Crystallization by diffusion

Crystal growth is a diffusion and integration process, modified by the effect of the solid surfaces on which it occurs (Figure 5.3). Solute molecules/ions reach the growing faces of a crystal by diffusion through the liquid phase. At the surface, they must become organized into the space lattice through an... 

Aza[60]fulleronium ion 28 has been isolated and characterized by X-ray crystallography via the oxidation of 2 with the radical cation hexabromo(phenyl)carbazole (HBPC ) in dry ODCB [27]. The counter-ion is the silver(I) complex carborane ion Ag(CBjjHgCl5)2]. The salt was crystallized as dark green crystals by diffusion of hexane vapor. The solid is reasonably air stable. has almost the same structure... 

Coordination polymer 6a was obtained as light-blue crystals by diffusion of dps into Ni(N03)2 6H2O in an ethanol solution. Figure 5(b) and (c) reveals the crystal... 

A dry cell is not truly dry, because the electrolyte is an aqueous paste. Solid-state batteries have been developed, however. One of these is a lithium-iodine battery, a voltaic cell in which the anode is lithium metal and the cathode is an I2 complex. These solid-state electrodes are separated by a thin crystalline layer of lithium iodide (Figure 20.11). Current is carried through the crystal by diffusion of Li" ions. Although the cell has high resistance and therefore low current, the battery is very reliable and is used to power heart pacemakers. The battery is implanted within the patient s chest and lasts about ten years before it has to be replaced. 

A pale bright blue suspension of Ni(Hdpa)2Cl2 (2.83 g, 6.00 mmol) in THF (60 mL) is cooled to —78°C by means of a dry ice/acetone bath. To this suspension is slowly added methyUithium (5.0 mL of a 1.6M solution in diethyl ether, 4.0 mmol), which causes the suspension to become lime green in color. The suspension is then allowed to warm to room temperature, at which point it becomes dark brown. After the brown mixture is stirred at room temperature for 30 min, it is heated to reflux for 12h, which causes the color to change to dark purple. The solvent is removed under reduced pressure leaving a dark purple residue. Extraction of this sohd with dichloromethane affords a purple solution, from which the dark purple-red product is crystallized by diffusion of hexanes. Crystals were collected by filtration and washed with hexanes. Yield 1.57 g (85%). 

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

Diffusion in the bulk of a crystal can occur by two mechanisms. The first is interstitial diffusion. Atoms in all crystals have spaces, or interstices, between them, and small atoms dissolved in the crystal can diffuse around by squeezing between atoms, jumping - when they have enough energy - from one interstice to another (Fig. 18.6). Carbon, a small atom, diffuses through steel in this way in fact C, O, N, B and H diffuse interstitially in most crystals. These small atoms diffuse very quickly. This is reflected in their exceptionally small values of Q/RTm, seen in the last column of Table 18.1. 

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

In order to answer these questions as directly as possible we begin by looking at diffusive and displacive transformations in pure iron (once we understand how pure iron transforms we will have no problem in generalising to iron-carbon alloys). Now, as we saw in Chapter 2, iron has different crystal structures at different temperatures. Below 914°C the stable structure is b.c.c., but above 914°C it is f.c.c. If f.c.c. iron is cooled below 914°C the structure becomes thermodynamically unstable, and it tries to change back to b.c.c. This f.c.c. b.c.c. transformation usually takes place by a diffusive mechanism. But in exceptional conditions it can occur by a displacive mechanism instead. To understand how iron can transform displacively we must first look at the details of how it transforms by diffusion. 

The diffusion of H and D atoms in the molecular crystals of hydrogen isotopes was explored with the EPR method. The atoms were generated by y-irradiation of crystals or by photolysis of a dopant. In the H2 crystals the initial concentration of the hydrogen atoms 4x 10 mol/cm is halved during 10 s at 4.2 K as well as at 1.9 K [Miyazaki et al. 1984 Itskovskii et al. 1986]. The bimolecular recombination (with rate constant /ch = 82cm mol s ) is limited by diffusion, where, because of the low concentration of H atoms, each encounter of the recombinating partners is preceded by 10 -10 hops between adjacent sites. 

