Crystal dimensions

These facts are connected through consideration of crystal dimensions. 

Melting occurs over a range of temperatures, as in Fig. 4.1. The range narrows as the crystallization temperature increases. This is probably due to a wider range of crystal dimensions and less perfect crystals under the lower temperatures of formation. 

We shall take up the kinetics of crystallization in detail in Secs. 4.5 and 4.6. For the present, our only interest is in examining what role kinetic factors play in complicating the crystal-liquid transition. In brief, the story goes like this. Polymers have a great propensity to supercool. If and when they do crystallize, it is an experimental fact that smaller crystal dimensions are obtained the lower the temperature at which the crystallization is carried out. The following considerations supply some additional details ... 

In the discussion of Table 4.1, we acknowledged that there might be some uncertainty in the values of the quantities tabulated, but we sidestepped the origin of the uncertainty. In the next section we shall consider one of these areas the effect of crystal dimensions of the value of T j,. 

Population density (n) has dimensions number/(volume)(length) it is a key quantity in the discussion of CSD, a function of the characteristic crystal dimension E, and it is defined so that it is independent of the magnitude of the system. When a total population density is used, the symbol is n and the units are number/length. Population density is defined by letting AiVbe the number of crystals per unit system volume in a size range from E to L + AL, so that... 

The dominant crystal size, is most often used as a representation of the product size, because it represents the size about which most of the mass in the distribution is clustered. If the mass density function defined in equation 33 is plotted for a set of hypothetical data as shown in Figure 10, it would typically be observed to have a maximum at the dominant crystal size. In other words, the dominant crystal size is that characteristic crystal dimension at which drajdL = 0. Also shown in Figure 10 is the theoretical result obtained when the mass density is determined for a perfectiy mixed, continuous crystallizer within which invariant crystal growth occurs. That is, mass density is found for such systems to foUow a relationship of the form m = aL exp —bL where a and b are system-dependent parameters. 

First, on a purely physical basis, we determine when departures from a linear growth rate may be expected, that is when the crystal dimensions do not increase proportionally with time, but also depend on the size of the crystal (and maybe even other factors). Then we show how these limits relate to the possible values of i and g. 

X-ray structural analysis. Suitable crystals of compound 14 were obtained from toluene/ether solutions. X-ray data were collected on a STOE-IPDS diffractometer using graphite monochromated Mo-Ka radiation. The structure was solved by direct methods (SHELXS-86)16 and refined by full-matrix-least-squares techniques against F2 (SHELXL-93).17 Crystal dimensions 0.3 0.2 0.1 mm, yellow-orange prisms, 3612 reflections measured, 3612 were independent of symmetry and 1624 were observed (I > 2ct(7)), R1 = 0.048, wR2 (all data) = 0.151, 295 parameters. 

Independent of crystallization conditions, whether from solutions or melt, the polymer molecules crystallize into thin lamellae. The lamellar thickness is about 10 nm, about two orders of magnitude smaller than values allowed by existing equilibrium considerations. This is in contrast to the case of crystallized short alkanes, where the lamellar thickness is proportional to the length of the molecules. Clearly the chains in the case of polymers should fold back and forth in the lamellae to support the experimentally observed lamellar thickness. It is believed in the literature [3-9] that the lamellar thickness is kinetically selected and that if enough time is permissible, the lamella would thicken to extended chain crystal dimension. What determines the spontaneous selection of lamellar thickness ... 

Fig. 6.9 Left Relationship between the Curie (Tc) and Morin (Tm) temperature of hematite and the extent of structural substitution of Fe " by Al, Ga, Cr and In (M) (Svab Kren, 1979, with permission). Right Relationship between the Morin temperature and the inverse mean crystal dimension (MCD) for different hematites ( ) natural from Elba ( ) heating lepido-...

Fig. 12. Views of flat (left) and perpendicular (right) glass spatulas constructed for crystallographic studies of plate-like crystals from Halobacterium marismortui 508 subunits at cryotemperature. The long c-axis (i.e. the shortest crystal dimension) will coincide with the spindle axis (and overlap problems will be less severe) when perpendicular spatulas are used...

Intercalation of single crystals of 2H(a)-TaS2 may be carried out in a similar manner, although it is possible that, if the crystals are too large in surface area, intercalation may proceed only around the edges. It should be noted that the time for full intercalation of crystals increases with crystal dimensions. 

Study of the effects of charge diam, crystal dimensions 8t nature of the gas present on the velocity of deton of crystd expls, such as PETN 2) A. Parisot 8t P. Lafitte, ComptRend 18eCongrlntemlChimlnd (Nancy, France), Sept-Oct 1938, 930-36 Si CA 33, 6049(1939) (Influence of cartridge diam on the vel of deton of expls) 3) Anon, La Chimica. e l ln-dustria 21, 546(1939) 8t SS 35, 83(1940) (Influence of charge diam on the deton velocity)... 

Study of the effects of crystal dimensions-, nature of the gas present and diam of the cartridge on the deton vel of crystd expls, such as PETN) 2) F.J. Martin et al, "The... 

CD films are often nanocrystalline. One very important use of XRD when dealing with nanocrystals is to estimate crystal dimensions through the Scherrer relationship ... 

Macromolecules are very much like the crystalline powder just described. A few polymers, usually biologically-active natural products like enzymes or proteins, have very specific structure, mass, repeat-unit sequence, and conformational architecture. These biopolymers are the exceptions in polymer chemistry, however. Most synthetic polymers or storage biopolymers are collections of molecules with different numbers of repeat units in the molecule. The individual molecules of a polymer sample thus differ in chain length, mass, and size. The molecular weight of a polymer sample is thus a distributed quantity. This variation in molecular weight amongst molecules in a sample has important implications, since, just as in the crystal dimension example, physical and chemical properties of the polymer sample depend on different measures of the molecular weight distribution. 

Crystal Dimension. 95% of the crysts shall have a max dimension becw 7 20 microns. The length of the crysts shall not be greater than 3 times it width... 

Appearance. The material shall be free from visible impurities and free from aggregates which are larger than the maximum allowable crystal dimensions permitted, as stated under "Crystal Dimension"... 

Crystal Dimension. The largest dimension of any crystal shall not exceed 0.5 mm... 

Crystal Dimensions. Using the same slide as above, measure the longest dimension of the largest crysts observed when scanning the field with the aid of... 

Kawakubo s fluorescence results 86> for methyl- and dimethylnaphthalene solids can be similarly related to the crystal structure. Both 2-and 2,6-substituted naphthalenes retain the same close-packed layer structure as seen in naphthalene. The only effect of the methyl substitution is to increase the crystal dimension along the naphthalene long axis87 . Less is known about the crystal structures of 1- and 1,6-substituted naphthalenes, except that the 1-substituent requires a different packing pattern than naphthalene and that 1- and 1,6-substituted naphthalenes have much lower melting points than the 2-substituted naphthalenes. The absence of sandwich pairs in 2- and 2,6-substituted naphthalene crystals certainly explains the lack of excimer fluorescence in the crystal spectra. Presumably, such pairs are also absent in crystalline 1-methylnaphthylene, but they seem to be present in glassy 1-methyl-naphthalene and in 1,6-dimethylnaphthalene solid. 

Molnar, E. Additional observations on bone crystal dimensions. Clin. Orthop. 17, 38 (1960)... 

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