Crystallization molar volume effect

For example, consider a binary alloy in which the stress-free molar volume is a function of concentration, V(cs). The linear expansion due to the composition change can be inferred from diffraction experiments under stress-free conditions (Vegard s effect) and is characterized by Vegard s parameter, ac [e.g., in cubic or isotropic crystals e ° = e°y 0 = = ac(c — c0)]. The assumption of coherency... 

Another way to achieve uniform illumination is to lower the optical density of the sample by increasing the effective molar volume. Solid solution of an absorbing guest in a transparent host in either a normal crystal or a molecular inclusion compound can achieve this end so can using a pure crystal of a much larger molecule which includes the chromophore of interest [27]. While it is harder to reach high dilution with the latter approach, it has the virtue that the initial compound is a pure crystal and thus better suited for definitive X-ray investigation. 

Many polymers arc crystal lizablc. The concept of the intrinsic crystallizability will be discussed in Section 6.1. When it exists, crystallinity can significantly affect the density, the molar volume, and more generally the PVT relationships. Equations-of-state are generally unable to describe the PVT behavior adequately in the presence of crystallinity because of the sudden change in density that usually accompanies crystallization. While a detailed treatment of these issues is beyond the scope of this book, the effects of crystallinity on the density at room temperature will be discussed in the next section to illustrate the most important trends. 

The above discussion is oversimplified since if a chain end is excluded, it must reach the surface. This requirement limits the size of the crystal and affects its surface energy. Exclusion is more likely with slow crystallization. On the ofrier hand, with fast crystallization, chain ends (and comonomer units) might be trapped within in the growing crystal. The derivation then assiunes that the molar volume of a chain end is the same as that of a monomer unit, but this is not necessarily so. The effect may depend on the nature of die chain end. 

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