Free energy-temperature diagrams

Free Energy - Temperature Diagrams (Ellingham Diagrams)... 

Figure 3.6 Free energy-temperature diagram with scales showing oxygen pressures, C0/C02 and H2/H20 pressure gas ratios.

Fig. 4.15 Characteristic free-energy temperature diagram (a) and DSC traces (b) for the enantiotropic relationship between polymorphs. The Gi and Gu curves cross at the transition temperature 7[ n below their melting points mpi, and mpn all indicated on the temperature axis. DSC trace A at the transition temperature modification I undergoes an endothermic transition to modification II, and the heat absorbed is A/fi n for that transition. Modification II then melts at mpn, with the accompanying AHfu. DSC trace B Modification I melts at mpi with A//n followed by crystaUization of II with A//ni at the intermediate temperature. Modification II then melts with details as above. DSC trace C modification II, metastable at room temperature, transforms exothermically to modification I with A/fn i at that transition temperature. Continued heating leads to the events in trace A. DSC trace D modification II exists at room temperature and no transition takes place prior to melting at mpn, with the appropriate A//ni- (After Giron 1995, with permission.)...

Fig. 9.2. Flowchart of prilocaine hydrochloride solid state forms and melt with transformation temperatures under ambient pressure conditions (left) and semi-schematic energy/temperature diagram of the polymorphs (right). Key H, enthalpy G, Gibbs free energy AHf, heat of fusion Liq, liquid phase (melt). Reproduced from [36]...

The subject matter is introduced by a short exposition of the Gibbs phase rule in Sec. 8.2. Unary component systems are discussed in Sec. 8.3. Binary and ternary systems are addressed in Secs. 8.4 and 8.5, respectively. Sec. 8.6 makes the connection between free energy, temperature, and composition, on one hand, and phase diagrams, on the other. 

Figure 8.12 Temperature versus composition phase diagram and corresponding free-energy composition diagrams at various temperatures. In the two-phase region, a mixture of the solid and liquid solution is the lowest-energy configuration.

Draw schematic free-energy-composition diagrams and plots of activity versus composition at representative temperatures for binary systems A-B that... 

Figure 6.17 Free-energy-composition diagrams corresponding to equilibria at selected temperatures on Figure 6.15 (a) Ti, (b) T2 and (c)r3.

Figure 2. Energy/temperature diagram for nimodipine. Form I has a melting point of 124°C, with heat of fusion of AH, . Form II has a melting point of 116°C and a heat of fusion of AH , n. The transition of Form I to Form II occurs at 88°C with a heat of transition of AHti n- The enthalpies are given by H, and H and the free energies by G j, G, and G, for the liquid and Forms I and II respectively. Reprinted from reference [18] with permission from Elsevier Science.

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

Figure 8.19 F.llingham diagram for the free energy of formation of metallic oxides. (After F. D. Richardson and J. H. F. Jeffes, J. Iron Steel Inst. 160, 261 (1948).) The oxygen dissociation pressure of a given M - MO system at a given temperature is obtained by joining on the lop left hand to the appropriate point on the M-MO frec-energy line, and extrapolating to the scale on the right hand ordinate for POi (atm).

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