Diffusion atomic

Write the expression for the diffusivity in terms of the principal diffusion coefficients for  

an orthorhombic crystal with diffusion along an arbitrary direction with direction cosines 1, ly, / )  

for a uniaxial crystal (hexagonal, tetragonal, trigonal) with unique axis c parallel to z. 

The diffusion coefficient for any arbitrary direction (Z, Zy, Iz) is obtained from  

For an isotropic medium (e.g. cubic crystal or icosahedral quasicrystal), D is 

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Fig. XVIII-15. Oxygen atom diffusion on a W(IOO) surface (a) variation of the activation energy for diffusion with d and (b) variation of o- (From Ref. 136. Reprinted with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

Using Fig. XVIII-15, calculate (D for O atom diffusion on W(IOO) as a function of 6. Comment on your results. 

The defects generated in ion—soHd interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10 s), the remaining vacancy—interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach (27). Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom and local kinetic processes can be described on the basis of ahquid-like diffusion formalism (28,29). 

Diffusion of Carbon. When carbon atoms are deposited on the surface of the austenite, these atoms locate in the interstices between the iron atoms. As a result of natural vibrations the carbon atoms rapidly move from one site to another, statistically moving away from the surface. Carbon atoms continue to be deposited on the surface, so that a carbon gradient builds up, as shown schematically in Figure 5. When the carbon content of the surface attains the equihbrium value, this value is maintained at the surface if the kinetics of the gas reactions are sufficient to produce carbon atoms at least as fast as the atoms diffuse away from the surface into the interior of the sample. 

TABLE 5-16 Atomic Diffusion Volumes for Use in Estimating Oab by the Method of Fuller/ Schettler/ and Giddings... 

Materials handbooks list data for Dq and Q for various atoms diffusing in metals and ceramics Table 18.1 gives some of the most useful values. Diffusion occurs in polymers, composites and glasses, too, but the data are less reliable. 

Diffusion in the bulk of a crystal can occur by two mechanisms. The first is interstitial diffusion. Atoms in all crystals have spaces, or interstices, between them, and small atoms dissolved in the crystal can diffuse around by squeezing between atoms, jumping - when they have enough energy - from one interstice to another (Fig. 18.6). Carbon, a small atom, diffuses through steel in this way in fact C, O, N, B and H diffuse interstitially in most crystals. These small atoms diffuse very quickly. This is reflected in their exceptionally small values of Q/RTm, seen in the last column of Table 18.1. 

Atoms diffuse away from the bottom of the halt plane. At high T/T this takes place mainly by bulk diffusion through the crystal... 

As the stress is reduced, the rate of power-law creep (eqn. (19.1)) falls quickly (remember n is between 3 and 8). But creep does not stop instead, an alternative mechanism takes over. As Fig. 19.4 shows, a polycrystal can extend in response to the applied stress, ct, by grain elongation here, cr acts again as a mechanical driving force but, this time atoms diffuse from one set of the grain faces to the other, and dislocations are not involved. At high T/Tm, this diffusion takes place through the crystal itself, that... 

Either the and the two e s diffuse outward through the film to meet the 0 at the outer surface, or the oxygen diffuses inwards (with two electron holes) to meet the at the inner surface. The concentration gradient of oxygen is simply the concentration in the gas, c, divided by the film thickness, x and the rate of growth of the film dx/dt is obviously proportional to the flux of atoms diffusing through the film. So, from Pick s Law (eqn. (18.1)) ... 

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 ... 

Among the alkali metals, Li, Na, K, Rb, and Cs and their alloys have been used as exohedral dopants for Cgo [25, 26], with one electron typically transferred per alkali metal dopant. Although the metal atom diffusion rates appear to be considerably lower, some success has also been achieved with the intercalation of alkaline earth dopants, such as Ca, Sr, and Ba [27, 28, 29], where two electrons per metal atom M are transferred to the Cgo molecules for low concentrations of metal atoms, and less than two electrons per alkaline earth ion for high metal atom concentrations. Since the alkaline earth ions are smaller than the corresponding alkali metals in the same row of the periodic table, the crystal structures formed with alkaline earth doping are often different from those for the alkali metal dopants. Except for the alkali metal and alkaline earth intercalation compounds, few intercalation compounds have been investigated for their physical properties. 

In some materials, semiconductors in particular, interstitial atoms play a crucial role in diffusion. Thus, Frank and Turnbull (1956) proposed that copper atoms dissolved in germanium are present both substitutionally (together with vacancies) and interstitially, and that the vacancies and interstitial copper atoms diffuse independently. Such diffusion can be very rapid, and this was exploited in preparing the famous micrograph of Figure 3.14 in the preceding chapter. Similarly, it is now recognised that transition metal atoms dissolved in silicon diffuse by a very fast, predominantly interstitial, mechanism (Weber 1988). 

In Section 4.2.2 the central role of atomic diffusion in many aspects of materials science was underlined. This is equally true for polymers, but the nature of diffusion is quite different in these materials, because polymer chains get mutually entangled and one chain cannot cross another. An important aspect of viscoelastic behavior of polymer melts is memory such a material can be deformed by hundreds of per cent and still recover its original shape almost completely if the stress is removed after a short time (Ferry 1980). This underlies the use of shrink-fit cling-film in supermarkets. On the other hand, because of diffusion, if the original stress is maintained for a long time, the memory of the original shape fades. 

Additionally, hydrogen atoms diffuse through metals and coalesce to form hydrogen molecules at certain preferred locations such as inclusions. 

In the chemical desorption step the adsorbed H atoms diffuse about on the metal surface, either by threading their way through adsorbed water molecules or by pushing them aside, until two collide to form an Hj molecule which escapes into the solution. This chemical step will be independent of overpotential, since charge transfer is not involved, and the rate will be proportional to the concentration or coverage of adsorbed H,, (see equation 20.39) and may occur at coverages that range from very small to almost complete. 

A possible layered precursor to the layered nanoproduct conversion mechanism is thus proposed. The silver clusters formed at the initial heating stage by the partial decomposition of AgSR serve as nuclei at further reaction stages, and their distribution naturally inherits the layered pattern of the precursor. The following growth is mainly controlled by the atom concentration and atom diffusion path, which are both constrained by the crystal structure of the precursor [9]. 

Hydrogen adsorbs dissociatively on almost all metals. At 500 K the H atoms diffuse freely over the surface. Desorption occurs associatively by recombination of two H atoms, while desorption of atomic hydrogen can be ignored. 

LEED patterns at 0 = 1 /4, but was identified at lower coverages in islands surrounded by mobile sulfur atoms at platinum, rhodium and rhenium surfaces. Sautet and co-workers42 have analysed the statistical correlations between the intensities of sulfur features in p(2 x 2) islands on rhenium surfaces and also of streaks in areas between islands, which they attribute to sulfur atoms diffusing under the tip (Figure 10.12). 

Table 8.5. Special atomic diffusion volumes (Fuller el al., 1966)...

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