Crystallization moments

The overall i-th moments are defined as summation of nucleated and seeded crystallization moments. 

The visible crystals that develop during a crystallization procedure are built up as a result of growth either on nuclei of the material itself or surfaces of foreign material serving the same purpose. Neglecting for the moment the matter of impurities, nucleation theory provides an explanation for certain qualitative observations in the case of solutions. 

The polarization properties of single-molecule fluorescence excitation spectra have been explored and utilized to detennine botli tlie molecular transition dipole moment orientation and tlie deptli of single pentacene molecules in a /7-teriDhenyl crystal, taking into account tlie rotation of tlie polarization of tlie excitation light by tlie birefringent... 

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

Iron(II) bromide [7789-46-0] FeBr2, can be prepared by reaction of iron and bromine ia a flow system at 200°C and purified by sublimation ia oitrogea or uader vacuum. Other preparative routes iaclude the reactioa of Fe202 with HBr ia a flow system at 200—350°C, reactioa of iroa with HBr ia methanol, and dehydration of hydrated forms. FeBr2 crystallizes ia a layered lattice of the Cdfy type and has a magnetic moment of... 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

It can be demonstrated that the total number of crystals, the total length, the total area, and the total volume of crystals, all in a unit of system volume, can be evaluated from the zero, first, second, and third moments of the population density function. 

Moments of the distribution can be calculated for MSMPR crystallizers by the simple expression... 

Properties of the distribution such as total number of crystals per unit volume, total length of crystals per unit volume, total area of crystals per unit volume, and total volume of soUds (crystals) per unit volume may be expUcitiy evaluated from the moment equations. 

The magma density Mj- (mass of crystals per unit volume of slurry or Hquor) may be obtained from the third moment of the population density function and is given by... 

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