Crystal density difference

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. 

Figures 14.2 and 14.3 show the main landscape for polymorphic pairs in organic compounds. 30% of polymorphic crystal stmcture pairs have one centrosymmetric and one non-centrosymmetric partner, and 25% of the cases show one partner with more than one molecule in the asymmetric unit. No correlation appears between crystal density differences, and either centrosymmetricity or difference in the number of molecules in the asymmetric unit. Crystal density differences range from 0 to 10%, and lattice energy differences, as computed in a preliminary way with atom-atom UNI...

Fig. 2.4. The structure of a typical grain boundary. In order to "bridge the gap" between two crystals of different orientation the atoms in the grain boundary have to be packed in a less ordered way. The packing density in the boundary is then as low as 50%.

Another velocity finally appears in a system where a liquid is in contact with an interface. The interface energy 7 then works as a static driving force. This can trigger a current which is damped by a dynamic force, the viscous friction, in the case of density difference between crystal and liquid. Taking the ratio... 

Figure 1. The charge-density difference (bonding charge density) between NiaX and the superposition of neutral Ni and X atomic charge densities on the (001) planes for (a) X = A1 and (b) X = Si. The solid (dotted) contours denote contours of increased (decreased) density as atoms are brought together to form the NiaX (X = Al, Si) crystal. Contours start from 4.0 X 10 e/(a.u.) cind increase successively by a factor of root 2.

The gravity sensor is unknown in Phycomyces. Statoliths have not been detected. Any particle with a density different from that of the average density of the cytoplasm could be a candidate, e.g., mitochondria, lipid droplets, nuclei or crystals. The work of Dennison (1961) has clearly shown that the gravity sensor must be inside the cell because the response is independent of the density of the medium outside the sporangiophore. 

The mechanism by which electrons interact with crystals is different from that of X-rays. X-rays detect electron density distribution in crystals, while electrons detect electrostatic potential distribution in crystals. Electron crystallography may be used for studying some special problems related to potential distribution such as the oxidation states of atoms in the crystal. 

EDSA of thin polycrystalline films has several advantages First of all the availability of a wide beam (100-400 pm in diameter) which irradiates a large area with a large amount of micro-crystals of different orientations [1, 2]. This results into a special t5q)e of diffraction patterns (DP) (see Fig.l). Thus it is possible to extract from a single DP a full 3D data set of structure amplitudes. That allows one to perform a detailed structure analysis with good resolution for determining structure parameters, reconstruction of ESP and electron density. 

Baum and Archibald reported the synthesis of 2,2,6,6-tetranitrobicyclo[3.3.1]nonane (142). This synthesis starts from the dioxime (140), which on halogenation with chlorine, followed by oxidation with hypochlorite and reductive dehalogenation with hydrogen in the presence of palladium on carbon, yields 2,6-dinitrobicyclo[3.3.1]nonane (141). Oxidative nitration of (141) with sodium nitrite and silver nitrate under alkaline conditions yields 2,2,6,6-tetranitrobi-cyclo[3.3.1]nonane (142). The greater molecular freedom in 2,2,6,6-tetranitrobicyclo[3.3.1] nonane (crystal density-1.45 g/cm ) compared to the isomeric 2,2,6,6-tetranitroadamantane (crystal density-1.75 g/cm ) is reflected is their considerably different crystal densities. 

Volume additivity methods generally do not take into account crystal packing efficiency or molecular conformation effects and thus will afford identical calculated densities for positional and conformational isomers and for compounds that possess different multiples of the same functional group composition. As an example, a volume additivity calculation predicts that l,3,5-trinitro-l,3,5-triazacyclohex-ane (RDX), l,3,5,7-tetranitro-l,3,-5,7-tetraazacyclooctane (a-HMX), and /3-HMX all will possess the same crystal density, 1.783 g/cm [32]. In fact, the experimentally observed densities of these three compounds differ markedly (i.e., 1.806 [33], 1.839 [34], and 1.902 [35], respectively). 

