Solid-state diffusion mechanisms

Some ceramic materials are not found widely or at all in nature, and thus are synthesized for use. To prepare more complex ceramic compositions such as perovskites of general structural formula ABO3, and ferrites, of formula MFc204, the individual oxides or salts of the cations A, B, and M are often combined as powders and then reacted at high temperature by a solid-state diffusion mechanism. Silicon nitride (Si3N4) can be manufactured from either the nitridation of silicon metal or from the reaction of silicon tetrachloride with ammonia. Silicon carbide (SiC) is obtained from the reduction of silica with a carbon containing source. 

V - Role of Defects in Solid State Diffusion Mechanisms... 

FIGURE 4.23 Two principal solid-state diffusion mechanisms (a) vacancy diffusion (b) interstitial diffusion. 

The mechanism of mechanochemical synthesis is not clear. One possibility is the occurrence of the reaction by a solid-state diffusion mechanism. Since diffusion is thermally activated, this would require a significant lowering of the activation energy, a considerable increase in the temperature existing in the mill. 

For a solid-state diffusion mechanism, the growth of the reaction product in powder systems occurs at the contact points and for nearly equal-sized spheres, the number of contact points is small. Nevertheless, for many systems, the Jander equation and the Carter equation give a good description of the reaction kinetics for at least the initial stages of the reaction. It appears that rapid surface diffusion provides a uniform supply of one of the reactants over the other. Alternatively, if the vapor pressure of one of the reactants is high enough [e.g., ZnO in Eq. (2.3)], condensation on the surface of the other reactant can also provide a uniform supply of the other reactant. In this case, the powder reaction can be better described as a gas-solid reaction rather than a solid-state reaction (32). 

In sintering, matter transport by evaporation and condensation is normally treated alongside the solid-state diffusion mechanisms. The rate of transport is taken as proportional to the equilibrium vapor pressure over the surface, which can be related to the value of /Xa - / v beneath the surface. Suppose a number dNa of atoms is removed from the vapor and added to the surface with an accompanying decrease in the number of vacancies beneath the surface. The free energy change for this virtual operation must be zero, so that... 

High temperatures are generally needed in solid state synthesis to improve reaction rates and to facilitate solid state diffusion. Solid state diffusion is typically very slow. Thus, mechanical grinding steps are important to homogenize the sample and encourage complete reaction. It is important to realize, however, that some phases decompose at elevated temperatures. For example, Ba CujOy is unstable above about 1050°C (1) and the related phase, BajYCUjOg is only stable to 860°C in one atmosphere of oxygen (2). Thus, efforts to prepare these phases require a balance between the heat put in to speed the reaction kinetics and the stability limits of the desired phase. 

As discussed in section 2.4, indications of high temperature ferromagnetism in (Ga,Mn)N have been reported by Sonoda et al. (2002) and Reed et al. (2001), whose layers grown by ammonia-MBE or prepared by solid state diffusion show ferromagnetism well above room temperature. Work is under way to rule out the influence of precipitations as well as to establish how 7c depends on the Mn and carrier concentration. Possible mechanisms accounting for the experimental observations have been put forward (Dietl etal. 2001b). 

Solid A Solid B S/S Corrosion, grain boundary passivation, adhesion, delamination, epitaxial growth, nucleation and growth abrasion, wear, friction, diffusion, boundary structure thin films, solid state devices, mechanical stability, creep. 

Autodoping of epi films can be explained by two mechanisms. For one, dopant could diffuse (solid state diffusion) from the buried layer to the epi film during its formation. Second, the dopant from the buried layer can vaporize, enter the reactor gas flow, and be incorporated as the surface reaction proceeds. The concensus seems to be that the latter effect is the predominant one. In fact, it is well known that coating the back of the wafer with oxide reduces the autodoping, and this can only relate to gas phase transport. 

Solid-state diffusion, which is involved in the release of oxygen, proceeds generally through the movement of point defects. The vacancy mechanism, the interstitial mechanism, and the interstitialcy mechanism can occur depending on the distortion of the solid lattice and the nature of the diffusing species. When one of the steps 1-5 is the slowest step representing the major resistance, that step is the rate-controlling one, which is not necessarily the chemical reaction (step 3). 

At the same time, mechanisms of the solid-state diffusion of ions in the intercalation electrodes are numerous and more complicated than the mechanisms of surface diffusion. Crystallographic fea-... 

Solid-solid synthesis reactions operate by different mechanisms, which include solid state diffusion and chemicsd reaction. Diffusion in ceramic solids is always ionic in nature and depends on defect or hole diffusivity, as well as, electron conductivity. Once the ionic reactants are in close association, chemical reactions can take place. 

The present day FCC eatalyst eonsists typically of a USY zeolite in a siliea-alumina matrix. The matrix ean have a range of surface area and cracking activity (11). At the regenerator temperature, sodium has a solid state diffusion eoeffieient of lO to 10 em s" (12) and is expected to move easily within a eatalyst particle. The distribution of Na between zeolite and matrix and its effect on the stability of each component under these conditions is of interest. Furthermore, in the presence of steam, interparticle migration of volatile Na species is expected. The mechanism of this process has not been investigated. 

According to this mechanism the rate determining step for the second stage of the sulphation of CaCOs is a solid state diffusion in which the diffusion species could be Ca, COa " or S04 . 

Nevertheless, this basic mechanism of using specific phases to concentrate nuclides chemically, followed by preferential extraction of those phases, is a process that is common to many of the models proposed for U-series excesses including the dynamic melting models (McKenzie, 1985 Williams and Gill, 1989) discussed in Section 3.14.4.3.1 as well as more recently proposed solid state, diffusion controlled models (e.g., Van Orman et al., 2002a Saal et al., 2002b Feineman et al., 2002)... 

Historically, stabilized (and partially stabilized) zirconia ceramics were prepared from powders in which the component oxides are mechanically blended prior to forming and sintering. Because solid state diffusion is sluggish, firing temperatures in excess of 1800°C are normally required. Furthermore, the dopant was nonuniformly distributed, leading to inferior electrical properties. Trace impurities in the raw materials can also lead to enhancement of electronic conductivity in certain temperature ranges, which is also undesirable. To overcome these problems, several procedures have been developed to prepare reactive (small particle size) and chemically pure and homogeneous precursor powders for both fully stabilized and partially stabilized material. Two of these are alkoxide synthesis and hydroxide coprecipitation. 

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