Coordinate system Gibbs triangle

Chemical system with three isomers (A) coordinates in balance triangle (simplex) (B) levels of the Gibbs free energy C (C) domain of inaccessibility in the vicinity of Aq point X, Y, and Z denote two-component mixtures with equal concentrations (ct/2) of both components ... 

A thermodynamic example may be illustrative. Consider Maxwell s model of the Gibbs USV surface for water (Fig. 1.1), as depicted schematically in Fig. 9.1. In this model, the physical (77, S, V) coordinates are associated with mutually perpendicular axes, and three chosen points on this surface form a triangle whose edges, angles, and area are as shown in Fig. 9.1a. However, the model might have been constructed (with equal thermodynamic justification) in a skewed /io/ orthogonal axis system (Fig. 9.1b) in which the... 

In Section 4.3.3, it was explained how to construct the reaction (diffusion) path for ternary and higher solid solution systems. In practice, one plots, for example, in a ternary system, the composition variables (measured along the pertinent space coordinate of the reacting solid) into a Gibbs phase triangle, noting that the spatial information is thereby lost. For certain boundary conditions, such a reaction path is independent of reaction time and therefore characterizes the diffusion process. For a one dimensional ternary system with stable interfaces, these boundary conditions are c,-( = oo,f) = c°( oo) q( <0,0) = c (-oo) c,(f>0,0) = c (+oo). 

For a three-component mixture, it is convenient to present the composition space C3 as an equilateral triangle, the height of which equals one (Fig. 1.1b). The triangle s vertexes represent pure components, the points within its sides, represent the binary constituents of the three-component mixture, and the inner points of triangle represent the three-component mixture compositions. The lengths of the perpendiculars to the triangle s sides correspond to the concentrations of the components indicated by the opposite vertexes. The described system of coordinates, which bears the name of the system of uniform coordinates, was introduced by Mobius and was further developed by Gibbs. 

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