Gibbs’s triangle

Fig. 1-10. Equilateral triangle (Gibb s triangle) for the representation of ternary mixtures.

The liquidus isotherms and solid-solution isoconcentration lines over the entire Gibbs composition triangle are shown in Fig. 28. A point to be elaborated upon further below is that in the Hg-Cd rich half the solid-solution isoconcentration lines turn to the Hg corner even for very high x values. An expanded plot near the -rich corner is shown in Fig. 29. The liquidus isotherms match Harman s (1980) experimental values for Cd < 0.005 and are close to his for 550 and 600°C. However, his 450 and 500°C isotherms are displaced from the calculated lines towards higher xCd by about 0.003 in xCd-The calculated isoconcentration lines agree with the composition analysis of films grown epitaxially upon CdTe substrates by Harman (1980) for x = 0.2 and 550°C, x = 0.3 and 575°C, x = 0.4 and 580°C, and x = 0.5 and 580°C. 

FIG. 7 The latent heat AQ per cubic centimeter of sample volume for the transition lam — Li is plotted as a function of ( )s at a fixed ratio < )o/< >w = 5.67. The squares are obtained from the calorimetric spectra, and the solid line is the prediction of Eq. (12) for the heat changes obtained from the interfacial model [29]. The inset shows the location of the sample compositions in the Gibbs phase triangle. 

Fig. 9 shows the ellipsometric isotherm A — Ao(triangles) of the cationic surfactant C12-DMP bromide. A pronounced non-monotonic behaviour is shown with an extremum at an intermidiate concentration far below the cmc. Also shown is the number density of amphiphiles adsorbed to the interface (circles) as determined by Surface second harmonic generation (SHG). At these bulk concentrations the measured number density equals the surface excess F. SHG reveals a monotoneous increase in the surface excess in qualitative agreement to a thermodynamic analysis within the Gibb s framework. The data also clearly prove that the ellipsometric quantity need not be proportional to the adsorbed amount for a soluble ionic surfactant. What causes the nonmonotonous behaviour and how can it be understood ... 

The solvent components in the feed and in the EA are chosen such that (a) the entire system formed by the starting polymer and the solvent components exhibits a miscibility gap at the temperature of operatimi (b) that, in the Gibb s phase triangle, the composititMi of the feed corresponds to a point outside of this miscibility gap and (c) that the EA is composed in such a way that the straight line drawn between feed and EA (working line) intersects the miscibility gap (Fig. 6). 

Figure 10 Dipolar solute equilibrium reorientation time at the water liquid/vapor interface. (a) The reorientation time T2 as a function of the solute s dipole moment. The solute is located in the bulk (B, squares), at the Gibbs surface region (G, circles) and 3.5A above the Gibbs surface (S, triangles), (b) the peak value of g(r) versus the dipole moment for all solute molecules studied. Squares, circles, and triangles correspond to regions B, G, and S, respectively. (Reprinted with permission from Ref. 478. Copyright 2007 American Institute of Physics.)...

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... 

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. 

Figure 3. The potential energy landscape and its connection to dynamics. Shown are (a) inherent structure energy cis. (b) configurational entropy S, and (c) diffiisivity D as functions of T for three isochores at p = 3.90 g/cm (5.13 cm /mol, triangles), p = 3.01 g/cm (6.65 cm /mol, squares), and p = 2.36 g/cm (8.50 cm /mol, circles). In panel (c). Sc is given per, Si02 unit. Panel (d) shows a test of the Adam-Gibbs relationship. Molar quantities are per mole ions.

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