Alloys, ordered

Other examples of order-disorder second-order transitions are found in the alloys CuPd and Fe Al. Flowever, not all ordered alloys pass tlirough second-order transitions frequently the partially ordered structure changes to a disordered structure at a first-order transition. 

We have studied the fee, bcc, and hep (with ideal eja ratio) phases as completely random alloys, while the a phase for off-stoichiometry compositions has been considered as a partially ordered alloy in the B2 structure with one sub-lattice (Fe for c < 50% and Co for c > 50%) fully occupied by the atoms with largest concentration, and the other sub-lattice randomly occupied by the remaining atoms. 

We have considered the fee and bee phases for both random and ordered (partially ordered) alloys. The ordered bee phase is based on the B2 structure. In this structure only the FcsoXso (X = Co, Ni or Cu) alloys can be perfectly ordered. For the off-stoichiometry compositions partially ordered alloys have been considered with one... 

Figure l.The CPA-LSDA-ASA results for the energy of bcc (fat lines) and fee (thin lines) random and ordered alloys. The fee random phase is the referenee energy and defines zero in the graph. The random phases are given in full drawn lines and the ordered phases are given in dashed lines. 

In a previous work we showed that we could reproduce qualitativlely the LMTO-CPA results for the Fe-Co system within a simple spin polarized canonical band model. The structural properties of the Fe-Co alloy can thus be explained from the filling of the d-band. In that work we presented the results in canonical units and we could of course not do any quantitative comparisons. To proceed that work we have here done calculations based on the virtual crystal approximation (VGA). In this approximation each atom in the alloy has the same surrounding neighbours, it is thus not possible to distinguish between random and ordered alloys, but one may analyze the energy difference between different crystal structures. 

Diffusion in Ordered Alloys and Intermetallic Compounds ed. by B. Fultz et al. TMS Publication, Warrendale, PA (1993), 79-90. 

It should be emphasized here that usual tracer diffusion experiments in LI2 ordered alloys due to diffusion of majority atoms mainly over their own sublattice do not give any of the strongly desired information about ordering kinetics. The study of order-order relaxations in contrast, yields a selective information Just about those atomic Jump processes which are related to ordering phenomena. 

R.W Cahn, Antiphase domains, disordered films and the ductility of ordered alloys based on Ni3 Al, Mai. Res. Soc. Symp. Proc. 81 27 (1987)... 

Behaviour in short-range ordered alloys, Phys. Rev. Lett. 70 3311 (1993). 

The second difficulty is where to locate the terminating planes. In the case of an ordered alloy the microscopic position of these planes with respect to the unit cell might make a difference to the result, and it has to be correctly chosen, as discussed in detail below. 

Formula for the chemical potentials have been derived in terms of the formation energy of the four point defects. In the process the conceptual basis for calculating point defect energies in ordered alloys and the dependence of point defect concentrations on them has been clarified. The statistical physics of point defects in ordered alloys has been well described before [13], but the present work represents a generalisation in the sense that it is not dependent on any particular model, such as the Bragg-Williams approach with nearest neighbour bond energies. It is hoped that the results will be of use to theoreticians as well as... 

In summary, the OP-term introduced by Brooks and coworkers has been transferred to a corresponding potential term in the Dirac equation. As it is demonstrated this approach allows to account for the enhancement of the spin-orbit induced orbital magnetic moments and related phenomena for ordered alloys as well as disordered. systems by a corresponding extension of the SPR-KKR-CPA method. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

The structures of the ordered alloys AuCu and AuCu3. At higher temperatures they are transformed to alloys which have all atomic positions statistically occupied by the Cu and Au atoms... 

Disordered alloys may form when two metals are mixed if both have body-centered cubic structures and if their atomic radii do not differ by much (e.g. K and Rb). The formation of ordered alloys, however, is usually favored at higher temperatures the tendency towards disordered structures increases. Such an arrangement can even be adopted if metals are combined which do not crystallize with body-centered cubic packings themselves, on condition of the appropriate composition. /J-Brass (CuZn) is an example below 300 °C it has a CsCl structure, but between 300 °C and 500 °C a A type transformation takes place resulting in a disordered alloy with a body-centered cubic structure. 

With this imaging system it is possible to study virtually all metals and alloys, many semiconductors and some ceramic materials. The image contrast from alloys and two-phase materials is difficult to predict quantitatively, as the effects of variations in chemistry on local field ion emission characteristics are not fully understood. However, in general, more refractory phases image more brightly in the FIM. Information regarding the structure of solid solutions, ordered alloys, and precipitates in alloys has been obtained by FIM. 

Although creating complex ternary and higher-order alloys with specific intermetallic phases was no longer required, the preparation of solutions with potentially harmful constituents was required. 

However, the predse structure of the catalyst and the precise role of CeC>2 in the present case and of Bi is not completely clear. In general terms, several explanations for the rate and selectivity enhancements by the promoter are possible [80] (a) geometric blocking of a fradion of sites and generation of specific surface ensembles, viz. formation of an ordered alloy (b) neighboring atom participation (Fig. 11.4), although the partial oxidized state of the promoter (Bix+) of the model is not confirmed by surface studies (LEED, XPS, EXAFS) (c) occurrence of bi-fundional catalysis, assuming that O or OH radicals formed on the promoter participate in the oxidation. 

A significant review of several aspects of the phase diagram computation (phase diagram calculations in teaching, research and industry) has been published by Chang (2006). The relationship between the characteristic features of a phase diagram and the relative thermodynamic stabilities of the phases involved has been there underlined and exemplified. Representative examples of binary, ternary and high-order alloy systems have been presented. Moreover a number of applications have... 

For a discussion on the trends of lattice parameter and volume changes consequent on disordering some types of structure see Bhatia and Cahn (2005). They observed that, when the more electropositive constituent of the alloy is a simple metal, a strong correlation may be observed between the volume increase on disordering and the formation volume of the ordered alloy. 

This is essentially the same expression already given for the BWG approximation (Eq. (7.3)) with an additional function that combines the various vibrational frequencies of different bonds. In an ordered alloy the A-B bonds are expected to be stiffer than those of the A-A and A-B bonds, so the vibrational entropy of the ordered state will be lower than that of the disordered state, thus lowering the critical ordering temperature. 

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