Dispersion orthorhombic crystals

Fig. 56. Dispersion of optic axes in orthorhombic crystals, a. p > u. b-d. Crossed axial plane dispersion.

When used as the dispersion formula for the phonons and polaritons in orthorhombic crystals, the symbols in Eq. (11.22) have the following meaning r)= 1,2,3 designates the three directions of the principal orthogonal axes. sv are the direction cosines of the normalized wave vector s = k/k with respect to the three principal axes of the crystal. If the unit vectors in the directions of these three principal axes are designated eue2,e3, one can write... 

Figure 2.18. Profile of isoenergetic surfaces of the excitonic dispersion in the vicinity of the bottom of the band in the model (2.139) of an orthorhombic crystal. We note the lengthening of the surfaces along c . Also, the wave vectors tend to orient perpendicular to d (or the b axis) in the vicinity of the point K = 0.

System Orthorhombic Crystal Habit columnar Optical Sign - Axial Angle 69 Optic orientation (assigned acc.to crystal habit) XX c YY a ZZ b. Dispersion None observed Refractive Indexes a (w) = 1.517 (3 ( e) = 1.567 y = 1.592 Density 1.379 Refraction Experimental = 111.90 Calculated = 113.99. 

Most organic compounds crystallize in the monoclinic or orthorhombic crystal systems, which contain substantial macroscopic anisotropies, and thus the singlecrystal CD technique cannot be applied, although our method of measurement may be useful if the macroscopic anisotropies are not very large. An alternative way to obtain crystalline-specific information is to examine the microcrystalline state. Measurements can be usually made either in nujol mull or KBr disc form, where microcrystals are dispersed randomly either in nujol or in a KBr microcrystalline matrix. The method was developed and applied to inorganic complexes by Mason [34], Bosnich [35], and Kuroda [9,10], and since then its application to metal complexes has been carried out sporadically [36,37]. Recently, the technique has become popular in the field of organic chemistry as well, probably stimulated by our work [38]. An alternative technique recently developed by us is diffuse reflectance CD (DRCD) which will be briefly described in V.B.2. 

The major constituents of waxes are esters of fatty acids, isolated from animals and plants. Thus, most of natural waxes are basically edible, such as those summarized in Table 25.2, but often indigestible. Among them, camauba, candeliUa, and beeswax have been frequently used for encapsulation by melt dispersion. Waxes crystallize mainly in an orthorhombic subcell arranganent and the polymorphic transition rate is low. ... 

Fig. VII.S. Frequency-dispersion relation of the orthorhombic crystal of perdeuterated polyethylene. Open circles are for experimental data of Feldkamp, Venkataraman, and King (1968) and solid lines are dispersion curves (and symmetry assigments) calculated by...

Eshelby used an orthorhombic crystal as an example to describe the spatial relationships of S. He also pointed out that they do not couple (51,1,2,2 52,2,i,i). Mori-Tanaka and Tandon-Weng refer to S as Eshelby s tensors or Eshelby s transformation tensors. Eshelby utilized direction cosines from an observation point to a volume element to evaluate the elastic fields in the dispersed phase. 5i,1,1,1, 52,2,2,2> 52,2,3,3, 52,2,i,i, and 5i,1,2,2 are needed to calculate K, K, and K2 for Equation (5.9). Their values for disk-shaped dispersed phases are provided in the Tandon-Weng and Eshelby publications. These values are solely a function of aspect ratio and Poisson s ratio. Knowing the proper S values, one can return to Equation (5.11) to calculate the strain in the dispersed phase as a function of the strain in the composite. 

Crystals of the compound of empirical formula FiiPtXe are orthorhombic with unit-cell dimensions a = 8-16, h = 16-81. c = 5-73 K, V = 785-4 A . The unit cell volume is consistent with Z = 4, since with 44 fluorine atoms in the unit cell the volume per fluorine atom has its usual value of 18 A. Successful refinement of the structure is proceeding in space group Pmnb (No. 62). Three-dimensional intensity data were collected with Mo-radiation on a G.E. spectrogoniometer equipped with a scintillation counter. For the subsequent structure analysis 565 observed reflexions were used. The platinum and xenon positions were determined from a three-dimensional Patterson map, and the fluorine atom positions from subsequent electron-density maps. Block diagonal least-squares refinement has led to an f -value of 0-15. Further refinements which take account of imaginary terms in the anomalous dispersion corrections are in progress. 

