Crystallization crystal shape factor

Crystal habit refers to the external appearance of the crystal. A quantitative description of a crystal means knowing the crystal faces present, their relative areas, the lengths of the axes in the three directions, the angles between the faces, and the shape factor of the crystal. Shape factors are a convenient mathematical way of... 

Determining the crystal structure of nanoparticles is a challenge, particularly, when the particles are <5 nm. The intensity-maxim observed in the x-ray or electron diffraction patterns of such small particles are broadened due to the crystal shape factor, which greatly reduced the accuracy of structure refinement. The quality of the HRTEM images of the particles is degraded because of the strong effect from the substrate. This difficulty arises in our recent study of CoO nanocrystals whose shape is dominated by tetrahedral of sizes <5 nm. Electron diffraction indicates that the crystal has a NaCl type of structure. To confirm that the synthesized nanocrystals are CoO, EELS is used to measure the valence state of Co. Figure 4.10... 

B = peak width K = crystal shape factor = 1 K = wavelength 0 = Bragg angle... 

The total crystal surface area per unit liquid volume, Ax, may be defined using a crystal shape factor y/ based on the surface area Up of a particle or a representative radius tp (definition (3.4.26)) ... 

The two density functions can be related through a simple shape factor as follows. Suppose the mass of a single crystal is and the characteristic dimension of that crystal is E. If the crystal is from a population in which shape is not a function of size, then the mass of any crystal from that population is related to characteristic dimension by a volume shape factor ... 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

Taking the crystal density as 1770 kg/m and the volume shape factor,/v, as 0.47 calculate... 

Take the crystal volume shape factor to be 0.4 and the crystal density to be 2600 kg/m. Solution... 

Why do we get differences in crystal shape or habit This may be a matter of directional rates of growth. Factors affecting directional rates will then affect the habit. Directional rates of growth can be illustrated with a relatively simple crystal structure, that of sodium chloride. 

A polymorph is a solid crystalline phase of a compound resulting from the possibility of at least two different crystal lattice arrangements of that compound in the solid state [42], Polymorphs of a compound are, however, identical in the liquid and vapor states. They usually melt at different temperatures but give melts of identical composition. Two polymorphs of a compound may be as different in structure and properties as crystals of two different compounds [43,44], Apparent solubility, melting point, density, hardness, crystal shape, optical and electrical properties, vapor pressure, etc. may all vary with the polymorphic form. The polymorphs that are produced depend upon factors such as storage temperature, recrystallization solvent, and rate of cooling. Table 2 suggests the importance of polymorphism in the field of pharmaceutics [45],... 

An MSMPR crystalliser operates with a steady nucleation rate of n = 1013/m4, a growth rate, Gd = 10-8 m/s and a mixed-product removal rate, based on clear liquor of 0.00017 m3/s. The volume of the vessel, again based on clear liquor, is 4 m3, the crystal density is 2660 kg/m3 and the volumetric shape factor is 0.7. Determine ... 

Table IV shows whole data relating to CSD and j, p values, the latters of which were mainly estimated by the relation between Sw-Sn (Figure 2), because that almost the same values were obtained with different methods, as shown in Table III. The data in Table IV are arranged in order of volumetric shape factor of crystals, fy. fv is unity...

The weight basis probability density function of crystals in exit stream, fw(L) is derived from in a similar way. Multiplying both sides of Equation a-6 by PcfyL, where rc and fy are the density and volumetric shape factor of crystals, respectively,... 

Volume shape factor. Figure 3 shows SEM microphotograph of the typical crystal of Mg(0H)2 obtained for series I. As the crystal form is composed of disklike units and the crystal structure of Mg(0H)2 is Cdl2 type, the standard unit of Mg(0H)2 crystal is considered to be a disk. The ratio of the length L to thickness D of the disk of crystal unit was measured for each experimental condition, so that it was found that L/D was nearly constant at 6.4. The crystal volumes were calculated for... 

Shape Factor of a Magnesium Sulfate Crystal Growing in Its Aqueous Solution... 

Variation of Shape Factor. Three typical variations In the shape factor of MgSOi 71120 crystal are shown In Figure 1. The factors show the results obtained from three experiments of crystal growth In the solution without gas admittance at a supersaturation degree (AC) of 1.78 kg m , and a temperature of 298.2 K. In this solution, secondary nuclei(4) were hardly found. The curves connecting the points In the figure were determined by Fourier series equations to... 

The MgS0i 7H20 crystal in an aqueous solution grew along a periodic oscillation curve of the shape factors. The variations in the curve suggest that a crystal exhibits an analogous shape almost periodically within a certain range of shape factors. 

As Is well known, the shape of MgS0 7H20 Is an orthorhombic crystal with three different lattice parameters(5), 11.86, 11.99, and 6.858. From these values, the shape factor can be calculated as 0.778. This value closely matches the upper lines of Figure 6. If crystals having a shape factor of 0.778 are wanted, the lower values should be raised so that the amplitude becomes more narrow and the... 

That Is9 a growing crystal takes on various shapes while displaying a periodic oscillation curve with a constant period, a constant amplitude, and a fixed axis at the steady state of the shape factor. The amplitude is altered by the temperature (we are currently researching the amplitudes of various other crystals, of which one example follows). 

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