. Eng., A 135 (1991), p. 83.
120. J.G. Li and H. Hausner, J. Europ. Ceram. Soc., 9 (1992), p. 101.
121. T.R. Jonas, J.A. Cornie, and K.C. Russel, Metall. Mater. Trans., 26A (1995), p. 1491.
122. L. Coudurier and N. Eustathopoulos, J. Mater. Sci., 24 (1989), p. 1109.
123. V. Laurent, D. Chatain, and N. Eustathopoulos, J. Mater. Sci., 22 (1987), p. 244.
124. V. Laurent, D. Chatain, and N. Eustathopoulos, Mater. Sci. Eng., A135 (1991), p. 89.
125. V. Laurent et al., Cast Reinforced Metal Composites, ed. S.G. Fishman and A.K. Dhingra (Materials Park, OH: ASM, 1988), p. 27.
126. V. Laurent et al., Acta Metall. Mater., 36 (1988), 1797.
127. D.J. Wang and S.T. Wu, Acta Metall. Mater., 42 (12) (1994), p. 4029.
128. Z. Lijun et al., Interfaces in Metal-Ceramic Composites, ed. R.Y. Lin et al. (Warrendale, PA: TMS, 1989), p. 213.
129. C.S. Kanetkar, A.S. Kacar, and D.M. Stefanescu, Metall. Trans., 19A (1988), p. 1833.
130. D. Xu, D. Wang, and D. Lin, Scripta Metall. Mater., 28 (1993), p. 599.
131. N. Eustathopoulos and B. Drevet, Compos. Interfaces, 2 (1) (1994), p. 29.
132. C. Rado, S. Kalogeropoulo, and N. Eustathopoulos, Acta Mater., 47 (2) (1999), p. 461.
133. A.M. Hadian and R.A.L. Drew, Mater. Sci. Eng., A189 (1994), p. 209.
134. C. Iwamoto, M. Nomura, and S.I. Tanaka, in Ref. 29, p. 106.
135. M. Nomura, C. Iwamoto, and S.I. Tanaka, in Ref. 29, p. 23.
136. M. Nomura, C. Iwamoto, and S.I. Tanaka, Acta Mater., 47 (2) (1999), p. 407.
137. A. Tsoga, A. Naomidis, and P. Nikolopoulos, Acta Mater., 44 (9) (1996), p. 3679.
138. P. Xiao and B. Derby, Acta Mater., 46 (10) (1998), p. 3491.
139. A. Meir, P.R. Chidamabaram, and G.R. Edwards, J. Mater. Sci., 30 (1995), p. 3791.
140. A.D. Panasyuk, I.P. Neshpor, and L.I. Struk, Powd. Met. & Metal Ceram., 32 (11) (1993), p. 924.
141. J.E. Lazaroff, P.D. Ownby, and D.A. Weirauch, J. Amer. Ceram. Soc., 78 (3) (1995), p. 539.
142. P.D. Ownby, K.W. Li, and D.A. Weirauch, J. Amer. Ceram. Soc., 74 (6) (1991), p. 1275.
143. N. Sobczak et al., Inzynieria Materialowa (NR 4/1998), p. 754.
144. N. Sobczak et al., Proc. Int. Conf. Composites Eng. (ICCE-3), ed. D. Hui, p. 111.
145. K. Nogi et al., Acta Mater., 46 (7) (1998), p. 2305.
146. N. Sobczak et al., Proc. Int. Conf. Cast Composites 95'.
147. D. Chatain et al., J. Amer. Ceram. Soc., 76 (6) (1993), p. 1568.
148. D.A. Weirauch and W.J. Krafick, Metall. Trans., 21A (1990), p. 1745.
149. J.F. Silvain, J.C. Bihr, and J. Douin, Composites, Part A, 29A (1998), p. 1175.
150. H. Ho and S. Wu, Mater. Sci. Eng., A248 (1998), p. 120.
151. W. Jung et al., Metall. Mater. Trans., 27B (1996), p. 51.
152. S. Hara, M. Okamoto, and T. Tanaka, in Ref. 29, p. 94.
153. N. Sobczak et al., in Ref. 29, p. 138.
154. V.S. Zhuravlev et al., in Ref. 29, p. 158.
155. N. Sobczak et al., in Ref. 29, p. 145.
156. E. Benko et al., in Ref. 29, p. 100.
157. Y.V. Naidich, V. Zhuravlev, and K. Krasovskaya, Mater. Sci. Eng., A245 (1998), p. 293.
158. H. Fuji et al., J. Mater. Sci., 34 (1999), p. 3165.
159. S. Lequeux et al., in Ref. 29, p. 112.
160. S.W. Ip et al., Mater. Sci. Eng., A244 (1998), p. 31.
161. N. Frumin et al., Scripta Mater., 37 (8) (1997), p. 1263.
162. P.R. Chidambaram, A. Meir, and G.R. Edwards, Mater. Sci. Eng., A206 (1996), p. 249.
