Crystallization thermodynamic considerations

Thermodynamic considerations postulate BjH to be a better boron source than BCl, in CVD of TaB2Using reaction (f) at < 1200 K deposits with extremely small crystal sizes are obtained on graphite substrates . They contain amorphous B at deposition temperatures < 873 K and are substoichiometric in B above this T. Carbon from the substrate substitutes for B, thereby stabilizing the diboride structure at high deposition T... 

Thermodynamic considerations imply that all crystals must contain a certain number of defects at nonzero temperatures (0 K). Defects are important because they are much more abundant at surfaces than in bulk, and in oxides they are usually responsible for many of the catalytic and chemical properties.15 Bulk defects may be classified either as point defects or as extended defects such as line defects and planar defects. Examples of point defects in crystals are Frenkel (vacancy plus interstitial of the same type) and Schottky (balancing pairs of vacancies) types of defects. On oxide surfaces, the point defects can be cation or anion vacancies or adatoms. Measurements of the electronic structure of a variety of oxide surfaces have shown that the predominant type of defect formed when samples are heated are oxygen vacancies.16 Hence, most of the surface models of... 

On the basis of thermodynamic considerations, some of the lattice sites in the crystal are vacant, and the number of vacant lattice sites generally is a function of temperature. The movement of a lattice atom into an adjacent vacant site is called vacancy diffusion. In addition to occupying lattice sites, atoms can reside in interstitial sites, the spaces between the lattice sites. These interstitial atoms can readily move to adjacent interstitial sites without displacing the lattice atoms. This process is called interstitial diffusion. The interstitial atoms may be impurity atoms or atoms of the host lattice, but in either case, interstitial atoms are generally present only in very dilute amounts. However, these atoms can be highly mobile, and in certain cases, interstitial diffusion is the dominant diffusion mechanism. 

Thermodynamic considerations. A rigorous thermodynamic analysis shows that empirical rules which consider bonding forces of ions in crystalline phases alone are invalid. It is necessary to compare binding forces of ions in a mineral and the medium from which that mineral crystallized. For transition elements, this requires information about relative CFSE s of the cations in coexisting minerals, silicate melts, aqueous solutions and hydrothermal fluids. 

The material in this section draws from similar material in the excellent book by Ewell and Scheel [28]. The shape of a ciystal (i.e., ciystal habit) can be controlled by either thermodynamics or kinetics. Only for crystals grown imder very, very low supersaturation ratios is a crystal habit established thermodynamic considerations. These crystals tend to be of mineralological origin. For most other crystal growth conditions, the kinetics of the slowest growing crystal frees give rise to a crystal shape. 

Conclusions based on the widest possible variety of experimental observations provide the most rehable mechanistic interpretations. The necessity for quantitative characterisation of the reactant, the products and any intermediates has been emphasised. This characterisation includes the chemical composition, impurities, imperfections, crystal sizes, lattice structures and physical textures of all participating phases and the determination of their roles in the reactions investigated. Any study directed towards determining the detailed chemical mechanism of a particular reaction must establish the stoichiometry and identify the initial products, which may differ from those at equilibrium. These products may be compared with those predicted from thermodynamic considerations. 

K. A. Kobe and W. G. Domask, Extractive Crystallization—A New Separation Process. Part B. Thermodynamic Considerations, Petroleum Refiner 31(5) 151—157 (1952). 

The coordination chemistry involves the oxidation states from -i-7 to -1. Coordination numbers from 4 to 9 are known. Crystal field considerations and magnetic susceptibility measurements show that technetium forms low-spin compounds. Dinuclcar complexes frequently display metal to metal bond character. There is some evidence that technetium complexes are thermodynamically less stable and kinctically more reactive than the corresponding complexes of rhenium. A multitude of coordination compounds of technetium has been synthesized and unambiguously characterized. Investigations of the complex chemistry have been enormously stimulated by the development of Tc radiopharmaccuticals. 

Two other important concentration effects are also worth noting (1) impurity uptake is proportional to the concentration of impurities in the crystallizer, x/iiq, thus efforts should be made to minimize their formation or introduction into the crystallization stage and (2) the segregation is predicted to improve with increasing solute concentration, XHHq- Thus, a few key thermodynamic considerations can be used to tailor solvents and processing conditions to greatly improve the purification of crystalline materials. 

