Graphic Delineation

Figure 19. Si02 lines on the RIE d planarizing layer crosses over topo graphic features on the wafer. The Si02 three-layer RIE PCM was used to delineate these 1.0-u lines. (Reproduced with permission from Ref. 34.)...

The ranges of Eh and pH over which a particular chemical species is thermodynamically expected to be dominant in a given aqueous system can be displayed graphically as stability fields in a Pourbaix diagram,10-14 These are constructed with the aid of the Nernst equation, together with the solubility products of any solid phases involved, for certain specified activities of the reactants. For example, the stability field of liquid water under standard conditions (partial pressures of H2 and 02 of 1 bar, at 25 °C) is delineated in Fig. 15.2 by... 

One experiment not shown graphically is an oxidation reaction which was initiated at 300°C. and 100% oxygen but which led quickly to a violent run-away combustion reaction. This result is of interest only inasmuch as it delineates the upper limiting conditions for controlled oxidation of the coal here under test. 

There are many ways of differentiating numerical and graphical data. We shall confine our discussions to the technique of equal-area differentiation. In the procedure delineated below we want to find the derivative of y with respect to x. 

Equation (4.33) and its alkaline or basic form, Eq. (4.34), delineate the stability of water in a reducing environment and are represented in a graphical form by the sloping line (a) on the Pourbaix diagram in Fig. 4.10. Below the equilibrium reaction shown as line (a) in this figure, the decomposition of H O into hydrogen is favored while water is thermodynamically stable above the same line (a). As potential becomes more positive or noble, water can be decomposed into its other constituent, oxygen, as illustrated in Eqs. (4.38) and (4.39) for respectively the acidic form and neutral or basic form of the same process. 

Often it is helpful to assess current and future states graphically. As can be seen in Chart 2.8, the current state is in red (a ranking of 3.9) and the future state is in yellow (a ranking of 7.1) (See web version to view colors.). This ranking process clearly delineates where we are now and where we project ourselves to be in the future. We are now ready to develop a strategy for the future, which will be covered in the next section of this chapter. 

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