The Crystal Surface

Figure 7.14a illustrates the insertion of a propylene monomer into an edge vacancy in a crystal adjacent to an alkylated titanium atom. In Fig. 7.14b a cross-sectional view of the same site shows how the preferential orientation of the coordinated monomer is dictated by constraints imposed by the protuberances on the crystal surface. 

Attenuated total reflection (ATR), also called internal reflection, is based on the phenomenon of total internal reflection. In ATR the infrared beam is directed into an infrared-transmitting crystal so that it strikes the crystal surface at less than the critical angle and undergoes total internal reflection. 

Structure Modification. Several types of stmctural defects or variants can occur which figure in adsorption and catalysis (/) surface defects due to termination of the crystal surface and hydrolysis of surface cations (2) stmctural defects due to imperfect stacking of the secondary units, which may result in blocked channels (J) ionic species, eg, OH , AIO 2, Na", SiO , may be left stranded in the stmcture during synthesis (4) the cation form, acting as the salt of a weak acid, hydrolyzes in aqueous suspension to produce free hydroxide and cations in solution and (5) hydroxyl groups in place of metal cations may be introduced by ammonium ion exchange, followed by thermal deammoniation. 

As in chemical sensitization, spectral sensitization is usually done after precipitation but before coating, and usually is achieved by adsorbing certain organic dyes to the silver haUde surfaces (47,48,212—229). Once the dye molecule is adsorbed to the crystal surface, the effects of electromagnetic radiation absorbed by the dye can be transferred to the crystal. As a result of this transfer, mobile electrons are produced in the conduction band of the silver haUde grain. Once in the conduction band, the electrons are available to initiate latent-image formation. 

V, is measured by striking one end of a bar of the material (by glueing a piezo-electric crystal there and applying a charge-difference to the crystal surfaces) and measuring the time sound takes to reach the other end (by attaching a second piezo-electric crystal there). Most moduli are measured by one of these last two methods. 

Charles Frank and his recognition, in 1949, that the observation of ready crystal growth at small supersaturations required the participation of screw dislocations emerging from the crystal surface (Section 3.2.3.3) in this way the severe mismatch with theoretical estimates of the required supersaturation could be resolved. 

The line which defines the crystal surface can have straight pieces ( facets ) as well as curved ones. The latter correspond to a rough surface, as explained in the next section. The point at which straight and curved pieces meet can be either a sharp corner or a smooth tangential connection like z [21], where x is the deviation from the contact point in the direction... 

One now wonders whether these two phenomena are to be observed also for the whole two-dimensional surface of a crystal non-locking of the crystal surface in spite of lattice periodicity, and divergence of the fluctuation-induced thickening of the interface (or crystal surface), and in consequence the absence of facets. The last seems to contradict experience crystals almost by definition have their charm simply due to the beautifully shining facets which has made them jewelry objects since ancient times. 

On a so-called vicinal face there are many steps running in parallel with almost the same separation or terrace width in between. At a finite temperature, these steps also fluctuate. But due to the high energy cost for the formation of overhangs on the crystal surface, steps cannot cross each other. This non-crossing condition suppresses the step fluctuation. 

One can now immediately deduce the normal growth rate of a crystal due to the screw dislocation. Whenever a step edge passes by a fixed point on the crystal surface, this point gains the height of a lattice unit. The normal growth rate V of the crystal is then... 

We have so far assumed that the atoms deposited from the vapor phase or from dilute solution strike randomly and balHstically on the crystal surface. However, the material to be crystallized would normally be transported through another medium. Even if this is achieved by hydrodynamic convection, it must nevertheless overcome the last displacement for incorporation by a random diffusion process. Therefore, diffusion of material (as well as of heat) is the most important transport mechanism during crystal growth. An exception, to some extent, is molecular beam epitaxy (MBE) (see [3,12-14] and [15-19]) where the atoms may arrive non-thermalized at supersonic speeds on the crystal surface. But again, after their deposition, surface diffusion then comes into play. 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

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