The impact of solvent on product quality should be given early consideration in process development efforts since it can have a significant effect on crystal size, morphology, and purity. A poor initial choice of solvent may thermodynamically limit the effectiveness of the separation, irrespective of all other factors, including crystallizer design and cost. In Section 3.5.1, the thermodynamic considerations for minimizing impurity incorporation are outlined based on solvent selection. 

As expected from crystal field considerations the low-spin iron(II) complexes are substitution inert, and thermodynamically very stable with respect to Fe " and the free ligand overall formation constants (jffj) can be as large as 10 The consecutive formation constants for iron(II) 2,2 -bipyridine and 1,10-phenanthroline complexes derived by Irving and Mellor are not in the usual order K > Ki> K, but rather K > (Table 12) and this was attributed to spin pairing on... 

Thermodynamic considerations suggest that such transformation phenomena are thermally controlled. In fact, amorphous phase coatings spontaneously crystallize above some critical temperature. The transformation is manifested in the Raman spectrum by dramatic band intensity increases and marked band narrowing (20). When metastable crystalline treated, recrystallization temperature phase occurs as the temperature-dependent spectra shown in Figure 13, which depicts the irreversible transformation of anatase to rutile in a thin titania film. 

Classification and Nomenclature of Supramolecular Compounds, p. 267 Clathrate Hydrates, p. 274 Crystal Growth Mechanisms, p. 364 Self-Assembly Definition and Kinetic and Thermodynamic Considerations, p. 1248 Self-Assembly in Biochemistry , p. 1257 Supramolecular Polymers, p. 1443... 

Classical Descriptions of Inclusion Compounds, p. 253 Clathrate Hydrates, p. 274 Concepts in Crystal Engineering, p. 319 Crown Ethers, p. 326 Cryptands, p. 334 DNA Nanotechnology, p. 475 Enzyme Mimics, p. 546 The Lock and Key Principle, p. 809 Molecular-level Machines, p. 931 Selectivity Thermodynamic and Kinetic, p. 1225 Self-Assembly Definition and Kinetic and Thermodynamic Considerations, p. 1248 Self-Assembly Terminology, p. 1263 Soft and Smart Materials, p. 1302 Spherands, p. 1344... 

Microporous framework solids are synthesised via solvent-mediated crystallisations from mixtures of reactive precursors. The reaction pathway is controlled by kinetic as well as thermodynamic considerations so that equilibrium phase diagrams, so relevant in the high-temperature preparation of ceramics, are not useful here. Rather, synthetic routes have been developed empirically via a major synthetic effort that continues today. The continuing industrial and academic interest in these materials provides a powerful incentive to understand the principles underlying their formation through the processes of gel formation and evolution, nucleation and crystal growth. 

When crystallizing from multicomponent systems, kinetic factors often override thermodynamic considerations (the so-called Ostwald rule of stages -section 5.7). The phase which crystallizes is not necessarily the one which is thermodynamically most stable, but the one which crystallizes the fastest. Numerous examples of this sort of behaviour are available. 

In Figure 6.43b, form II is stable at temperatures below the transition temperature T and form I is stable above T. At the transition temperature both forms have the same solubility and reversible transformation between these two enantiotropic forms I and II can be effected by temperature manipulation. Figure 6.43c, however, depicts the intervention of metastable phases (the broken line extensions to the two solubility curves) which bear evidence of the importance of kinetic factors which for a time may override thermodynamic considerations. For example, if a solution of composition and temperature represented by point A (supersaturated with respect to both I and II) is allowed to crystallize it would not be unusual if the metastable form I crystallized out first even though the temperature would suggest that form II is the stable form. This would simply be an example of Ostwald s rule (section 5.7) being followed. This behaviour would occur, for example, if form II had the faster nucleation and/or crystal growth rates. However, if the crystals of form I were kept in contact with the mother liquor, transformation could occur as the more soluble form I crystals dissolve and the less soluble form II crystals nucleate and grow. 

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