Rhombohedral particle

Texture. All limestones are crystalline, but there is tremendous variance in the size, uniformity, and arrangement of their crystal lattices. The crystals of the minerals calcite, magnesite, and dolomite are rhombohedral those of aragonite are orthorhombic. The crystals of chalk and of most quick and hydrated limes are so minute that these products appear amorphous, but high powered microscopy proves them to be cryptocrystalline. Hydrated lime is invariably a white, fluffy powder of micrometer and submicrometer particle size. Commercial quicklime is used in lump, pebble, ground, and pulverized forms. 

The reaction conditions are critical, as hydrated iron oxide, Fe202 H20, can also precipitate. The particles are either spherical or rhombohedral, depending on the nucleating material. 

SEM observations showed that the most crystals obtained in the absence and the low concentration of the G4.5 PAMAM dendrimer were rhombohedral. In the high concentration of the G4.5 PAMAM dendrimer, the vaterite products were spherical. Each shape of CaCOj is a typical morphology for each polymorph. The particle sizes of the spherical vaterite particles obtained in the presence of the PAMAM dendrimer were depended on the concentration of the dendrimer. As the concentration of -COONa increased from 5.3 to 10.6 mmol/1, the particle sizes of the spherical vaterite particles were reduced from 8.7 1.0 to 5.2 3.0 pm. 

A special group of particles that are often produced are the icosahedral (I5) and decahedral (D5) structures shown in Fig. 9. These particles have a fivefold symetry axis which is forbidden for infinite crystals. Yang (1 0) has described these particles using a non-Fcc model. The particles are composed by five (D5) and twenty (I5) tetrahedral units in twin relationship. However the units have a non-Fcc structure. The decahedral is composed by body-centered orthorhombic units and the icosahedral by rhombohedral... 

Figure 16.5. Packing of spherical particles, (a) Cubic arrangement, one sphere touching six others. (b) Rhombohedral packing, one sphere touching twelve others, with layers arranged in rhombic formation...

Chromium(III) oxide crystallizes in the rhombohedral structure of the corundum type space group D3d-R3c, Q 5.2 g/cm3. Because of its high hardness (ca. 9 on the Mohs scale) the abrasive properties of the pigment must be taken into account in certain applications [3.44], It melts at 2435 °C but starts to evaporate at 2000 °C. Depending on the manufacturing conditions, the particle sizes of chromium oxide pigments are in the range 0.1-3 pm with mean values of 0.3-0.6 pm. Most of the particles are isometric. Coarser chromium oxides are produced for special applications, e.g., for applications in the refractory area. 

A review of the alleged allotropes of phosphorus reduces their number to four, namely, the a- and/3-forms of yellow phosphorus, red or violet phosphorus, and black phosphorus. Most of the work of various investigators has been directed towards elucidating the nature of red phosphorus, and of the transformation of yellow to red phosphorus and conversely. Red phosphorus was formerly considered to be amorphous, and it was often called amorphous phosphorus. The term amorphous, however, here referred more to the general appearance of the powder rather than to its minute structure. J. W. Retgers 5 showed that the particles of ordinary red phosphorus are rhombohedral crystals, which are well developed in those of W. Hittorf s violet phosphorus. All four varieties are therefore crystalline. J. W. Terwen has reviewed this subject in a general way and M. Copisarow discussed the theory of allotropy,... 

Special Treatment of Voids— An interesting concept of voids in a regular array of spherical particles has been presented by W. O. Smith et al (1929). Assume a rhombohedral array such as shown in Figure 30, where the spacing is d + h between the particle centers, and 6 is adjusted to the observed porosity. From geometry, the number of spheres per unit-volume is equal to V2/ d + 5)3 and the total sphere volume is this quantity multiplied by (7t/6)dz. Hence, if the observed void is ... 

The boron so formed resembled other amorphous borons in appearance and was found to be similar in structure to jS-rhombohedral boron. Individual particles were random in shape, consisting mainly of platelets between 200 and 7500 A in diameter. The presence of regular dodecagonal platelets of boron was also observed, in the product, which had typical diameters of 7000 A and a unit cell lattice constant of 30 A. This unit cell dimension is considerably larger than any previously reported form of boron and was considered to be a further modification of known boron structures. 

Famularo [35] investigated the problem further and found values of the constant for different assemblies as follows cubic, 1.91 rhombohedral, 1.79 random, 1.30. Burgers [36] considered a random assembly of particles and replaced the second term in the denominator with 6.88c. The numerical constant has been questioned by Hawksley [17 pl31] who suggested that in practice the particles would accelerate to an equilibrium arrangement with a reduced constant of 4.5. The form of expression has also been criticized by Happel and Brenner [7]. 

The Fluorination of Platinum in the Presence of Powdered Glass.—Fluorine, diluted with nitrogen, was passed in a slow stream over a heated mixture of powdered glass and platinum at 400° and a mixture of pale brown and black particles was left. J -Ray powder photographs showed these particles were two phases. A simple pattern, characteristic of the black material, was indexed on the basis of a rhombohedral unit-cell, a = 5-39 i 0 02 A, a = 54-7 i 0-2°, / = 97 A. Observed and calculated Ijd" values are in Table 3. The complex pattern of the light brown phase was identical with that of platinum oxide trifluoride. 

Fig. 17.5 The preparation of epitaxially grown In O thin-film model catalysts, (a) Electron micrograph of an In O thin film prepared on NaCl(OOl) in lO Pa O at 600 K. (b) The corresponding SAED pattern with the inset showing the (200) weak-beam dark-field image of a pyramidal IHjOj nanocrystal, (c) An atomically resolved TEM micrograph of a single rhombohedral In O particle with the corresponding fast Fourier transform (EFT) (inset), (d) Temperature-programmed reaction of MSR measured on the In Oj particles shown in (a). Adapted in part from [33] with permission. Copyright (2008) Elsevier...

Zinc suspension Lente 7.0-7.5 Acetate Amorphous particles (30%) Rhombohedral crystals (70%) -2 24... 

A method for determining the particle size distribution from a single X-ray diffraction profile when strain is present was applied to co-precipitated nickel oxide on alumina and silica. Appreciable strain occurred in the NiO, possibly due to the pressure developed in the small particles to balance the surface tension forces and the distortion produced by the deformation of the f.c.c. structure into a rhombohedral form. Apart from errors in the size distribution created by neglected lattice strain, the measurement of strain itself is important because its correlation with catalytic activity has been suggested. 

Figures 5.7, 5.8 and 5.9 show the diffraction pattern and transmission electron micrograph of the particles in the carbyne films produced by the combustion flame method. In Figures 5.7 and 5.8, the d-spacing of our particles is in good agreement with values of the a-modification of carbyne [47]. The evaluated lattice parameters were aQ = 0.892 nm, co=1.536nm. Figure 5.8 also shows that the interplanar spacing (21.0) and (30.0) of carbyne monocrystal obtained by combustion flame is coinciding with the value obtained by Heimann et al. [46]. The transmission electron micrograph shows the rhombohedral crystal flake of carbyne with a size of 230 X 274 nm.

Properties Specific surface area 0.3 mVg, particle size 1 pm, tetragonal and rhombohedral forms (x= 1) [1736]. 

The rhombohedral lattice arrangement gives the maximum concentration for a given interparticle spacing. This is assumed in arriving at the relation between the average inter-particle clearance C and the porosity. This relation is... 

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