Alloying model

Fig. 1. Equilibrium phase diagram T, c)=iT/Tc,c) for the alloy model used in Ref.. Solid lines boundaries of the disordered (a) and homogeneously ordered (6) fields areas c, d and e corre.spond to the two-phase region. Dashed line i.s the ordering spinodal separating the metastable disordered area c from the. spinodal decompo.sition area d. Dot-dashed line is the conditional spinodal that separate.s the area d from the ordered metastable area e.

Some evolution types observed in our simulations are shown in Figs. 2-7. The simulations were performed for the same 2D alloy model as that used in Refs. , on a square lattice of 128x128 sites with periodic boundary conditions. The as-quenched distribution Ci(0) was characterized by its mean value c and small random fluctuations Sci = 0.01. The intersite atomic jumps were supposed to occur only between nearest neighbors and we used the reduced time variable t = <7,m-... 

Fig. 8. Temporal evolution of q for the alloy model described in text after the quench from T = 0.9 to T = 0.61. at following times t after the quench (a) 0, (b) 120, (c) 260, and (d) 1000.

To examine replication of IPBs we made MFKEi-based simulations using the simplest 2D alloy model with the nearest-neighbor interaction. Some results are presented in Figs. 8-10. The lower row in Fig. 10 illustrates possible effects of thermal fluctuations, similar to those discussed in Sec. 3 for the replication of APBs. The figure shows that peculiar features of microstructural evolution are preserved even under rather strong thermal fluctuations used in this simulation. 

Fig. 12. Temporal evolution of q = cf (upper row) and c- (lower row) for the alloy model described in text, at T = 0.4, c = 0.35, = 0.01, and following values of the reduced time...

Application of Eqs. (21)-(27) to the calculations of the nucleation rates J for various alloy models revealed a number of interesting results, in particular, sharp dependence of J and embryo characteristics on the supersaturation, temperature, interaction radius, etc. These results will be described elsewhere. 

POLYMERIC ALLOYS MODEL MATERIALS FOR THE UNDERSTANDING OF THE STATISTICAL THERMODYNAMICS OF MIXTURES... 

R. Yang, S.V. Parker, J.A. Leake, R.W. Cahn, New metastable phases in nickel -rich Ni-Al-Ti alloys, in Alloy Modelling and Design, ed.G.M.Stocks and P.A. Turchi, The Minerals, Metals Materials Society (1994), p.303. 

J.S.Faulkner,Yang Wang and G.M.Stocks, in Alloy Modeling and Design edited by G.M.Stocks, C.T.Liu and P.E.A.Turchi, The Minerals, Metals and Materials Society, Warrendale, Pennsylvania (1995) ... 

Using in situ STM also makes it possible to monitor the growth of supported alloy model catalysts. The simplest way to synthesize supported alloy model catalysts is to... 

In this section, we extend the above formalism to that for an alloy surface within the CPA, which serves as the model for the pre-chemisorption substrate. The model discussed here is based on that of Ueba and Ichimura (1979a,b) and Parent et al (1980). For a comprehensive introduction to alloy surfaces see Turek et al (1996). A feature of surface-alloy models, which is different from bulk ones, is that the CP in layers near the surface is different from that in the bulk, due to the surface perturbation. Moreover, the alloy concentration in the surface layers may be quite different from that in the bulk, a feature known as surface segregation. (See Ducastelle et al 1990 and Modrak 1995 for recent reviews.) We assume that both of these surface effects are confined to the first surface layer only. 

I4Y. Liang, and, P. Sofronis, Micromechanics and Numerical Modeling of the Hydrogen-Particle-Matrix Interactions in Nickel-Base Alloys, Model. Simul. Mater. Sci. Eng., 11, 523-551 (2003). 

Both L coefficients and / factors can, in principle, be calculated from microscopic models. For the evaluation of L,j, the random-alloy model [J. R. Manning (1968) A. R. Allnatt, A. B. Lidiard (1987)] is sometimes used. For the evaluation of thermodynamic factors, one takes advantage of the empirical rule that in extended solid solutions AO-BO, the cation vacancy concentration and the oxygen potential are related to each other as... 

Let us present D explicitly for the condition d//0 = 0, omitting all details of the lengthy derivation. By application of Manning s random-alloy model [A. R. Allnatt, A.B. Lidiard (1987)], and by inserting Eqns. (5.126) and (5.131) into Eqn. (5.132), for a constant oxygen potential across the diffusion zone, a Darken type equation is obtained... 

The coherent potential approximation (1, 2) is a consistent theoretical frame, which unifies the different alloy models. In order to account for changes in the electronic nature of the atoms, the coherent potential approximation for a disordered alloy appears at present to be the best. It has been applied to single- and two-band systems (130a 130c). 

Fig. 4 The (01) crystal truncation rod of the Ag(lll)-(V3x /3)R30°-Sb structure. The experimental data points, shown as solid circles, are compared with the results of calculations for optimised versions of the faulted (solid curve) and unfaulted (dashed line) surface alloy models.

Tan and co-workers have studied the stabilty of the c(4x4) and c(2x2) phases using Monte-Carlo simulations with Lennard-Jones potentials confirming that a de-alloying transition occurs between 0.375 and 0.50 ML [117]. Within the surface alloy model the outermost mixed layer was found to be strongly buckled with Pb atoms outermost by about 0.8 A compared with the LEED value of 0.66 A. A modulation of the top layer Cu chains was also detected in agreement with experiment. The distance between neighbouring Pb atoms was found to be bi-modal with values of 3.08 and 3.22 A compared to the experimental value of 3.4 0.15 A by LEED [113] and 3.3 0.15 A by STM [115]. 

Jerdev D, Olivas A, Koel BE (2002) Hydrogenation of crotonaldehyde over Sn/Pt(l 11) alloy model catalysts. J Catal 205 278... 

The sequence of elementary steps shown in Fig. 13.2 suggests that one can formulate the problem of carbon poisoning in terms of the selectivity associated with the formation of C-0 vs. C-C bonds on Ni. In order to prevent carbon-induced deactivation, a catalyst should be able to selectively oxidize C atoms (and CH fragments) rather than form C-C bonds. This elementary step mechanism was the basis for the DFT calculations that focused on the identification of catalysts (mainly Ni-containing alloys), which preferentially oxidize C atoms rather than form C-C bonds [15, 16]. In these DFT calculations, the potential energy surfaces for the formation of C-C and C-0 bonds were calculated for different Ni alloys. The alloy model system used in these calculations contained mainly Ni, with some Ni atoms displaced by another atom in the surface layer. While we have examined a number of different alloys, we will focus our discussion on the alloy material (Sn/Ni). We note that this alloy material has also been studied by others previously [35, 38, 41, 49, 50]. 

Figure 17 Two possible structures for the c(2 x 2) Sn-Pt(lOO) surface, (a) Overlayer model with the Sn atoms located above the Pt(l 11) surface plane in threefold hollow sites, (b) Surface alloy model with the Sn atoms replacing every second Pt atom in the surface plane, (c) ALISS is ideally suited to distinguish between these two structures with high accuracy, as indicated by the shift in the critical angle for Sn-scattering upon alloying between 720-760 K. (From Ref. 73.)...

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