Crystals densities

One of the things that can be done with a knowledge of the unit cell dimensions is to calculate the crystal density. This is examined in the following example. 

Use the unit cell dimensions cited above to determine the crystal density of polyethylene. Examine Fig. 4.10 to decide the number of repeat units per unit cell. 

Table 20. Calculated Crystal Densities and Releasable Energy Density for HEDCs and In-Service Explosives...

The crystal stmcture of PPT is pseudo-orthorhombic (essentially monoclinic) with a = 0.785/nm b = 0.515/nm c (fiber axis) = 1.28/nm and d = 90°. The molecules are arranged in parallel hydrogen-bonded sheets. There are two chains in a unit cell and the theoretical crystal density is 1.48 g/cm. The observed fiber density is 1.45 g/cm. An interesting property of the dry jet-wet spun fibers is the lateral crystalline order. Based on electron microscopy studies of peeled sections of Kevlar-49, the supramolecular stmcture consists of radially oriented crystaUites. The fiber contains a pleated stmcture along the fiber axis, with a periodicity of 500—600 nm. 

This stmcture was first proposed in 1924 (3). The stacking arrangement is ABAB with atoms in alternate planes aligning with each other. Interlayer spacing is 0.3354 nm and interatomic distance within the planes 0.1415 nm. The crystal density is 2.25 g/cm compared to 3.51 g/cm for diamond. 

I = tip speed of the propeller or impeller, m/s p = crystal density, g/ciTr... 

Calculate the population density, growth, and nucleation rates for a crystal sample of urea for which there is the following information. These data are from Bennett and Van Biiren [Chem. Eng. Frvg. Symp. Ser., 65(95), 44 (1969)]. Slurry density = 450 g/L Crystal density = 1.335 g/cm ... 

Diamond is an important commodity as a gemstone and as an industrial material and there are several excellent monographs on the science and technology of this material [3-5]. Diamond is most frequently found in a cubic form in which each carbon atom is linked to fom other carbon atoms by sp ct bonds in a strain-free tetrahedral array. Fig. 2A. The crystal stmcture is zinc blende type and the C-C bond length is 154 pm. Diamond also exists in an hexagonal form (Lonsdaleite) with a wurtzite crystal structure and a C-C bond length of 152 pm. The crystal density of both types of diamond is 3.52 g-cm. ... 

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... 

In most cases crystal densities differ from the densities of amorphous polymers. This leads to differences in refractive index, which in turn cause scatter of light at boundaries between amorphous and crystalline zones. Such materials are opaque except in certain instances where the crystal structure can be carefully oriented to prevent such scatter of light. 

Thiourea and selenourea both form canal inclusion compounds. The selenourea compounds, reported only briefly 37), appear to be isostructural with the rhombo-hedral thiourea compounds, although with larger dimensions which are more susceptible to the sizes of guest molecules. For urea, thiourea and selenourea the crystal densities of the compounds are significantly less than those of the hosts values (g cm - 3) for the pairs host/complex are 1.30/1.20 1.40/1.10 2.08/1.60-1.65 for urea, thiourea, selenourea, respectively37). 

The quantities defined by Eqs. (2)—(7) plus Vs max, Vs min, and the positive and negative areas, A and, enable detailed characterization of the electrostatic potential on a molecular surface. Over the past ten years, we have shown that subsets of these quantities can be used to represent analytically a variety of liquid-, solid-, and solution-phase properties that depend on noncovalent interactions [14-17, 84] these include boiling points and critical constants, heats of vaporization, sublimation and fusion, solubilities and solvation energies, partition coefficients, diffusion constants, viscosities, surface tensions, and liquid and crystal densities. 

Although the unit cell dimensions shown in Table 11.3 appear to be reasonably close to each other, the calculated cell volumes and crystal densities are divided... 

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