Solid solutions formation

The likelihood of forming a substitutional solid solution between two metals will depend on a variety of chemical and physical properties, which are discussed in Chapter 6 (see the Hume-Rothery solubility rules in Section 6.1.4). Broadly speaking, substitutional solid solution in metallic systems is more likely when  

The solids occurring in nature are seldom pure solid phases. Isomorphous replacement by a foreign constituent in the crystalline lattice is an important factor by which the activity of the solid phase may be decreased. If the solids are homogeneous, that is, contain no concentration gradient, one speaks of homogeneous solid solutions. The thermodynamics of solid solution formation has been discussed by Vaslow and Boyd (1952) for solid solutions formed by AgCI(s) and AgBr(s). 

To express theoretically the relationship involved we consider a two-phase system where AgBr(s) as solute becomes dissolved in solid AgCI as solvent. This corresponds to the reaction that takes place if AgCI(s) is shaken with a solution containing Br. The reaction might formally be characterized by the equilibrium 

1) We follow here essentially the discussion presented in Stumm and Morgan (1981). 

The equilibrium constant for this reaction, that is, the distribution constant D is given by 

The activity ratio of the solids may be replaced by the ratio of the mole fractions (XAgCi = nAgci/ (HAgci + nAgBr) multiplied by activity coefficients  

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The stoichiometry must be exact. Coprecipitation by solid-solution formation, foreign ion entrapment, and adsorption are possible sources of error. 

The temperature dependence of electrical conductivity has been used [365] to distinguish between the possible structural modifications of the Mn02 yielded by the thermal decomposition of KMn04. In studies involving additives, it is possible to investigate solid-solution formation, since plots of electrical conductivity against concentration of additive have a characteristic V-shape [366]. 

Measurements of photoconductivity and of the Hall potential [367] are accurate and unambiguous methods of detecting electronic conduction in ionic solids. Kabanov [351] emphasizes, however, that the absence of such effects is not conclusive proof to the contrary. From measurements of thermal potential [368], it is possible to detect solid-solution formation, to distinguish between electronic and positive hole conductivity in semi-conductors and between interstitial and vacancy conductivity in ionic conductors. 

Reactions of the general type A + B -> AB may proceed by a nucleation and diffusion-controlled growth process. Welch [111] discusses one possible mechanism whereby A is accepted as solid solution into crystalline B and reacts to precipitate AB product preferentially in the vicinity of the interface with A, since the concentration is expected to be greatest here. There may be an initial induction period during solid solution formation prior to the onset of product phase precipitation. Nuclei of AB are subsequently produced at surfaces of particles of B and growth may occur with or without maintained nucleation. 

For a range of simple substitutional solid solutions to form, certain requirements must be met. First, the ions that replace each other must be isovalent. If this were not the case, other structural changes (e.g., vacancies or interstitials) would be required to maintain electroneutrality. Second, the ions that replace each other must be fairly similar in size. From a review of the experimental results on metal alloy formation, it has been suggested that 15% size difference can be tolerated for the formation of a substantial range of substitutional solid solutions. For solid solutions in nomnetal-lic systems, the limiting difference in size appears to be somewhat larger than 15%, although it is very difficult to quantify this. To a certain extent, this is because it is difficult to quantify the sizes of the ions themselves, but also because solid solution formation is very temperature dependent. 

Cation Vacancies If the cation of the host structure has a lower charge than the cation that is replacing it, cation vacancies may be introduced for the preservation of electroneutrality. Alternatively, the substitution of an anion by one of lower charge may also achieve this in certain systems. For example, NaCl is able to dissolve a small amount of CaCl2, and the mechanism of solid-solution formation involves the replacement of two Na+ ions by one Ca ion, leaving one vacancy on the Na" sublattice, Nai 2xCa Cl (where x denotes a vacancy). 

Kellogg RM, Kaptein B, Vries TR (2007) Dutch Resolution of Racemates and the Roles of Solid Solution Formation and Nucleation Inhibition. 269 159-197 Kessler H, see Weide T (2007) 272 1-50... 

Davis J.A., Fuller C.C., Cook A.D. A model for trace metal sorption processes th the calcite surface Adosprtion of Cd2+ and subsequent solid solution formation. Geochim Cosmochim Acta 1987 51 1477-1490. 

Nikitin, B. A., Chemistry of the Inert Gases. IV. Solid-Solution Formation Between Inert Gases and Other Substances, Doklad. Akad. Nauk SSSR 24 562-564 (1939). 

Alkaline earth oxides (AEO = MgO, CaO, and SrO) doped with 5 mol% Nd203 have been synthesised either by evaporation of nitrate solutions and decomposition, or by sol-gel method. The samples have been characterised by chemical analysis, specific surface area measurement, XRD, CO2-TPD, and FTIR spectroscopy. Their catalytic properties in propane oxidative dehydrogenation have been studied. According to detailed XRD analyses, solid solution formation took place, leading to structural defects which were agglomerated or dispersed, their relative amounts depending on the preparation procedure and on the alkaline-earth ion size match with Nd3+. Relationships between catalyst synthesis conditions, lattice defects, basicity of the solids and catalytic performance are discussed. 

