Solid-state atomic diffusion

The formation free radicals in solid state,the diffusion of free radicals into polymer matrix,the kinetics of hydrogen atom abstraction. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

Figure 19.2 shows, at a microscopic level, what is going on. Atoms diffuse from the grain boundary which must form at each neck (since the particles which meet there have different orientations), and deposit in the pore, tending to fill it up. The atoms move by grain boundary diffusion (helped a little by lattice diffusion, which tends to be slower). The reduction in surface area drives the process, and the rate of diffusion controls its rate. This immediately tells us the two most important things we need to know about solid state sintering ... 

Many metals and metallic alloys show martensitic transformations at temperatures below the melting point. Martensitic transformations are structural phase changes of first order which belong to the broader class of diffusion js solid-state phase transformations. These are structural transformations of the crystal lattice, which do not involve long-range atomic movements. A recent review of the properties and the classification of diffusionless transformations has been given by Delayed... 

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

The solid state sensor consists of a Wheatstone Bridge circuit shown in Figure 6.9 which is diffused into a silicon chip, thereby becoming a part of the atomic structure of the... 

The materials for solid solutions of transition elements in j3-rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by erystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (V ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, (2o, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V . Boron is a brittle material, indicating the accommodation of transition-element atoms in the -rh boron structure is associated with an increase in the cohesion energy of the solid. 

We find that this solid state reaction is very slow, even at 800 °C., and occurs at the interface of the two types of particles. The reaction is slow because it is diffusion-limited. What is happening is that since the silica-network is three-dimensionally bound, the only reaction that occurs is caused by the difiusion of Ba2+ atoms within the network, as shown in the following ... 

The BaO is produced in the form of very small particles of nearly atomic proportions which react immediately to form the silicate. Actually, the rate of reaction is proportional to the number of nuclei produced per unit vdlume. A nucleus is a point where atoms or ions have reacted and begun the formation of the product structure. In the case of the BaO reaction, the number of nuclei formed per unit of time is small and formation of the structure is diffusion limited. In the case of BaCOa decomposition, the atomic-proportioned BaO reacts nearly as fast as it is formed so that the number of nuclei per unit volume is enormously increased. It is thus apparent that if we wish to increase solid state reaction rates, one way to do so is to use a decomposition reaction to supply the reacting species, we will further address this type of reaction later on in our discussion. 

In 1902, Wagner published an analysis, based on diffusion reactions, of the oxidation of the surface of a metal. His interpretation has remained a classic in solid state diffusion analysis. The surface of a metal consists of metal atoms bound to the inner structure by a series of hybrid-bonds. If oxygen gas is present (air), the metal can form an oxide coating ... 

For phase-boundary controlled reactions, the situation differs somewhat. Diffusion of species is fast but the reaction is slow so that the dlfiusing species pile up. That is, the reaction to rearrange the structure is slow in relation to the arrival of the diffusing ions or atoms. TTius, a phaseboundary (difference in structure) focus exists which controls the overall rate of solid state reaction. This rate may be described by ... 

The very fine particles of nearly atomic proportions react almost immediately. Because the BaO product hcis an extremely large surface area, the solid state reaction Is not diffusion limited. In the last method (see 4.9.18.), we might use a precipitated product to use as the basis to form the desired compound. We might precipitate ... 

Crystalline solids are built up of regular arrangements of atoms in three dimensions these arrangements can be represented by a repeat unit or motif called a unit cell. A unit cell is defined as the smallest repeating unit that shows the fuU symmetry of the crystal structure. A perfect crystal may be defined as one in which all the atoms are at rest on their correct lattice positions in the crystal structure. Such a perfect crystal can be obtained, hypothetically, only at absolute zero. At all real temperatures, crystalline solids generally depart from perfect order and contain several types of defects, which are responsible for many important solid-state phenomena, such as diffusion, electrical conduction, electrochemical reactions, and so on. Various schemes have been proposed for the classification of defects. Here the size and shape of the defect are used as a basis for classification. 

---