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intimacy of contact—much less than that between a solid and a liquid or gas.

Applications of ceramic materials commonly involve thermal gradients. Under such conditions, it is possible for one component of a multicomponent material to diffuse selectively along the thermal gradient. This phenomenon is called thermal diffusion or the Sorét effect. This diffusion along thermal gradients is not well understood, especially for ceramic materials. See Sec. 2.9 for a discussion of diffusion.

2.5 SURFACE EFFECTS

2.5.1 Surface Charge

Gibson and LaFemina [2.104] offered an excellent discussion of the various aspects of mineral surfaces and how these affect dissolution. Surfaces that have the same atomic structure (i.e., symmetry) as the bulk are termed relaxed. Those that are different are termed reconstructed. There is an excess electronic charge density associated with the broken or dangling bonds at the surface that is not present with bonds within the bulk. Different crystal faces exhibit different numbers of dangling bonds for the ions. If electrons can transfer between dangling bonds of anions and cations, then a situation arises where one ion has completely filled bonds and the other has completely empty bonds. When this occurs, the surface is charge-neutral. This will occur for surfaces that have a stoichiometric ratio of anions to cations. If the contribution of electrons from the different ions causes an excess charge density, then the surface becomes charged. The atoms on the surface will move to minimize the excess charge density associated with the dangling bonds and thus cause a localized strain. Dissolution of mineral surfaces depends upon the surface structure or arrangement of the atoms on the surface [2.105]. Gibson and LaFemina reported that the exact chemical species forming the surface is of secondary importance and that it is the atomic connectivity that dominates surface relaxations. This is important since one

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need not have data on a specific material, chemically, but only on one of identical structure to estimate its dissolution characteristics.

2.5.2 Porosity and Surface Area

The corrosion of ceramics (i.e., weight gain/loss) is proportional to the porosity; the more porous the sample, the more corrosion that is exhibited. This is in reality related to the surface area exposed to corrosion. The fact that one material may yield a better corrosion resistance than another does not necessarily make it the better material, if the two materials have different porosities. This is very important, for example, when comparing different sintering aids for silicon nitride and their effects upon oxidation. The more oxidation-resistant material may not be due to the chemical species of the sintering aid used, but, in actuality, may be due to the fact that one particular sintering aid yields a denser sintered ceramic. One must remember that it is not the total porosity that is important, but the surface area of the total porosity, thus making the pore size distribution an important parameter to determine.

The porosity of a ceramic can affect the overall corrosion only if the attacking medium can penetrate the porosity. Washburn [2.106] derived the following equation to determine the pore size distribution by mercury intrusion:

(2.41)

where P is the pressure required to force liquid into a cylindrical pore of radius r, γ is the surface tension of the liquid, and φ is the contact angle between the liquid and the ceramic. Although some have applied this equation to liquids other than mercury, the results are generally inaccurate due to the wetting of the solid by the liquid. Several assumptions were made by Washburn; the applied force required to force a nonwetting liquid into the pore is equal to the opposing capillary force, the void space is one of nonintersecting cylindrical pores, and

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that the pores exist in a graded array with the largest ones toward the outside of the ceramic as shown in Fig. 2.10. A quick glance at Fig. 2.10 should convince anyone that Washburn’s assumptions are far from reality.

One of the more controversial aspects of this technique is the discrepancy between intrusion and extrusion data, which has been explained by contact angle hysteresis by Smithwick and Fuller [2.107]. Conner et al. [2.108] have shown the sensitivity of this technique to pore morphology. Moscou and Lub [2.109] reported that the hysteresis stems from a combination of both contact angle differences for intrusion and extrusion and pore morphology.

Lapidus et al. [2.110] and Conner and Lane [2.111] have compared computer simulations of mercury flow through a pore space assumed to be a pore-throat network to actual porosimetry data and found that the throats determine the intrusion behavior and the pores determine extrusion behavior. The reader is referred to any of several review papers for more detailed information [109, 112, 113].

FIGURE 2.10 Nonintersecting cylindrical pores in a graded array becoming larger as the surface is approached, as assumed by Washburn.

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One effect that is directly related to the pore size distribution is a phenomenon called thermal transpiration. This is the transport of gases through a ceramic caused by a thermal gradient. The relationship between pressure and temperature is given by:

(2.42)

where the subscript 1 denotes the hot face. If the gas pressure is essentially the same on both sides, gases will migrate up the thermal gradient in an attempt to make the pressure on the hot face higher. The rate of migration is inversely proportional to the square root of the molecular weight of the gas. Pore size will affect the migration since very fine pores create too great a resistance to flow and very large pores allow ordinary flow due to pressure differences. Thus at some intermediate pore size, transpiration will occur. In ceramics with a large pore size distribution, ordinary flow tends to equalize the pressures, minimizing flow by transpiration. There are no known reports in the literature indicating that thermal transpiration influences corrosion of ceramics; however, it may suggest a means to minimize the effects from corrosive ordinary flow. If sufficient flow of the transpiring gas is present, dilution of the corrosive gas at the hot face may lower the corrosion rate to an acceptable level.

The manufacturers of flat glass by one of the float processes* are well aware of the problems that thermal transpiration may cause. Although not a corrosion process, defective glass has been produced by gases transpiring up through the tin bath bottom blocks, rising through the tin, and then causing an indent in the bottom surface of the glass. In some cases, the gas pressure has been sufficient to puncture completely through

* Two somewhat different processes are currently being used today to manufacture flat glass by floating molten glass onto molten tin.

Copyright © 2004 by Marcel Dekker, Inc.