Gibbs free energy alloying

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

This is but one possible expression for the Gibbs free energy. We could write an expression in terms of changes in other state variables, such as temperature and pressure. Furthermore, we must account for the possibility that a component may be distributed among or transported between several phases within the system (e.g., alloys). Alternatively, many reactions of interest to the materials... 

The dependence of the Gibbs free energy pathway on electrode potential (Figure 3.3.10A) manifests itself directly in the experimental current potential characteristic illustrated in Figure 3.3.10B. At 1.23 V, no ORR current is measureable, while with decreasing electrode potentials the ORR current increases exponentially until at +0.81 V, processes other than surface kinetics (e.g. mass transport) begin to limit the overall reaction rate. Figure 3.3.10B represents a typical performance characteristic of a Pt or Pt-alloy electrocatalyst for the ORR. 

On the basis of Eqs. (20.1)-(20.3), we had suggested [81] a set of thermodynamic rules for a prescreening evaluation of appropriate metals that could be alloyed to Pt. According to these rules, the relative Gibbs free energies, AAG (n = 1 and 3), are defined taking Pt as a reference ... 

Figure 6.3 Schematic dependence of Gibbs free energy on composition. Quasiequilibrium concentration of Cu in the alloy near the substrate (C ), in the intermetallic joint CueSns or rj phase (Q) and in the alloy with stable equilibrium with the planar rj phase [C ).

Figure 13.9 g(c) Gibbs free energy (per atom) as a function of composition for old and new phases Ago is the isothermal Gibbs free energy density of the cr-alloy from pure solid components. Q is the initial composition of the parent phase, Cp is the... 

Here, Ago, Agj, and Ag2 are the isothermal Gibbs free energy densities of formation of the corresponding alloys from the pure solid components ... 

Significantly different thermodynamic properties of nanocrystaiiine materials are expected to increase the Gibbs free energy of the materials alloys which can be represented as per... 

Thus, an incorporation of more active metals (e.g., Co) into Pd could facilitate the dissociative adsorption of O2 to form dissociated oxygen atoms (Oads) and these Oad atoms could migrate from the Co site to Pd site where electroreduction could occur with less polarization. Based on Gibbs free energy considerations Pd-Co, Pd-li, Pd-Co-Au, and Pd-Co-Mo are good ORR catalysts. Investigations of Pd-Co-Au (7 2 1)/C Pd-Co-Mo(7 2 l)/C ternary catalysts, and Pd-Ti binary catalyst as cathode materials in PEMFCs [150-152] showed the comparable ORR performance to that of commercial Pt/C but good methanol tolerance and stability than Pt/C [150-152]. Similar results with Pd-Co alloys dispersed on C were also found by others [153-155]. 

For the Pd-M alloy system, Wang and Balbuena [156] have proposed a thermodynamic guideline. According to them when a catalyst consists of two metals, one with a low occupancy of d-orbitals (Co, Ni, Cr, or V) and the other with fully occupied d-orbitals (Pd, Au, and Ag) the d-orbital coupling decreases the Gibbs free energy of the electron transfer steps in ORR, resulting in an enhanced ORR kinetics. 

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