Solid solution disorder

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,... 

In order to clearly differentiate between the contributions from solid solution, disorder-order and precipitation strengthening contributions in such alloys, homogenized (i.e., solution annealed) and quickly quenched samples need to be investigated and compared with subsequently aged samples. 

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. 

Figure 1 Intrinsic stacking fault energy for chemically disordered solid solution Al-X (where X=Cu or Mg) as a function of composition.

In the case of lithium orthoniobate, Li3Nb04, no meta-stable phase was found that had a rock-salt crystal structure with disordered cation distribution [268]. Nevertheless, solid solutions Li2+xTii-4xNb3x03, where 0 < x < 0.22, have a monoclinic structure at low temperatures and undergo transformation to a disordered NaCl type structure at high temperatures [274]. 

Because the appearance of a superlattice is usually well characterized qualitatively in terms of an interaction parameter w which has nothing to do, in the usual treatments, with the melting of the parent solid solution, one does not expect to find a simple relationship between the critical temperature for disordering of the superlattice, and Ts, the solidus temperature of the corresponding solid... 

Four of the solid solutions of Table III have excess entropies of solution which include contributions from magnetic disordering in both the alloy and in one or both of the pure components. These contributions can be quite large, and since there is no assurance... 

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. 

Anion Interstitials The other mechanism by which a cation of higher charge may substitute for one of lower charge creates interstitial anions. This mechanism appears to be favored by the fluorite structure in certain cases. For example, calcium fluoride can dissolve small amounts of yttrium fluoride. The total number of cations remains constant with Ca +, ions disordered over the calcium sites. To retain electroneutrality, fluoride interstitials are created to give the solid solution formula... 

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. 

At variance with the evaporated samples, Am and did not change much for the sol-gel ones, in spite of the difference between AE cation radii size (Fig. lb, c). It can be suggested that the sol-gel method succeeded in better introduction of Nd into a solid solution (supported by the TPD results) which also depended to a lower extent on the cation radii size match. The increase of the lattice anisotropy AO (Fig. Id) and the trend of the local strain values to decrease or remain about constant (Fig. lc) indicated that there was competition between disorder sources of different nature dispersed lattice defects and Nd3+ agglomerates. 

Taking into account thatiVAA = /VBB and Nm =zN - /VAA - NBB the energy of the disordered solid solution becomes... 

The extent of solute disorder is high before crystallization, because each ion or molecule resides in solution, and thereby experiences the same freedom as a molecule of liquid. Conversely, the extent of disorder after crystallization will inevitably be much smaller, since solute is incorporated within a solid comprising a regular repeat lattice. 

Ihe present paper is intended to review the most important literature in this field and to extend the theory from the widely accepted ideal solid solutions to the more general models of regular solid solutions ( 5), with and without ordering (6 ) or substitutional disorder (2, b, 1). 

DISTRIBUTION LAWS AND SUBSTITUTIONAL DISORDER Driessens (2 ) has discussed the consequences of substitutional disorder on component activities in solid solutions. For example, solid solutions of the Formula ... 

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

This is also valid for the more complex spinel solid solutions of FejO, Mn304 and CO3O4, in which electron exchange occurs in addition to substitutional disorder (2). 

Substitutional Disorder In Regular Solid Solutions. Most simple ionic solutions in which substitution occurs in one sublattice only are not ideal, but regular 2, J3) Most complex ionic solid solutions in which substitution occurs in more than one sublattice are not only regular in the sense of Hildebrand s definition (15) but also exhibit substitutional disorder. The Equations describing the activities of the components as a function of the composition of their solid solutions are rather complex ( 7, V7, 1 ), and these can be evaluated best for each individual case. Both type II and type III distributions can result from these conditions. 

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 situation in the solid state is generally more complex. Several examples of binary systems were seen in which, in the solid state, a number of phases (intermediate and terminal) are formed. See for instance Figs 2.18-2.21. Both stoichiometric phases (compounds) and variable composition phases (solid solutions) may be considered and, as for their structures, both fully ordered or more or less completely disordered phases. This variety of types is characteristic for the solid alloys. After a few comments on liquid alloys, particular attention will therefore be dedicated in the following paragraphs to the description and classification of solid intermetallic phases. 

For these phases the reported formulae generally correspond to an average composition within a solid solution field. This also in relation to a (partially) disordered occupation of the different sites. 

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