Metal disorder, solid solutions

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

DISORDERED SOLID SOLUTION OF H IN "SIMPLE" METALS 3.1 Hydrogen Potential... 

Finally, Section 2.6, after some concluding remarks, proposes some ideas for future work that particularly concern the high-temperature oxidation of intermetallic compounds that are not considered in the present overview. Contrary to the case of pure metals or disordered solid solutions, vacancies in intermetallic compounds cannot be considered as non-conservative species. Indeed, their equilibrium molar fraction depends not only on temperature and stress state but also on the local chemical composition, which corresponds to a situation drastically different from that of a pure metal or a disordered solid solutions. 

The schematization of Fig. 2.5 and relation [2.1] remain valid for the selective oxidation of ideal disordered solid solutions. Indeed, the total volume of such an ideal solid solution does not depend on the spatial distribution of its constituents, as the partial molar volume of each constituent is equal to its molar volume. Therefore, there is no difference between the pure metal and an ideal solid solution regarding the definition and location of planes il/and Km- In relation [2.1], the value of 0 is then that of the selectively oxidized constituent. 

In the examples given below, the physical effects are described of an order-disorder transformation which does not change the overall composition, the separation of an inter-metallic compound from a solid solution the range of which decreases as the temperature decreases, and die separation of an alloy into two phases by spinodal decomposition. 

G. Foumet, Order-disorder phenomena in solid solutions, in. Phase Stability in Metals and Alloys", P S. 

Whereas the quasi-chemical theory has been eminently successful in describing the broad outlines, and even some of the details, of the order-disorder phenomenon in metallic solid solutions, several of its assumptions have been shown to be invalid. The manner of its failure, as well as the failure of the average-potential model to describe metallic solutions, indicates that metal atom interactions change radically in going from the pure state to the solution state. It is clear that little further progress may be expected in the formulation of statistical models for metallic solutions until the electronic interactions between solute and solvent species are better understood. In the area of solvent-solute interactions, the elastic model is unfruitful. Better understanding also is needed of the vibrational characteristics of metallic solutions, with respect to the changes in harmonic force constants and those in the anharmonicity of the vibrations. 

Different metals can very frequently be mixed with each other in the molten state, i.e. they form homogeneous solutions. A solid solution is obtained by quenching the liquid in the disordered alloy obtained this way, the atoms are distributed randomly. When cooled slowly, in some cases solid solutions can also be obtained. However, it is more common that a segregation takes place, in one of the following ways ... 

Two metals that are chemically related and that have atoms of nearly the same size form disordered alloys with each other. Silver and gold, both crystallizing with cubic closest-packing, have atoms of nearly equal size (radii 144.4 and 144.2 pm). They form solid solutions (mixed crystals) of arbitrary composition in which the silver and the gold atoms randomly occupy the positions of the sphere packing. Related metals, especially from the same group of the periodic table, generally form solid solutions which have any composition if their atomic radii do not differ by more than approximately 15% for example Mo +W, K + Rb, K + Cs, but not Na + Cs. If the elements are less similar, there may be a limited miscibility as in the case of, for example, Zn in Cu (amount-of-substance fraction of Zn maximally 38.4%) and Cu in Zn (maximally 2.3% Cu) copper and zinc additionally form intermetallic compounds (cf. Section 15.4). 

The hardness shear modulus ratio in this case is similar to the one for metallic glasses. This suggests that the structure in the KCl-KBr solid solution is highly disordered i.e., glassy. 

Mutual solid-state solubility a simple structural representation - order/ disorder. In a number of systems such as the previously described V-Mo and Cs-Rb, continuous solid solutions are formed in the whole range of compositions, characteristics and structures of which will be discussed in more detail in Chapter 3. These result from two metals having the same crystal structure, which is maintained for all the intermediate compositions, due to a continuous random substitution of the atoms of one kind for another and vice versa. 

The methodology for obtaining the partial atomic volume and its application as a realistic measure of atomic size in metals and alloys has been discussed by Bhatia and Cahn (2005) they illustrated its use as a powerful tool in understanding the behaviour of solid solutions in both ordered and disordered states. 

In the context of bidentate ligands, and in a similar vein to the polyfunctional aryloxides discussed above [141, 142, 146, 147], the chelation of a metal centre by deprotonated j5-diketones is a recurrent feature of monomeric organooxide complexes of aluminium. The employment of such ligands results in the observation of simple hexa-coordinate complexes which incorporate three [RC(0)C(H)C(0)R ] moieties (R = R = Me [177,178], CF3 [179], Ph [180, 181] R = f-Bu, R = CF3 [182]). More recently, the cocrystallisation of M(acac)3 (M = Al, Cr) has allowed the crystallographic study of metal disorder in a series of solid solutions of stoichiometry Ali, cCi x(acac)3 (x = 0.02-0.91) [183, 184]. Chelation of the metal centre similar to that reported in monomeric ] -diketonates has also been noted in the presence of... 

As the amount of Fe is increased, the (111) peak shifts to smaller d-spacings, reflecting a contraction of the lattice. The (111) peak positions in Fig. 11.5 show a continuous shift from pure Pt to pure Fe. The Pt-Fe XRD patterns are consistent with a single-phase, substitutional solid solution (disordered alloy) over the entire compositional range. In contrast, Fig. 11.6 clearly displays diffraction from inter-metallic compounds of lower symmetry. Post-deposition annealing has resulted in an ordering of the Pt and Fe atoms, the effect of which is the crystallization of an ordered metal alloy of lower symmetry than 100% Pt. In essence, the applied vacuum deposition method is ideally suited for the preparation of multi-component,... 

Figure 22 Depiction of the arrangements of metal atoms in solid solutions of gold copper alloys (a) disordered stmcture in which the metal atoms are statistically distrihuted and (b) the ordered stmcture with copper atoms (filled circles) are in the face centers and gold atoms (open circles) at the cube comers...

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