Multi-component solids

Solid-state NMR can be applied equally well to both crystalline and amorphous solids (10-17), and can be used to distinguish and quantify the crystalline and amorphous components of multi-component solids. Here we describe the... 

Stoichiometric saturation defines equilibrium between an aqueous solution and homogeneous multi-component solid of fixed composition (10). At stoichiometric saturation the composition of the solid remains fixed even though the mineral is part of a continuous compositional series. Since, in this case, the composition of the solid is invariant, the solid may be treated as a one-component phase and Equation 6 is the only equilibrium criteria applicable. Equations 1 and 2 no longer apply at stoichiometric saturation because, owing to kinetic restrictions, the solid and saturated solution compositions are not free to change in establishing an equivalence of individual component chemical potentials between solid and aqueous solution. The equilibrium constant, K(x), is defined identically for both equilibrium and stoichiometric saturation. 

The more components in a system, the more complex are the phase equilibria and it is more difficult to represent phases graphically. Descriptions of multi-component solid-liquid diagrams and their uses have been given by Mullin 3, Findlay and Campbell , Ricci , Null(10) and Nyvlt 11 1 and techniques for predicting multi-component solid-liquid phase equilibria have been presented by Hormeyer et alS12 Kusik el al.(n), and Sander et al.(U). 

FE data have been collected from the fracture of a wide variety of single and multi-component solids, ranging from single crystals of molecular solids to fiber-reinforced composites, and also from the peeling of adhesives 0-16 ). In this paper, we will restrict our attention to FE arising from the failure of polymer composites (fibrous and particulate), and the individual components thereof (fibers and matrix resins). 

Since linear variation of hardness is not always the case, equation (5.7) is approximate. But Glazov and Vigdorovich consider that the production of many very complex solid solution systems does require some method if only rough, for hardness analysis of such systems. They formulate the additivity principle for multicomponent systems as follows the numerical increase in hardness of multi-component solid solutions equals the sum of hardness increments in bi-component solutions... 

In the "Ammoniak laboratory at Oppau, a multitude of projects, including many of a non-catalytic nature, were investigated under Mittasch s administration. Yet, the study of catalysis remained closest to his heart. To an increasing extent he initiated theoretical studies to shed some light on the chemical and physical factors that make a multi-component solid catalyze a specific reaction. Primarily, these scientific investigations centered around those catalysts that had previously been found by empirical methods at the Ammoniak laboratory. 

In both solid and gaseous solutions, virial equation-based Raoultian coefficients have often been proposed. For example, the Margules equations, often used in binary and sometimes in ternary solid solutions and which have a virial equation basis, were proposed originally for gaseous solutions. However, there is no satisfactory general model for Raoultian coefficients in multi-component solid solutions, and the tendency in modeling has been to treat these solutions as ideal (i.e., to use the mole fraction of a solid solution component as its activity see Equation (3.13)). 

Stoichiometric saturation was formally defined by Thorstenson and Plummer (1). These authors argued that solid-solution compositions typically remain invariant during solid aqueous-phase reactions in low-temperature geological environments, thereby preventing attainment of thermodynamic equilibrium. Thorstenson and Plummer defined stoichiometric saturation as the pseudoequilibrium state which may occur between an aqueous-phase and a multi-component solid-solution, "in situations where the composition of the solid phase remains invariant, owing to kinetic restrictions, even though the solid phase may be a part of a continuous compositional scries". 

The second hypothesis considers the solid as a multi-component solid-solution, capable of adjusting its composition in response to the aqueous solution composition, given the long equilibration period, the relatively high solubility of the solid and relatively low solid to solution ratio. In this case, the assumption of thermodynamic equilibrium may apply. If the equilibration period is too short for thermodynamic equilibrium to have been achieved, but if an outer surface layer of the solid has been able to recrystallise (because of the high solubility of the solid), the concept of primary saturation may apply. 

Another method by which metals can be protected from corrosion is called alloying. An alloy is a multi-component solid solution whose physical and chemical properties can be tailored by varying the alloy composition. 

One of the problems of trying to establish reliable phase equilibria in multi-component solid-liquid systems is that very long periods of contact between crystals and solution are often necessary before the equilibrium state is approached. In fact, some systems can appear to be unable to achieve a stable equilibrium, in which case a meaningful phase diagram cannot be constructed. 

Thermodynamic data for multi-component solid phases and for multi-ligand aquo-conq)lexes... 

Khougaz K, Clas S-D (2000) Crystalhzation inhibition in solid dispersions of MK-0591 and poly(vinylpyrrolidone) polymers. J Pharm Sci 89 1325-1334 Kissick DJ, Wanapun D, Simpson GJ (2011) Second-order nonlinear optical imaging of chiral crystals. Annu Rev Anal Chem (Palo Alto, Cahf.) 4 419-437 Klama F (2010) NMR-studies of multi component solids. M. Sc. Dissertation, University of East Anglia, p 186... 

In this subsection we show an example of the thermodynamical restrictions required to derive the constitutive equation for a multi-component solid under small strain conditions with chemical processes included. 

Salts, and more recently co-crystals, have attracted much interest in the pharmaceutical industry for their promise in tailoring the physical properties of an active pharmaceutical ingredient (API) to meet the needs of the drug product and ultimately the patient.Salt forms, produced by add (A)-base (B) reactions in the solid state, are multi-component solids comprising minimally an A B pair they may be crystalline or amorphous. The term co-crystal, on the other hand, refers specifically to crystalline molecular complexes, which may include an A B pair among the different components and by definition necessarily include solvates (hydrates), inclusion compounds, clathrates and solid solutions. 

Defect concentrations of Fe in Fei xO are usually measured by chemical analysis. It is impossible to determine the compositions of non-stoichiometric compounds, because the error of an ordinary quantitative analysis is about 10, while the deviation of a crystal with intrinsic defect from its stoichiometric composition is about <10. Nevertheless, it is possible for chemical analysis to determine if the metal atoms in non-stoichiometric compounds are excessive or less. Because a non-stoichiometric compound, in common, is a multi-component solid solution in which the different components have different valences, e.g., Fei xO can be viewed as a solid solution which consists of Fe +O and Fe2" 03. Deviation of those types of compounds can directly be determined by measuring of the concentration of an atom that shows an abnormal valence in it. For example, it forms the solutions containing large amounts of Fe + ion and less amounts of Fe + ion, when Fei xO (catalyst) is solved by hydrochloric acid solution under conditions with the absence of air or oxygen. Among these ions, the contents of both Fe + and Fe + can be determined by a titration of EDTA, but the Fe + needs to be oxidated to Fe + by ammonium persulfate prior to titration. The volume ratio of EDTA solutions that are consumed by Fe + and Fe + ions respectively is the ratio of Fe + and Fe + in sample, namely defect concentration of Fe, i.e., x = 1/(3 - - 2Fe +/Fe +). There is also Kulun titration or polarographic analysis except for oxidation-reduction titration which can be used for such measurement of an ion with abnormal valence in the solution of a solid sample. 

Zaharov, M. A. Grid models of multi-component solid solutions statistic thermodynamics and kinetics. Abstract of doctoral thesis. Novgorod State University 2008,36 p. 

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