glasses were reacted, a semicrystalline or gel calcium phosphate formed that had a composition very similar to hydroxyapatite. Although early work by Hench et al. has indicated the need for the formation of a silica gel surface layer for silicate glasses to be bioactive, the work of Day et al. has indicated that a silica gel is not always necessary for bioactivity.

In addition to the beneficial bioactive glasses discussed above, there is the extremely important area of hazardous health effects from glasses. One such case is that of inhalation of glass fibers. The dissolution of these fibers is very critical in determining their health risk. Bauer [2.89] reported the work of Eastes and Hadley that glass fibers greater than 20 µm, if inhaled, have been correlated to respiratory disease in laboratory animals. The dissolution was dependent upon the fiber surface chemistry and physical nature. The continuous movement of fluids in the human lung can increase the dissolution rate and also transport the dissolved species to other parts of the body via the blood stream. Aluminosilicate fibers were the most durable, while the dissolution rate of borosilicate fibers (e.g., home insulation) was 1000 times greater. The biopersistence of 1-µm diameter fibers varied from several days to as long as 14 years depending upon their chemistry.

Annealing fibers at temperatures below the transition temperature decreased the dissolution rate in simulated extracellular fluid (pH=7.4) by 2 to 3 times. The fact that they have not shown any major adverse reaction in human lungs was attributed by Bauer to the high dissolution rate of glass fibers.

2.3 CORROSION BY GAS

2.3.1 Crystalline Materials

The corrosion of a polycrystalline ceramic by vapor attack can be very serious, much more so than attack by either liquids or solids. One of the most important material properties related

* The phosphorus is from a phosphate-buffered saline simulated physiological liquid.

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to vapor attack is that of porosity or permeability. If the vapor can penetrate the material, the surface area exposed to attack is greatly increased and corrosion proceeds rapidly. It is the total surface area exposed to attack that is important. Thus not only is the volume of porosity important, but the pore size distribution is also important. See Chap. 3, page 137, PorositySurface Area, for a discussion on porosity determination.

Vapor attack can proceed by producing a reaction product that may be either solid, liquid, or gas, as in the equation:

(2.26)

As an example, the attack of SiO2 by Na2O vapors can produce a liquid sodium silicate.

In another type of vapor attack, which is really a combined sequential effect of vapor and liquid attack, the vapor may penetrate a material under thermal gradient to a lower temperature, condense, and then dissolve material by liquid solution. The liquid solution can then penetrate further along temperature gradients until it freezes. If the thermal gradient of the material is changed, it is possible for the solid reaction products to melt, causing excessive corrosion and spalling at the point of melting.

The driving force for ionic diffusion through a surface reaction layer and for continued growth is thermal energy. If sufficient thermal energy is not provided, layer growth falls off rapidly. Across very thin (<5nm) films at low temperatures, strong electric fields may exist that act to pull cations through the film, much like that which occurs in the room-temperature oxidation of metals [2.90]. The growth of the reaction layer generally can be represented by one of the following equations for thin films:

(2.27)

(2.28)

(2.29)

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and for thick films:

(2.30)

(2.31)

Oxidation processes are generally more complex than the simple mechanism of a single species diffusing through an oxide layer. Preferential diffusion along grain boundaries can alter the oxide layer growth substantially. Grain boundary diffusion is a lower energy process than bulk diffusion and thus will be more important at lower temperatures. Quite often, a higher reaction rate will be observed at lower temperatures than expected if one were to extrapolate from high-temperature reaction rates. Thus the microstructure of the layer, especially grain size, is particularly important. In addition, fully stoichiometric reaction layers provide more resistance to diffusion than anionand/or cation-deficient layers, which provide easy paths for diffusion.

Readey [2.91] has listed the possible steps that might be rate-controlling in the kinetics of gas-solid reactions. These are given below:

1.Diffusion of the gas to the solid

2.Adsorption of the gas molecule onto the solid surface

3.Surface diffusion of the adsorbed gas

4.Decomposition of reactants at surface-specific sites

5.Reaction at the surface

6.Removal of products from reaction site

7.Surface diffusion of products

8.Desorption of gas molecules from the surface

9.Diffusion away from solid

Any one of these may control the rate of corrosion.

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Much attention has been given recently to the oxidation of nonoxide ceramics, especially silicon carbide and nitride. In general, the stability of nonoxides toward oxidation is related to the relative free energy of formation between the oxide and nonoxide phases. When studying the oxidation of nitrides, one must not overlook the possibility of the formation of an oxynitride, either as the final product or as an intermediate. The stability of the oxide vs. the nitride, for example, can be represented by the following equation:

(2.32)

As the difference in free energy of formation between the oxide and the nitride becomes more negative, the greater is the tendency for the reaction to proceed toward the right. Expressing the free energy change of the reaction in terms of the partial pressures of oxygen and nitrogen, one obtains:

(2.33)

One can then calculate the partial pressure ratio required for the oxide or nitride to remain stable at any temperature of interest. For example, the oxidation of silicon nitride to silica at 1800 K yields a partial pressure ratio of nitrogen to oxygen of about 107. Thus very high nitrogen pressures are required to stabilize the nitride. Anytime the permeability of the product gas through the reaction layer is less than that of the reactant gas, the product gas pressure can build at the interface to very high levels with the result being bubbles and/or cracks in the reaction interface layer. This subsequently leads to continued reaction.

