Diffusion mechanism direct

In order to answer these questions as directly as possible we begin by looking at diffusive and displacive transformations in pure iron (once we understand how pure iron transforms we will have no problem in generalising to iron-carbon alloys). Now, as we saw in Chapter 2, iron has different crystal structures at different temperatures. Below 914°C the stable structure is b.c.c., but above 914°C it is f.c.c. If f.c.c. iron is cooled below 914°C the structure becomes thermodynamically unstable, and it tries to change back to b.c.c. This f.c.c. b.c.c. transformation usually takes place by a diffusive mechanism. But in exceptional conditions it can occur by a displacive mechanism instead. To understand how iron can transform displacively we must first look at the details of how it transforms by diffusion. 

We are now ready to consider some soUd state reactions that relate more directly to the real world. These include the tarnishing reaction and Pick s Laws of Diffusion. Both of these scientific areas have been rigorously studied because of their importcmce in revealing how diffusion mechanisms are related to everyday solid state reactions which occur on a daily basis. 

One type of diffusion mechanism is known as the interstitial mechanism because it involves movement of a lattice member from one interstitial position to another. When diffusion involves the motion of a particle from a regular lattice site into a vacancy, the vacancy then is located where the site was vacated by the moving species. Therefore, the vacancy moves in the opposite direction to that of the moving lattice member. This type of diffusion is referred to as the vacancy mechanism. In some instances, it is possible for a lattice member to vacate a lattice site and for that site to be filled simultaneously by another unit. In effect, there is a "rotation" of two lattice members, so this mechanism is referred to as the rotation mechanism of diffusion. 

In the case of interstitials—self-interstitials, impurities, or dopants—two diffusion mechanisms can be envisaged. In the simplest case, an interstitial can jump to a neighboring interstitial position (Fig. 5.8a). This is called interstitial diffusion and is sometimes referred to as direct diffusion to distinguish it from vacancy diffusion (indirect diffusion). 

Beside the partial pressure differences between the various gas components, the total pressure on both sides of the membrane is also important. Though mean total pressure does not directly affect the permeation rate in the case of a Knudsen diffusion mechanism, it governs the gas flow through... 

The speed of provision of the feed molecules to the adsorption/catalytic sites must be balanced with engineering issues such as pressure drop in a reactor/ adsorber, so the parhcle size and pore structure of engineered forms must be optimized for each appHcation. A hierarchy of diffusion mechanisms interplays in processes using formed zeoHtes. Micropore, molecular, Knudsen and surface diffusion mechanisms are all more or less operative, and the rate Hmifing diffusion mechanism in each case is directly affected by synthesis and post-synthesis manufacturing processes. Additional details are provided in Chapter 9. 

The two starting components were packed into a glass capillary from opposite ends until they met in the centre. A coloured reaction product was observed visually after 7 to 10 min at the reactant interface. As time progressed, the product interface was observed to advance in the direction of the picric acid reactant. Further study of this reaction supported a vapour diffusion mechanism, bolstered in part by the observation that complexation proceeds even if a small gap of space exists between the two reactants [12]. The nature of the complex was investigated in additional work, whereby it was proposed that a donor/acceptor 71-complex was produced [13]. A crystal structure confirming this deduction was later published [14]. 

Figure 11.9(b) shows that when p, is calculated with N=8, it resembles a high-temperature probability density function. The peaks are broader and two of them are linked by bridges along the c direction, the direction of easy Mg diffusion. Figure 11.9(b) suggests a diffusion mechanism in which Mgl, but not Mg2, moves between its regular sites via the vacant hole in the structure. 

A great role in substantiating the importance of electron tunneling reactions was played by the work of De Vault and Chance in 1966 where the characteristic time, t1/z, of electron transfer from the heme site of the cytochrome molecule to the chlorophyll molecule in a bacterium was shown to be constant within the temperature range of 130 to 4.2 K [4]. The temperature independence of t1/2 permitted one to reject a diffusion mechanism for the process. However, it was still impossible to exclude the possibility of the reaction to proceeding via direct contact between the active sites of the reacting molecules. 

If diffusive combustion occurs and the flame does not move with respect to the gas, then convective flows will carry it upward such a flame can not propagate downward. Therefore we relate the dependence of the limits on the direction of propagation to the possibility of a diffusive mechanism, and we compare the theory of limits of normal propagation ( 1.4 and 1.5) with data relating to downward propagation. 

On the basis of the theory developed above we foresaw and realized experimentally (in Drozdov s work in our laboratory) a new kind of mixture which exhibits a significant dependence of the limit on the direction of propagation such mixtures do not contain hydrogen, and the diffusion mechanism in them facilitates combustion due to kinetic, rather than thermal factors. 

It is easy to believe that the grain-boundary diffusion mechanism was the major one to be considered, as described in equation (9.1). The direct effect of fine grain size alone on the rate of deformation can be obtained from the °c d 3 relationship. Therefore the 100 nm sized 3Y-TZP material should exhibit some 40 times higher rates of deformation in comparison with the 0.35 pm grain-sized ones, under similar conditions. 

Because numerical errors due to discretization of a convective term introduce an additional, unphysical diffusion mechanism, termed numerical diffusion (ND), the diffusion coefficient D was set to zero [152], The resulting concentration fields nonetheless are indicative of the distribution of a solute within the micro channel volume. In this way, convective patterns can be derived for the redistribution of the liquid transverse to the flow direction. Accordingly, the stretching, tilting and thinning of liquid lamellae can be followed. 

The first attempts in the direction of simulating theoretically at an atomistic level the diffusion of simple gas molecules in a polymer matrix were made more than two decades ago (100). But, the systematic development of ab initio computer simulations of penetrant diffusion in polymeric systems dates only from the late 80 s (101-104). At the beginning of the 90 s it was achieved to simulate some qualitative aspects such as the diffusion mechanism, temperature, and pressure dependence of diffusion coefficients (105-109). The polymers chosen for investigation mainly fell into two categories either they were easily described (model elastomers or polyethylene) or they were known to have, for simple permanent gases like H2, 02, N2, H20 or CH4,... 

In Section 3 we derive that for the vacancy-mediated diffusion mechanism, one expects the shape of the jump length distribution to be that of a modified Bessel function of order zero. Both distributions can be fit very well with the modified Bessel function, again confirming the vacancy-mediated diffusion mechanism for both cases. The only free parameter used in the fits is the probability prec for vacancies to recombine at steps, between subsequent encounters with the same embedded atom [33]. This probability is directly related to the average terrace width and variations in this number can be ascribed to the proximity of steps. The effect of steps will be discussed in more detail in Section 4. 

Figure 3 Defects and associated diffusion mechanism 1 and 2, diffusion mechanism by direct exchange 3, diffusion through vacancy 4, direct interstitial mechanism 5, indirect interstitial or caterpillar mechanism 6, Frenkel defect 7, indirect exchange 8, Schottky defect. (Ref 9. Reproduced by permission of Cambridge University Press)...

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