Crystallization criteria

The properties of fillers which induence a given end use are many. The overall value of a filler is a complex function of intrinsic material characteristics, eg, tme density, melting point, crystal habit, and chemical composition and of process-dependent factors, eg, particle-si2e distribution, surface chemistry, purity, and bulk density. Fillers impart performance or economic value to the compositions of which they are part. These values, often called functional properties, vary according to the nature of the appHcation. A quantification of the functional properties per unit cost in many cases provides a vaUd criterion for filler comparison and selection. The following are summaries of key filler properties and values. 

Qian, R., Chen, Z., Ni, H., Fan, Z. and Cai, F., 1987. Crystallization kinetics of potassium chloride from brine and scale-up criterion. American Institution of Chemical Engineers Journal, 33, 1690-1697. 

It should be noted that, whereas ferroelectrics are necessarily piezoelectrics, the converse need not apply. The necessary condition for a crystal to be piezoelectric is that it must lack a centre of inversion symmetry. Of the 32 point groups, 20 qualify for piezoelectricity on this criterion, but for ferroelectric behaviour a further criterion is required (the possession of a single non-equivalent direction) and only 10 space groups meet this additional requirement. An example of a crystal that is piezoelectric but not ferroelectric is quartz, and ind this is a particularly important example since the use of quartz for oscillator stabilization has permitted the development of extremely accurate clocks (I in 10 ) and has also made possible the whole of modern radio and television broadcasting including mobile radio communications with aircraft and ground vehicles. 

Eristfm., abbrev. (Kristallform) crystal form. Kriterium, n. criterion. 

By definition, this is equal to the substrate, or persistence, length Lp (see Sect. 3.4.2) which by this criterion can easily take values so large that nonlinear growth should be observed for small crystals in regime I. 

Sometimes the atomic arrangement of a crystal is such as not to permit the formulation of a covalent structure. This is the case for the sodium chloride arrangement, as the alkali halides do not contain enough electrons to form bonds between each atom and its six equivalent nearest neighbors. This criterion must be applied with caution, however, for in some cases electron pairs may jump around in the crystal, giving more bonds than there are electron pairs, each bond being of an intermediate type. It must also be mentioned that determinations of the atomic arrangement are sometimes not sufficiently accurate to provide evidence on this point an atom reported equidistant from six others may be somewhat closer to three, say, than to the other three. 

In Table XVIII are given values of the radius ratio for the salts of beryllium, magnesium and calcium (those of barium and strontium, with the sodium chloride structure, also obviously satisfy the radius ratio criterion). It is seen that all of the sodium chloride type crystals containing eight-shell cations have radius ratios greater than the limit 0.33, and the beryl-... 

The radius ratios for sphalerite and wurzite type crystals with eighteen-shell cations do not conform to our criterion, so that some other influence must be operative. Without doubt this is deformation. Here again it is seen that the tetrahedral structure is particularly favorable to deformation, for the observed Zn++—O distance (1.93 A.) is 0.21 A. shorter than the theoretical one, while in cadmium oxide, with the sodium chloride structure, the difference is only 0.01 A. 

The hemispherands, spherands, calixarenes, and related derivatives. A number of hosts for which the pre-organization criterion is half met (the hemispherands) (Cram et al., 1982) or fully met (the spherands) (Cram, Kaneda, Helgeson Lein, 1979) have been synthesized. An example of each of these is given by (251) and (252), respectively. In (251), the three methoxyl groups are conformationally constrained whereas the remaining ether donors are not fixed but can either point in or out of the ring. This system binds well to alkali metal ions such as sodium and potassium as well as to alkylammonium ions. The crystal structure of the 1 1 adduct with the f-butyl ammonium cation indicates that two linear +N-H - 0... 

Finally, if the temperature increases, becomes larger until the crystal melts. The Lindemann criterion predicts that melting sets in when becomes about 0.25 a2, where a is the interatomic distance of the metal. Because the mean squared displacements of surface atoms is higher we expect that the surface melts at lower temperatures than the bulk does [2]. Indeed, evidence has been presented that the (110) surface of lead starts to melt at 560 K whereas the bulk melting temperature is about 600 K [13]. 

Numerous disperse dyes are marketed in a metastable crystalline form that gives significantly higher uptake than the corresponding more stable modification. The molar free enthalpy difference can be used as a criterion of the relative thermodynamic stabilities of two different modifications [53]. Certain dyes can be isolated in several different morphological forms. For example, an azopyrazole yellow disperse dye (3.52) was prepared in five different crystal forms and applied to cellulose acetate fibres. Each form exhibited a different saturation limit, the less stable modifications giving the higher values [54]. 

More recent quantum-based MD simulations were performed at temperatures up to 2000 K and pressures up to 30 GPa.73,74 Under these conditions, it was found that the molecular ions H30+ and OH are the major charge carriers in a fluid phase, in contrast to the bcc crystal predicted for the superionic phase. The fluid high-pressure phase has been confirmed by X-ray diffraction results of water melting at ca. 1000 K and up to 40 GPa of pressure.66,75,76 In addition, extrapolations of the proton diffusion constant of ice into the superionic region were found to be far lower than a commonly used criterion for superionic phases of 10 4cm2/s.77 A great need exists for additional work to resolve the apparently conflicting data. 

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