Crystals equilibrium

Bowen N. L. and Schairer I F. (1938). Crystallization equilibrium in nepheline-albite-silica mixtures with fayalite. J. Geol, 46 397-411. 

The common ion effect must also be considered, since it affects each one of the crystallization equilibrium, both in supercritical and subcritical water. Adding sodium acetate, for instance, to a solution containing sodium salts would favour sodium bicarbonate precipitation (formed from oxidation of acetate), thus avoiding the precipitation of more corrosive salts, such as the chloride or sulfate [28],... 

The following discussion is excerpted from Mullin (1993) and Elwell and Scheel (1975). Diffusional boundary theory is well-established (see e.g., Bird et al., 1960) and the concept of a boundary unstirred layer was introduced a century ago. Noyes and Whitney (1897) proposed that the change in the rate of crystal growth (dm/dt) was controlled by diffusion from the bulk concentration to the crystal (equilibrium) interface. 

In this section the broad spectrum of melting of one-component macromolecular systems is described by means of several specific polymers. The description starts with polyethylene, the most analyzed polymer. It continues with two sections that present several special effects seen in the thermal analysis of polymers including some examples of detailed analyses by TMDSC, documenting the locally reversible melting and crystallization equilibrium within a globally metastable structure. Then illustrations of poly(oxymethylene) and PEEK are given as typical common polymeric materials. This is followed in the last section with the discussion of special effects seen in drawn polymers, as are commonly found in fibers and films. 

Wolff, G.A., Gualtieri, J.G. (1962). PBC vector, critical bond energy ratio and crystal equilibrium form. American Mineralogist, 47, 562-584. 

Figure 1.20. Surf2u e defined by Equation 1.2 34 to characterize the gas and liquid states of a onc-component system in the coordinates P V-T (a). Surface defined by Equation 1.2-33 for the crystal and liquid states (6). ACD is the binodal of liquid-vapour phase equilibria BCC is the spinodal of liquid-vapour phase transition Be and Ff are fragments of the binodal of the crystal-liquid phase equilibria Kj is the spinodal of the crystal-liquid phase transition GAD is the straight line of three-phase (vapour-liquid-crystal) equilibrium at the triple point (Skripov and Koverda, 1984)...

In crystallization equilibrium is attained when the solution or mother liquor is saturated. This is represented by a solubility curve. Solubility is dependent mainly upon temperature. Pressure has a negligible effect on solubility. Solubility data are given in the form of curves where solubilities in some convenient units are plotted versus temperature. Tables of solubilities are given in many chemical handbooks (PI). Solubility curves for some typical salts in water were given in Fig 8.1-1. In general, the solubilities of most salts Increase slightly or markedly with increasing temp>erature. 

The stereochemical similarity between the additive and the crystal structure of one of the enantiomorphic substrates was found to be of paramount importance [8], while parameters like temperature, concentration or nature of the medium had only a quantitative effect on the induction in this system. Further kinetic and mechanistic studies resulted in the formulation of a mechanism according to which the additive is enantioselectively adsorbed in small amounts at the surface of the growing crystal of the same absolute configuration. The adsorption of the chiral additive causes a drastic decrease in the rate of growth of this same crystal, thus shifting the crystallization equilibrium towards the unaffected enantiomorphous phase. This is illustrated in Scheme 2, where the achiral monomer is represented as a fast racemizing... 

Prigogine, 1. and Defay, R. (1954) Solution-crystal equilibrium eutectics, in Chemical Thermodynamics, Longmans, Green, London, pp. 357-367. 

We considered above the calculation of observables requiring the first-order derivatives of the total energy. For the equilibrium structure of crystal (equilibrium nuclear coordinates and unit-cell parameters) the total-energy derivatives with respect to nuclear coordinates r and lattice parameters o equal zero at constant temperature T ... 

This is a non-equilibrium phase, both with respect to liquid-crystal and crystal equilibrium. The explanation of the fact that precisely this phase, and not the liquid-crystalline (or crystalline, of course) phase, is first formed, is that the rate of nucleation of the amorphous phase is much higher than the rate of formation of the liquid-crystalline and crystalline phases, especially in spinodal separation. The probability of nucleation is lower, the higher the phase order. 

Table 33 shows the coefficients of the interpolation equations (0.18)-(0.21) for the temperature dependencies of saturated vapor pressure and for three functions in the ideal gas state, enthalpy, heat capacity, and entropy. Since the state of crystal equilibrium at 0 K is taken as a beginning for enthalpy calculations, the numerical value of coefficient a in equation (0.18) is replaced by the value... 

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