The Alloy Free Energy

In eq. (1) the ETT order parameter z = s(p-Pc) measures, in a convenient direction, the chemical potential from that corresponding to the ETT. From the values given in Table I for the above s and q, we readily see that the occurrence of the ETTs discussed in this paper always implies an increase of the alloy free energy. Thus, CuPt random alloys, that just below and above the equiatomic concentration present both the relevant ETT s, are less stable than CuPd or AgPd and, thus more likely to be destabilised. Moreover, the proximity to both the critical concentrations implies large contributions to the BSE from the X and L points. Now, the concentration wave susceptibility, Xcc(q). as observed by Gyorffy and Stocks, is proportional to... 

The solution of these problems has been performed by calculation and analysis of crystal free energy (1). The alloy free energy has been found by the configurational method within the approximation of the pair interaction of nearest atoms without considering geometric distortion of lattice. This structure B8i has two types of tetrahedral T2,T4 interstitial sites, defined by different type site surroundings, and one type of octahedral 02 interstitial site... 

On the practical side, the difficulties involved in constructing the alloy free energy are related to the fact that somehow the effective Hamiltonian must be informed on the basis of a relatively small set of calculations. For concreteness, we consider a binary alloy in which there are two different chemical constituents. For a lattice built up of N sites, the freedom to distribute the two constituents on these N sites results in 2 configurations (i.e. each site may be assigned one of... 

In general, once both the effective cluster interactions and the statistical treatment resulting from the cluster variation method are in hand, the alloy free energy can be written as... 

The broken bond approach has been extended by Nason and co-workers (see Ref. 85) to calculate as a function of surface composition for alloys. The surface free energy follows on adding an entropy of mixing term, and the free energy is then minimized. 

Discuss the role of the surface free-energy in phenomena such as alloy segregation, surface reconstruction, faceting and sintering of small particles. How does a gas environment (air, vacuum) affect the surface composition of alloys ... 

Figure 3.18 Spectrum of free energies of hydrogen adsorption, AGh, on binary surface alloys at r = 298K. The vertical axis shows the number of elements with free energies within 0.1 eV windows (O.O-O.l eV, 0.1-0.2 eV, etc.). The sohd vertical line indicates AGh = 0- The dashed vertical line gives the hydrogen free energy adsorption for pure Pt. AU free energies are referenced to gas phase H2. Adapted from [Greeley and Nprskov, 2007] see this reference for more details.

One of the important differences between calciothermic and aluminothermic reduction of oxides concerns the interaction between the reduced metal and the reductant. Calcium does not form stable solid solutions or alloys with the reduced metals calcium contamination in the metal is, therefore, relatively small. Aluminum, on the other hand, readily forms solid solutions with the reduced metals, and the product generally contains appreciable quantities of residual aluminum. This is not a serious problem because in many cases either a certain aluminum content is desired in the reduced metal or the residual aluminum can be effectively removed in post-reduction purification operations. The extent of the contamination of a reduced metal with the reductant can be related to factors such as the reaction temperature, the standard free energy change associated with the reaction, and the slag composition. Let the following generalized reaction be considered ... 

This paper addresses two different sets of observations on the anisotropy of wetting of Pb crystals by its own melt and by Ga-Pb alloys. The observed anisotropies in these cases are due to the anisotropy of the surface free energy of solid Pb and to the intervention of surface phase transitions. 

Solution. Important assumptions include that the interfacial free energy is isotropic, that elastic strain energy is unimportant, and that the nucleation rates mentioned are for steady-state nucleation. The critical barrier to nucleation, AQe, can be calculated for the 0.3 atomic fraction B alloy using the tangent-to-curve construction on the curves in Fig. 19.18b to provide the value Aga = —9 x 107 Jm-3 for the chemical driving force for this supersaturation at 800 K. AQc is given for a spherical critical nucleus by... 

Find activity of copper in the alloy of the solidus composition, relative to the pure solid copper standard state. The standard free energy of fusion of copper is given by... 

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. 

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