Crystal growth thermodynamics

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Grzegory I, Jun J, Bockowski M, Krukowski S, Wroblewski M, Lucznik B and Porowski S 1995 lll-V nitrides-thermodynamics and crystal growth at high N2 pressure J. Phys. Chem. Solids 56 639... 

The relaxation of a thermodynamic system to an equilibrium configuration can be conveniently described by a master equation [47]. The probability of finding a system in a specific state increases by the incoming jump from adjacent states, and decreases by the outgoing jump from this state to the others. From now on we shall be specific for the lattice-gas model of crystal growth, described in the previous section. At the time t the system will be found in the state. S/ with a probability density t), and its evolution... 

There is little data available to quantify these factors. The loss of catalyst surface area with high temperatures is well-known (136). One hundred hours of dry heat at 900°C are usually sufficient to reduce alumina surface area from 120 to 40 m2/g. Platinum crystallites can grow from 30 A to 600 A in diameter, and metal surface area declines from 20 m2/g to 1 m2/g. Crystal growth and microstructure changes are thermodynamically favored (137). Alumina can react with copper oxide and nickel oxide to form aluminates, with great loss of surface area and catalytic activity. The loss of metals by carbonyl formation and the loss of ruthenium by oxide formation have been mentioned before. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

Snow crystals [4] Their macroscopic structure is different from a bulk three-dimensional ice crystal, but they are formed by homologous pair-pair interaction between water molecules and are static and in thermodynamic equilibrium. It should be noted, however, that dendritic crystal growth is a common phenomenon for metals [5-7] and polymers. The crystals grow under non-equilibrium conditions, but the final crystal is static. 

The problem is basically similar to preventing scale inhibition in washing machines therefore similar chemicals are used to prevent scale deposition. Scale inhibition can be achieved either by adding substances that react with potential scale-forming substances so that from a thermodynamics standpoint the stable region is reached or by adding substances that suppress crystal growth. 

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

Nucleation is defined as the point where the protonucleus is sufficiently large that its surface area to volume ratio exceeds a critical point, and further growth results in a reduction in global free energy surface effects are now small compared to the inside of the crystal. This is the point where enthalpy dominates over entropy. Subsequent crystal growth and further nucleation events will occur until thermodynamic equilibria is reached, as defined by Eq. 3. The rate of nucleation is defined as the rate at which clusters grow through this critical point. 

It is clear that kinetic effects must be utilized in the design of a process to make the commercially available Form A, because it is never the most thermodynamically stable form. Information from the literature and patents in reference [14] indicates that Form A can be successfully isolated from Acetonitrile, Acetone, Methyl isobutyl ketone, Toluene, the C2 to C4 alkenols, Ethanol, Methanol and Propan-2-ol. In these solvents it is likely that solvation is favourable to the nucleation rate of Form A or detrimental to crystal growth of the other forms, or both. For a new development compound there should be similar solvent interaction data available from polymorph screening experiments. 

SOLUTION BEHAVIOR. Biomineralization is dominated by physical chemical considerations , and we begin with a discussion of real electrolyte solutions in which the concentration of a substance exceeds its thermodynamically defined solubility. In such a case, the presence of a coexisting crystal surface will lead to crystal growth. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

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