MIR), requires the introduction of new x-ray scatterers into the unit cell of the crystal. These additions should be heavy atoms (so that they make a significant contribution to the diffraction pattern) there should not be too many of them (so that their positions can be located) and they should not change the structure of the molecule or of the crystal cell—in other words, the crystals should be isomorphous. In practice, isomorphous replacement is usually done by diffusing different heavy-metal complexes into the channels of preformed protein crystals. With luck the protein molecules expose side chains in these solvent channels, such as SH groups, that are able to bind heavy metals. It is also possible to replace endogenous light metals in metal-loproteins with heavier ones, e.g., zinc by mercury or calcium by samarium. 

Ionic transport in solid electrolytes and electrodes may also be treated by the statistical process of successive jumps between the various accessible sites of the lattice. For random motion in a three-dimensional isotropic crystal, the diffusivity is related to the jump distance r and the jump frequency v by [3] ... 

Baranowski [680] concluded that the decomposition of nickel hydride was rate-limited by a volume diffusion process the first-order equation [eqn. (15)] was obeyed and E = 56 kJ mole-1. Later, Pielaszek [681], using volumetric and X-ray diffraction measurements, concluded from observations of the effect of copper deposited at dislocations that transportation was not restricted to imperfect zones of the crystal but also occurred by diffusion from non-defective regions. The role of nickel hydride in catalytic processes has been reviewed [663]. 

Time is an essential part of the crystallization process. A large crystal cannot form spontaneously. It must start with a nucleus which grows by addition. As the solution immediately adjacent to the growing crystal face is depleted of building blocks, more must be supplied by diffusion through the liquid. 

It is usually believed that the growth of dendritic crystals is controlled by a bulk diffusion-controlled process which is defined as a process controlled by a transportation of solute species by diffusion from the bulk of aqueous solution to the growing crystals (e.g., Strickland-Constable, 1968 Liu et al., 1976). The appearances of feather- and star-like dendritic shapes indicate that the concentrations of pertinent species (e.g., Ba +, SO ) in the solution are highest at the corners of crystals. The rectangular (orthorhombic) crystal forms are generated where the concentrations of solute species are approximately the same for all surfaces but it cannot be homogeneous when the consumption rate of solute is faster than the supply rate by diffusion (Nielsen, 1958). 

U-series elements are unusual in that, although they are trapped as one species at the time of crystal growth, they will decay to a different species with time. Consequently, the possibility exists for a highly compatible parent to decay to a highly incompatible daughter nuclide. With time the daughter will be expelled from the lattice, typically by diffusion. This creates a balance between uptake and decay that is not a consideration for stable trace elements, and so deserves brief mention here. 

Two crystallographic forms of lead azide are important, the ordinary alpha form which is orthorhombic and the beta form which is monoclinic. The densities of these forms are 4-71 and 4-93 respectively. It was for many years believed that the beta form is the more sensitive to friction and impact and accounted for detonations which have occurred in the manufacture and handling of the substance. It is now known that the beta form is in fact no more sensitive than the alpha. Even the alpha form, when present as large crystals, is very sensitive and conditions can arise (particularly when the formation of the lead azide is controlled by diffusion effects) where spontaneous detonation occurs. Although with modern knowledge these hazards can be avoided, pure lead azide is nevertheless a dangerous compound and is now made only for military purposes. 

Purified MeHNL was crystallized by the sitting-drop vapor-diffusion method. The 10-20 mm bipyramidal crystals formed were cross-linked with glutaraldehyde and used as biocatalyst for the synthesis of optically active cyanohydrins. The cross-linked crystals were more stable than Celite-immobilized enzymes when incubated in organic solvents, especially in polar solvents. After six consecutive batch reactions in dibutyl ether, the remaining activity of the cross-linked crystals was more than 70 times higher than for the immobilized enzymes. Nevertheless, the specific activity of the cross-linked crystals per milligram protein was reduced compared with the activity of Celite-immobilized enzymes [53],... 

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