Solid diagrams

Figure 2.3 (a) Isometric projection (solid diagram) for a hypothetical ternary system (b) isotherm (horizontal section) (c) binary-phase subset (d) liquidus surface. 

We now describe the phase behavior exhibited by binary mixtures at modest pressures. The kinds of behavior observed in Nature include vapor-liquid equilibria (VLE, 9.3.1-9.3.3), azeotropes ( 9.3.4), critical points ( 9.3.5), liquid-liquid equilibria (LLE, 9.3.6), and vapor-liquid-liquid equilibria (VLLE, 9.3.7). When solid-fluid equilibria occur ( 9.4), many (but not all) of the resulting phase diagrams are analogous to their counterparts in fluid-fluid equilibria for example, many liquid-solid diagrams are analogous to vapor-liquid diagrams. 

Second, recall the many analogies that occur in the phase behavior of binary mixtures. For example, many features that occur on binary vapor-liquid phase diagrams have counterparts on liquid-solid diagrams. Some of those equivalent features are listed in Table 9.2. Furthermore, such equivalences include not only the kinds of behavior but may also extend to the general shapes of two-phase lines. That is, many... 

Txy diagrams for vapor-liquid equilibria are equivalent to Txx diagrams for liquid-solid equilibria we merely relabel the lines and regions. When two structures are the same but have different labels, we say the structures are isomorphisms an example is shown in Figure 9.29. However, we caution that not all liquid-solid diagrams are isomorphic to vapor-liquid diagrams liquid-solid systems can also display phase behavior, such as peritectics, that rarely or never occurs in vapor-liquid systems. 

Asphaltenes are obtained in the laboratory by precipitation in normal heptane. Refer to the separation flow diagram in Figure 1.2. They comprise an accumulation of condensed polynuclear aromatic layers linked by saturated chains. A folding of the construction shows the aromatic layers to be in piles, whose cohesion is attributed to -it electrons from double bonds of the benzene ring. These are shiny black solids whose molecular weight can vary from 1000 to 100,000. 

Fig. 1 shows the block diagram of the vibrometer, in which the most sensible to small phase variations interferometric scheme is employed. It consists of the microwave and the display units. The display unit consists of the power supply 1, controller 2 of the phase modulator 3, microprocessor unit 9 and low-frequency amplifier 10. The microwave unit contains the electromechanical phase modulator 3, a solid-state microwave oscillator 4, an attenuator 5, a bidirectional coupler 6, a horn antenna 7 and a microwave detector 11. The horn antenna is used for transmitting the microwave and receiving the reflected signal, which is mixed with the reference signal in the bidirectional coupler. In the reference channel the electromechanical phase modulator is used to provide automatic calibration of the instrument. To adjust the antenna beam to the object under test, the microwave unit is placed on the platform which can be shifted in vertical and horizontal planes. 

Figure Al.7.11. Schematic diagram of a generic surface science experiment. Particles, such as photons, electrons, or ions, are mcident onto a solid surface, while the particles emitted from the surface are collected and measured by the detector.

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

Figure A2.5.16. The coexistence curve, = KI(2R) versus mole fraction v for a simple mixture. Also shown as an abscissa is the order parameter s, which makes the diagram equally applicable to order-disorder phenomena in solids and to ferromagnetism. The dotted curve is the spinodal.

Figure Bl.1.3. State energy diagram for a typical organic molecule. Solid arrows show radiative transitions A absorption, F fluorescence, P phosphorescence. Dotted arrows non-radiative transitions.

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

Figure Bl.26.18. Schematic diagram of the energy levels in a solid.

Figure B3.3.9. Phase diagram for polydisperse hard spheres, in the volume fraction ((]))-polydispersity (s) plane. Some tie-lines are shown connecting coexistmg fluid and solid phases. Thanks are due to D A Kofke and P G Bolhuis for this figure. For frirther details see [181. 182].

Figure C2.4.5. Horizontal transfer on a hydrophobic substrate. This metliod is useful for very rigid films tliat are in tire solid state in the ji-A-diagram.

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

Figure C2.6.9. Phase diagram of charged colloidal particles. The solid lines are predictions by Robbins et al [85]. Fluid phase (open circles), fee crystal (solid circles) and bee crystal (triangles). is tire interaction energy at tire...

System in which the solid phases consist of the pure components and the components are completely miscible in the liquid phase. We may now conveniently consider the general case of a system in which the two components A and B are completely miscible in the liquid state and the solid phases consist of the pure components. The equilibrium diagram is shown in Fig. 1,12, 1. Here the points A and B are the melting points of the pure components A and B respectively. If the freezing points of a series of liquid mixtures, varying in composition from pure A to pure B, are determined, the two curves represented by AC and BC will be obtained. The curve AC expresses the compositions of solutions which are in equilibrium, at different temperatures, with the solid component A, and, likewise, the curve BC denotes the compositions... 

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the sohd state and also in the hquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 7, 76, 1. The hquidus curve portrays the composition of the hquid phase in equihbrium with sohd, the composition of... 

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