It may be argued that London dispersion forces and multipole forces 51 would add energy to that computed from Kapustins-kiVs equation. This may be so, but this additional term is unlikely to exceed the enthalpy of formation of orthorhombic PtFe crystals from the vapor (i.e., -11 kcal-moIe-J) . Furthermore it is probable that reaction (1) is more exothermic than —25 kcal-mole , since the solid is not sublimable in vacuo below 90 C 2l. Even allowing for additional lattice energy terms, it is probable that E(PtF6) well exceeds —156 kcal-mole i. 

X-ray diffraction of sulfur particles excreted by Thiobacillus sp. showed the presence of orthorhombic sulfur crystals. The solubility of crystalline orthorhombic sulfur in water is known to be only 5 /tg 1 [42]. In the solubility test shown in Fig. 7 it was seen that the biologically produced sulfur particles can be dispersed in water but not in hexadecane, whereas crystalline orthorhombic sulfur is soluble in hexadecane but not in water. The reason for the observed hydrophilicity of the biologically produced sulfur particles has to be attributed to the hydrophilic properties of the surface of the sulfur particles. Because of the relatively high stability of the biologically produced sulfur particles at high salt concentrations, it is concluded that the colloidal stability is not merely based on electrostatic repulsion. It is known that hydrophobic sulfur can be wetted by Thiobacillus thiooxidans bacteria due to formation of organic surface-active substances [43, 44]. 

Dawsonite [Named after the Canadian geologist John William Dawson (1820-1899), principal of McGill University, Montreal, Canada] (ICSD 100140 and PDF 42-1346) NaAl(C03)(OH), M= 144.00 15.97 wt.% Na 8.34 wt.% C 18.74 wt.% Al 1.40 wt.%H 55.56 wt.%0 Orthorhombic a = 673 pm bs 1036 pm c 558 pm P.G. 2/m2/m2/m S.G. Imam (Z= 4) Barentsite type Biaxial (-) a= 1.462 P= 1.542 Y= 1-596 5=0.130 27=76.75" Dispersion weak <3 2420 (2434) Habit thin encrustations, bladed, needle-hke or radial crystals. Color colorless to white. Diaphaneity transparent. Luster vitreous to silky. Fracture uneven. Cleavage [110] Perfect. Streak colorless. Other fluorescent under short-wavelength UV with dull white. Occurrence low-temperature hydrothermal mineral. 

It can be seen that a rather wide range of predicted values is obtained that is partly due to choice of different force constants. The results are also sensitive to the details of the assumed crystal unit cell structure, especially the angle made by the plane of the planar zigzag polyethylene chain with the b-axis of the orthorhombic unit cell. The overall pattern of elastic anisotropy is however clear. The stiffness in the chain axis direction C33 is by far the greatest value, and the shear stiffnesses C44, C55 and Cee are the lowest values. This reflects the major differences between the intramolecular bond stretching and valence bond bending forces and the intermolecular dispersion forces, which determine the shear stiffnesses. The lateral stiffnesses also relate primarily to dispersion forces and are correspondingly low. 

Fig. V.4(a) 4(h). Frequency-dispersion curves of the orthorhombic polyethylene crystal. From Kitagawa (1969), Kitagawa and Miyazawa (1968 a)...

The previously addressed problem of the critical SAS behavior of PCM-PVP solid dispersions out of a pure ethanol solution did not occur as soon as a certain amount of acetone is added in the initial solution composition. The addition of acetone does affect both solutes separately in different ways as discussed in the chapters concerning the behavior of both solutes in the SAS process. What they have in common is that they show different solvatimi phenomena in C02-expanded organic solution as originally published by Sala et al. [40] and previously discussed in the context of the PCM and PVP behavior in the SAS [10,41]. In the case of PVP, this effect can be used to tailor the mean particle size of the generated amorphous polymer particles. Varying the content of acetone in the initial solvent compositiOTi at SAS crystallization of PCM does enable the manipulation of the crystalline structure of PCM from the monoclinic form I to the orthorhombic form n. 

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