Diffusion crystalline solids, mechanisms

When determining the solubility and dissolution rate of amorphous or partially crystalline solids, the metastability of these phases with respect to the highly crystalline solid must be considered. While the low diffusivity of the molecules in the solid state can kinetically stabilize these metastable forms, contact with the solution, for example during measurements of solubility and dissolution rate, or with the vapor, if the solid has an appreciable vapor pressure, may provide a mechanism for mass transfer and crystallization. Less crystalline material dissolves or sublimes whereas more crystalline material crystallizes out. The equilibrium solubility measured will therefore approach that of the highly crystalline solid. The initial dissolution rate of the metastable form tends to reflect its higher... 

R.W. Balluffi. Grain boundary diffusion mechanisms in metals. In G.E. Murch and A.S. Nowick, editors, Diffusion in Crystalline Solids, pages 319-377, Orlando, FL, 1984. Academic Press. 

A number of diffusion mechanisms in crystalline solids are possible. Atoms vibrate in their equilibrium sites after that, periodically, these oscillations turn out to be large enough to give rise to a jump from one site to the other. The order of magnitude of the frequency of these oscillations is about 1012-1013 Hz. In this regard, it has been shown that the jump rate at which an atom jumps into an empty neighboring site is given by [30]... 

Diffusion of atoms or ions in crystalline solids can occur by at least three possible mechanisms, as shown schematically in Figure 2.7. In some solids, transport proceeds primarily by the vacancy mechanism, in which an atom jumps into an adjacent, energetically equivalent vacant lattice site. The vacancy mechanism is generally much slower than the interstitial mechanism (discussed below). Nonetheless, it is thought to be responsible for self-diffusion in all pure metals and for most substitutional alloys (Shewmon, 1989). 

Figure 2.7 Diffusion of atoms or ions in crystalline solids can occur by at least three possible mechanisms illustrated here. In the vacancy mechanism (bottom arrow), an atom in a lattice site jumps to an adjacent vacant lattice site. In the interstitial mechanism (middle arrow), an interstitial atom jumps to an adjacent vacant interstitial site. In the intersitialcy mechanism (top two arrows), an interstitial atom pushes an atom residing in a lattice site into an adjacent vacant interstitial site and occupies the displaced atom s former site. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)...

Ordinary diffusion can be defined as the transport of a particular species relative to an appropriate reference plane owing to the random motion of molecules in a region of space in which a composition gradient exists. Although the mechanisms by which the molecular motion occurs may vaty greatly from those in a gas to those in a crystalline solid, the essential features of a random molecular motion in a composition gradient are the same, as will be seen in the simplified derivations discussed here. 

In modelling crystalline solids, the MC technique is of particular value in three distinct fields. The first concerns studies of sorbed systems, e.g. micropo-rous solids loaded with organic molecules. MC techniques are particularly suitable for studying the variation with temperature of the distribution of sorbed molecules in such systems (Yashonath et al., 1988). Secondly, the method has been fruitfully applied to the study of atomic diffusion. In this case the moves are atomic jumps of defined frequencies. In complex solids (including, e.g., alloys and ionic conductors), use of the MC technique allows accurate sampling of all the different jump mechanisms contributing to the diffusion, as shown in several studies of Murch and coworkers (e.g. Murch, 1982). 

Diffusion through nonporous crystalline solids depends markedly on the crystal lattice structure and the diffusing entity. The mechanisms of diffusion in crystalline solids include (Seader and Henley, 2006) ... 

It is necessary to emphasize that the effect of uphill diffusion should be distinguished from the directional diffusion of point defects that can also take place under conditions of a homogeneous stressed state (diffusive creep). Nevertheless, the indicated mechanisms of plastic deformation have a lot in common, because they both are diffusive mechanisms of plastic deformation of crystalline solids. 

As discussed before, the free surface of a crystalline solid is not a perfectly flat plane, which could contain vacancies, terraces, kinks, edges, and adatoms. The migration of vacancies and the movement of adatoms facilitate the mechanisms of surface diffusion. The diffusion process is usually confined to a thin layer near the surface with a thickness of 0.5-1 nm. 

In theory, heat in crystalline solids is transferred by three mechanisms (i) electrons (ii) lattice vibrations and (iii) radiation [44], Since zirconia is an electronic insulator (electrical conductivity occurring at high temperatures by oxygen ion diffusion), electrons play no part in the total thermal conductivity of the system. Hence, thermal conduction in zirconia-based ceramics is mainly by lattice vibrations (phonons) or by radiation (photons). 

Figure 7.4 shows an initial nonuniform distribution of element i in a medium of j. Atoms of species i diffuse from the region of high concentration to the region of low concentration and establish a more imiform concentration distribution of the species. Self-diffusion also takes place in a relatively pure crystalline solid material controlled by a process known as vacancy mechanism or the hopping process. The ion transport in crystalline electrolyte is controlled by this vacancy diffusion or hopping diffusion mechanism. In this... 

Reactions of the general type A + B -> AB may proceed by a nucleation and diffusion-controlled growth process. Welch [111] discusses one possible mechanism whereby A is accepted as solid solution into crystalline B and reacts to precipitate AB product preferentially in the vicinity of the interface with A, since the concentration is expected to be greatest here. There may be an initial induction period during solid solution formation prior to the onset of product phase precipitation. Nuclei of AB are subsequently produced at surfaces of particles of B and growth may occur with or without maintained nucleation. 

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