163. E. Saiz, A.P. Tomsia, and R.M. Cannon, Acta Mater., 46 (7) (1998), p. 2349.
164. O. Dezellus and N. Eustathopoulos, Scripta Mater., 40 (11) (1999), p. 1283.
165. K. Landry, C. Rado, and N. Eustathopoulos, Metall. Mater. Trans., 27A (1996), p. 3181.
166. V. Laurent, C. Rado, and N. Eustathopoulos, Mater. Sci. Eng., A205 (1996), p. 1.
167. V.M. Perevertailo, A.A. Smekhnov, and O.B. Loginova, in Ref. 29, p. 127.
168. A.P. Tomsia et al., in Ref. 29.
169. N. Sobczak, Interfacial Science in Ceramic Joining, ed. A. Bellosi, T. Kosmac, and A.P. Tomsia, NATO ASI Series, High Technology-vol 58 (Dordrecht, Netherlands: Kluwer Academic Publishers, 1997), p. 27.
170. N. Grigorenko et al., in Ref. 29, p. 27.
171. F.G. Yost, P.A. Sackinger, and E.J. O'Toole, Acta Mater., 46 (7) (1998), p. 2329.
172. J.A. Warren, W.J. Boettinger, and A.R. Roosen, Acta Mater., 46 (9) (1998), p. 3247.
173. R. Asthana, "Dissolutive Capillary Penetration with Expanding Pores and Transient Contact Angles," J. Colloid Interface Sci. (December 1999, submitted).
174. R. Asthana, "An Analysis for the Capillary Rise of Reactive Melts," Metall. Mater. Trans. (in press).
175. W.A. Zisman, Advances in Chemistry, 43 (1964), p. 1.
176. E. Ricci and A. Passerone, Mater. Sci. Eng., A161 (1993), p. 31.
177. N. Sobczak, Trans. Foundry Research Institute, XLIV (4) (1994), p. 221.
178. J.F. Mcdonald and J.G. Eberhart, Trans. AIME, 233 (1965), p. 512.
179. A.W. Neumann et al., J. Colloid Interface Sci., 49 (2) (1974), p. 291.
180. S.N. Omenyi and A.W. Neumann, J. Appl. Phys., 47 (9) (1976), p. 3956.
181. S.N. Omenyi, R.P. Smith, and A.W. Neumann, J. Colloid Interface Sci., 75 (1) (1980), p. 117.
182. D. Li and A.W. Neumann, J. Colloid Interface Sci., 137 (1) (1990), p. 304.
183. D.M. Stefanescu et al., Metall. Trans., 21A (1990), p. 231.
184. R. Asthana, Metall. Mater. Trans., 25A (1994), p. 225.
185. R. Asthana, J. Colloid Interface Sci., 165 (1994), p. 256.
186. E. Moy and A.W. Neumann, J. Colloid Interface Sci., 119 (1) (1987), p. 296.
187. T.G.M. Van de Ven, J. Colloid Interface Sci., 102 (1) (1984), p. 301.
188. T.G.M. Van de Ven et al., J. Colloid Interface Sci., 91 (1) (1983), p. 297.
189. R.J. Good, J. Colloid and Interface Sci., 59 (1977), p. 398.
190. S. Wu, J. Colloid Interface Sci., 71 (3) (1979), p. 605.
191. S.K. Rhee, Mater. Sci. Eng., 16 (1974), p. 45.
192. S.K. Rhee, J. Amer. Ceram. Soc., 54 (8), p. 376.
193. R. Warren, J. Mater. Sci., 15 (1980), p. 2489.
194. A.R. Miedema and R. Boom, Z. Metallkde., 69 (1978), p. 183.
195. A.R. Miedema and F.J.A. de Broeder, Z. Metallkde., 70 (1979), p. 14.
196. E.M. Washburn, Phys. Rev., 17 (1921), p. 374.
197. G.P. Martins, D.L. Olson, and G.R. Edwards, Metall. Trans., 19B (1988), p. 95.
198. K.A. Semlak and F.N. Rhines, Trans. AIME, 21 (1958), p. 325.
199. R. Asthana, Solidification Processing of Reinforced Metals (Switzerland: Trans Tech Publications, 1997), pp. 421.
200. R.P. Messner and Y-.M. Chiang, J. Amer. Ceram. Soc., 73 (5) (1990), p. 1193.
201. V.N. Eremenko and L.D. Lesnik, The Role of Surface Phenomena in Metallurgy, ed. V.N. Eremenko (New York: Consultant Bureau, English Translation), p. 102.