Todd, A. C. and M. Yuan, 1990, Barium and strontium sulphate solid-solution formation in relation to North Sea scaling problems. SPE Production Engineering 5, 279-285. 

The qualitative significance of solid solution formation can be demonstrated with the help of this simplified equation, using the following numerical example. 

The composition of the equilibrium mixture shows that Br has been enriched significantly in the solid phase in comparison to the liquid phase (D > 1). If one considered the concentrations of aqueous [Br"] and [Ag+], one would infer, by neglecting to consider the presence of a solid solution phase, that the solution is undersaturated with respect to AgBr ([Ag+] [Br ]/KsoA Br = 0.1). Because the aqueous solution is in equilibrium with a solid solution, however, the aqueous solution is saturated with Br. Although the solubility of the salt that represents the major component of the solid phase is only slightly affected by the formation of solid solutions, the solubility of the minor component is appreciably reduced. The observed occurrence of certain metal ions in sediments formed from solutions that appear to be formally (in the absence of any consideration of solid solution formation) unsaturated with respect to the impurity can, in many cases, be explained by solid solution formation. 

It may be noted that, since the distribution coefficient is smaller than unity, the solid phase becomes depleted in strontium relative to the concentration in the aqueous solution. The small value of D may be interpreted in terms of a high activity coefficient of strontium in the solid phase, /srco3 38. If the strontium were in equilibrium with strontianite, [Sr2+] 10 3-2 M, that is, its concentration would be more than six times larger than at saturation with Cao.996Sro.oo4C03(s). This is an illustration of the consequence of solid solution formation where with Xcaco3 /caC03 -1 ... 

We already touched on some aspects of carbonate surface chemistry e.g., in Chapter 3.4. We have already illustrated some of the factors that affect surface charge and the point of zero charge, pHpzc, in Chapter 3.5, and have discussed certain elementary aspects of CaC03 nucleation in Chapter 6.5 and of coprecipitation (and solid solution formation) in Chapter 6.7. 

Recent work by Stipp and Hochella (1991) provide evidence for the processes of reconfiguration and hydration at the calcite surface. These results may provide a basis for future spectroscopic studies of trace metal adsorption and subsequent solid-solution formation. 

Davis, J. A., C. C. Fuller, and A. D. Cook (1987), "A Model for Trace Metal Sorption Processes at the Calcite Surface Adsorption of Cd2+ and Subsequent Solid Solution Formation", Geochim. Cosmochim. Acta 51, 1477-1490. 

This book deals only with the chemistry of the mineral-water interface, and so at first glance, the book might appear to have a relatively narrow focus. However, the range of chemical and physical processes considered is actually quite broad, and the general and comprehensive nature of the topics makes this volume unique. The technical papers are organized into physical properties of the mineral-water interface adsorption ion exchange surface spectroscopy dissolution, precipitation, and solid solution formation and transformation reactions at the mineral-water interface. The introductory chapter presents an overview of recent research advances in each of these six areas and discusses important features of each technical paper. Several papers address the complex ways in which some processes are interrelated, for example, the effect of adsorption reactions on the catalysis of electron transfer reactions by mineral surfaces. 

First rule Effect of the size factor. If the atomic sizes of the two components differ more than 15%, extended solid solution formation is not expected. 

Second rule Effect of the electrochemical nature. If the electrochemical characteristics of the two elements are similar, solid solution formation may be expected, otherwise compound formation is more probable. 

Some aspects of the mentioned relationships have been presented in previous chapters while discussing special characteristics of the alloying behaviour. The reader is especially directed to Chapter 2 for the role played by some factors in the definition of phase equilibria aspects, such as compound formation capability, solid solution formation and their relationships with the Mendeleev Number and Pettifor and Villars maps. Stability and enthalpy of formation of alloys and Miedema s model and parameters have also been briefly commented on. In Chapter 3, mainly dedicated to the structural characteristics of the intermetallic phases, a number of comments have been reported about the effects of different factors, such as geometrical factor, atomic dimension factor, etc. on these characteristics. 

Many solid-state reactions may be pictured as proceeding in two steps. First a homogeneous process leads to product molecules dissolved in residual parent matrix. Curtin and Paul, in a review on thermal solid-state reactions (6), divide this step into a number of stages First, there is a loosening of the molecules at the reaction site to be, then molecular change (the true reaction), and finally solid-solution formation. When the concentration of the accumulated product exceeds the solubility limit the second step, the decomposition of this solid solution into separate reactant and product phases, occurs. However, in some cases the solubility limit is very low, so that the overall process appears to become simpler ... 

Fig. 2.2 Solid solution formation by doping with aliovalent ions.

Wolska, E. Schwertmann, U. (1993) The mechanism of solid solution formation between goethite and diaspore. Neues Jahrb. Miner. Monatsh. 5 213-233... 

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