Materials surface: diffusion

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

Sintering consists of heating a mixture of fine materials to an elevated temperature without complete fusion. Surface diffusion and some incipient fusion cause the soHd particles in contact with one another to adhere and form larger aggregates. In the processing of hematite, Fe202, or magnetite,... 

Numerical values for solid diffusivities D,j in adsorbents are sparse and disperse. Moreover, they may be strongly dependent on the adsorbed phase concentration of solute. Hence, locally conducted experiments and interpretation must be used to a great extent. Summaries of available data for surface diffusivities in activated carbon and other adsorbent materials and for micropore diffusivities in zeolites are given in Ruthven, Yang, Suzuki, and Karger and Ruthven (gen. refs.). 

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. 

The PLAP applies a short duration (100 ps 10 ns) laser pulse to the apex of the specimen. The heat generated is sufficient to promote the field evaporation at the standing voltage of the specimen. The specimens need only to be sufficiently conductive to permit field ion imaging. The peak temperature in the PLAP is only 300 K for a period of a few nanoseconds, which is not sufficiently high for surface diffusion on semiconductor materials, and so the spatial resolution is not downgraded. 

There are, in principle, three ways in which material may be transported to the electrode surface diffusion, convection and migration. Of these, perhaps the most straightforward is migration, which simply consists of the movement of a charged particle under the influence of an electric field. Experimentally, it is well established that after an extremely short time an ion in solution in an electric field will behave as if it had acquired a steady velocity in the direction of the field. The reason why a steady velocity is established rather... 

The gradient of chemical potential along the surface may also drive surface diffusion. The gradient of V2h is therefore a driving force for a flux Ns of material parallel to the surface. A differential material balance gives,... 

While modeling the structure and properties of porous materials one usually is interested in structural properties of a desirable hierarchical level. For example, for chemical properties the molecular structure is major, and the specific adsorption and catalytic properties are guided by the structure and composition of particle surface. Diffusion permeability is determined by the supramolecular... 

During the constant rate period, it is assumed that drying takes place from a saturated surface of the material by diffusion of the water vapour through a stationary air film into the air stream. Gilliland(8) has shown that the rates of drying of a variety of materials in this stage are substantially the same as shown in Table 16.1. 

In both situations the interaction of the medium inside the pore with the pore wall (1) is increased (2) or changed which affect the transport and separation properties (surface diffusion, multilayer adsorption) and/or help overcome equilibrium constraints in membrane reactors. Membrane modifications can be performed by depositing material in the internal pore structure from liquids (impregnation, adsorption) or gases. Several modification possibilities are schematically shown in Figure 2.3. Some results obtained by Burggraaf, Keizer and coworkers are summarized in Table 2.7. Composite structures on a scale of 1-5 nm were obtained. 

The maximum rise of number of mobile dislocations in the deformed materials occurs in the range of 10-20 % [9, 10]. Such processes influence on kinetic of phase formation that results in the accelerated growth of s- and y-nitrides and in increase of microhardness of the surface diffusion layers. 

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