Crystal fragmentation

The excess energy of a real crystal fragment depends on how this was obtained usually, the fracture surface is imagined to be perfectly smooth, but real surfaces are rough, have steps, and so on. The surfaces assumed in theoretical calculations are not in contact with any other substance. If a gas, however, is admitted, then the unsaturated valencies will be saturated with adsorbed gas molecules, and the asymmetry of the field will be reduced. Thus the structure calculated for the external layer may be in equilibrium only in excellent vacuum, and the duration of this equilibrium would depend on how rapidly gases and vapors leak into the evacuated vessel. This remark shows, by the way, how illogical are the attempts to correlate the experimental estimates of ys or 7 with those calculated from the theories of Chapter II. 

Fig. 2.89 Lattice images from a crystal fragment with a structure of... 333444... containing stacking defects." These pictures were obtained from another part of the same crystal as that of Fig. 2.88(c). The basic unit of structure MY5 is seen.

When the Gandolfi camera is used, a single crystal or crystal fragment is mounted on a glass capillary (Refs 11 19). This camera is thus of great value when a very small amount of the phase to be investigated is available... 

The vibration directions and refractive indices of crystal fragments of mon ammonium phosphate lying on a microscope slide in any orientation are given by the indicatrix in the following way. A crystal fragment, oriented with its unique axis at any angle 6 to the line of vision, is mentally replaced by the indicatrix (Fig. 48). Perpendicular to the... 

So far it has been assumed that well-formed crystals with plane faces, suitable for accurate setting by the optical method, are available. Such crystals form the ideal experimental material for any detailed crystallographic investigation but it is possible, even when the crystal symmetry is low, to proceed with far less promising material—with ill-formed crystals, or writh irregular crystal fragments, or even with polycrystalline specimens. The additional problems presented by such specimens will now be considered. 

The parameters of Hamiltonians (1) and (2) are determined in our approach by pure theoretical way using different quantum chemical models and calculations unlike the traditional fitting the experimental thermodynamic and dielectric data. Our method of the many-pseudospin clusters [ 1,4] seems to be the most reliable way of determination. The latter are obtained in this case within the static approximation from the system of equations for a typical crystal fragment (cluster) for all possible proton distributions on H-bonds. The left-hand side of any equation expresses the cluster total energy in terms of Jy, while the right-hand side is determined by means of the quantum chemical calculation of this energy. 

Microcline, albite and labradorite were obtained from Ward s Canada Limited. Cleaved crystal fragments and 60 mesh-sized samples were ultrasonically cleaned prior to use. Powdered samples (particle size < 25 ym) were prepared by grinding in a tungsten carbide ball mill, wet-sieving and washing in water. 

The curves in Fig. 15 show the different hydrated forms which are in equilibrium with the saturated solution at different temperatures. It will be seen that the dekahydrate is the stable hydrate only below 33°. In the following preparation, if barely enough water to form the dekahydrate were added to the anhydrous soda ash and the mixture heated to 100°, a complete solution would not be obtained because some monohydrate would separate. Enough water, therefore, is taken to hold all the monohydrate in solution at the boiling point. When this solution cools to below 33° it may become highly supersaturated with the dekahydrate unless a few crystal fragments of the dekahydrate are added. It occasionally happens that if no seed crystals are added the heptahydrate... 

The surface will certainly contain crystal fragments of copper, and perhaps also some amorphous material,1 in all possible orientations. The activating power of the various parts of the surface may well depend on the spacing of the surface atoms of copper, on which the alcohol molecules are adsorbed, and on the amount of distortion (electrical or mechanical) imposed on the adsorbed molecules as they are made to fit the surface of the crystalline fragments in their various orientations. This distortion probably lowers the additional amount of energy, or the heat of activation, required to activate the adsorbed molecules. Though the heat of activation on any particular active patch could not be determined, the... 

Olivine clasts are typically single-crystal fragments, varying in composition from P092 to Eosg. Mesosiderites also contain fine-grained olivine. Most literature analyses are of unspecified grains, and metamorphic equilibration may have altered... 

Amelin Y. V. (1998) Geochronology of the Jack Hills detrital zircons by precise U-Pb isotope dilution analysis of crystal fragments. Chem. Geol. 146, 25—38. 

Debye and Scherrer (1917) used the reflection of a monochromatic beam of X-rays falling on a powder of small crystals or crystal fragments. The random arrangement ensures that sufficient layers of atoms present suitable angles for all reflections to occur. 

Figure 2 High-resolution image of a crystal fragment from a preparation of composition (Ti,Fe)Oi. 9o heated at 1773 K/or 24 h. Perfectly sinusoidal wavelike CS boundaries are seen, oscillating from k(041) to k(04T) with (020) as the mean plane. The wavelength is approximately 25 nm and the amplitude 2.5 nm (Reproduced by permission from Nature London), 1978, 272, 405)...

Figure 5 Electron micrograph showing CS planes in a crystal fragment from a sample o overall composition Tio.osWOs. The orientation of the CS planes changes from 103 in th bottom right corner to (001 in the top left...

Figure 10 A quadruple SiO chain defect in a matrix of double (Si04) chains of the amphibole type is shown (a) as a drawing of packing polyhedra and (b) occurring naturally in a crystal fragment of nephrite jade. In (b) the lower inset shows a superposition of the drawing in (a) at a reduced scale and the upper inset shows the computed image of such a defect (Reproduced by permission from Contrib. Mineral. Petrol., 1978, 66, 1)...

Figure 21 Longitudinal and vertical faults separating ordered regions in a crystal fragment containing mostly the phase (Ba3Nb6Si4026)6. BajNb Ti Oii (Reproduced by permission from Phys. Status Solidi, 1978, 49, 189)...

Figure 27 A crystal fragment o/SrTiOa containing isolated bands o/SrsTiaO (Reproduced by permission from J. Solid State Chem., 1977, 21, 293)...

Figure 36 Electron micrograph of a crystal fragment of the mineral chloritoid. The crystal is mainly composed of one polytypic stacking sequence, but three others, labelled Al, A2, and A3, are also present and exist as coherent intergrowths in the parent matrix (Reproduced by permission from Proc. R. Soc. London, Ser. A, 1978, 36, 399)...

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