The reduction of oxide ceramics at various partial pressures of oxygen may also be of interest and can be obtained from the examination of Ellingham plots of ∆G°=-RT In pO2 vs. temperature (see Fig. 2.14 in Sec. 2.7.2). If one is interested in the reduction of a binary compound, such as mullite, the presence of a second more stable oxide that forms the

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compound increases the stability of the less stable oxide by decreasing RT In pO2. Although increasing the stability of the less stable oxide, the magnitude of this change is not large enough to increase the stability of the more stable oxide. Thus the free energy of formation of mullite will be between that of silica and alumina but closer to that of silica.

The reduction of binary compounds can take place by one of the constituent oxides being reduced with decreasing oxygen partial pressure:

(2.34)

a reaction that is very common when transition metals are present. These reactions become very important when applications of double oxides (or multicomponent oxides) require placement in an environment containing an oxygen potential gradient. In more general terms, this is true for any gaseous potential gradient if the gas phase is one of the constituents of the solid.

As reported by Yokokawa et al. [2.92], a double oxide may decompose kinetically even if the oxygen potential gradient is within the stability region of the double oxide. This kinetic decomposition is due to cation diffusivity differences along the oxygen potential gradient.

Another factor that might enhance the reduction of an oxide is the formation of a more stable lower oxide and the vaporization of the reaction products. An example of this is the reduction of silica by hydrogen at elevated temperature to the monoxide, which is highly volatile above 300°C.

A loss of weight by oxidation to a higher oxide that is volatile can also occur. A good example of this is the assumed vaporization of Cr2O3 that actually occurs through oxidation to CrO3 gas by the following equation:

(2.35)

This reaction is one that is not easily proven experimentally since CrO3 upon deposition/condensation dissociates to Cr2O3

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and O2. CrO3 gas; however, it has been identified by mass spectrometry [2.93]. Diffusion of CrO3 gas through a stagnant gaseous boundary layer was determined to be rate-controlling as opposed to the surface reaction for the reaction above [2.94].

A gas that is often encountered in practical applications is water vapor. An increase in corrosion rates when moisture is present has been reported by many investigators. This is apparently related to the ease with which gaseous hydroxide species can form.

A possible rate-controlling step in vapor attack is the rate of arrival of a gaseous reactant and also possibly the rate of removal of a gaseous product. One should realize that many intermediate steps (i.e., diffusion through a gaseous boundary layer) are possible in the overall reaction, and any one of these may also be rate-controlling. It is obvious that a reaction cannot proceed any faster than the rate at which reactants are added, but it may proceed much more slowly. The maximum rate of arrival of a gas can be calculated from the Hertz-Langmuir equation:

(2.36)

where:

Z= moles of gas that arrive at surface in unit time and over unit area

Using P and M of the product gas, the rate of removal of gas product can be calculated using the same equation. To determine if service life was acceptable, these rates may be all that would be needed. Actual observed rates of removal may not agree with those calculated if some surface reaction must take place to produce the species that vaporizes. The actual difference between observed and calculated rates depends on the activation energy of the surface reaction. If the gaseous

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reactant was at a lower temperature than the solid material, an additional factor of heat transfer to the gas must also be considered and may limit the overall reaction.

According to Readey [2.91] in the corrosion of spheres, the rate of corrosion is proportional to the square root of the gas velocity. If the gas vapor pressure and velocity were held constant, the corrosion rate then would be proportional to the square root of the temperature. At low gas vapor pressures, transport of the gas to the surface controls the corrosion rate. At high vapor pressures, the reaction at the surface is controlling. The gaseous reaction products many times cause formation of pits and/or intergranular cracking. This can be very important for materials containing second phases (e.g., composites) that produce gaseous reaction products.

Pilling and Bedworth [2.95] have reported the importance of knowing the relative volumes occupied by the reaction products and reactants. Knowing these volumes can aid in determining the mechanism of the reaction. When the corrosion of a solid by a gas produces another solid, the reaction proceeds only by diffusion of a reactant through the boundary layer when the volume of the solid reactant is less than the volume of the solid reaction product. In such a case, the reaction rate decreases with time. If the volume of the reactant is greater than the product, the reaction rate is usually linear with time. These rates are only guidelines since other factors can keep a tight layer from forming (i.e., thermal expansion mismatch).

When a surface layer is formed by the reaction through which a gas must diffuse for the reaction to continue, the reaction can generally be represented by the parabolic rate law, which is discussed in more detail in Sec. 2.8. Jorgensen et al. [2.96] have shown that the theory put forth by Engell and Hauffe [2.97] that described the formation of a thin oxide film on metals was applicable to the oxidation of nonoxide ceramics. In this case, the rate constant being dependent upon oxygen partial pressure had the form:

(2.37)

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