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equilibrium. Many reactions, however, closely approach equilibrium, and thus the condition of equilibrium should be considered only as a limitation, not as a barrier to interpretation of the data.
2.7.2 Graphical Representation
The thermodynamics of reactions between ceramics and their environments can be best represented by one of several different types of stability diagrams. Graphs provide the same information as the mathematical equations; however, they can display unexpected relationships that provide new insight into solving a problem. Various types of graphical representations emphasize different aspects of the information and thus are well suited only to a specific problem. Fig. 2.13 is a schematic representation for each of the various types of diagrams that one may find in the literature. Probably the most common type of graphical representation of thermodynamic data is the equilibrium phase diagram [2.1]. These are based upon the Gibbs Phase Rule, which relates the physical state of a mixture with the number of substances or components that make up the mixture and with the environmental conditions of temperature and/or pressure. The region above the solidus is of greatest importance in most corrosion studies. The liquidus lines or the boundary curves between the region of 100% liquid and the region of liquid plus solid determine the amount of solid that can be dissolved into the liquid (i.e., saturation composition) at any temperature. For this reason, these curves are also called solubility or saturation curves. Thus, these curves give the mole fraction (or weight fraction) at saturation as a function of temperature. To obtain concentrations, one must also know the density of the compositions in question.
Another type of diagram is a graphical representation of the standard free energy of formation of the product between a metal and 1 mol of oxygen as a function of temperature at a constant total pressure. These are called Ellingham diagrams [2.131]. Richardson and Jeffes [2.132] added an oxygen
Copyright © 2004 by Marcel Dekker, Inc.
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FIGURE 2.13 Representation of thermodynamic data: a) phase equilibrium diagram, b) Ellingham diagram, c) Darken and Gurry modified Ellingham diagram, d) Lou et al. modified Ellingham diagram, e) volatility diagram, f) stability diagram, g) phase stability or Kellogg diagram, h) Pourbaix diagram.
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nomograph scale to the Ellingham diagram so that one could also determine the reaction for a certain partial pressure of oxygen in addition to the temperature. Since CO/CO2 and H2/ H2O ratios are often used in practice to obtain various partial pressures of oxygen (especially the very low values), Darken and Gurry [2.133] added nomograph scales for these ratios. These diagrams now can be found in many places containing various numbers of oxidation/reduction reactions and have been referred to as Ellingham, Ellingham-Richardson, Darken and Gurry, or modified Ellingham diagrams. On these plots (Fig. 2.14), the intercept at T=0 K is equal to ∆H° and the slope is equal to -∆S°.
To use the diagram shown in Fig. 2.14, one needs only to connect the point representing zero free energy at the absolute zero of temperature (e.g., the point labeled O to the left of the diagram) and the point of intersection of the reaction and temperature in question. As an example, for alumina at 1400°C, this line intersects the pO2 scale at about 10-24 atm, the equilibrium partial pressure of oxygen for the oxidation of aluminum metal to alumina. Any pressure lower than this will cause alumina to be reduced to the metal. This leads to the general tendency for oxides to be reduced at higher temperatures at constant oxygen partial pressures. One should also be aware that any metal will reduce any oxide above it in this diagram.
One should remember that all condensed phases of the reactions plotted in Fig. 2.14 are assumed to be pure phases and therefore at unit activity. Deviations from unit activity are encountered in most practical reactions. The correction that is applied is proportional to the activities of the products to that of the reactants by use of Eqs. (2.55) and (2.58). As an example for the manufacture of glass containing nickel, the NiO activity is less than unity due to its solution in the glass. The correction term would then be negative and the free energy plot would be rotated clockwise. This change in slope can considerably affect the equilibrium partial pressure of oxygen required to maintain the nickel in the oxidized state. In this case, the lower activity
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FIGURE 2.14 The standard free energy of formation of many metal oxides as a function of temperature. (From Ref. 2.133, reproduced with permission of McGraw-Hill Companies.)
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is beneficial since the nickel will remain in the oxidized state at lower partial pressures of oxygen at any given temperature. Many reactions that do or do not occur based upon examination of Fig. 2.14 can be explained by nonunit activities.
Since greater values of negative ∆G° indicate greater stability of an oxide with respect to its elements, Ellingham diagrams are excellent for determining the relative stability of oxides in contact with metals; however, they contain no information about the various vapor species that may form. Lou et al. [2.134] have described a modified Ellingham diagram containing vapor pressure information. They have combined the information of volatility diagrams (isothermal plots of partial pressure relationships between two gaseous species in equilibrium with the condensed phases) with that of Ellingham-type information to derive a diagram for the free energy changes vs. temperature at various vapor pressures for individual oxides. The example for aluminum is shown in Fig. 2.15. This diagram is a plot of pO2 (actually, RT In pO2) and temperature for various pAlOx values. Line 6 is the boundary for the transition from Al solid or liquid to Al2O3 solid or liquid; line 7 is the boundary for transition of the principal vapors from Al to AlO2. The vapor pressure of Al over solid Al2O3 is shown as a series of lines sloping toward the right in the center portion of the diagram. The upper dashed line is the isomolar line that defines the maximum pAl over Al2O3 in a nonreactive system (i.e., vacuum or inert gas). The lower dashed line is constructed from isobaric points that represent the maximum Al vapor pressure allowed for any hydrogen pressure at a particular temperature (based upon the reaction Al2O3+3H2→2Al(g)+3H2O(g)). For example, at 1800°C, the maximum predicted vapor pressure of Al over solid Al2O3 would be 10–3 Pa and the maximum pO2 would be 10–3.3 Pa.
The free energy is also related to the dissociation pressure of the product; thus other types of graphical representations are also available in the literature. These are generally isothermal plots of the gaseous partial pressures in equilibrium with the condensed phases and have been called volatility diagrams,
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FIGURE 2.15 Ellingham type diagram for the Al–O system. (From Ref. 2.134, reprinted with permission of The American Ceramic Society, www.ceramics.org. Copyright © 1985. All rights reserved.)
volatility maps, or phase stability diagrams [2.132,2.133]. A similar type of diagram can be obtained when two oxidants are present (i.e., O2 and N2) as long as all possible condensed phases are known. Diagrams for systems such as metal-oxygen-carbon are available [2.135]. An assumption that is usually made that is not always true is that the condensed phases are at unit activity.
Unit activity should be applied only to species in the pure state.
Copyright © 2004 by Marcel Dekker, Inc.