202. R. Asthana, "An Analysis for the Capillarity Penetration Kinetics in Reactive Couples" (Paper to be presented at the 2000 TMS Annual Meeting, Nashville, TN, 12-16 March, 2000).
203. R. Asthana and S.N. Tewari, Compos. Manuf., 4 (1) (1993), p. 3.
204. K. Nogi and K. Ogino, Adv. Structural Materials, ed. D.S. Wilkinson (New York: Pergamon, 1988), p. 97.
205. M. Shimbo, M. Naka, and I. Okamoto, J. Mater. Sci. Lett., 8 (1989), p.663.
206. R. Warren and C.H. Anderson, Composites, 15 (1984), p. 101.
207. W. Kohler, Aluminium, 51 (1975), p. 443.
208. D.S. Han, H. Jones, and H.V. Atkinson, J. Mater. Sci., 28 (1993), p. 2654.
209. J. Narcisco et al., Scripta Metall. Mater., 31 (11) (1994), p. 1495.
210. R. Asthana and P.K. Rohatgi, Compos. Manuf., 3 (2) (1992), p. 119.
211. R. Asthana and P.K. Rohatgi, Z. Metallkde., 83 (12) (1992), p. 887.
212. B.M. Gallois, JOM, 49 (6) (1997), p. 48.
213. A.C.D. Chaklader, A.M. Armstrong, and S.K. Mishra, J. Amer. Ceram. Soc., 51 (11) (1968), p. 630.
214. A.C.D. Chaklader, W.W. Gill, and S.P. Mehrotra, Interfaces in Ceramics.
215. J.J. Brennan and J.A. Pask, J. Amer. Ceram. Soc., 51 (10) (1968), p. 569.
216. J.A. Champion, B.J. Keene, and J.M. Silwood, J. Mater. Sci., 4 (1969), p. 39.
217. J. Goicoechea et al., Scripta Metall. Mater., 25 (1991), p. 479.
218. R.D. Carnaham, T.L. Johnson, and C.H. Li, J. Amer. Ceram. Soc., 41 (958) p. 343.
219. Y.V. Naidich et al., Poroshkovaya Metallurgiya, 246 (6) (1983), p. 67.
220. P.J. Bunyan and S.H. Huo, Advanced Composites '93, ed. T. Chandra and A.K. Dhingra (Warrendale, PA: TMS, 1993), p. 1009.
221. E. Saez and A.P. Tomsia, J. Amer. Ceram. Soc., 81 (9) (1998), p. 2381.
222. W.G. Fahrenholtz et al., Ceramic Microstructure: Control at the Atomic Level, ed. A.P. Tomsia and A. Glaeser (New York: Plenum Press, 1988), p. 749.
223. R.E. Loehman, K.G. Ewsuk, and A.P. Tomsia, J. Amer. Ceram. Soc., 79 (1) (1996), p. 27.
224. K. Fujita, Y. Sawada, and K. Honjo, J. Jpn. Soc. Compos. Mater., 17 (2) (1991), p. 80.
225. P. Rocher, J.M. Quenisset, and R. Naslain, J. Mater. Sci. Lett., 4 (1985), p. 1527.
226. I.L. Kalnin, U.S. patent 4,056,874 (1977).
227. A.P. Levitt, E. DiCesare, and S.M. Wolf, Metall. Trans., 3 (1972), p.2455.
228. R.T. Pepper and E.G. Kendall, U.S. patent 4,082,864 (1978).
229. O. Remondier et al., Developments in Sci. & Tech. of Compos. Mater. (ECCM-I), ed. A.R. Bunsell et al., p. 732.
230. J.P. Rocher et al., Memoires et etudes Scientifiques Revue de Metallurgie (February 1986), p. 69.
231. U. Gangopadhyaya and P. Wynblatt, J. Mater. Sci., (1995), p. 94.
232. T.J. Whalen and A.T. Anderson, J. Amer. Ceram. Soc., 58 (9) (1975), p. 396.
233. C. Zhongyu, W. Jimbo, and H. Xiangui, Interfaces in Metal Ceramic Composites, ed. R.Y. Lin et al. (Warrendale, PA: TMS, 1988), p. 233.
234. N. Sobczak et al., Materials Science Forum, Part I, 217-222, p. 153.
235. M. Nicholas and D. Mortimer, Proc. Int. Conf. Carbon Fibers, Their Compos. and Applic. (London: Plastics Institute, 1971), p. 129.
