Falling crystallization

Convective crystal dissolution means that crystal dissolution is controlled by convection, which requires (i) a high interface reaction rate so that crystal dissolution is controlled by mass transport (see previous section), and (ii) that mass transport be controlled by convection. In nature, convective crystal dissolution is common. In aqueous solutions, the dissolution of a falling crystal with high solubility (Figure 1-12) is convective. In a basaltic melt, the dissolution of most minerals is likely convection-controlled. 

For the calculation of convective dissolution rate of a falling crystal in a silicate melt, the diffusion is multicomponent but is treated as effective binary diffusion of the major component. The diffusivity of the major component obtained from diffusive dissolution experiments of the same mineral in the same silicate melt is preferred. Diffusivities obtained from diffusion-couple experiments or other types of experiments may not be applicable because of both compositional effect... 

Dissolution distance in 18,000 s would be 174/im, greater than the diffusive dissolution distance of 48 ixm obtained earlier. There are no experimental data to compare. The convective dissolution rate can be applied only when the diffusion distance (Dt) is greater than the boundary layer thickness. If diffusion distance (Dt) is smaller than the boundary layer thickness (86.4 fim), i.e., if t< 1408 s, the dissolution would be controlled by diffusion even for a falling crystal, and the method in Section 4.2.2.3 should be used. 

Convective melting of a rising or falling crystal in its own melt... 

Equations 7 and 8 describe a circle having a center at coordinates (a, 0) and a radius of [(.r — a) + 2/o ] . The falling crystal follows this circle at the same angular velocity as the fluid rotates that is, the rotation of the crystal about (a, 0) has the same period as the fluid rotating about (0, 0). Where x = Vgl6 and /o = 0 the crystal carries out a circle of zero radius, a point at (a, 0). 

The equations have been verified experimentally in apparatus to be described later. After the cylinder begins rotating, only a few minutes are needed for the falling crystal to establish an orbit. The rotation rate of the crystal matches that of the mechanics, for the 1-mm crystals to... 

Most solid surfaces are marred by small cracks, and it appears clear that it is often because of the presence of such surface imperfections that observed tensile strengths fall below the theoretical ones. For sodium chloride, the theoretical tensile strength is about 200 kg/mm [136], while that calculated from the work of cohesion would be 40 kg/mm [137], and actual breaking stresses are a hundreth or a thousandth of this, depending on the surface condition and crystal size. Coating the salt crystals with a saturated solution, causing surface deposition of small crystals to occur, resulted in a much lower tensile strength but not if the solution contained some urea. 

Many-body problems wnth RT potentials are notoriously difficult. It is well known that the Coulomb potential falls off so slowly with distance that mathematical difficulties can arise. The 4-k dependence of the integration volume element, combined with the RT dependence of the potential, produce ill-defined interaction integrals unless attractive and repulsive mteractions are properly combined. The classical or quantum treatment of ionic melts [17], many-body gravitational dynamics [18] and Madelung sums [19] for ionic crystals are all plagued by such difficulties. 

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

Prepare two solutions, one containing i g. of diphenylamine in 8 ml. of warm ethanol, and the other containing 0-5 g. of sodium nitrite in i ml. of water, and cool each solution in ice-water until the temperature falls to 5°. Now add o 8 ml. of concentrated hydrochloric acid steadily with stirring to the diphenylamine solution, and then without delay (otherwise diphenylamine hydrochloride may crystallise out) pour the sodium nitrite solution rapidly into the weil-stirred mixture. The temperature rises at once and the diphenylnitrosoamine rapidly crystallises out. Allow the mixture to stand in the ice-water tor 15 minutes, and then filter off the crystals at the pump, drain thoroughly, wash with water to remove sodium chloride, and then drain again. Recrystallise from methylated spirit. Diphenylnitrosoamine is thus obtained as very pale yellow crystals, m.p. 67 68° yield, 0 9-1 o g. 

Fit securely to the lower end of the condenser (as a receiver) a Buchner flask, the side-tube carrying a piece of rubber tubing which falls well below the level of the bench. Steam-distil the ethereal mixture for about 30 minutes discard the distillate, which contains the ether, possibly a trace of unchanged ethyl benzoate, and also any biphenyl, CeHs CgHs, which has been formed. The residue in the flask contains the triphenyl carbinol, which solidifies when the liquid is cooled. Filter this residual product at the pump, wash the triphenyl-carbinol thoroughly with water, drain, and then dry by pressing between several layers of thick drying-paper. Yield of crude dry product, 8 g. The triphenyl-carbinol can be recrystallised from methylated spirit (yield, 6 g.), or, if quite dry, from benzene, and so obtained as colourless crystals, m.p. 162. ... 

Figure 8.28 shows how the X-rays fall on the solid or liquid sample which then emits X-ray fluorescence in the region 0.2-20 A. The fluorescence is dispersed by a flat crystal, often of lithium fluoride, which acts as a diffraction grating (rather like the quartz crystal in the X-ray monochromator in Figure 8.3). The fluorescence may be detected by a scintillation counter, a semiconductor detector or a gas flow proportional detector in which the X-rays ionize a gas such as argon and the resulting ions are counted.

Glass-Ceramics Based on Silicate Crystals. The principal commercial glass-ceramics fall into this category. These can be grouped by composition, simple siUcates, fluorosiUcates, and aluminosihcates, and by the crystal stmctures of these phases. 

If all the molecules are perfectly parallel, S would equal 1. In an isotropic Hquid, f 6) is constant so that < cos 0 > equals 1/3 and S is therefore 2ero. The order parameter for Hquid crystals falls somewhere between these limits and decreases somewhat with increasing temperature. 

X-ray, uv, optical, in, and magnetic resonance techniques are used to measure the order parameter in Hquid crystals. Values of S for a typical Hquid crystal are shown in Figure 3. The compound, -methoxyben2yHdene-/) - -butylaniHne (MBBA) is mesomorphic around room temperature. The order parameter ranges from 0.7 to 0.3 and discontinuously falls to 2ero at T, which is sometimes called the clearing temperature (1). 

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