The crystallization of the D-enantiomer is therefore considered to be induced by crystal growth on the surface of the seed crystal and at the same time initial breeding may play a role that causes small crystals near the seed crystal. The propagation of nucleation in distance from the seed may be caused by convective flow of the solution due to density difference during the crystal growth. 

Finally, it should be mentioned that polymers can exhibit polymorphism, i.e., they can crystallize in different types of lattices. The different crystal forms generally differ in their physical properties, e.g., crystallite melting point and density. 

Because the crystal density usually differs significantly from that of the melt, it is necessary to distinguish the crystal growth rate and the melt consumption rate (or melt dissolution rate). The latter equals pcryst/pmeit times the crystal growth rate. Because we are interested in the melt phase, u in the above equation is specified as the melt consumption rate. 

Mathematically, diffusive crystal dissolution is a moving boundary problem, or specifically a Stefan problem. It was treated briefly in Section 3.5.5.1. During crystal dissolution, the melt grows. Hence, there are melt growth distance and also crystal dissolution distance. The two distances differ because the density of the melt differs from that of the crystal. For example, if crystal density is 1.2 times melt density, dissolution of 1 fim of the crystal would lead to growth of 1.2 fim of the melt. Hence, AXc = (pmeit/pcryst) where Ax is the dissolution distance of the crystal and Ax is the growth distance of the melt. 

The crystal dissolution distance Ax and rate are different from the melt growth distance and rate because of density difference. Hence, the crystal dissolution distance and rate are... 

The boundary layer thickness 5. For convective crystal dissolution, the steady-state boundary layer thickness increases slowly with increasing viscosity and decreasing density difference between the crystal and the fluid. It does not depend strongly on the crystal size. Typical boundary layer thickness is 10 to 100/rm. For diffusive crystal dissolution, the boundary layer thickness is proportional to square root of time. 

Crystai growth distance and behavior of major component This problem is similar to diffusive crystal dissolution. Hence, only a summary is shown here. Consider the principal equilibrium-determining component, which can be treated as effective binary diffusion. The density of the melt is often assumed to be constant. The density difference between the crystal and melt is accounted for. 

Figures 9 10 show A B s results in the form of P vs h plots for a number of different explosives at around 90% crystal density. They claim that for PETN, RDX HMX, P is un- affected (within a 10% experimental uncertainty) if particle size distribution is varied from 1-10p in one series of experiments to 315-400p in a-second series. They also claim that P is the same (within experimental error) for pressed wafers...

After the crystal structure of the compound has been solved, or deduced, from the X-ray data, the initial parameters (atomic positions, bond lengths, and bond angles) are only approximate and have to be improved. The usual method employed is that of least-squares refinement, although electron-density difference-maps and trial-and-error procedures are also used. Electron-density difference-maps give the approximate difference between the actual structure and the trial structure. 

In experimental studies, metal-sulfide liquids form rounded globules that will sink through a silicate matrix that is itself partly molten (e.g. Walker and Agee, 1988). The density difference is sufficient that segregation of a metallic core though a mush of liquid and crystals should be rapid. However, sinking of metallic liquid through a solid or mostly... 

Several different types of reaction patterns may form on the sphere as the reaction proceeds. In cases where the reaction products actually build up on the surface of the metal, as in oxidation, the oxide film will form more rapidly on one face than on another. When the films are in the range of 200 to 2,500 A. and the sphere is examined by placing a tube of white paper over the crystal, the different thicknesses of oxide on the different faces appear as a regular pattern of interference colors of great beauty. The symmetry of one of these highly colored patterns is shown in Fig. 1. In electrodeposition on a crystal sphere at a low current density the metal will deposit more rapidly on one face than another, and the sphere is converted into a polyhedron, or small facets are formed on the different faces which may be seen under the microscope. 

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