236. K. Nogi, Y. Osugi, and K. Ogino, J. Iron Steel Inst. Japan (ISIJ), 30 (1) (1990), p. 64.
237. W.B. Hillig et al., Ceram. Bull., 54 (1975), p. 1054.
238. M.C. Breslin et al., Ceram. Eng. Sci. Proc., 15 (4) (1994), p. 104.
239. F.P. Chiaramonte and B.N. Rosenthal, J. Amer. Ceram. Soc., 74 (3) (1991), p. 658.
240. H. Fuji, H. Nakae, and K. Okada, Acta Metall. Mater., 41 (10) (1993), p. 2963.
241. A.D. Panasyuk, I.P. Neshpor, and L.I. Struk, Powd. Met. Metal Ceram., 32 (11/12) (1993), p. 924.
242. C.R. Manning and T.B. Gurganus, J. Amer. Ceram. Soc., 52 (1969), p. 115.
243. S.W. Ip, M. Kuchanski, and J.M. Toguri, J. Mater. Sci. Lett., 12 (1993), p. 1699.
244. N. Kishaporov et al., Sov. Powd. Met. Metal Ceram., 11 (1984), p. 869.
245. K. Kobashi and T. Choh, J. Mater. Sci., 28 (3) (1993), p. 684.
246. H. John and H. Hausner, J. Mater. Sci. Lett., 5 (1986), p. 549.
247. H. Katzman, U.S. patent 4,376,803 (1983).
248. H. Katzman, J. Mater. Sci., 22 (1987), p. 144.
249. B. Kindl et al., Composite Sci. Tech., 43 (1) (1992), pages.
250. M. Entezarian and R.A.L. Drew, Mater. Sci. Eng., A212 (1996), p. 206.
251. N. Sobczak et al., Proc. Third Conf. Surface Phenomena in Foundry Processes (Poznan-Kolobrzeg, Poland, 1996), p. 193.
252. N. Sobczak et al., in Ref. 251, p. 201.
253. N. Sobczak, unpublished data (1999).
254. N. Sobczak et al., Proc. Annual Meeting of American Vacuum Soc. (New York: AVS, 1995).
255. N. Sobczak et al., to be published in J. Foundry Research Institute (Poland).
256. N. Sobczak, Proc. Int. Conf. Light Alloys and Composites (Zakopane, Poland, 1999), p. 341.
257. N. Sobczak et al.,in Ref. 251, p. 193.
258. B.J. Dalgleish et al., Scripta Metall., 31 (8) (1994), p. 1109.
259. J.T. Klomp, MRS Symp. Proc., 40 (Pittsburgh, PA: MRS, 1985), p. 381.
260. R. Asthana, J. Mater. Sci., 33 (1998), p. 1959.
261. R. Asthana, R. Tiwari, and S.N. Tewari, Metall. Mater. Trans., 26A (1995), p. 2175.
262. S.N. Tewari et al., Metall. Mater. Trans., 26A (1995), p. 477.
263. J.M. Howe, Int. Mater. Revs., 38 (5) (1993), p. 233.
264. M. Ueki, M. Naka, and I. Okamoto, J. Mater. Sci. Lett., 5 (1986), p. 1261.
265. M. Nicholas, P.R.D. Forgan, and D.M. Poole, J. Mater. Sci., 3 (1968), p. 9.
266. M. Nicholas, J. Mater. Sci., 5 (1970), p. 571.
267. P.K. Rohatgi et al., Mater. Sci. Eng., A162 (1993), p. 163.
268. A.G. Evans et al., Mater. Sci. Eng., A126 (1990), p. 53.
269. A.G. Evans et al., Metall. Trans., 21A (1990), p. 2419.
270. F. Ernst, Mater. Sci. Eng., R14 (1995), p. 97.
271. R. Asthana, S.N. Tewari, and S.L. Draper, Metall. Trans. A, 29A (1998), p. 1527.
272. T.P.D. Rajan, R.M. Pillai, and B.C. Pai, J. Mater. Sci., 33 (1998), p. 3491.
273. R.E. Baier, E.G. Shafrin, and W.A. Zisman, Science, 162 (1968), p. 1360.

Rajiv Asthana is an associate professor of manufacturing engineering in the Technology Department at University of Wisconsin-Stout. Natalia Sobczak is head of the Laboratory for Physical Chemistry of Metals and Alloys at the Foundry Research Institute in Krakow, Poland.

For more information, contact R. Asthana, University of Wisconsin at Stout, Manufacturing Engineering, Technology Department, 326 Fryklund Hall, Menomonee, Wisconsin 54751; (715) 232-2152; fax (715) 232-1330; e-mail asthanar@uwstout.edu.


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