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the glass ribbon. To eliminate this problem, bath bottom blocks are manufactured to a specific pore size distribution.

A purely surface area effect, which is very important in the corrosion of asbestos or chrysotile fibrils, is that related to ledge effects. As one can see from Fig. 2.11, ledges can greatly increase the exposed surface area. This is extremely important in the dissolution of spiral fibrils and their related health effects.

Similar structural effects can be present due to dislocations and other defects (see Fig. 2.11a). Chrysotile is a two-layer sheet silicate with a dimensional misfit between the octahedral and tetrahedral layers. This causes the sheet to curl forming spiral fibrils. This property causes some confusion since chrysotile is a sheet silicate, not a chain silicate, although both have properties related to fibrous materials.

Surface areas determined from sample geometry are generally many times smaller than that determined from BET measurements. This difference can be attributed to the presence of microscopic surface features. Thus one must be careful how surface areas are determined and how these data are related to the subsequent dissolution data.

2.5.3 Surface Energy

The surface energy of a material is the ratio of the potential energy difference obtained when moving an atom from the bulk to the surface to the area of the surface. A term that is closely related is the surface tension, which is the force required to move the atom to the surface divided by its diameter. Since liquids cannot maintain a shear stress, the surface energy and surface tension of liquids are equivalent. This is not the case for solids where the surface energy is generally greater than the surface tension. In general, the symbol used to represent surface tension is σ, whereas the one used to represent surface energy is γ.

One area where the surface energies play a very important role is in the movement of liquids into capillaries. For ceramics,

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FIGURE 2.11 Surface area increase (a) due to dislocations and defects and (b) due to ledge effect in fibrils.

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capillaries can be considered to be very small connected pores. Equation (2.43) represents the equilibrium pressure difference at the interface (i.e., liquid-vapor) due to surface energy:

(2.43)

where:

∆P = pressure drop across interface

γ= surface energy of liquid

φ= contact angle of meniscus at wall of capillary

R = radius of capillary

In actual materials, the porosity is not a cylindrical cavity and therefore one must use an effective radius that represents the weighted average of the contributing porosity. In addition, Eq. (2.43) is valid for only an empty capillary. As soon as any liquid penetrates the capillary, the driving force, ∆P, decreases.

The relationship of the surface energies among the solidvapor interface, solid-liquid interface, and the liquid-vapor interface is given by:

(2.44)

When the contact angle, φ, is less than 90°, capillary attraction will allow the liquid to fill the pores displacing the gas within without any applied force. When the contact angle is greater than 90°, an applied force, P, is required to force the liquid into the pores. The pressure exerted upon a ceramic in service will depend upon the height and density of the liquid. When this pressure is greater than P, the liquid will enter the pores that have a radius greater than R.

Carrying this one step further, the penetration of liquids between like grains of a ceramic can be predicted from the interfacial surface energies of the liquid-solid and solid-solid interfaces according to Smith [2.114] since if:

(2.45)

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complete wetting will occur. If

(2.46)

solid-solid contact is present and the liquid will occur in discrete pockets. A balance offerees exists when:

(2.47)

where φ is the dihedral angle between several grains and the liquid. Thus Eq. (2.45) is valid when and Eq. (2.46) is valid when . For this reason, 60° has been called the critical dihedral angle that separates the conditions of complete wetting and nonpenetration of the second phase between grains of the major phase. Although some data on dihedral angles exist as discussed later, very little actual data have been reported. The general factors that cause variation in the dihedral angle, however, are often mentioned (see discussion below).

The balance of forces (see Fig. 2.12) holds well for grains that tend to be rounded. If marked crystallographic faces exist, Eq. (2.47) is no longer valid. Surface forces are then no longer tangential and isotropic, which was assumed in the derivation of Eq. (2.47). However, if

(2.48)

the liquid occurs only at three grain intersections or triple points. Thus one would desire that γss be <2γsl and at least to minimize liquid penetration into the ceramic. This balance of forces is affected, however, by many things, one important factor being the temperature. Composition and grain size will also affect the overall balance of forces as discussed below.

Due to the random orientation of the three-grain junctions in polished sections, the determination of φ varies between 0° and 180°, even when it is constant throughout the structure.

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FIGURE 2.12 Balance of surface energy forces between a major and a secondary grain boundary phase (α=solid grains; ß=liquid grain boundary phase; γss=surface energy between two solid grains; γsl=surface energy between solid and liquid; and (φ=dihedral angle).

In this case, the median of a large number of determinations is taken as the dihedral angle value.*

White [2.115], in his studies of refractory systems, has shown that as the temperature increased, the dihedral angle decreased. He has also shown the effects of composition upon the dihedral angle in 85% MgO–15% Ca–Mg–silicate liquids at 1550°C in air. These effects are shown in Table 2.6. White reported that as the concentration of solid in the saturated liquid increased, the dihedral angle decreased, which is the same as the effect of temperature. Since the curvature of the grains must decrease as the dihedral angle increases, larger grains will produce a smaller dihedral angle. In addition, White showed

* The evaluation of a 3-D parameter by use of a 2-D array will always lead to a variation in values. Obtaining a representative value requires the determination of a large number of individual dihedral angles. The final average value is never the same as the actual value, but something less.

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TABLE 2.6 Effects of Composition upon the Dihedral Angle

a Substitution for MgO in an 85% MgO-15% CMS composition. Source: Ref. 2.115.

that the dihedral angle between like grains was smaller than that between unlike grains, indicating that the penetration of liquid between unlike grains should be less than between like grains.

The nature of the bonding type of the solid being attacked compared to that of the attacking medium often can give an indication as to the extent of wetting that may take place. For example, transition metal borides, carbides, and nitrides, which contain some metallic bond character, are wet much better by molten metals than are oxides, which have ionic bond character [2.116]. Various impurities, especially oxygen, dissolved in the molten metal can have a significant effect upon the interfacial surface energies. For example, Messier [2.117] reported that silicon wet silicon nitride at 1500°C in vacuum but did not spread due to oxygen contamination. In most cases, it is the nature of the grain boundary or secondary phases that is the controlling factor.

Puyane and Trojer [2.118] examined the possibility of altering the wettability of alumina by using additives to their glass composition. They found that V2O5 and CeO2 additions changed the surface tension of the glass in opposite directions, with V2O5 decreasing it and CeO2 increasing it. They concluded that the glass characteristics were more important than the solid parameters in corrosion.

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