Ternary Electrodes Under Equilibrium or Near-Equilibrium Conditions
The previous chapter described binary electrodes, in which the microstructure is composed of phases made up of two elements. It was pointed out that there are also cases in which three elements are present, but only partial equilibrium can be obtained in
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Ternary Electrodes Under Equilibrium or Near-Equilibrium Conditions
12.1
Introduction
The previous chapter described binary electrodes, in which the microstructure is composed of phases made up of two elements. It was pointed out that there are also cases in which three elements are present, but only partial equilibrium can be obtained in experiments, so the electrode behaves as though it were composed of two, rather than three, components. This chapter discusses active materials that contain three elements, but have kinetic behavior such that they behave as true ternary systems. As before, it will be seen that phase diagrams and equilibrium electrochemical titration curves are very useful thinking tools in understanding the potentials and capacities of electrodes containing such materials. It is generally more difficult to obtain complete equilibrium in ternary systems than in binary systems, so that much of the available equilibrium, or nearequilibrium, information stems from experiments at elevated temperatures. Selective, or partial, equilibrium is much more common at ambient temperatures. This will be discussed in another chapter.
12.2
Ternary Phase Diagrams and Phase Stability Diagrams
In order to represent compositions in a three-component system one must have a figure that represents the concentrations of three components. This can be done by using a two-dimensional figure, as will be seen shortly. However, if information about the influence of temperature is also desired, a three-dimensional figure is required. This is often done in metallurgical and ceramic systems in which experiments commonly involve changes in the temperature. Most electrochemical © Springer International Publishing Switzerland 2016 R.A. Huggins, Energy Storage, DOI 10.1007/978-3-319-21239-5_12
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Ternary Electrodes Under Equilibrium or Near-Equilibrium Conditions C Loci of different atom % C
Loci of different atom % A
A
B
Fig. 12.1 General coordinate scheme used to depict compositions and phase equilibria in ternary systems on isothermal Gibbs triangles
systems operate at or near constant temperatures, so three-dimensional figures are not generally considered necessary. Compositions in isothermal ternary systems can be represented on paper by using a triangular coordinate system. The method that is commonly employed in materials systems involves the use of isothermal Gibbs triangles. This scheme is illustrated in Fig. 12.1. Compositions are expressed in terms of the atomic percent of each of the three components, indicated as A, B, and C in this case. For the purposes of this discussion it is desirable to have elements as components, so that three elements are placed at the corners, and the atomic percent of an element varies from zero along the opposite side to 100 % at its corner. Thus the position of each point within the triangle represents the atomic fraction of each of the elements present in the system. Although phases in ternary systems often have ranges of composition, as they do in binary systems, it
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