Compositional variations in solid solutions

The particular evolution phenomena in material systems considered in this chapter include the transition from a nominally flat surface to a wavy surface in a stressed solid, the spontaneous growth of epitaxial islands due to deposition of a material on a substrate with lattice mismatch, stress relaxation by grain boundary diffusion, the role of stress in altering compositional variations in solid solutions, and stress-assisted diffusion in the presence of an electric field or electromigration. 

Compositional variations in solid solutions 9.6.2 Stability of a uniform composition... 

Integral and partial molar enthalpies of mixing in solid solutions may be derived by similar investigations of a series of solid solutions with systematic variation in composition. 

It should be noted, however, that in a multisite substitution where cation ordering occurs, a heat of mixing term could arise even in the absence of a compositional variation of the CFSE. For example, the excess CFSE of mixing would increase to about -8.20 kJ/mole in solid-solution formation of the liebenbergite (Mg0 49Ni0 51)2SiO4, eq. (7.14), if the CFSE of Ni2+ ions in the Ml and M2 sites were to remain constant at -143.1 and -113.2 kJ/mole, respectively. 

Pure crystals that are formed by the above rales are rare, and in most crystals, the minerals exhibit wide-ranging compositional variation. In these minerals, a given ion at a given site is substituted by another similar ion, and hence, a mineral is characterized by percent substitution of impurities or atomic percentage of one metal for another. The resulting mineral forms are called solid solutions . 

G.16 W. B. Pearson. A Handbook of Lattice Spacings and Structures of Metals and Alloys (New York Pergamon Press, 1958). A most useful source of information. Gives the crystal structures of intermediate phases, and the variation of lattice parameter with composition in solid solutions, of binary and ternary alloys. Also gives the crystal structures of metal borides, carbides, hydrides, nitrides, and binary oxides. 

Application of EQ3/6 to many important problems will depend critically on the ability to model compositional variation in clays and zeolites. Thermodynamic data for 2 1 clays, and to a lesser extent zeolites, are not sufficiently abundant or of high enough quality to construct definitive solid solution models for these phases. Nevertheless, incorporation of reasonable models into EQ3/6 is a prerequisite to assessing the sensitivity of the geochemical modeling results to different solid solution approaches and for testing predictions against experimental and field observations. 

It is not possible to detail all of the factors that may influence the complex chemical variation in apatites (see also reviews by McConnell 1973 Roy et al. 1978 Elliott 1994), especially because data for many solid solutions are either incomplete or absent. Accordingly, we have selected the uptake of REEs in FAp, OHAp, and ClAp as examples to illustrate some of the important factors, both intrinsic (crystal-chemical) and external (P-T-X), that control the compositional variation in apatites. 

The general issue of stability of composition of a solid solution is pursued further in the next subsection. Two potentially important physical effects are not taken into account in the discussion of energy variations with composition above. One of these effects arises from the possibility of atomic misfit of one species in the solution with respect to the other. The average unit cell dimension of a solid solution may depend on the composition, so that there is a stress-free volume change (or a more complex stress-free strain, perhaps) with change in concentration. For a spatially nonuniform composition, the associated stress-free strain field will be incompatible, in general, giving rise to a residual stress distribution. 

The technically important interstitial carbides usually exhibit three distinct phase ranges dependent on M C ratio. First M takes up carbon in solid solution to produce the a-phase with an expanded metal structure. When the solubility limit is passed in the range 5-10%, conversion to the )8-phase occurs which is a nonstoichiometric phase around MC0.5 composition. The width of the composition variation is temperature dependent and... 

The two main wrought copper-nickel alloys chosen for seawater service contain 10 and 30% percent nickel, respectively. When comparing international specifications, the compositional ranges of the two alloys vary slightly between specifications, as can be seen in Tables 8.15 and 8.16 for 90-10 and 70-30 copper-nickel alloys. In practice, these variations have little influence on the overall service performance of the alloys. Iron is essential for both alloys because it provides added resistance to corrosion caused by velocity effects called impingement attack. An optimum level is between 1.5 and 2.5% iron, probably as a result of solid solubility. The corrosion resistance improves with increasing iron so long as it remains in solid solution. The specification limits for alloys were set by this observation. 

In the case of solid solutions, when they become non stoichiometric in composition, variation in composition can have large effect. For example, when UO2 is made into UO2+X, the conductivity decreases by 75%. When it is made in a solid solution with Th02, conductivity is further reduced. The lowest observed conductivity for an O-deficient Th-U composition has a value of about 0.003 cal/cm °C. 

Take F as the component (element of stmcture) which leaves the solid it can be either a main constituent in the case of the variation of stoichiometry or a foreign element in the case of the variation of composition of a solid solution. The reaction can be written as ... 

Alloys of lead and thallium have a structure based upon cubic closest packing from 0 to about 87-5 atomic percent thallium. The variation of the lattice constant with composition gives strong indication that ordered structures PbTl, and PbTl, exist. In the intermediate ranges, solid solutions of the types Pb(Pb,Tl)a and Pb(Pb,Tl)TlB exist. Interpretation of interatomic distances indicates that thallium atoms present in low concentration in lead assume the same valence as lead, about 2-14, and that the valence of thallium increases with increase in the mole fraction of thallium present, having the same value, about 2-50, in PbTls and PbTl, as in pure thallium. A theory of the structure of the alloys is presented which explains the observed phase diagram,... 

The band gap of the LED varies with composition for both these solid solutions, as shown in the figure below. The cause of the variation is different for the two substances. Semiconductor band gaps increase when orbital overlap decreases. A decrease in orbital overlap can arise from increased spacing between atoms or increased ionic character of the bonds. 

Solid solutions are very common among structurally related compounds. Just as metallic elements of similar structure and atomic properties form alloys, certain chemical compounds can be combined to produce derivative solid solutions, which may permit realization of properties not found in either of the precursors. The combinations of binary compounds with common anion or common cation element, such as the isovalent alloys of IV-VI, III-V, II-VI, or I-VII members, are of considerable scientific and technological interest as their solid-state properties (e.g., electric and optical such as type of conductivity, current carrier density, band gap) modulate regularly over a wide range through variations in composition. A general descriptive scheme for such alloys is as follows [41]. 

An expansion of the solution TMP approach involves a cothermolytic strategy, whereby two or more molecular species that thermally convert to materials under mild heating are converted simultaneously in the same solution [83,128-130]. This cothermolysis method allows the composition of the final material to be tuned to variable stoichiometries, and has proven useful in the generation of catalytic materials where even small variations in elemental content can lead to dramatic performance changes. The remainder of this section serves to provide examples of the materials that can be formed via simple solid phase or solution TMP routes. 

The variations in Fe and Mg contents of the 14 A Fe-chlorite-14 A Mg-chlorite solid solution are considered here. However, structural formulae for chlorite are not as simple as those considered here. As mentioned by Walshe and Solomon (1981), Stoesell (1984), Cathelineau and Nieva (1985) and Walshe (1986), chlorite solid solution may be represented by six components, and accurate thermochemical data on each end-member component at the hydrothermal conditions of concern are necessary to provide a far more rigorous calculation of the equilibrium between chlorite and hydrothermal solution. However, the above argument demonstrates that the composition of chlorite is a highly useful indicator of physicochemical conditions of hydrothermal solution and extent of water-rock interaction. 

---