Triangular phase diagram

Figure 8.10 (o) Three-dimensional representation of a ternary phase diagram. (/>) Triangular grid for representing compositions in a three-component system, (c) Two-dimensional representation of part (a) where boundary curves between two surfaces are drawn as heavy lines and temperature is represented by a series of lines corresponding to various isotherms. " (ct) Isothermal section of a ternary system that includes a ternary AO BO and a quaternary phase AO 2MO BO. The compatibility triangles are drawn with solid lines. 

Figure 4. Triangular phase diagram, showing partitions of R q, and Rq, at fixed...

Except for a few special cases (most notably, /inear rules (see below) and the P2 = I line for the isotropic peripheral PCA discussed above, which happens to be an endpoint of a disorder line of an exactly solved 2-dim Ising model on a triangular lattice and can be solved exactly [kinzel85b]), phase-diagrams for PCA... 

Transition probability, non-adiabatic coupling, Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 152-155 Triangular phase diagram, geometric phase... 

Figure 4. Triangular phase diagram, showing partitions of R2ar. / gc, and at fixed Q > ab + bc + ca- Physically allowed combinations lie inside the circle, with the conical intersection, corresponding to equilateral triangular ABC, at the center.

Fig. 20. Phase diagram of the triangular lattice gas model with nearest-neighbor repulsion and next-nearest neighbor attraction, for JmJJ = — 1, in the coverage-temperature plane. For fl=0.5 a Kost tz-Thouless transition occurs at Ti and a commensurate-incommensurate transition at Tj. Two commensurate. 3 x 3 phases (with ideal coverages of 1/3 and 2/3, respectively) occur, as well as several two-phase regions, as indicated in the figure. Here l.g. stands for lattice gas and LI for lattice liquid . (From Landau. )...

Figure 4.14. Phase diagram, coverage vs. temperature, of N2 physisorbed on graphite. Symbols used fluid without any positional or orientational order (F), reentrant fluid (RF), commensurate orientationally disordered solid (CD), commensurate herringbone ordered solid (HB), uniaxial incommensurate orientation-ally ordered (UlO) and disordered (UID) solid, triangular incommensurate orientationally ordered (lO) and disordered (ID) solid, second-layer liquid (2L), second-layer vapour (2V), second-layer fluid (2F), bilayer orientationally ordered (2SO) and disordered (2SD) solid. Solid lines are based on experimental results whereas the dashed lines are speculative. Adapted from Marx Wiechert, 1996.

The aim of the experiment is to determine the microemulsion (i.e. clear, single-phase) region for the three components already discussed and map out the results on a triangular phase diagram. The microemulsion region is determined by making up a series of mixtures in lOcm stoppered Erlenmeyer flasks with compositions that span the anticipated range. The procedure is to start with a volume of about 2cm of oil... 

Fig. 9. Phase diagrams of quasi-ternary systems containing two different molecular weight samples a PHIC-toluene with (Ni, N2) = (4.46,0.38) [73] b schizophyllan-water system with (Nt, N2) = (0.930, 0.0765) [75,76]. (O, A) experimental coexisting isotropic phase ( , , ) experimental coexisting anisotropic phase dashed segments, experimental tie lines the shadowed triangular region, the IAA triphasic region thick full curves, theoretical binodals thin full segments, theoretical tie lines...

The phase diagram shown in Figure 8.7 is simpler than many other ternary phase diagrams inasmuch as only one liquid crystal phase exists, and there are no three-phase triangles. By contrast, the water-decanol-sodium-caprylate phase diagram at 20°C shows 5 different liquid crystal phases and 10 triangular regions, in each of which 3 different sets of phases are in equilibrium. 

Historically, however, it has been much more common for experimentalists to introduce a new variable into Figure 1, changing either the temperature of one or more samples of fixed composition, or the electrolyte concentration in a series of samples of fixed amphiphile—oil—water ratio. The former constitutes a temperature scan the latter experiment is widely known as a salinity scan. When the temperature of an amphiphile—oil—water system is varied, the phase diagram can be plotted as a triangular prism (because temperature is an intensive or field variable). When a fourth component (eg, NaCl) is added at constant temperature, tetrahedral coordinates, are appropriate (conjugate phases have different salinities, and the planes of different tietriangles are no longer parallel). 

All the solutions which are necessary to form an equilateral triangular llxllxll, 61-element ternary phase diagram were prepared automatically by a liquid dispensing machine. Mixtures with compositions of each component ranged from 0 to 100% in 10% increments. On the 3 in quartz wafer used, 144 wells form a 12 x 12 square grid for the catalyst spots. Each of these elements has a diameter of 3 mm. The whole array is calcined at 500 °C for 12 h and subsequently for an additional 12 h at 800 °C under a 6% H2 in argon atmosphere [80],... 

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